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43
44	#ifndef OPENCV_CALIB3D_HPP
45	#define OPENCV_CALIB3D_HPP
46
47	#include "opencv2/core.hpp"
48	#include "opencv2/core/types.hpp"
49	#include "opencv2/features2d.hpp"
50	#include "opencv2/core/affine.hpp"
51	#include "opencv2/core/utils/logger.hpp"
52
53	/**
54	@defgroup calib3d Camera Calibration and 3D Reconstruction
55
56	The functions in this section use a so-called pinhole camera model. The view of a scene
57	is obtained by projecting a scene's 3D point \f$P_w\f$ into the image plane using a perspective
58	transformation which forms the corresponding pixel \f$p\f$. Both \f$P_w\f$ and \f$p\f$ are
59	represented in homogeneous coordinates, i.e. as 3D and 2D homogeneous vector respectively. You will
60	find a brief introduction to projective geometry, homogeneous vectors and homogeneous
61	transformations at the end of this section's introduction. For more succinct notation, we often drop
62	the 'homogeneous' and say vector instead of homogeneous vector.
63
64	The distortion-free projective transformation given by a pinhole camera model is shown below.
65
66	\f[s \; p = A \begin{bmatrix} R|t \end{bmatrix} P_w,\f]
67
68	where \f$P_w\f$ is a 3D point expressed with respect to the world coordinate system,
69	\f$p\f$ is a 2D pixel in the image plane, \f$A\f$ is the camera intrinsic matrix,
70	\f$R\f$ and \f$t\f$ are the rotation and translation that describe the change of coordinates from
71	world to camera coordinate systems (or camera frame) and \f$s\f$ is the projective transformation's
72	arbitrary scaling and not part of the camera model.
73
74	The camera intrinsic matrix \f$A\f$ (notation used as in @cite Zhang2000 and also generally notated
75	as \f$K\f$) projects 3D points given in the camera coordinate system to 2D pixel coordinates, i.e.
76
77	\f[p = A P_c.\f]
78
79	The camera intrinsic matrix \f$A\f$ is composed of the focal lengths \f$f_x\f$ and \f$f_y\f$, which are
80	expressed in pixel units, and the principal point \f$(c_x, c_y)\f$, that is usually close to the
81	image center:
82
83	\f[A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1},\f]
84
85	and thus
86
87	\f[s \vecthree{u}{v}{1} = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1} \vecthree{X_c}{Y_c}{Z_c}.\f]
88
89	The matrix of intrinsic parameters does not depend on the scene viewed. So, once estimated, it can
90	be re-used as long as the focal length is fixed (in case of a zoom lens). Thus, if an image from the
91	camera is scaled by a factor, all of these parameters need to be scaled (multiplied/divided,
92	respectively) by the same factor.
93
94	The joint rotation-translation matrix \f$[R|t]\f$ is the matrix product of a projective
95	transformation and a homogeneous transformation. The 3-by-4 projective transformation maps 3D points
96	represented in camera coordinates to 2D points in the image plane and represented in normalized
97	camera coordinates \f$x' = X_c / Z_c\f$ and \f$y' = Y_c / Z_c\f$:
98
99	\f[Z_c \begin{bmatrix}
100	x' \\
101	y' \\
102	1
103	\end{bmatrix} = \begin{bmatrix}
104	1 & 0 & 0 & 0 \\
105	0 & 1 & 0 & 0 \\
106	0 & 0 & 1 & 0
107	\end{bmatrix}
108	\begin{bmatrix}
109	X_c \\
110	Y_c \\
111	Z_c \\
112	1
113	\end{bmatrix}.\f]
114
115	The homogeneous transformation is encoded by the extrinsic parameters \f$R\f$ and \f$t\f$ and
116	represents the change of basis from world coordinate system \f$w\f$ to the camera coordinate sytem
117	\f$c\f$. Thus, given the representation of the point \f$P\f$ in world coordinates, \f$P_w\f$, we
118	obtain \f$P\f$'s representation in the camera coordinate system, \f$P_c\f$, by
119
120	\f[P_c = \begin{bmatrix}
121	R & t \\
122	0 & 1
123	\end{bmatrix} P_w,\f]
124
125	This homogeneous transformation is composed out of \f$R\f$, a 3-by-3 rotation matrix, and \f$t\f$, a
126	3-by-1 translation vector:
127
128	\f[\begin{bmatrix}
129	R & t \\
130	0 & 1
131	\end{bmatrix} = \begin{bmatrix}
132	r_{11} & r_{12} & r_{13} & t_x \\
133	r_{21} & r_{22} & r_{23} & t_y \\
134	r_{31} & r_{32} & r_{33} & t_z \\
135	0 & 0 & 0 & 1
136	\end{bmatrix},
137	\f]
138
139	and therefore
140
141	\f[\begin{bmatrix}
142	X_c \\
143	Y_c \\
144	Z_c \\
145	1
146	\end{bmatrix} = \begin{bmatrix}
147	r_{11} & r_{12} & r_{13} & t_x \\
148	r_{21} & r_{22} & r_{23} & t_y \\
149	r_{31} & r_{32} & r_{33} & t_z \\
150	0 & 0 & 0 & 1
151	\end{bmatrix}
152	\begin{bmatrix}
153	X_w \\
154	Y_w \\
155	Z_w \\
156	1
157	\end{bmatrix}.\f]
158
159	Combining the projective transformation and the homogeneous transformation, we obtain the projective
160	transformation that maps 3D points in world coordinates into 2D points in the image plane and in
161	normalized camera coordinates:
162
163	\f[Z_c \begin{bmatrix}
164	x' \\
165	y' \\
166	1
167	\end{bmatrix} = \begin{bmatrix} R|t \end{bmatrix} \begin{bmatrix}
168	X_w \\
169	Y_w \\
170	Z_w \\
171	1
172	\end{bmatrix} = \begin{bmatrix}
173	r_{11} & r_{12} & r_{13} & t_x \\
174	r_{21} & r_{22} & r_{23} & t_y \\
175	r_{31} & r_{32} & r_{33} & t_z
176	\end{bmatrix}
177	\begin{bmatrix}
178	X_w \\
179	Y_w \\
180	Z_w \\
181	1
182	\end{bmatrix},\f]
183
184	with \f$x' = X_c / Z_c\f$ and \f$y' = Y_c / Z_c\f$. Putting the equations for instrincs and extrinsics together, we can write out
185	\f$s \; p = A \begin{bmatrix} R|t \end{bmatrix} P_w\f$ as
186
187	\f[s \vecthree{u}{v}{1} = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}
188	\begin{bmatrix}
189	r_{11} & r_{12} & r_{13} & t_x \\
190	r_{21} & r_{22} & r_{23} & t_y \\
191	r_{31} & r_{32} & r_{33} & t_z
192	\end{bmatrix}
193	\begin{bmatrix}
194	X_w \\
195	Y_w \\
196	Z_w \\
197	1
198	\end{bmatrix}.\f]
199
200	If \f$Z_c \ne 0\f$, the transformation above is equivalent to the following,
201
202	\f[\begin{bmatrix}
203	u \\
204	v
205	\end{bmatrix} = \begin{bmatrix}
206	f_x X_c/Z_c + c_x \\
207	f_y Y_c/Z_c + c_y
208	\end{bmatrix}\f]
209
210	with
211
212	\f[\vecthree{X_c}{Y_c}{Z_c} = \begin{bmatrix}
213	R|t
214	\end{bmatrix} \begin{bmatrix}
215	X_w \\
216	Y_w \\
217	Z_w \\
218	1
219	\end{bmatrix}.\f]
220
221	The following figure illustrates the pinhole camera model.
222
223	
224
225	Real lenses usually have some distortion, mostly radial distortion, and slight tangential distortion.
226	So, the above model is extended as:
227
228	\f[\begin{bmatrix}
229	u \\
230	v
231	\end{bmatrix} = \begin{bmatrix}
232	f_x x'' + c_x \\
233	f_y y'' + c_y
234	\end{bmatrix}\f]
235
236	where
237
238	\f[\begin{bmatrix}
239	x'' \\
240	y''
241	\end{bmatrix} = \begin{bmatrix}
242	x' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6} + 2 p_1 x' y' + p_2(r^2 + 2 x'^2) + s_1 r^2 + s_2 r^4 \\
243	y' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6} + p_1 (r^2 + 2 y'^2) + 2 p_2 x' y' + s_3 r^2 + s_4 r^4 \\
244	\end{bmatrix}\f]
245
246	with
247
248	\f[r^2 = x'^2 + y'^2\f]
249
250	and
251
252	\f[\begin{bmatrix}
253	x'\\
254	y'
255	\end{bmatrix} = \begin{bmatrix}
256	X_c/Z_c \\
257	Y_c/Z_c
258	\end{bmatrix},\f]
259
260	if \f$Z_c \ne 0\f$.
261
262	The distortion parameters are the radial coefficients \f$k_1\f$, \f$k_2\f$, \f$k_3\f$, \f$k_4\f$, \f$k_5\f$, and \f$k_6\f$
263	,\f$p_1\f$ and \f$p_2\f$ are the tangential distortion coefficients, and \f$s_1\f$, \f$s_2\f$, \f$s_3\f$, and \f$s_4\f$,
264	are the thin prism distortion coefficients. Higher-order coefficients are not considered in OpenCV.
265
266	The next figures show two common types of radial distortion: barrel distortion
267	(\f$ 1 + k_1 r^2 + k_2 r^4 + k_3 r^6 \f$ monotonically decreasing)
268	and pincushion distortion (\f$ 1 + k_1 r^2 + k_2 r^4 + k_3 r^6 \f$ monotonically increasing).
269	Radial distortion is always monotonic for real lenses,
270	and if the estimator produces a non-monotonic result,
271	this should be considered a calibration failure.
272	More generally, radial distortion must be monotonic and the distortion function must be bijective.
273	A failed estimation result may look deceptively good near the image center
274	but will work poorly in e.g. AR/SFM applications.
275	The optimization method used in OpenCV camera calibration does not include these constraints as
276	the framework does not support the required integer programming and polynomial inequalities.
277	See [issue #15992](https://github.com/opencv/opencv/issues/15992) for additional information.
278
279	
280	
281
282	In some cases, the image sensor may be tilted in order to focus an oblique plane in front of the
283	camera (Scheimpflug principle). This can be useful for particle image velocimetry (PIV) or
284	triangulation with a laser fan. The tilt causes a perspective distortion of \f$x''\f$ and
285	\f$y''\f$. This distortion can be modeled in the following way, see e.g. @cite Louhichi07.
286
287	\f[\begin{bmatrix}
288	u \\
289	v
290	\end{bmatrix} = \begin{bmatrix}
291	f_x x''' + c_x \\
292	f_y y''' + c_y
293	\end{bmatrix},\f]
294
295	where
296
297	\f[s\vecthree{x'''}{y'''}{1} =
298	\vecthreethree{R_{33}(\tau_x, \tau_y)}{0}{-R_{13}(\tau_x, \tau_y)}
299	{0}{R_{33}(\tau_x, \tau_y)}{-R_{23}(\tau_x, \tau_y)}
300	{0}{0}{1} R(\tau_x, \tau_y) \vecthree{x''}{y''}{1}\f]
301
302	and the matrix \f$R(\tau_x, \tau_y)\f$ is defined by two rotations with angular parameter
303	\f$\tau_x\f$ and \f$\tau_y\f$, respectively,
304
305	\f[
306	R(\tau_x, \tau_y) =
307	\vecthreethree{\cos(\tau_y)}{0}{-\sin(\tau_y)}{0}{1}{0}{\sin(\tau_y)}{0}{\cos(\tau_y)}
308	\vecthreethree{1}{0}{0}{0}{\cos(\tau_x)}{\sin(\tau_x)}{0}{-\sin(\tau_x)}{\cos(\tau_x)} =
309	\vecthreethree{\cos(\tau_y)}{\sin(\tau_y)\sin(\tau_x)}{-\sin(\tau_y)\cos(\tau_x)}
310	{0}{\cos(\tau_x)}{\sin(\tau_x)}
311	{\sin(\tau_y)}{-\cos(\tau_y)\sin(\tau_x)}{\cos(\tau_y)\cos(\tau_x)}.
312	\f]
313
314	In the functions below the coefficients are passed or returned as
315
316	\f[(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f]
317
318	vector. That is, if the vector contains four elements, it means that \f$k_3=0\f$ . The distortion
319	coefficients do not depend on the scene viewed. Thus, they also belong to the intrinsic camera
320	parameters. And they remain the same regardless of the captured image resolution. If, for example, a
321	camera has been calibrated on images of 320 x 240 resolution, absolutely the same distortion
322	coefficients can be used for 640 x 480 images from the same camera while \f$f_x\f$, \f$f_y\f$,
323	\f$c_x\f$, and \f$c_y\f$ need to be scaled appropriately.
324
325	The functions below use the above model to do the following:
326
327	- Project 3D points to the image plane given intrinsic and extrinsic parameters.
328	- Compute extrinsic parameters given intrinsic parameters, a few 3D points, and their
329	projections.
330	- Estimate intrinsic and extrinsic camera parameters from several views of a known calibration
331	pattern (every view is described by several 3D-2D point correspondences).
332	- Estimate the relative position and orientation of the stereo camera "heads" and compute the
333	*rectification* transformation that makes the camera optical axes parallel.
334
335	<B> Homogeneous Coordinates </B><br>
336	Homogeneous Coordinates are a system of coordinates that are used in projective geometry. Their use
337	allows to represent points at infinity by finite coordinates and simplifies formulas when compared
338	to the cartesian counterparts, e.g. they have the advantage that affine transformations can be
339	expressed as linear homogeneous transformation.
340
341	One obtains the homogeneous vector \f$P_h\f$ by appending a 1 along an n-dimensional cartesian
342	vector \f$P\f$ e.g. for a 3D cartesian vector the mapping \f$P \rightarrow P_h\f$ is:
343
344	\f[\begin{bmatrix}
345	X \\
346	Y \\
347	Z
348	\end{bmatrix} \rightarrow \begin{bmatrix}
349	X \\
350	Y \\
351	Z \\
352	1
353	\end{bmatrix}.\f]
354
355	For the inverse mapping \f$P_h \rightarrow P\f$, one divides all elements of the homogeneous vector
356	by its last element, e.g. for a 3D homogeneous vector one gets its 2D cartesian counterpart by:
357
358	\f[\begin{bmatrix}
359	X \\
360	Y \\
361	W
362	\end{bmatrix} \rightarrow \begin{bmatrix}
363	X / W \\
364	Y / W
365	\end{bmatrix},\f]
366
367	if \f$W \ne 0\f$.
368
369	Due to this mapping, all multiples \f$k P_h\f$, for \f$k \ne 0\f$, of a homogeneous point represent
370	the same point \f$P_h\f$. An intuitive understanding of this property is that under a projective
371	transformation, all multiples of \f$P_h\f$ are mapped to the same point. This is the physical
372	observation one does for pinhole cameras, as all points along a ray through the camera's pinhole are
373	projected to the same image point, e.g. all points along the red ray in the image of the pinhole
374	camera model above would be mapped to the same image coordinate. This property is also the source
375	for the scale ambiguity s in the equation of the pinhole camera model.
376
377	As mentioned, by using homogeneous coordinates we can express any change of basis parameterized by
378	\f$R\f$ and \f$t\f$ as a linear transformation, e.g. for the change of basis from coordinate system
379	0 to coordinate system 1 becomes:
380
381	\f[P_1 = R P_0 + t \rightarrow P_{h_1} = \begin{bmatrix}
382	R & t \\
383	0 & 1
384	\end{bmatrix} P_{h_0}.\f]
385
386	@note
387	- Many functions in this module take a camera intrinsic matrix as an input parameter. Although all
388	functions assume the same structure of this parameter, they may name it differently. The
389	parameter's description, however, will be clear in that a camera intrinsic matrix with the structure
390	shown above is required.
391	- A calibration sample for 3 cameras in a horizontal position can be found at
392	opencv_source_code/samples/cpp/3calibration.cpp
393	- A calibration sample based on a sequence of images can be found at
394	opencv_source_code/samples/cpp/calibration.cpp
395	- A calibration sample in order to do 3D reconstruction can be found at
396	opencv_source_code/samples/cpp/build3dmodel.cpp
397	- A calibration example on stereo calibration can be found at
398	opencv_source_code/samples/cpp/stereo_calib.cpp
399	- A calibration example on stereo matching can be found at
400	opencv_source_code/samples/cpp/stereo_match.cpp
401	- (Python) A camera calibration sample can be found at
402	opencv_source_code/samples/python/calibrate.py
403
404	@{
405	@defgroup calib3d_fisheye Fisheye camera model
406
407	Definitions: Let P be a point in 3D of coordinates X in the world reference frame (stored in the
408	matrix X) The coordinate vector of P in the camera reference frame is:
409
410	\f[Xc = R X + T\f]
411
412	where R is the rotation matrix corresponding to the rotation vector om: R = rodrigues(om); call x, y
413	and z the 3 coordinates of Xc:
414
415	\f[\begin{array}{l} x = Xc_1 \\ y = Xc_2 \\ z = Xc_3 \end{array} \f]
416
417	The pinhole projection coordinates of P is [a; b] where
418
419	\f[\begin{array}{l} a = x / z \ and \ b = y / z \\ r^2 = a^2 + b^2 \\ \theta = atan(r) \end{array} \f]
420
421	Fisheye distortion:
422
423	\f[\theta_d = \theta (1 + k_1 \theta^2 + k_2 \theta^4 + k_3 \theta^6 + k_4 \theta^8)\f]
424
425	The distorted point coordinates are [x'; y'] where
426
427	\f[\begin{array}{l} x' = (\theta_d / r) a \\ y' = (\theta_d / r) b \end{array} \f]
428
429	Finally, conversion into pixel coordinates: The final pixel coordinates vector [u; v] where:
430
431	\f[\begin{array}{l} u = f_x (x' + \alpha y') + c_x \\
432	v = f_y y' + c_y \end{array} \f]
433
434	Summary:
435	Generic camera model @cite Kannala2006 with perspective projection and without distortion correction
436
437	@}
438	*/
439
440	namespace cv
441	{
442
443	//! @addtogroup calib3d
444	//! @{
445
446	//! type of the robust estimation algorithm
447	enum { LMEDS = 4, //!< least-median of squares algorithm
448	RANSAC = 8, //!< RANSAC algorithm
449	RHO = 16, //!< RHO algorithm
450	USAC_DEFAULT = 32, //!< USAC algorithm, default settings
451	USAC_PARALLEL = 33, //!< USAC, parallel version
452	USAC_FM_8PTS = 34, //!< USAC, fundamental matrix 8 points
453	USAC_FAST = 35, //!< USAC, fast settings
454	USAC_ACCURATE = 36, //!< USAC, accurate settings
455	USAC_PROSAC = 37, //!< USAC, sorted points, runs PROSAC
456	USAC_MAGSAC = 38 //!< USAC, runs MAGSAC++
457	};
458
459	enum SolvePnPMethod {
460	SOLVEPNP_ITERATIVE = 0, //!< Pose refinement using non-linear Levenberg-Marquardt minimization scheme @cite Madsen04 @cite Eade13 \n
461	//!< Initial solution for non-planar "objectPoints" needs at least 6 points and uses the DLT algorithm. \n
462	//!< Initial solution for planar "objectPoints" needs at least 4 points and uses pose from homography decomposition.
463	SOLVEPNP_EPNP = 1, //!< EPnP: Efficient Perspective-n-Point Camera Pose Estimation @cite lepetit2009epnp
464	SOLVEPNP_P3P = 2, //!< Complete Solution Classification for the Perspective-Three-Point Problem @cite gao2003complete
465	SOLVEPNP_DLS = 3, //!< **Broken implementation. Using this flag will fallback to EPnP.** \n
466	//!< A Direct Least-Squares (DLS) Method for PnP @cite hesch2011direct
467	SOLVEPNP_UPNP = 4, //!< **Broken implementation. Using this flag will fallback to EPnP.** \n
468	//!< Exhaustive Linearization for Robust Camera Pose and Focal Length Estimation @cite penate2013exhaustive
469	SOLVEPNP_AP3P = 5, //!< An Efficient Algebraic Solution to the Perspective-Three-Point Problem @cite Ke17
470	SOLVEPNP_IPPE = 6, //!< Infinitesimal Plane-Based Pose Estimation @cite Collins14 \n
471	//!< Object points must be coplanar.
472	SOLVEPNP_IPPE_SQUARE = 7, //!< Infinitesimal Plane-Based Pose Estimation @cite Collins14 \n
473	//!< This is a special case suitable for marker pose estimation.\n
474	//!< 4 coplanar object points must be defined in the following order:
475	//!< - point 0: [-squareLength / 2, squareLength / 2, 0]
476	//!< - point 1: [ squareLength / 2, squareLength / 2, 0]
477	//!< - point 2: [ squareLength / 2, -squareLength / 2, 0]
478	//!< - point 3: [-squareLength / 2, -squareLength / 2, 0]
479	SOLVEPNP_SQPNP = 8, //!< SQPnP: A Consistently Fast and Globally OptimalSolution to the Perspective-n-Point Problem @cite Terzakis2020SQPnP
480	#ifndef CV_DOXYGEN
481	SOLVEPNP_MAX_COUNT //!< Used for count
482	#endif
483	};
484
485	enum { CALIB_CB_ADAPTIVE_THRESH = 1,
486	CALIB_CB_NORMALIZE_IMAGE = 2,
487	CALIB_CB_FILTER_QUADS = 4,
488	CALIB_CB_FAST_CHECK = 8,
489	CALIB_CB_EXHAUSTIVE = 16,
490	CALIB_CB_ACCURACY = 32,
491	CALIB_CB_LARGER = 64,
492	CALIB_CB_MARKER = 128,
493	CALIB_CB_PLAIN = 256
494	};
495
496	enum { CALIB_CB_SYMMETRIC_GRID = 1,
497	CALIB_CB_ASYMMETRIC_GRID = 2,
498	CALIB_CB_CLUSTERING = 4
499	};
500
501	enum { CALIB_NINTRINSIC = 18,
502	CALIB_USE_INTRINSIC_GUESS = 0x00001,
503	CALIB_FIX_ASPECT_RATIO = 0x00002,
504	CALIB_FIX_PRINCIPAL_POINT = 0x00004,
505	CALIB_ZERO_TANGENT_DIST = 0x00008,
506	CALIB_FIX_FOCAL_LENGTH = 0x00010,
507	CALIB_FIX_K1 = 0x00020,
508	CALIB_FIX_K2 = 0x00040,
509	CALIB_FIX_K3 = 0x00080,
510	CALIB_FIX_K4 = 0x00800,
511	CALIB_FIX_K5 = 0x01000,
512	CALIB_FIX_K6 = 0x02000,
513	CALIB_RATIONAL_MODEL = 0x04000,
514	CALIB_THIN_PRISM_MODEL = 0x08000,
515	CALIB_FIX_S1_S2_S3_S4 = 0x10000,
516	CALIB_TILTED_MODEL = 0x40000,
517	CALIB_FIX_TAUX_TAUY = 0x80000,
518	CALIB_USE_QR = 0x100000, //!< use QR instead of SVD decomposition for solving. Faster but potentially less precise
519	CALIB_FIX_TANGENT_DIST = 0x200000,
520	// only for stereo
521	CALIB_FIX_INTRINSIC = 0x00100,
522	CALIB_SAME_FOCAL_LENGTH = 0x00200,
523	// for stereo rectification
524	CALIB_ZERO_DISPARITY = 0x00400,
525	CALIB_USE_LU = (1 << 17), //!< use LU instead of SVD decomposition for solving. much faster but potentially less precise
526	CALIB_USE_EXTRINSIC_GUESS = (1 << 22) //!< for stereoCalibrate
527	};
528
529	//! the algorithm for finding fundamental matrix
530	enum { FM_7POINT = 1, //!< 7-point algorithm
531	FM_8POINT = 2, //!< 8-point algorithm
532	FM_LMEDS = 4, //!< least-median algorithm. 7-point algorithm is used.
533	FM_RANSAC = 8 //!< RANSAC algorithm. It needs at least 15 points. 7-point algorithm is used.
534	};
535
536	enum HandEyeCalibrationMethod
537	{
538	CALIB_HAND_EYE_TSAI = 0, //!< A New Technique for Fully Autonomous and Efficient 3D Robotics Hand/Eye Calibration @cite Tsai89
539	CALIB_HAND_EYE_PARK = 1, //!< Robot Sensor Calibration: Solving AX = XB on the Euclidean Group @cite Park94
540	CALIB_HAND_EYE_HORAUD = 2, //!< Hand-eye Calibration @cite Horaud95
541	CALIB_HAND_EYE_ANDREFF = 3, //!< On-line Hand-Eye Calibration @cite Andreff99
542	CALIB_HAND_EYE_DANIILIDIS = 4 //!< Hand-Eye Calibration Using Dual Quaternions @cite Daniilidis98
543	};
544
545	enum RobotWorldHandEyeCalibrationMethod
546	{
547	CALIB_ROBOT_WORLD_HAND_EYE_SHAH = 0, //!< Solving the robot-world/hand-eye calibration problem using the kronecker product @cite Shah2013SolvingTR
548	CALIB_ROBOT_WORLD_HAND_EYE_LI = 1 //!< Simultaneous robot-world and hand-eye calibration using dual-quaternions and kronecker product @cite Li2010SimultaneousRA
549	};
550
551	enum SamplingMethod { SAMPLING_UNIFORM=0, SAMPLING_PROGRESSIVE_NAPSAC=1, SAMPLING_NAPSAC=2,
552	SAMPLING_PROSAC=3 };
553	enum LocalOptimMethod {LOCAL_OPTIM_NULL=0, LOCAL_OPTIM_INNER_LO=1, LOCAL_OPTIM_INNER_AND_ITER_LO=2,
554	LOCAL_OPTIM_GC=3, LOCAL_OPTIM_SIGMA=4};
555	enum ScoreMethod {SCORE_METHOD_RANSAC=0, SCORE_METHOD_MSAC=1, SCORE_METHOD_MAGSAC=2, SCORE_METHOD_LMEDS=3};
556	enum NeighborSearchMethod { NEIGH_FLANN_KNN=0, NEIGH_GRID=1, NEIGH_FLANN_RADIUS=2 };
557	enum PolishingMethod { NONE_POLISHER=0, LSQ_POLISHER=1, MAGSAC=2, COV_POLISHER=3 };
558
559	struct CV_EXPORTS_W_SIMPLE UsacParams
560	{ // in alphabetical order
561	CV_WRAP UsacParams();
562	CV_PROP_RW double confidence;
563	CV_PROP_RW bool isParallel;
564	CV_PROP_RW int loIterations;
565	CV_PROP_RW LocalOptimMethod loMethod;
566	CV_PROP_RW int loSampleSize;
567	CV_PROP_RW int maxIterations;
568	CV_PROP_RW NeighborSearchMethod neighborsSearch;
569	CV_PROP_RW int randomGeneratorState;
570	CV_PROP_RW SamplingMethod sampler;
571	CV_PROP_RW ScoreMethod score;
572	CV_PROP_RW double threshold;
573	CV_PROP_RW PolishingMethod final_polisher;
574	CV_PROP_RW int final_polisher_iterations;
575	};
576
577	/** @brief Converts a rotation matrix to a rotation vector or vice versa.
578
579	@param src Input rotation vector (3x1 or 1x3) or rotation matrix (3x3).
580	@param dst Output rotation matrix (3x3) or rotation vector (3x1 or 1x3), respectively.
581	@param jacobian Optional output Jacobian matrix, 3x9 or 9x3, which is a matrix of partial
582	derivatives of the output array components with respect to the input array components.
583
584	\f[\begin{array}{l} \theta \leftarrow norm(r) \\ r \leftarrow r/ \theta \\ R = \cos(\theta) I + (1- \cos{\theta} ) r r^T + \sin(\theta) \vecthreethree{0}{-r_z}{r_y}{r_z}{0}{-r_x}{-r_y}{r_x}{0} \end{array}\f]
585
586	Inverse transformation can be also done easily, since
587
588	\f[\sin ( \theta ) \vecthreethree{0}{-r_z}{r_y}{r_z}{0}{-r_x}{-r_y}{r_x}{0} = \frac{R - R^T}{2}\f]
589
590	A rotation vector is a convenient and most compact representation of a rotation matrix (since any
591	rotation matrix has just 3 degrees of freedom). The representation is used in the global 3D geometry
592	optimization procedures like @ref calibrateCamera, @ref stereoCalibrate, or @ref solvePnP .
593
594	@note More information about the computation of the derivative of a 3D rotation matrix with respect to its exponential coordinate
595	can be found in:
596	- A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates, Guillermo Gallego, Anthony J. Yezzi @cite Gallego2014ACF
597
598	@note Useful information on SE(3) and Lie Groups can be found in:
599	- A tutorial on SE(3) transformation parameterizations and on-manifold optimization, Jose-Luis Blanco @cite blanco2010tutorial
600	- Lie Groups for 2D and 3D Transformation, Ethan Eade @cite Eade17
601	- A micro Lie theory for state estimation in robotics, Joan Solà, Jérémie Deray, Dinesh Atchuthan @cite Sol2018AML
602	*/
603	CV_EXPORTS_W void Rodrigues( InputArray src, OutputArray dst, OutputArray jacobian = noArray() );
604
605
606
607	/** Levenberg-Marquardt solver. Starting with the specified vector of parameters it
608	optimizes the target vector criteria "err"
609	(finds local minima of each target vector component absolute value).
610
611	When needed, it calls user-provided callback.
612	*/
613	class CV_EXPORTS LMSolver : public Algorithm
614	{
615	public:
616	class CV_EXPORTS Callback
617	{
618	public:
619	virtual ~Callback() {}
620	/**
621	computes error and Jacobian for the specified vector of parameters
622
623	@param param the current vector of parameters
624	@param err output vector of errors: err_i = actual_f_i - ideal_f_i
625	@param J output Jacobian: J_ij = d(ideal_f_i)/d(param_j)
626
627	when J=noArray(), it means that it does not need to be computed.
628	Dimensionality of error vector and param vector can be different.
629	The callback should explicitly allocate (with "create" method) each output array
630	(unless it's noArray()).
631	*/
632	virtual bool compute(InputArray param, OutputArray err, OutputArray J) const = 0;
633	};
634
635	/**
636	Runs Levenberg-Marquardt algorithm using the passed vector of parameters as the start point.
637	The final vector of parameters (whether the algorithm converged or not) is stored at the same
638	vector. The method returns the number of iterations used. If it's equal to the previously specified
639	maxIters, there is a big chance the algorithm did not converge.
640
641	@param param initial/final vector of parameters.
642
643	Note that the dimensionality of parameter space is defined by the size of param vector,
644	and the dimensionality of optimized criteria is defined by the size of err vector
645	computed by the callback.
646	*/
647	virtual int run(InputOutputArray param) const = 0;
648
649	/**
650	Sets the maximum number of iterations
651	@param maxIters the number of iterations
652	*/
653	virtual void setMaxIters(int maxIters) = 0;
654	/**
655	Retrieves the current maximum number of iterations
656	*/
657	virtual int getMaxIters() const = 0;
658
659	/**
660	Creates Levenberg-Marquard solver
661
662	@param cb callback
663	@param maxIters maximum number of iterations that can be further
664	modified using setMaxIters() method.
665	*/
666	static Ptr<LMSolver> create(const Ptr<LMSolver::Callback>& cb, int maxIters);
667	static Ptr<LMSolver> create(const Ptr<LMSolver::Callback>& cb, int maxIters, double eps);
668	};
669
670
671
672	/** @example samples/cpp/tutorial_code/features2D/Homography/pose_from_homography.cpp
673	An example program about pose estimation from coplanar points
674
675	Check @ref tutorial_homography "the corresponding tutorial" for more details
676	*/
677
678	/** @brief Finds a perspective transformation between two planes.
679
680	@param srcPoints Coordinates of the points in the original plane, a matrix of the type CV_32FC2
681	or vector\<Point2f\> .
682	@param dstPoints Coordinates of the points in the target plane, a matrix of the type CV_32FC2 or
683	a vector\<Point2f\> .
684	@param method Method used to compute a homography matrix. The following methods are possible:
685	- **0** - a regular method using all the points, i.e., the least squares method
686	- @ref RANSAC - RANSAC-based robust method
687	- @ref LMEDS - Least-Median robust method
688	- @ref RHO - PROSAC-based robust method
689	@param ransacReprojThreshold Maximum allowed reprojection error to treat a point pair as an inlier
690	(used in the RANSAC and RHO methods only). That is, if
691	\f[\| \texttt{dstPoints} _i - \texttt{convertPointsHomogeneous} ( \texttt{H} \cdot \texttt{srcPoints} _i) \|_2 > \texttt{ransacReprojThreshold}\f]
692	then the point \f$i\f$ is considered as an outlier. If srcPoints and dstPoints are measured in pixels,
693	it usually makes sense to set this parameter somewhere in the range of 1 to 10.
694	@param mask Optional output mask set by a robust method ( RANSAC or LMeDS ). Note that the input
695	mask values are ignored.
696	@param maxIters The maximum number of RANSAC iterations.
697	@param confidence Confidence level, between 0 and 1.
698
699	The function finds and returns the perspective transformation \f$H\f$ between the source and the
700	destination planes:
701
702	\f[s_i \vecthree{x'_i}{y'_i}{1} \sim H \vecthree{x_i}{y_i}{1}\f]
703
704	so that the back-projection error
705
706	\f[\sum _i \left ( x'_i- \frac{h_{11} x_i + h_{12} y_i + h_{13}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2+ \left ( y'_i- \frac{h_{21} x_i + h_{22} y_i + h_{23}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2\f]
707
708	is minimized. If the parameter method is set to the default value 0, the function uses all the point
709	pairs to compute an initial homography estimate with a simple least-squares scheme.
710
711	However, if not all of the point pairs ( \f$srcPoints_i\f$, \f$dstPoints_i\f$ ) fit the rigid perspective
712	transformation (that is, there are some outliers), this initial estimate will be poor. In this case,
713	you can use one of the three robust methods. The methods RANSAC, LMeDS and RHO try many different
714	random subsets of the corresponding point pairs (of four pairs each, collinear pairs are discarded), estimate the homography matrix
715	using this subset and a simple least-squares algorithm, and then compute the quality/goodness of the
716	computed homography (which is the number of inliers for RANSAC or the least median re-projection error for
717	LMeDS). The best subset is then used to produce the initial estimate of the homography matrix and
718	the mask of inliers/outliers.
719
720	Regardless of the method, robust or not, the computed homography matrix is refined further (using
721	inliers only in case of a robust method) with the Levenberg-Marquardt method to reduce the
722	re-projection error even more.
723
724	The methods RANSAC and RHO can handle practically any ratio of outliers but need a threshold to
725	distinguish inliers from outliers. The method LMeDS does not need any threshold but it works
726	correctly only when there are more than 50% of inliers. Finally, if there are no outliers and the
727	noise is rather small, use the default method (method=0).
728
729	The function is used to find initial intrinsic and extrinsic matrices. Homography matrix is
730	determined up to a scale. If \f$h_{33}\f$ is non-zero, the matrix is normalized so that \f$h_{33}=1\f$.
731	@note Whenever an \f$H\f$ matrix cannot be estimated, an empty one will be returned.
732
733	@sa
734	getAffineTransform, estimateAffine2D, estimateAffinePartial2D, getPerspectiveTransform, warpPerspective,
735	perspectiveTransform
736	*/
737	CV_EXPORTS_W Mat findHomography( InputArray srcPoints, InputArray dstPoints,
738	int method = 0, double ransacReprojThreshold = 3,
739	OutputArray mask=noArray(), const int maxIters = 2000,
740	const double confidence = 0.995);
741
742	/** @overload */
743	CV_EXPORTS Mat findHomography( InputArray srcPoints, InputArray dstPoints,
744	OutputArray mask, int method = 0, double ransacReprojThreshold = 3 );
745
746
747	CV_EXPORTS_W Mat findHomography(InputArray srcPoints, InputArray dstPoints, OutputArray mask,
748	const UsacParams &params);
749
750	/** @brief Computes an RQ decomposition of 3x3 matrices.
751
752	@param src 3x3 input matrix.
753	@param mtxR Output 3x3 upper-triangular matrix.
754	@param mtxQ Output 3x3 orthogonal matrix.
755	@param Qx Optional output 3x3 rotation matrix around x-axis.
756	@param Qy Optional output 3x3 rotation matrix around y-axis.
757	@param Qz Optional output 3x3 rotation matrix around z-axis.
758
759	The function computes a RQ decomposition using the given rotations. This function is used in
760	#decomposeProjectionMatrix to decompose the left 3x3 submatrix of a projection matrix into a camera
761	and a rotation matrix.
762
763	It optionally returns three rotation matrices, one for each axis, and the three Euler angles in
764	degrees (as the return value) that could be used in OpenGL. Note, there is always more than one
765	sequence of rotations about the three principal axes that results in the same orientation of an
766	object, e.g. see @cite Slabaugh . Returned three rotation matrices and corresponding three Euler angles
767	are only one of the possible solutions.
768	*/
769	CV_EXPORTS_W Vec3d RQDecomp3x3( InputArray src, OutputArray mtxR, OutputArray mtxQ,
770	OutputArray Qx = noArray(),
771	OutputArray Qy = noArray(),
772	OutputArray Qz = noArray());
773
774	/** @brief Decomposes a projection matrix into a rotation matrix and a camera intrinsic matrix.
775
776	@param projMatrix 3x4 input projection matrix P.
777	@param cameraMatrix Output 3x3 camera intrinsic matrix \f$\cameramatrix{A}\f$.
778	@param rotMatrix Output 3x3 external rotation matrix R.
779	@param transVect Output 4x1 translation vector T.
780	@param rotMatrixX Optional 3x3 rotation matrix around x-axis.
781	@param rotMatrixY Optional 3x3 rotation matrix around y-axis.
782	@param rotMatrixZ Optional 3x3 rotation matrix around z-axis.
783	@param eulerAngles Optional three-element vector containing three Euler angles of rotation in
784	degrees.
785
786	The function computes a decomposition of a projection matrix into a calibration and a rotation
787	matrix and the position of a camera.
788
789	It optionally returns three rotation matrices, one for each axis, and three Euler angles that could
790	be used in OpenGL. Note, there is always more than one sequence of rotations about the three
791	principal axes that results in the same orientation of an object, e.g. see @cite Slabaugh . Returned
792	three rotation matrices and corresponding three Euler angles are only one of the possible solutions.
793
794	The function is based on #RQDecomp3x3 .
795	*/
796	CV_EXPORTS_W void decomposeProjectionMatrix( InputArray projMatrix, OutputArray cameraMatrix,
797	OutputArray rotMatrix, OutputArray transVect,
798	OutputArray rotMatrixX = noArray(),
799	OutputArray rotMatrixY = noArray(),
800	OutputArray rotMatrixZ = noArray(),
801	OutputArray eulerAngles =noArray() );
802
803	/** @brief Computes partial derivatives of the matrix product for each multiplied matrix.
804
805	@param A First multiplied matrix.
806	@param B Second multiplied matrix.
807	@param dABdA First output derivative matrix d(A\*B)/dA of size
808	\f$\texttt{A.rows*B.cols} \times {A.rows*A.cols}\f$ .
809	@param dABdB Second output derivative matrix d(A\*B)/dB of size
810	\f$\texttt{A.rows*B.cols} \times {B.rows*B.cols}\f$ .
811
812	The function computes partial derivatives of the elements of the matrix product \f$A*B\f$ with regard to
813	the elements of each of the two input matrices. The function is used to compute the Jacobian
814	matrices in #stereoCalibrate but can also be used in any other similar optimization function.
815	*/
816	CV_EXPORTS_W void matMulDeriv( InputArray A, InputArray B, OutputArray dABdA, OutputArray dABdB );
817
818	/** @brief Combines two rotation-and-shift transformations.
819
820	@param rvec1 First rotation vector.
821	@param tvec1 First translation vector.
822	@param rvec2 Second rotation vector.
823	@param tvec2 Second translation vector.
824	@param rvec3 Output rotation vector of the superposition.
825	@param tvec3 Output translation vector of the superposition.
826	@param dr3dr1 Optional output derivative of rvec3 with regard to rvec1
827	@param dr3dt1 Optional output derivative of rvec3 with regard to tvec1
828	@param dr3dr2 Optional output derivative of rvec3 with regard to rvec2
829	@param dr3dt2 Optional output derivative of rvec3 with regard to tvec2
830	@param dt3dr1 Optional output derivative of tvec3 with regard to rvec1
831	@param dt3dt1 Optional output derivative of tvec3 with regard to tvec1
832	@param dt3dr2 Optional output derivative of tvec3 with regard to rvec2
833	@param dt3dt2 Optional output derivative of tvec3 with regard to tvec2
834
835	The functions compute:
836
837	\f[\begin{array}{l} \texttt{rvec3} = \mathrm{rodrigues} ^{-1} \left ( \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \mathrm{rodrigues} ( \texttt{rvec1} ) \right ) \\ \texttt{tvec3} = \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \texttt{tvec1} + \texttt{tvec2} \end{array} ,\f]
838
839	where \f$\mathrm{rodrigues}\f$ denotes a rotation vector to a rotation matrix transformation, and
840	\f$\mathrm{rodrigues}^{-1}\f$ denotes the inverse transformation. See #Rodrigues for details.
841
842	Also, the functions can compute the derivatives of the output vectors with regards to the input
843	vectors (see #matMulDeriv ). The functions are used inside #stereoCalibrate but can also be used in
844	your own code where Levenberg-Marquardt or another gradient-based solver is used to optimize a
845	function that contains a matrix multiplication.
846	*/
847	CV_EXPORTS_W void composeRT( InputArray rvec1, InputArray tvec1,
848	InputArray rvec2, InputArray tvec2,
849	OutputArray rvec3, OutputArray tvec3,
850	OutputArray dr3dr1 = noArray(), OutputArray dr3dt1 = noArray(),
851	OutputArray dr3dr2 = noArray(), OutputArray dr3dt2 = noArray(),
852	OutputArray dt3dr1 = noArray(), OutputArray dt3dt1 = noArray(),
853	OutputArray dt3dr2 = noArray(), OutputArray dt3dt2 = noArray() );
854
855	/** @brief Projects 3D points to an image plane.
856
857	@param objectPoints Array of object points expressed wrt. the world coordinate frame. A 3xN/Nx3
858	1-channel or 1xN/Nx1 3-channel (or vector\<Point3f\> ), where N is the number of points in the view.
859	@param rvec The rotation vector (@ref Rodrigues) that, together with tvec, performs a change of
860	basis from world to camera coordinate system, see @ref calibrateCamera for details.
861	@param tvec The translation vector, see parameter description above.
862	@param cameraMatrix Camera intrinsic matrix \f$\cameramatrix{A}\f$ .
863	@param distCoeffs Input vector of distortion coefficients
864	\f$\distcoeffs\f$ . If the vector is empty, the zero distortion coefficients are assumed.
865	@param imagePoints Output array of image points, 1xN/Nx1 2-channel, or
866	vector\<Point2f\> .
867	@param jacobian Optional output 2Nx(10+\<numDistCoeffs\>) jacobian matrix of derivatives of image
868	points with respect to components of the rotation vector, translation vector, focal lengths,
869	coordinates of the principal point and the distortion coefficients. In the old interface different
870	components of the jacobian are returned via different output parameters.
871	@param aspectRatio Optional "fixed aspect ratio" parameter. If the parameter is not 0, the
872	function assumes that the aspect ratio (\f$f_x / f_y\f$) is fixed and correspondingly adjusts the
873	jacobian matrix.
874
875	The function computes the 2D projections of 3D points to the image plane, given intrinsic and
876	extrinsic camera parameters. Optionally, the function computes Jacobians -matrices of partial
877	derivatives of image points coordinates (as functions of all the input parameters) with respect to
878	the particular parameters, intrinsic and/or extrinsic. The Jacobians are used during the global
879	optimization in @ref calibrateCamera, @ref solvePnP, and @ref stereoCalibrate. The function itself
880	can also be used to compute a re-projection error, given the current intrinsic and extrinsic
881	parameters.
882
883	@note By setting rvec = tvec = \f$[0, 0, 0]\f$, or by setting cameraMatrix to a 3x3 identity matrix,
884	or by passing zero distortion coefficients, one can get various useful partial cases of the
885	function. This means, one can compute the distorted coordinates for a sparse set of points or apply
886	a perspective transformation (and also compute the derivatives) in the ideal zero-distortion setup.
887	*/
888	CV_EXPORTS_W void projectPoints( InputArray objectPoints,
889	InputArray rvec, InputArray tvec,
890	InputArray cameraMatrix, InputArray distCoeffs,
891	OutputArray imagePoints,
892	OutputArray jacobian = noArray(),
893	double aspectRatio = 0 );
894
895	/** @example samples/cpp/tutorial_code/features2D/Homography/homography_from_camera_displacement.cpp
896	An example program about homography from the camera displacement
897
898	Check @ref tutorial_homography "the corresponding tutorial" for more details
899	*/
900
901	/** @brief Finds an object pose from 3D-2D point correspondences.
902
903	@see @ref calib3d_solvePnP
904
905	This function returns the rotation and the translation vectors that transform a 3D point expressed in the object
906	coordinate frame to the camera coordinate frame, using different methods:
907	- P3P methods (@ref SOLVEPNP_P3P, @ref SOLVEPNP_AP3P): need 4 input points to return a unique solution.
908	- @ref SOLVEPNP_IPPE Input points must be >= 4 and object points must be coplanar.
909	- @ref SOLVEPNP_IPPE_SQUARE Special case suitable for marker pose estimation.
910	Number of input points must be 4. Object points must be defined in the following order:
911	- point 0: [-squareLength / 2, squareLength / 2, 0]
912	- point 1: [ squareLength / 2, squareLength / 2, 0]
913	- point 2: [ squareLength / 2, -squareLength / 2, 0]
914	- point 3: [-squareLength / 2, -squareLength / 2, 0]
915	- for all the other flags, number of input points must be >= 4 and object points can be in any configuration.
916
917	@param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or
918	1xN/Nx1 3-channel, where N is the number of points. vector\<Point3d\> can be also passed here.
919	@param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
920	where N is the number of points. vector\<Point2d\> can be also passed here.
921	@param cameraMatrix Input camera intrinsic matrix \f$\cameramatrix{A}\f$ .
922	@param distCoeffs Input vector of distortion coefficients
923	\f$\distcoeffs\f$. If the vector is NULL/empty, the zero distortion coefficients are
924	assumed.
925	@param rvec Output rotation vector (see @ref Rodrigues ) that, together with tvec, brings points from
926	the model coordinate system to the camera coordinate system.
927	@param tvec Output translation vector.
928	@param useExtrinsicGuess Parameter used for #SOLVEPNP_ITERATIVE. If true (1), the function uses
929	the provided rvec and tvec values as initial approximations of the rotation and translation
930	vectors, respectively, and further optimizes them.
931	@param flags Method for solving a PnP problem: see @ref calib3d_solvePnP_flags
932
933	More information about Perspective-n-Points is described in @ref calib3d_solvePnP
934
935	@note
936	- An example of how to use solvePnP for planar augmented reality can be found at
937	opencv_source_code/samples/python/plane_ar.py
938	- If you are using Python:
939	- Numpy array slices won't work as input because solvePnP requires contiguous
940	arrays (enforced by the assertion using cv::Mat::checkVector() around line 55 of
941	modules/calib3d/src/solvepnp.cpp version 2.4.9)
942	- The P3P algorithm requires image points to be in an array of shape (N,1,2) due
943	to its calling of #undistortPoints (around line 75 of modules/calib3d/src/solvepnp.cpp version 2.4.9)
944	which requires 2-channel information.
945	- Thus, given some data D = np.array(...) where D.shape = (N,M), in order to use a subset of
946	it as, e.g., imagePoints, one must effectively copy it into a new array: imagePoints =
947	np.ascontiguousarray(D[:,:2]).reshape((N,1,2))
948	- The methods @ref SOLVEPNP_DLS and @ref SOLVEPNP_UPNP cannot be used as the current implementations are
949	unstable and sometimes give completely wrong results. If you pass one of these two
950	flags, @ref SOLVEPNP_EPNP method will be used instead.
951	- The minimum number of points is 4 in the general case. In the case of @ref SOLVEPNP_P3P and @ref SOLVEPNP_AP3P
952	methods, it is required to use exactly 4 points (the first 3 points are used to estimate all the solutions
953	of the P3P problem, the last one is used to retain the best solution that minimizes the reprojection error).
954	- With @ref SOLVEPNP_ITERATIVE method and `useExtrinsicGuess=true`, the minimum number of points is 3 (3 points
955	are sufficient to compute a pose but there are up to 4 solutions). The initial solution should be close to the
956	global solution to converge.
957	- With @ref SOLVEPNP_IPPE input points must be >= 4 and object points must be coplanar.
958	- With @ref SOLVEPNP_IPPE_SQUARE this is a special case suitable for marker pose estimation.
959	Number of input points must be 4. Object points must be defined in the following order:
960	- point 0: [-squareLength / 2, squareLength / 2, 0]
961	- point 1: [ squareLength / 2, squareLength / 2, 0]
962	- point 2: [ squareLength / 2, -squareLength / 2, 0]
963	- point 3: [-squareLength / 2, -squareLength / 2, 0]
964	- With @ref SOLVEPNP_SQPNP input points must be >= 3
965	*/
966	CV_EXPORTS_W bool solvePnP( InputArray objectPoints, InputArray imagePoints,
967	InputArray cameraMatrix, InputArray distCoeffs,
968	OutputArray rvec, OutputArray tvec,
969	bool useExtrinsicGuess = false, int flags = SOLVEPNP_ITERATIVE );
970
971	/** @brief Finds an object pose from 3D-2D point correspondences using the RANSAC scheme.
972
973	@see @ref calib3d_solvePnP
974
975	@param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or
976	1xN/Nx1 3-channel, where N is the number of points. vector\<Point3d\> can be also passed here.
977	@param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
978	where N is the number of points. vector\<Point2d\> can be also passed here.
979	@param cameraMatrix Input camera intrinsic matrix \f$\cameramatrix{A}\f$ .
980	@param distCoeffs Input vector of distortion coefficients
981	\f$\distcoeffs\f$. If the vector is NULL/empty, the zero distortion coefficients are
982	assumed.
983	@param rvec Output rotation vector (see @ref Rodrigues ) that, together with tvec, brings points from
984	the model coordinate system to the camera coordinate system.
985	@param tvec Output translation vector.
986	@param useExtrinsicGuess Parameter used for @ref SOLVEPNP_ITERATIVE. If true (1), the function uses
987	the provided rvec and tvec values as initial approximations of the rotation and translation
988	vectors, respectively, and further optimizes them.
989	@param iterationsCount Number of iterations.
990	@param reprojectionError Inlier threshold value used by the RANSAC procedure. The parameter value
991	is the maximum allowed distance between the observed and computed point projections to consider it
992	an inlier.
993	@param confidence The probability that the algorithm produces a useful result.
994	@param inliers Output vector that contains indices of inliers in objectPoints and imagePoints .
995	@param flags Method for solving a PnP problem (see @ref solvePnP ).
996
997	The function estimates an object pose given a set of object points, their corresponding image
998	projections, as well as the camera intrinsic matrix and the distortion coefficients. This function finds such
999	a pose that minimizes reprojection error, that is, the sum of squared distances between the observed
1000	projections imagePoints and the projected (using @ref projectPoints ) objectPoints. The use of RANSAC
1001	makes the function resistant to outliers.
1002
1003	@note
1004	- An example of how to use solvePNPRansac for object detection can be found at
1005	opencv_source_code/samples/cpp/tutorial_code/calib3d/real_time_pose_estimation/
1006	- The default method used to estimate the camera pose for the Minimal Sample Sets step
1007	is #SOLVEPNP_EPNP. Exceptions are:
1008	- if you choose #SOLVEPNP_P3P or #SOLVEPNP_AP3P, these methods will be used.
1009	- if the number of input points is equal to 4, #SOLVEPNP_P3P is used.
1010	- The method used to estimate the camera pose using all the inliers is defined by the
1011	flags parameters unless it is equal to #SOLVEPNP_P3P or #SOLVEPNP_AP3P. In this case,
1012	the method #SOLVEPNP_EPNP will be used instead.
1013	*/
1014	CV_EXPORTS_W bool solvePnPRansac( InputArray objectPoints, InputArray imagePoints,
1015	InputArray cameraMatrix, InputArray distCoeffs,
1016	OutputArray rvec, OutputArray tvec,
1017	bool useExtrinsicGuess = false, int iterationsCount = 100,
1018	float reprojectionError = 8.0, double confidence = 0.99,
1019	OutputArray inliers = noArray(), int flags = SOLVEPNP_ITERATIVE );
1020
1021
1022	/*
1023	Finds rotation and translation vector.
1024	If cameraMatrix is given then run P3P. Otherwise run linear P6P and output cameraMatrix too.
1025	*/
1026	CV_EXPORTS_W bool solvePnPRansac( InputArray objectPoints, InputArray imagePoints,
1027	InputOutputArray cameraMatrix, InputArray distCoeffs,
1028	OutputArray rvec, OutputArray tvec, OutputArray inliers,
1029	const UsacParams &params=UsacParams());
1030
1031	/** @brief Finds an object pose from 3 3D-2D point correspondences.
1032
1033	@see @ref calib3d_solvePnP
1034
1035	@param objectPoints Array of object points in the object coordinate space, 3x3 1-channel or
1036	1x3/3x1 3-channel. vector\<Point3f\> can be also passed here.
1037	@param imagePoints Array of corresponding image points, 3x2 1-channel or 1x3/3x1 2-channel.
1038	vector\<Point2f\> can be also passed here.
1039	@param cameraMatrix Input camera intrinsic matrix \f$\cameramatrix{A}\f$ .
1040	@param distCoeffs Input vector of distortion coefficients
1041	\f$\distcoeffs\f$. If the vector is NULL/empty, the zero distortion coefficients are
1042	assumed.
1043	@param rvecs Output rotation vectors (see @ref Rodrigues ) that, together with tvecs, brings points from
1044	the model coordinate system to the camera coordinate system. A P3P problem has up to 4 solutions.
1045	@param tvecs Output translation vectors.
1046	@param flags Method for solving a P3P problem:
1047	- @ref SOLVEPNP_P3P Method is based on the paper of X.S. Gao, X.-R. Hou, J. Tang, H.-F. Chang
1048	"Complete Solution Classification for the Perspective-Three-Point Problem" (@cite gao2003complete).
1049	- @ref SOLVEPNP_AP3P Method is based on the paper of T. Ke and S. Roumeliotis.
1050	"An Efficient Algebraic Solution to the Perspective-Three-Point Problem" (@cite Ke17).
1051
1052	The function estimates the object pose given 3 object points, their corresponding image
1053	projections, as well as the camera intrinsic matrix and the distortion coefficients.
1054
1055	@note
1056	The solutions are sorted by reprojection errors (lowest to highest).
1057	*/
1058	CV_EXPORTS_W int solveP3P( InputArray objectPoints, InputArray imagePoints,
1059	InputArray cameraMatrix, InputArray distCoeffs,
1060	OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs,
1061	int flags );
1062
1063	/** @brief Refine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame
1064	to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution.
1065
1066	@see @ref calib3d_solvePnP
1067
1068	@param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel,
1069	where N is the number of points. vector\<Point3d\> can also be passed here.
1070	@param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
1071	where N is the number of points. vector\<Point2d\> can also be passed here.
1072	@param cameraMatrix Input camera intrinsic matrix \f$\cameramatrix{A}\f$ .
1073	@param distCoeffs Input vector of distortion coefficients
1074	\f$\distcoeffs\f$. If the vector is NULL/empty, the zero distortion coefficients are
1075	assumed.
1076	@param rvec Input/Output rotation vector (see @ref Rodrigues ) that, together with tvec, brings points from
1077	the model coordinate system to the camera coordinate system. Input values are used as an initial solution.
1078	@param tvec Input/Output translation vector. Input values are used as an initial solution.
1079	@param criteria Criteria when to stop the Levenberg-Marquard iterative algorithm.
1080
1081	The function refines the object pose given at least 3 object points, their corresponding image
1082	projections, an initial solution for the rotation and translation vector,
1083	as well as the camera intrinsic matrix and the distortion coefficients.
1084	The function minimizes the projection error with respect to the rotation and the translation vectors, according
1085	to a Levenberg-Marquardt iterative minimization @cite Madsen04 @cite Eade13 process.
1086	*/
1087	CV_EXPORTS_W void solvePnPRefineLM( InputArray objectPoints, InputArray imagePoints,
1088	InputArray cameraMatrix, InputArray distCoeffs,
1089	InputOutputArray rvec, InputOutputArray tvec,
1090	TermCriteria criteria = TermCriteria(TermCriteria::EPS + TermCriteria::COUNT, 20, FLT_EPSILON));
1091
1092	/** @brief Refine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame
1093	to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution.
1094
1095	@see @ref calib3d_solvePnP
1096
1097	@param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel,
1098	where N is the number of points. vector\<Point3d\> can also be passed here.
1099	@param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
1100	where N is the number of points. vector\<Point2d\> can also be passed here.
1101	@param cameraMatrix Input camera intrinsic matrix \f$\cameramatrix{A}\f$ .
1102	@param distCoeffs Input vector of distortion coefficients
1103	\f$\distcoeffs\f$. If the vector is NULL/empty, the zero distortion coefficients are
1104	assumed.
1105	@param rvec Input/Output rotation vector (see @ref Rodrigues ) that, together with tvec, brings points from
1106	the model coordinate system to the camera coordinate system. Input values are used as an initial solution.
1107	@param tvec Input/Output translation vector. Input values are used as an initial solution.
1108	@param criteria Criteria when to stop the Levenberg-Marquard iterative algorithm.
1109	@param VVSlambda Gain for the virtual visual servoing control law, equivalent to the \f$\alpha\f$
1110	gain in the Damped Gauss-Newton formulation.
1111
1112	The function refines the object pose given at least 3 object points, their corresponding image
1113	projections, an initial solution for the rotation and translation vector,
1114	as well as the camera intrinsic matrix and the distortion coefficients.
1115	The function minimizes the projection error with respect to the rotation and the translation vectors, using a
1116	virtual visual servoing (VVS) @cite Chaumette06 @cite Marchand16 scheme.
1117	*/
1118	CV_EXPORTS_W void solvePnPRefineVVS( InputArray objectPoints, InputArray imagePoints,
1119	InputArray cameraMatrix, InputArray distCoeffs,
1120	InputOutputArray rvec, InputOutputArray tvec,
1121	TermCriteria criteria = TermCriteria(TermCriteria::EPS + TermCriteria::COUNT, 20, FLT_EPSILON),
1122	double VVSlambda = 1);
1123
1124	/** @brief Finds an object pose from 3D-2D point correspondences.
1125
1126	@see @ref calib3d_solvePnP
1127
1128	This function returns a list of all the possible solutions (a solution is a <rotation vector, translation vector>
1129	couple), depending on the number of input points and the chosen method:
1130	- P3P methods (@ref SOLVEPNP_P3P, @ref SOLVEPNP_AP3P): 3 or 4 input points. Number of returned solutions can be between 0 and 4 with 3 input points.
1131	- @ref SOLVEPNP_IPPE Input points must be >= 4 and object points must be coplanar. Returns 2 solutions.
1132	- @ref SOLVEPNP_IPPE_SQUARE Special case suitable for marker pose estimation.
1133	Number of input points must be 4 and 2 solutions are returned. Object points must be defined in the following order:
1134	- point 0: [-squareLength / 2, squareLength / 2, 0]
1135	- point 1: [ squareLength / 2, squareLength / 2, 0]
1136	- point 2: [ squareLength / 2, -squareLength / 2, 0]
1137	- point 3: [-squareLength / 2, -squareLength / 2, 0]
1138	- for all the other flags, number of input points must be >= 4 and object points can be in any configuration.
1139	Only 1 solution is returned.
1140
1141	@param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or
1142	1xN/Nx1 3-channel, where N is the number of points. vector\<Point3d\> can be also passed here.
1143	@param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
1144	where N is the number of points. vector\<Point2d\> can be also passed here.
1145	@param cameraMatrix Input camera intrinsic matrix \f$\cameramatrix{A}\f$ .
1146	@param distCoeffs Input vector of distortion coefficients
1147	\f$\distcoeffs\f$. If the vector is NULL/empty, the zero distortion coefficients are
1148	assumed.
1149	@param rvecs Vector of output rotation vectors (see @ref Rodrigues ) that, together with tvecs, brings points from
1150	the model coordinate system to the camera coordinate system.
1151	@param tvecs Vector of output translation vectors.
1152	@param useExtrinsicGuess Parameter used for #SOLVEPNP_ITERATIVE. If true (1), the function uses
1153	the provided rvec and tvec values as initial approximations of the rotation and translation
1154	vectors, respectively, and further optimizes them.
1155	@param flags Method for solving a PnP problem: see @ref calib3d_solvePnP_flags
1156	@param rvec Rotation vector used to initialize an iterative PnP refinement algorithm, when flag is @ref SOLVEPNP_ITERATIVE
1157	and useExtrinsicGuess is set to true.
1158	@param tvec Translation vector used to initialize an iterative PnP refinement algorithm, when flag is @ref SOLVEPNP_ITERATIVE
1159	and useExtrinsicGuess is set to true.
1160	@param reprojectionError Optional vector of reprojection error, that is the RMS error
1161	(\f$ \text{RMSE} = \sqrt{\frac{\sum_{i}^{N} \left ( \hat{y_i} - y_i \right )^2}{N}} \f$) between the input image points
1162	and the 3D object points projected with the estimated pose.
1163
1164	More information is described in @ref calib3d_solvePnP
1165
1166	@note
1167	- An example of how to use solvePnP for planar augmented reality can be found at
1168	opencv_source_code/samples/python/plane_ar.py
1169	- If you are using Python:
1170	- Numpy array slices won't work as input because solvePnP requires contiguous
1171	arrays (enforced by the assertion using cv::Mat::checkVector() around line 55 of
1172	modules/calib3d/src/solvepnp.cpp version 2.4.9)
1173	- The P3P algorithm requires image points to be in an array of shape (N,1,2) due
1174	to its calling of #undistortPoints (around line 75 of modules/calib3d/src/solvepnp.cpp version 2.4.9)
1175	which requires 2-channel information.
1176	- Thus, given some data D = np.array(...) where D.shape = (N,M), in order to use a subset of
1177	it as, e.g., imagePoints, one must effectively copy it into a new array: imagePoints =
1178	np.ascontiguousarray(D[:,:2]).reshape((N,1,2))
1179	- The methods @ref SOLVEPNP_DLS and @ref SOLVEPNP_UPNP cannot be used as the current implementations are
1180	unstable and sometimes give completely wrong results. If you pass one of these two
1181	flags, @ref SOLVEPNP_EPNP method will be used instead.
1182	- The minimum number of points is 4 in the general case. In the case of @ref SOLVEPNP_P3P and @ref SOLVEPNP_AP3P
1183	methods, it is required to use exactly 4 points (the first 3 points are used to estimate all the solutions
1184	of the P3P problem, the last one is used to retain the best solution that minimizes the reprojection error).
1185	- With @ref SOLVEPNP_ITERATIVE method and `useExtrinsicGuess=true`, the minimum number of points is 3 (3 points
1186	are sufficient to compute a pose but there are up to 4 solutions). The initial solution should be close to the
1187	global solution to converge.
1188	- With @ref SOLVEPNP_IPPE input points must be >= 4 and object points must be coplanar.
1189	- With @ref SOLVEPNP_IPPE_SQUARE this is a special case suitable for marker pose estimation.
1190	Number of input points must be 4. Object points must be defined in the following order:
1191	- point 0: [-squareLength / 2, squareLength / 2, 0]
1192	- point 1: [ squareLength / 2, squareLength / 2, 0]
1193	- point 2: [ squareLength / 2, -squareLength / 2, 0]
1194	- point 3: [-squareLength / 2, -squareLength / 2, 0]
1195	*/
1196	CV_EXPORTS_W int solvePnPGeneric( InputArray objectPoints, InputArray imagePoints,
1197	InputArray cameraMatrix, InputArray distCoeffs,
1198	OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs,
1199	bool useExtrinsicGuess = false, SolvePnPMethod flags = SOLVEPNP_ITERATIVE,
1200	InputArray rvec = noArray(), InputArray tvec = noArray(),
1201	OutputArray reprojectionError = noArray() );
1202
1203	/** @brief Finds an initial camera intrinsic matrix from 3D-2D point correspondences.
1204
1205	@param objectPoints Vector of vectors of the calibration pattern points in the calibration pattern
1206	coordinate space. In the old interface all the per-view vectors are concatenated. See
1207	#calibrateCamera for details.
1208	@param imagePoints Vector of vectors of the projections of the calibration pattern points. In the
1209	old interface all the per-view vectors are concatenated.
1210	@param imageSize Image size in pixels used to initialize the principal point.
1211	@param aspectRatio If it is zero or negative, both \f$f_x\f$ and \f$f_y\f$ are estimated independently.
1212	Otherwise, \f$f_x = f_y \cdot \texttt{aspectRatio}\f$ .
1213
1214	The function estimates and returns an initial camera intrinsic matrix for the camera calibration process.
1215	Currently, the function only supports planar calibration patterns, which are patterns where each
1216	object point has z-coordinate =0.
1217	*/
1218	CV_EXPORTS_W Mat initCameraMatrix2D( InputArrayOfArrays objectPoints,
1219	InputArrayOfArrays imagePoints,
1220	Size imageSize, double aspectRatio = 1.0 );
1221
1222	/** @brief Finds the positions of internal corners of the chessboard.
1223
1224	@param image Source chessboard view. It must be an 8-bit grayscale or color image.
1225	@param patternSize Number of inner corners per a chessboard row and column
1226	( patternSize = cv::Size(points_per_row,points_per_colum) = cv::Size(columns,rows) ).
1227	@param corners Output array of detected corners.
1228	@param flags Various operation flags that can be zero or a combination of the following values:
1229	- @ref CALIB_CB_ADAPTIVE_THRESH Use adaptive thresholding to convert the image to black
1230	and white, rather than a fixed threshold level (computed from the average image brightness).
1231	- @ref CALIB_CB_NORMALIZE_IMAGE Normalize the image gamma with #equalizeHist before
1232	applying fixed or adaptive thresholding.
1233	- @ref CALIB_CB_FILTER_QUADS Use additional criteria (like contour area, perimeter,
1234	square-like shape) to filter out false quads extracted at the contour retrieval stage.
1235	- @ref CALIB_CB_FAST_CHECK Run a fast check on the image that looks for chessboard corners,
1236	and shortcut the call if none is found. This can drastically speed up the call in the
1237	degenerate condition when no chessboard is observed.
1238	- @ref CALIB_CB_PLAIN All other flags are ignored. The input image is taken as is.
1239	No image processing is done to improve to find the checkerboard. This has the effect of speeding up the
1240	execution of the function but could lead to not recognizing the checkerboard if the image
1241	is not previously binarized in the appropriate manner.
1242
1243	The function attempts to determine whether the input image is a view of the chessboard pattern and
1244	locate the internal chessboard corners. The function returns a non-zero value if all of the corners
1245	are found and they are placed in a certain order (row by row, left to right in every row).
1246	Otherwise, if the function fails to find all the corners or reorder them, it returns 0. For example,
1247	a regular chessboard has 8 x 8 squares and 7 x 7 internal corners, that is, points where the black
1248	squares touch each other. The detected coordinates are approximate, and to determine their positions
1249	more accurately, the function calls #cornerSubPix. You also may use the function #cornerSubPix with
1250	different parameters if returned coordinates are not accurate enough.
1251
1252	Sample usage of detecting and drawing chessboard corners: :
1253	@code
1254	Size patternsize(8,6); //interior number of corners
1255	Mat gray = ....; //source image
1256	vector<Point2f> corners; //this will be filled by the detected corners
1257
1258	//CALIB_CB_FAST_CHECK saves a lot of time on images
1259	//that do not contain any chessboard corners
1260	bool patternfound = findChessboardCorners(gray, patternsize, corners,
1261	CALIB_CB_ADAPTIVE_THRESH + CALIB_CB_NORMALIZE_IMAGE
1262	+ CALIB_CB_FAST_CHECK);
1263
1264	if(patternfound)
1265	cornerSubPix(gray, corners, Size(11, 11), Size(-1, -1),
1266	TermCriteria(CV_TERMCRIT_EPS + CV_TERMCRIT_ITER, 30, 0.1));
1267
1268	drawChessboardCorners(img, patternsize, Mat(corners), patternfound);
1269	@endcode
1270	@note The function requires white space (like a square-thick border, the wider the better) around
1271	the board to make the detection more robust in various environments. Otherwise, if there is no
1272	border and the background is dark, the outer black squares cannot be segmented properly and so the
1273	square grouping and ordering algorithm fails.
1274
1275	Use gen_pattern.py (@ref tutorial_camera_calibration_pattern) to create checkerboard.
1276	*/
1277	CV_EXPORTS_W bool findChessboardCorners( InputArray image, Size patternSize, OutputArray corners,
1278	int flags = CALIB_CB_ADAPTIVE_THRESH + CALIB_CB_NORMALIZE_IMAGE );
1279
1280	/*
1281	Checks whether the image contains chessboard of the specific size or not.
1282	If yes, nonzero value is returned.
1283	*/
1284	CV_EXPORTS_W bool checkChessboard(InputArray img, Size size);
1285
1286	/** @brief Finds the positions of internal corners of the chessboard using a sector based approach.
1287
1288	@param image Source chessboard view. It must be an 8-bit grayscale or color image.
1289	@param patternSize Number of inner corners per a chessboard row and column
1290	( patternSize = cv::Size(points_per_row,points_per_colum) = cv::Size(columns,rows) ).
1291	@param corners Output array of detected corners.
1292	@param flags Various operation flags that can be zero or a combination of the following values:
1293	- @ref CALIB_CB_NORMALIZE_IMAGE Normalize the image gamma with equalizeHist before detection.
1294	- @ref CALIB_CB_EXHAUSTIVE Run an exhaustive search to improve detection rate.
1295	- @ref CALIB_CB_ACCURACY Up sample input image to improve sub-pixel accuracy due to aliasing effects.
1296	- @ref CALIB_CB_LARGER The detected pattern is allowed to be larger than patternSize (see description).
1297	- @ref CALIB_CB_MARKER The detected pattern must have a marker (see description).
1298	This should be used if an accurate camera calibration is required.
1299	@param meta Optional output arrray of detected corners (CV_8UC1 and size = cv::Size(columns,rows)).
1300	Each entry stands for one corner of the pattern and can have one of the following values:
1301	- 0 = no meta data attached
1302	- 1 = left-top corner of a black cell
1303	- 2 = left-top corner of a white cell
1304	- 3 = left-top corner of a black cell with a white marker dot
1305	- 4 = left-top corner of a white cell with a black marker dot (pattern origin in case of markers otherwise first corner)
1306
1307	The function is analog to #findChessboardCorners but uses a localized radon
1308	transformation approximated by box filters being more robust to all sort of
1309	noise, faster on larger images and is able to directly return the sub-pixel
1310	position of the internal chessboard corners. The Method is based on the paper
1311	@cite duda2018 "Accurate Detection and Localization of Checkerboard Corners for
1312	Calibration" demonstrating that the returned sub-pixel positions are more
1313	accurate than the one returned by cornerSubPix allowing a precise camera
1314	calibration for demanding applications.
1315
1316	In the case, the flags @ref CALIB_CB_LARGER or @ref CALIB_CB_MARKER are given,
1317	the result can be recovered from the optional meta array. Both flags are
1318	helpful to use calibration patterns exceeding the field of view of the camera.
1319	These oversized patterns allow more accurate calibrations as corners can be
1320	utilized, which are as close as possible to the image borders. For a
1321	consistent coordinate system across all images, the optional marker (see image
1322	below) can be used to move the origin of the board to the location where the
1323	black circle is located.
1324
1325	@note The function requires a white boarder with roughly the same width as one
1326	of the checkerboard fields around the whole board to improve the detection in
1327	various environments. In addition, because of the localized radon
1328	transformation it is beneficial to use round corners for the field corners
1329	which are located on the outside of the board. The following figure illustrates
1330	a sample checkerboard optimized for the detection. However, any other checkerboard
1331	can be used as well.
1332
1333	Use gen_pattern.py (@ref tutorial_camera_calibration_pattern) to create checkerboard.
1334	
1335	*/
1336	CV_EXPORTS_AS(findChessboardCornersSBWithMeta)
1337	bool findChessboardCornersSB(InputArray image,Size patternSize, OutputArray corners,
1338	int flags,OutputArray meta);
1339	/** @overload */
1340	CV_EXPORTS_W inline
1341	bool findChessboardCornersSB(InputArray image, Size patternSize, OutputArray corners,
1342	int flags = 0)
1343	{
1344	return findChessboardCornersSB(image, patternSize, corners, flags, meta: noArray());
1345	}
1346
1347	/** @brief Estimates the sharpness of a detected chessboard.
1348
1349	Image sharpness, as well as brightness, are a critical parameter for accuracte
1350	camera calibration. For accessing these parameters for filtering out
1351	problematic calibraiton images, this method calculates edge profiles by traveling from
1352	black to white chessboard cell centers. Based on this, the number of pixels is
1353	calculated required to transit from black to white. This width of the
1354	transition area is a good indication of how sharp the chessboard is imaged
1355	and should be below ~3.0 pixels.
1356
1357	@param image Gray image used to find chessboard corners
1358	@param patternSize Size of a found chessboard pattern
1359	@param corners Corners found by #findChessboardCornersSB
1360	@param rise_distance Rise distance 0.8 means 10% ... 90% of the final signal strength
1361	@param vertical By default edge responses for horizontal lines are calculated
1362	@param sharpness Optional output array with a sharpness value for calculated edge responses (see description)
1363
1364	The optional sharpness array is of type CV_32FC1 and has for each calculated
1365	profile one row with the following five entries:
1366	* 0 = x coordinate of the underlying edge in the image
1367	* 1 = y coordinate of the underlying edge in the image
1368	* 2 = width of the transition area (sharpness)
1369	* 3 = signal strength in the black cell (min brightness)
1370	* 4 = signal strength in the white cell (max brightness)
1371
1372	@return Scalar(average sharpness, average min brightness, average max brightness,0)
1373	*/
1374	CV_EXPORTS_W Scalar estimateChessboardSharpness(InputArray image, Size patternSize, InputArray corners,
1375	float rise_distance=0.8F,bool vertical=false,
1376	OutputArray sharpness=noArray());
1377
1378
1379	//! finds subpixel-accurate positions of the chessboard corners
1380	CV_EXPORTS_W bool find4QuadCornerSubpix( InputArray img, InputOutputArray corners, Size region_size );
1381
1382	/** @brief Renders the detected chessboard corners.
1383
1384	@param image Destination image. It must be an 8-bit color image.
1385	@param patternSize Number of inner corners per a chessboard row and column
1386	(patternSize = cv::Size(points_per_row,points_per_column)).
1387	@param corners Array of detected corners, the output of #findChessboardCorners.
1388	@param patternWasFound Parameter indicating whether the complete board was found or not. The
1389	return value of #findChessboardCorners should be passed here.
1390
1391	The function draws individual chessboard corners detected either as red circles if the board was not
1392	found, or as colored corners connected with lines if the board was found.
1393	*/
1394	CV_EXPORTS_W void drawChessboardCorners( InputOutputArray image, Size patternSize,
1395	InputArray corners, bool patternWasFound );
1396
1397	/** @brief Draw axes of the world/object coordinate system from pose estimation. @sa solvePnP
1398
1399	@param image Input/output image. It must have 1 or 3 channels. The number of channels is not altered.
1400	@param cameraMatrix Input 3x3 floating-point matrix of camera intrinsic parameters.
1401	\f$\cameramatrix{A}\f$
1402	@param distCoeffs Input vector of distortion coefficients
1403	\f$\distcoeffs\f$. If the vector is empty, the zero distortion coefficients are assumed.
1404	@param rvec Rotation vector (see @ref Rodrigues ) that, together with tvec, brings points from
1405	the model coordinate system to the camera coordinate system.
1406	@param tvec Translation vector.
1407	@param length Length of the painted axes in the same unit than tvec (usually in meters).
1408	@param thickness Line thickness of the painted axes.
1409
1410	This function draws the axes of the world/object coordinate system w.r.t. to the camera frame.
1411	OX is drawn in red, OY in green and OZ in blue.
1412	*/
1413	CV_EXPORTS_W void drawFrameAxes(InputOutputArray image, InputArray cameraMatrix, InputArray distCoeffs,
1414	InputArray rvec, InputArray tvec, float length, int thickness=3);
1415
1416	struct CV_EXPORTS_W_SIMPLE CirclesGridFinderParameters
1417	{
1418	CV_WRAP CirclesGridFinderParameters();
1419	CV_PROP_RW cv::Size2f densityNeighborhoodSize;
1420	CV_PROP_RW float minDensity;
1421	CV_PROP_RW int kmeansAttempts;
1422	CV_PROP_RW int minDistanceToAddKeypoint;
1423	CV_PROP_RW int keypointScale;
1424	CV_PROP_RW float minGraphConfidence;
1425	CV_PROP_RW float vertexGain;
1426	CV_PROP_RW float vertexPenalty;
1427	CV_PROP_RW float existingVertexGain;
1428	CV_PROP_RW float edgeGain;
1429	CV_PROP_RW float edgePenalty;
1430	CV_PROP_RW float convexHullFactor;
1431	CV_PROP_RW float minRNGEdgeSwitchDist;
1432
1433	enum GridType
1434	{
1435	SYMMETRIC_GRID, ASYMMETRIC_GRID
1436	};
1437	GridType gridType;
1438
1439	CV_PROP_RW float squareSize; //!< Distance between two adjacent points. Used by CALIB_CB_CLUSTERING.
1440	CV_PROP_RW float maxRectifiedDistance; //!< Max deviation from prediction. Used by CALIB_CB_CLUSTERING.
1441	};
1442
1443	#ifndef DISABLE_OPENCV_3_COMPATIBILITY
1444	typedef CirclesGridFinderParameters CirclesGridFinderParameters2;
1445	#endif
1446
1447	/** @brief Finds centers in the grid of circles.
1448
1449	@param image grid view of input circles; it must be an 8-bit grayscale or color image.
1450	@param patternSize number of circles per row and column
1451	( patternSize = Size(points_per_row, points_per_colum) ).
1452	@param centers output array of detected centers.
1453	@param flags various operation flags that can be one of the following values:
1454	- @ref CALIB_CB_SYMMETRIC_GRID uses symmetric pattern of circles.
1455	- @ref CALIB_CB_ASYMMETRIC_GRID uses asymmetric pattern of circles.
1456	- @ref CALIB_CB_CLUSTERING uses a special algorithm for grid detection. It is more robust to
1457	perspective distortions but much more sensitive to background clutter.
1458	@param blobDetector feature detector that finds blobs like dark circles on light background.
1459	If `blobDetector` is NULL then `image` represents Point2f array of candidates.
1460	@param parameters struct for finding circles in a grid pattern.
1461
1462	The function attempts to determine whether the input image contains a grid of circles. If it is, the
1463	function locates centers of the circles. The function returns a non-zero value if all of the centers
1464	have been found and they have been placed in a certain order (row by row, left to right in every
1465	row). Otherwise, if the function fails to find all the corners or reorder them, it returns 0.
1466
1467	Sample usage of detecting and drawing the centers of circles: :
1468	@code
1469	Size patternsize(7,7); //number of centers
1470	Mat gray = ...; //source image
1471	vector<Point2f> centers; //this will be filled by the detected centers
1472
1473	bool patternfound = findCirclesGrid(gray, patternsize, centers);
1474
1475	drawChessboardCorners(img, patternsize, Mat(centers), patternfound);
1476	@endcode
1477	@note The function requires white space (like a square-thick border, the wider the better) around
1478	the board to make the detection more robust in various environments.
1479	*/
1480	CV_EXPORTS_W bool findCirclesGrid( InputArray image, Size patternSize,
1481	OutputArray centers, int flags,
1482	const Ptr<FeatureDetector> &blobDetector,
1483	const CirclesGridFinderParameters& parameters);
1484
1485	/** @overload */
1486	CV_EXPORTS_W bool findCirclesGrid( InputArray image, Size patternSize,
1487	OutputArray centers, int flags = CALIB_CB_SYMMETRIC_GRID,
1488	const Ptr<FeatureDetector> &blobDetector = SimpleBlobDetector::create());
1489
1490	/** @brief Finds the camera intrinsic and extrinsic parameters from several views of a calibration
1491	pattern.
1492
1493	@param objectPoints In the new interface it is a vector of vectors of calibration pattern points in
1494	the calibration pattern coordinate space (e.g. std::vector<std::vector<cv::Vec3f>>). The outer
1495	vector contains as many elements as the number of pattern views. If the same calibration pattern
1496	is shown in each view and it is fully visible, all the vectors will be the same. Although, it is
1497	possible to use partially occluded patterns or even different patterns in different views. Then,
1498	the vectors will be different. Although the points are 3D, they all lie in the calibration pattern's
1499	XY coordinate plane (thus 0 in the Z-coordinate), if the used calibration pattern is a planar rig.
1500	In the old interface all the vectors of object points from different views are concatenated
1501	together.
1502	@param imagePoints In the new interface it is a vector of vectors of the projections of calibration
1503	pattern points (e.g. std::vector<std::vector<cv::Vec2f>>). imagePoints.size() and
1504	objectPoints.size(), and imagePoints[i].size() and objectPoints[i].size() for each i, must be equal,
1505	respectively. In the old interface all the vectors of object points from different views are
1506	concatenated together.
1507	@param imageSize Size of the image used only to initialize the camera intrinsic matrix.
1508	@param cameraMatrix Input/output 3x3 floating-point camera intrinsic matrix
1509	\f$\cameramatrix{A}\f$ . If @ref CALIB_USE_INTRINSIC_GUESS
1510	and/or @ref CALIB_FIX_ASPECT_RATIO, @ref CALIB_FIX_PRINCIPAL_POINT or @ref CALIB_FIX_FOCAL_LENGTH
1511	are specified, some or all of fx, fy, cx, cy must be initialized before calling the function.
1512	@param distCoeffs Input/output vector of distortion coefficients
1513	\f$\distcoeffs\f$.
1514	@param rvecs Output vector of rotation vectors (@ref Rodrigues ) estimated for each pattern view
1515	(e.g. std::vector<cv::Mat>>). That is, each i-th rotation vector together with the corresponding
1516	i-th translation vector (see the next output parameter description) brings the calibration pattern
1517	from the object coordinate space (in which object points are specified) to the camera coordinate
1518	space. In more technical terms, the tuple of the i-th rotation and translation vector performs
1519	a change of basis from object coordinate space to camera coordinate space. Due to its duality, this
1520	tuple is equivalent to the position of the calibration pattern with respect to the camera coordinate
1521	space.
1522	@param tvecs Output vector of translation vectors estimated for each pattern view, see parameter
1523	describtion above.
1524	@param stdDeviationsIntrinsics Output vector of standard deviations estimated for intrinsic
1525	parameters. Order of deviations values:
1526	\f$(f_x, f_y, c_x, c_y, k_1, k_2, p_1, p_2, k_3, k_4, k_5, k_6 , s_1, s_2, s_3,
1527	s_4, \tau_x, \tau_y)\f$ If one of parameters is not estimated, it's deviation is equals to zero.
1528	@param stdDeviationsExtrinsics Output vector of standard deviations estimated for extrinsic
1529	parameters. Order of deviations values: \f$(R_0, T_0, \dotsc , R_{M - 1}, T_{M - 1})\f$ where M is
1530	the number of pattern views. \f$R_i, T_i\f$ are concatenated 1x3 vectors.
1531	@param perViewErrors Output vector of the RMS re-projection error estimated for each pattern view.
1532	@param flags Different flags that may be zero or a combination of the following values:
1533	- @ref CALIB_USE_INTRINSIC_GUESS cameraMatrix contains valid initial values of
1534	fx, fy, cx, cy that are optimized further. Otherwise, (cx, cy) is initially set to the image
1535	center ( imageSize is used), and focal distances are computed in a least-squares fashion.
1536	Note, that if intrinsic parameters are known, there is no need to use this function just to
1537	estimate extrinsic parameters. Use @ref solvePnP instead.
1538	- @ref CALIB_FIX_PRINCIPAL_POINT The principal point is not changed during the global
1539	optimization. It stays at the center or at a different location specified when
1540	@ref CALIB_USE_INTRINSIC_GUESS is set too.
1541	- @ref CALIB_FIX_ASPECT_RATIO The functions consider only fy as a free parameter. The
1542	ratio fx/fy stays the same as in the input cameraMatrix . When
1543	@ref CALIB_USE_INTRINSIC_GUESS is not set, the actual input values of fx and fy are
1544	ignored, only their ratio is computed and used further.
1545	- @ref CALIB_ZERO_TANGENT_DIST Tangential distortion coefficients \f$(p_1, p_2)\f$ are set
1546	to zeros and stay zero.
1547	- @ref CALIB_FIX_FOCAL_LENGTH The focal length is not changed during the global optimization if
1548	@ref CALIB_USE_INTRINSIC_GUESS is set.
1549	- @ref CALIB_FIX_K1,..., @ref CALIB_FIX_K6 The corresponding radial distortion
1550	coefficient is not changed during the optimization. If @ref CALIB_USE_INTRINSIC_GUESS is
1551	set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
1552	- @ref CALIB_RATIONAL_MODEL Coefficients k4, k5, and k6 are enabled. To provide the
1553	backward compatibility, this extra flag should be explicitly specified to make the
1554	calibration function use the rational model and return 8 coefficients or more.
1555	- @ref CALIB_THIN_PRISM_MODEL Coefficients s1, s2, s3 and s4 are enabled. To provide the
1556	backward compatibility, this extra flag should be explicitly specified to make the
1557	calibration function use the thin prism model and return 12 coefficients or more.
1558	- @ref CALIB_FIX_S1_S2_S3_S4 The thin prism distortion coefficients are not changed during
1559	the optimization. If @ref CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the
1560	supplied distCoeffs matrix is used. Otherwise, it is set to 0.
1561	- @ref CALIB_TILTED_MODEL Coefficients tauX and tauY are enabled. To provide the
1562	backward compatibility, this extra flag should be explicitly specified to make the
1563	calibration function use the tilted sensor model and return 14 coefficients.
1564	- @ref CALIB_FIX_TAUX_TAUY The coefficients of the tilted sensor model are not changed during
1565	the optimization. If @ref CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the
1566	supplied distCoeffs matrix is used. Otherwise, it is set to 0.
1567	@param criteria Termination criteria for the iterative optimization algorithm.
1568
1569	@return the overall RMS re-projection error.
1570
1571	The function estimates the intrinsic camera parameters and extrinsic parameters for each of the
1572	views. The algorithm is based on @cite Zhang2000 and @cite BouguetMCT . The coordinates of 3D object
1573	points and their corresponding 2D projections in each view must be specified. That may be achieved
1574	by using an object with known geometry and easily detectable feature points. Such an object is
1575	called a calibration rig or calibration pattern, and OpenCV has built-in support for a chessboard as
1576	a calibration rig (see @ref findChessboardCorners). Currently, initialization of intrinsic
1577	parameters (when @ref CALIB_USE_INTRINSIC_GUESS is not set) is only implemented for planar calibration
1578	patterns (where Z-coordinates of the object points must be all zeros). 3D calibration rigs can also
1579	be used as long as initial cameraMatrix is provided.
1580
1581	The algorithm performs the following steps:
1582
1583	- Compute the initial intrinsic parameters (the option only available for planar calibration
1584	patterns) or read them from the input parameters. The distortion coefficients are all set to
1585	zeros initially unless some of CALIB_FIX_K? are specified.
1586
1587	- Estimate the initial camera pose as if the intrinsic parameters have been already known. This is
1588	done using @ref solvePnP .
1589
1590	- Run the global Levenberg-Marquardt optimization algorithm to minimize the reprojection error,
1591	that is, the total sum of squared distances between the observed feature points imagePoints and
1592	the projected (using the current estimates for camera parameters and the poses) object points
1593	objectPoints. See @ref projectPoints for details.
1594
1595	@note
1596	If you use a non-square (i.e. non-N-by-N) grid and @ref findChessboardCorners for calibration,
1597	and @ref calibrateCamera returns bad values (zero distortion coefficients, \f$c_x\f$ and
1598	\f$c_y\f$ very far from the image center, and/or large differences between \f$f_x\f$ and
1599	\f$f_y\f$ (ratios of 10:1 or more)), then you are probably using patternSize=cvSize(rows,cols)
1600	instead of using patternSize=cvSize(cols,rows) in @ref findChessboardCorners.
1601
1602	@note
1603	The function may throw exceptions, if unsupported combination of parameters is provided or
1604	the system is underconstrained.
1605
1606	@sa
1607	calibrateCameraRO, findChessboardCorners, solvePnP, initCameraMatrix2D, stereoCalibrate,
1608	undistort
1609	*/
1610	CV_EXPORTS_AS(calibrateCameraExtended) double calibrateCamera( InputArrayOfArrays objectPoints,
1611	InputArrayOfArrays imagePoints, Size imageSize,
1612	InputOutputArray cameraMatrix, InputOutputArray distCoeffs,
1613	OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs,
1614	OutputArray stdDeviationsIntrinsics,
1615	OutputArray stdDeviationsExtrinsics,
1616	OutputArray perViewErrors,
1617	int flags = 0, TermCriteria criteria = TermCriteria(
1618	TermCriteria::COUNT + TermCriteria::EPS, 30, DBL_EPSILON) );
1619
1620	/** @overload */
1621	CV_EXPORTS_W double calibrateCamera( InputArrayOfArrays objectPoints,
1622	InputArrayOfArrays imagePoints, Size imageSize,
1623	InputOutputArray cameraMatrix, InputOutputArray distCoeffs,
1624	OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs,
1625	int flags = 0, TermCriteria criteria = TermCriteria(
1626	TermCriteria::COUNT + TermCriteria::EPS, 30, DBL_EPSILON) );
1627
1628	/** @brief Finds the camera intrinsic and extrinsic parameters from several views of a calibration pattern.
1629
1630	This function is an extension of #calibrateCamera with the method of releasing object which was
1631	proposed in @cite strobl2011iccv. In many common cases with inaccurate, unmeasured, roughly planar
1632	targets (calibration plates), this method can dramatically improve the precision of the estimated
1633	camera parameters. Both the object-releasing method and standard method are supported by this
1634	function. Use the parameter **iFixedPoint** for method selection. In the internal implementation,
1635	#calibrateCamera is a wrapper for this function.
1636
1637	@param objectPoints Vector of vectors of calibration pattern points in the calibration pattern
1638	coordinate space. See #calibrateCamera for details. If the method of releasing object to be used,
1639	the identical calibration board must be used in each view and it must be fully visible, and all
1640	objectPoints[i] must be the same and all points should be roughly close to a plane. **The calibration
1641	target has to be rigid, or at least static if the camera (rather than the calibration target) is
1642	shifted for grabbing images.**
1643	@param imagePoints Vector of vectors of the projections of calibration pattern points. See
1644	#calibrateCamera for details.
1645	@param imageSize Size of the image used only to initialize the intrinsic camera matrix.
1646	@param iFixedPoint The index of the 3D object point in objectPoints[0] to be fixed. It also acts as
1647	a switch for calibration method selection. If object-releasing method to be used, pass in the
1648	parameter in the range of [1, objectPoints[0].size()-2], otherwise a value out of this range will
1649	make standard calibration method selected. Usually the top-right corner point of the calibration
1650	board grid is recommended to be fixed when object-releasing method being utilized. According to
1651	\cite strobl2011iccv, two other points are also fixed. In this implementation, objectPoints[0].front
1652	and objectPoints[0].back.z are used. With object-releasing method, accurate rvecs, tvecs and
1653	newObjPoints are only possible if coordinates of these three fixed points are accurate enough.
1654	@param cameraMatrix Output 3x3 floating-point camera matrix. See #calibrateCamera for details.
1655	@param distCoeffs Output vector of distortion coefficients. See #calibrateCamera for details.
1656	@param rvecs Output vector of rotation vectors estimated for each pattern view. See #calibrateCamera
1657	for details.
1658	@param tvecs Output vector of translation vectors estimated for each pattern view.
1659	@param newObjPoints The updated output vector of calibration pattern points. The coordinates might
1660	be scaled based on three fixed points. The returned coordinates are accurate only if the above
1661	mentioned three fixed points are accurate. If not needed, noArray() can be passed in. This parameter
1662	is ignored with standard calibration method.
1663	@param stdDeviationsIntrinsics Output vector of standard deviations estimated for intrinsic parameters.
1664	See #calibrateCamera for details.
1665	@param stdDeviationsExtrinsics Output vector of standard deviations estimated for extrinsic parameters.
1666	See #calibrateCamera for details.
1667	@param stdDeviationsObjPoints Output vector of standard deviations estimated for refined coordinates
1668	of calibration pattern points. It has the same size and order as objectPoints[0] vector. This
1669	parameter is ignored with standard calibration method.
1670	@param perViewErrors Output vector of the RMS re-projection error estimated for each pattern view.
1671	@param flags Different flags that may be zero or a combination of some predefined values. See
1672	#calibrateCamera for details. If the method of releasing object is used, the calibration time may
1673	be much longer. CALIB_USE_QR or CALIB_USE_LU could be used for faster calibration with potentially
1674	less precise and less stable in some rare cases.
1675	@param criteria Termination criteria for the iterative optimization algorithm.
1676
1677	@return the overall RMS re-projection error.
1678
1679	The function estimates the intrinsic camera parameters and extrinsic parameters for each of the
1680	views. The algorithm is based on @cite Zhang2000, @cite BouguetMCT and @cite strobl2011iccv. See
1681	#calibrateCamera for other detailed explanations.
1682	@sa
1683	calibrateCamera, findChessboardCorners, solvePnP, initCameraMatrix2D, stereoCalibrate, undistort
1684	*/
1685	CV_EXPORTS_AS(calibrateCameraROExtended) double calibrateCameraRO( InputArrayOfArrays objectPoints,
1686	InputArrayOfArrays imagePoints, Size imageSize, int iFixedPoint,
1687	InputOutputArray cameraMatrix, InputOutputArray distCoeffs,
1688	OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs,
1689	OutputArray newObjPoints,
1690	OutputArray stdDeviationsIntrinsics,
1691	OutputArray stdDeviationsExtrinsics,
1692	OutputArray stdDeviationsObjPoints,
1693	OutputArray perViewErrors,
1694	int flags = 0, TermCriteria criteria = TermCriteria(
1695	TermCriteria::COUNT + TermCriteria::EPS, 30, DBL_EPSILON) );
1696
1697	/** @overload */
1698	CV_EXPORTS_W double calibrateCameraRO( InputArrayOfArrays objectPoints,
1699	InputArrayOfArrays imagePoints, Size imageSize, int iFixedPoint,
1700	InputOutputArray cameraMatrix, InputOutputArray distCoeffs,
1701	OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs,
1702	OutputArray newObjPoints,
1703	int flags = 0, TermCriteria criteria = TermCriteria(
1704	TermCriteria::COUNT + TermCriteria::EPS, 30, DBL_EPSILON) );
1705
1706	/** @brief Computes useful camera characteristics from the camera intrinsic matrix.
1707
1708	@param cameraMatrix Input camera intrinsic matrix that can be estimated by #calibrateCamera or
1709	#stereoCalibrate .
1710	@param imageSize Input image size in pixels.
1711	@param apertureWidth Physical width in mm of the sensor.
1712	@param apertureHeight Physical height in mm of the sensor.
1713	@param fovx Output field of view in degrees along the horizontal sensor axis.
1714	@param fovy Output field of view in degrees along the vertical sensor axis.
1715	@param focalLength Focal length of the lens in mm.
1716	@param principalPoint Principal point in mm.
1717	@param aspectRatio \f$f_y/f_x\f$
1718
1719	The function computes various useful camera characteristics from the previously estimated camera
1720	matrix.
1721
1722	@note
1723	Do keep in mind that the unity measure 'mm' stands for whatever unit of measure one chooses for
1724	the chessboard pitch (it can thus be any value).
1725	*/
1726	CV_EXPORTS_W void calibrationMatrixValues( InputArray cameraMatrix, Size imageSize,
1727	double apertureWidth, double apertureHeight,
1728	CV_OUT double& fovx, CV_OUT double& fovy,
1729	CV_OUT double& focalLength, CV_OUT Point2d& principalPoint,
1730	CV_OUT double& aspectRatio );
1731
1732	/** @brief Calibrates a stereo camera set up. This function finds the intrinsic parameters
1733	for each of the two cameras and the extrinsic parameters between the two cameras.
1734
1735	@param objectPoints Vector of vectors of the calibration pattern points. The same structure as
1736	in @ref calibrateCamera. For each pattern view, both cameras need to see the same object
1737	points. Therefore, objectPoints.size(), imagePoints1.size(), and imagePoints2.size() need to be
1738	equal as well as objectPoints[i].size(), imagePoints1[i].size(), and imagePoints2[i].size() need to
1739	be equal for each i.
1740	@param imagePoints1 Vector of vectors of the projections of the calibration pattern points,
1741	observed by the first camera. The same structure as in @ref calibrateCamera.
1742	@param imagePoints2 Vector of vectors of the projections of the calibration pattern points,
1743	observed by the second camera. The same structure as in @ref calibrateCamera.
1744	@param cameraMatrix1 Input/output camera intrinsic matrix for the first camera, the same as in
1745	@ref calibrateCamera. Furthermore, for the stereo case, additional flags may be used, see below.
1746	@param distCoeffs1 Input/output vector of distortion coefficients, the same as in
1747	@ref calibrateCamera.
1748	@param cameraMatrix2 Input/output second camera intrinsic matrix for the second camera. See description for
1749	cameraMatrix1.
1750	@param distCoeffs2 Input/output lens distortion coefficients for the second camera. See
1751	description for distCoeffs1.
1752	@param imageSize Size of the image used only to initialize the camera intrinsic matrices.
1753	@param R Output rotation matrix. Together with the translation vector T, this matrix brings
1754	points given in the first camera's coordinate system to points in the second camera's
1755	coordinate system. In more technical terms, the tuple of R and T performs a change of basis
1756	from the first camera's coordinate system to the second camera's coordinate system. Due to its
1757	duality, this tuple is equivalent to the position of the first camera with respect to the
1758	second camera coordinate system.
1759	@param T Output translation vector, see description above.
1760	@param E Output essential matrix.
1761	@param F Output fundamental matrix.
1762	@param rvecs Output vector of rotation vectors ( @ref Rodrigues ) estimated for each pattern view in the
1763	coordinate system of the first camera of the stereo pair (e.g. std::vector<cv::Mat>). More in detail, each
1764	i-th rotation vector together with the corresponding i-th translation vector (see the next output parameter
1765	description) brings the calibration pattern from the object coordinate space (in which object points are
1766	specified) to the camera coordinate space of the first camera of the stereo pair. In more technical terms,
1767	the tuple of the i-th rotation and translation vector performs a change of basis from object coordinate space
1768	to camera coordinate space of the first camera of the stereo pair.
1769	@param tvecs Output vector of translation vectors estimated for each pattern view, see parameter description
1770	of previous output parameter ( rvecs ).
1771	@param perViewErrors Output vector of the RMS re-projection error estimated for each pattern view.
1772	@param flags Different flags that may be zero or a combination of the following values:
1773	- @ref CALIB_FIX_INTRINSIC Fix cameraMatrix? and distCoeffs? so that only R, T, E, and F
1774	matrices are estimated.
1775	- @ref CALIB_USE_INTRINSIC_GUESS Optimize some or all of the intrinsic parameters
1776	according to the specified flags. Initial values are provided by the user.
1777	- @ref CALIB_USE_EXTRINSIC_GUESS R and T contain valid initial values that are optimized further.
1778	Otherwise R and T are initialized to the median value of the pattern views (each dimension separately).
1779	- @ref CALIB_FIX_PRINCIPAL_POINT Fix the principal points during the optimization.
1780	- @ref CALIB_FIX_FOCAL_LENGTH Fix \f$f^{(j)}_x\f$ and \f$f^{(j)}_y\f$ .
1781	- @ref CALIB_FIX_ASPECT_RATIO Optimize \f$f^{(j)}_y\f$ . Fix the ratio \f$f^{(j)}_x/f^{(j)}_y\f$
1782	.
1783	- @ref CALIB_SAME_FOCAL_LENGTH Enforce \f$f^{(0)}_x=f^{(1)}_x\f$ and \f$f^{(0)}_y=f^{(1)}_y\f$ .
1784	- @ref CALIB_ZERO_TANGENT_DIST Set tangential distortion coefficients for each camera to
1785	zeros and fix there.
1786	- @ref CALIB_FIX_K1,..., @ref CALIB_FIX_K6 Do not change the corresponding radial
1787	distortion coefficient during the optimization. If @ref CALIB_USE_INTRINSIC_GUESS is set,
1788	the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
1789	- @ref CALIB_RATIONAL_MODEL Enable coefficients k4, k5, and k6. To provide the backward
1790	compatibility, this extra flag should be explicitly specified to make the calibration
1791	function use the rational model and return 8 coefficients. If the flag is not set, the
1792	function computes and returns only 5 distortion coefficients.
1793	- @ref CALIB_THIN_PRISM_MODEL Coefficients s1, s2, s3 and s4 are enabled. To provide the
1794	backward compatibility, this extra flag should be explicitly specified to make the
1795	calibration function use the thin prism model and return 12 coefficients. If the flag is not
1796	set, the function computes and returns only 5 distortion coefficients.
1797	- @ref CALIB_FIX_S1_S2_S3_S4 The thin prism distortion coefficients are not changed during
1798	the optimization. If @ref CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the
1799	supplied distCoeffs matrix is used. Otherwise, it is set to 0.
1800	- @ref CALIB_TILTED_MODEL Coefficients tauX and tauY are enabled. To provide the
1801	backward compatibility, this extra flag should be explicitly specified to make the
1802	calibration function use the tilted sensor model and return 14 coefficients. If the flag is not
1803	set, the function computes and returns only 5 distortion coefficients.
1804	- @ref CALIB_FIX_TAUX_TAUY The coefficients of the tilted sensor model are not changed during
1805	the optimization. If @ref CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the
1806	supplied distCoeffs matrix is used. Otherwise, it is set to 0.
1807	@param criteria Termination criteria for the iterative optimization algorithm.
1808
1809	The function estimates the transformation between two cameras making a stereo pair. If one computes
1810	the poses of an object relative to the first camera and to the second camera,
1811	( \f$R_1\f$,\f$T_1\f$ ) and (\f$R_2\f$,\f$T_2\f$), respectively, for a stereo camera where the
1812	relative position and orientation between the two cameras are fixed, then those poses definitely
1813	relate to each other. This means, if the relative position and orientation (\f$R\f$,\f$T\f$) of the
1814	two cameras is known, it is possible to compute (\f$R_2\f$,\f$T_2\f$) when (\f$R_1\f$,\f$T_1\f$) is
1815	given. This is what the described function does. It computes (\f$R\f$,\f$T\f$) such that:
1816
1817	\f[R_2=R R_1\f]
1818	\f[T_2=R T_1 + T.\f]
1819
1820	Therefore, one can compute the coordinate representation of a 3D point for the second camera's
1821	coordinate system when given the point's coordinate representation in the first camera's coordinate
1822	system:
1823
1824	\f[\begin{bmatrix}
1825	X_2 \\
1826	Y_2 \\
1827	Z_2 \\
1828	1
1829	\end{bmatrix} = \begin{bmatrix}
1830	R & T \\
1831	0 & 1
1832	\end{bmatrix} \begin{bmatrix}
1833	X_1 \\
1834	Y_1 \\
1835	Z_1 \\
1836	1
1837	\end{bmatrix}.\f]
1838
1839
1840	Optionally, it computes the essential matrix E:
1841
1842	\f[E= \vecthreethree{0}{-T_2}{T_1}{T_2}{0}{-T_0}{-T_1}{T_0}{0} R\f]
1843
1844	where \f$T_i\f$ are components of the translation vector \f$T\f$ : \f$T=[T_0, T_1, T_2]^T\f$ .
1845	And the function can also compute the fundamental matrix F:
1846
1847	\f[F = cameraMatrix2^{-T}\cdot E \cdot cameraMatrix1^{-1}\f]
1848
1849	Besides the stereo-related information, the function can also perform a full calibration of each of
1850	the two cameras. However, due to the high dimensionality of the parameter space and noise in the
1851	input data, the function can diverge from the correct solution. If the intrinsic parameters can be
1852	estimated with high accuracy for each of the cameras individually (for example, using
1853	#calibrateCamera ), you are recommended to do so and then pass @ref CALIB_FIX_INTRINSIC flag to the
1854	function along with the computed intrinsic parameters. Otherwise, if all the parameters are
1855	estimated at once, it makes sense to restrict some parameters, for example, pass
1856	@ref CALIB_SAME_FOCAL_LENGTH and @ref CALIB_ZERO_TANGENT_DIST flags, which is usually a
1857	reasonable assumption.
1858
1859	Similarly to #calibrateCamera, the function minimizes the total re-projection error for all the
1860	points in all the available views from both cameras. The function returns the final value of the
1861	re-projection error.
1862	*/
1863	CV_EXPORTS_AS(stereoCalibrateExtended) double stereoCalibrate( InputArrayOfArrays objectPoints,
1864	InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2,
1865	InputOutputArray cameraMatrix1, InputOutputArray distCoeffs1,
1866	InputOutputArray cameraMatrix2, InputOutputArray distCoeffs2,
1867	Size imageSize, InputOutputArray R, InputOutputArray T, OutputArray E, OutputArray F,
1868	OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs, OutputArray perViewErrors, int flags = CALIB_FIX_INTRINSIC,
1869	TermCriteria criteria = TermCriteria(TermCriteria::COUNT+TermCriteria::EPS, 30, 1e-6) );
1870
1871	/// @overload
1872	CV_EXPORTS_W double stereoCalibrate( InputArrayOfArrays objectPoints,
1873	InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2,
1874	InputOutputArray cameraMatrix1, InputOutputArray distCoeffs1,
1875	InputOutputArray cameraMatrix2, InputOutputArray distCoeffs2,
1876	Size imageSize, OutputArray R,OutputArray T, OutputArray E, OutputArray F,
1877	int flags = CALIB_FIX_INTRINSIC,
1878	TermCriteria criteria = TermCriteria(TermCriteria::COUNT+TermCriteria::EPS, 30, 1e-6) );
1879
1880	/// @overload
1881	CV_EXPORTS_W double stereoCalibrate( InputArrayOfArrays objectPoints,
1882	InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2,
1883	InputOutputArray cameraMatrix1, InputOutputArray distCoeffs1,
1884	InputOutputArray cameraMatrix2, InputOutputArray distCoeffs2,
1885	Size imageSize, InputOutputArray R, InputOutputArray T, OutputArray E, OutputArray F,
1886	OutputArray perViewErrors, int flags = CALIB_FIX_INTRINSIC,
1887	TermCriteria criteria = TermCriteria(TermCriteria::COUNT+TermCriteria::EPS, 30, 1e-6) );
1888
1889	/** @brief Computes rectification transforms for each head of a calibrated stereo camera.
1890
1891	@param cameraMatrix1 First camera intrinsic matrix.
1892	@param distCoeffs1 First camera distortion parameters.
1893	@param cameraMatrix2 Second camera intrinsic matrix.
1894	@param distCoeffs2 Second camera distortion parameters.
1895	@param imageSize Size of the image used for stereo calibration.
1896	@param R Rotation matrix from the coordinate system of the first camera to the second camera,
1897	see @ref stereoCalibrate.
1898	@param T Translation vector from the coordinate system of the first camera to the second camera,
1899	see @ref stereoCalibrate.
1900	@param R1 Output 3x3 rectification transform (rotation matrix) for the first camera. This matrix
1901	brings points given in the unrectified first camera's coordinate system to points in the rectified
1902	first camera's coordinate system. In more technical terms, it performs a change of basis from the
1903	unrectified first camera's coordinate system to the rectified first camera's coordinate system.
1904	@param R2 Output 3x3 rectification transform (rotation matrix) for the second camera. This matrix
1905	brings points given in the unrectified second camera's coordinate system to points in the rectified
1906	second camera's coordinate system. In more technical terms, it performs a change of basis from the
1907	unrectified second camera's coordinate system to the rectified second camera's coordinate system.
1908	@param P1 Output 3x4 projection matrix in the new (rectified) coordinate systems for the first
1909	camera, i.e. it projects points given in the rectified first camera coordinate system into the
1910	rectified first camera's image.
1911	@param P2 Output 3x4 projection matrix in the new (rectified) coordinate systems for the second
1912	camera, i.e. it projects points given in the rectified first camera coordinate system into the
1913	rectified second camera's image.
1914	@param Q Output \f$4 \times 4\f$ disparity-to-depth mapping matrix (see @ref reprojectImageTo3D).
1915	@param flags Operation flags that may be zero or @ref CALIB_ZERO_DISPARITY . If the flag is set,
1916	the function makes the principal points of each camera have the same pixel coordinates in the
1917	rectified views. And if the flag is not set, the function may still shift the images in the
1918	horizontal or vertical direction (depending on the orientation of epipolar lines) to maximize the
1919	useful image area.
1920	@param alpha Free scaling parameter. If it is -1 or absent, the function performs the default
1921	scaling. Otherwise, the parameter should be between 0 and 1. alpha=0 means that the rectified
1922	images are zoomed and shifted so that only valid pixels are visible (no black areas after
1923	rectification). alpha=1 means that the rectified image is decimated and shifted so that all the
1924	pixels from the original images from the cameras are retained in the rectified images (no source
1925	image pixels are lost). Any intermediate value yields an intermediate result between
1926	those two extreme cases.
1927	@param newImageSize New image resolution after rectification. The same size should be passed to
1928	#initUndistortRectifyMap (see the stereo_calib.cpp sample in OpenCV samples directory). When (0,0)
1929	is passed (default), it is set to the original imageSize . Setting it to a larger value can help you
1930	preserve details in the original image, especially when there is a big radial distortion.
1931	@param validPixROI1 Optional output rectangles inside the rectified images where all the pixels
1932	are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller
1933	(see the picture below).
1934	@param validPixROI2 Optional output rectangles inside the rectified images where all the pixels
1935	are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller
1936	(see the picture below).
1937
1938	The function computes the rotation matrices for each camera that (virtually) make both camera image
1939	planes the same plane. Consequently, this makes all the epipolar lines parallel and thus simplifies
1940	the dense stereo correspondence problem. The function takes the matrices computed by #stereoCalibrate
1941	as input. As output, it provides two rotation matrices and also two projection matrices in the new
1942	coordinates. The function distinguishes the following two cases:
1943
1944	- **Horizontal stereo**: the first and the second camera views are shifted relative to each other
1945	mainly along the x-axis (with possible small vertical shift). In the rectified images, the
1946	corresponding epipolar lines in the left and right cameras are horizontal and have the same
1947	y-coordinate. P1 and P2 look like:
1948
1949	\f[\texttt{P1} = \begin{bmatrix}
1950	f & 0 & cx_1 & 0 \\
1951	0 & f & cy & 0 \\
1952	0 & 0 & 1 & 0
1953	\end{bmatrix}\f]
1954
1955	\f[\texttt{P2} = \begin{bmatrix}
1956	f & 0 & cx_2 & T_x \cdot f \\
1957	0 & f & cy & 0 \\
1958	0 & 0 & 1 & 0
1959	\end{bmatrix} ,\f]
1960
1961	\f[\texttt{Q} = \begin{bmatrix}
1962	1 & 0 & 0 & -cx_1 \\
1963	0 & 1 & 0 & -cy \\
1964	0 & 0 & 0 & f \\
1965	0 & 0 & -\frac{1}{T_x} & \frac{cx_1 - cx_2}{T_x}
1966	\end{bmatrix} \f]
1967
1968	where \f$T_x\f$ is a horizontal shift between the cameras and \f$cx_1=cx_2\f$ if
1969	@ref CALIB_ZERO_DISPARITY is set.
1970
1971	- **Vertical stereo**: the first and the second camera views are shifted relative to each other
1972	mainly in the vertical direction (and probably a bit in the horizontal direction too). The epipolar
1973	lines in the rectified images are vertical and have the same x-coordinate. P1 and P2 look like:
1974
1975	\f[\texttt{P1} = \begin{bmatrix}
1976	f & 0 & cx & 0 \\
1977	0 & f & cy_1 & 0 \\
1978	0 & 0 & 1 & 0
1979	\end{bmatrix}\f]
1980
1981	\f[\texttt{P2} = \begin{bmatrix}
1982	f & 0 & cx & 0 \\
1983	0 & f & cy_2 & T_y \cdot f \\
1984	0 & 0 & 1 & 0
1985	\end{bmatrix},\f]
1986
1987	\f[\texttt{Q} = \begin{bmatrix}
1988	1 & 0 & 0 & -cx \\
1989	0 & 1 & 0 & -cy_1 \\
1990	0 & 0 & 0 & f \\
1991	0 & 0 & -\frac{1}{T_y} & \frac{cy_1 - cy_2}{T_y}
1992	\end{bmatrix} \f]
1993
1994	where \f$T_y\f$ is a vertical shift between the cameras and \f$cy_1=cy_2\f$ if
1995	@ref CALIB_ZERO_DISPARITY is set.
1996
1997	As you can see, the first three columns of P1 and P2 will effectively be the new "rectified" camera
1998	matrices. The matrices, together with R1 and R2 , can then be passed to #initUndistortRectifyMap to
1999	initialize the rectification map for each camera.
2000
2001	See below the screenshot from the stereo_calib.cpp sample. Some red horizontal lines pass through
2002	the corresponding image regions. This means that the images are well rectified, which is what most
2003	stereo correspondence algorithms rely on. The green rectangles are roi1 and roi2 . You see that
2004	their interiors are all valid pixels.
2005
2006	
2007	*/
2008	CV_EXPORTS_W void stereoRectify( InputArray cameraMatrix1, InputArray distCoeffs1,
2009	InputArray cameraMatrix2, InputArray distCoeffs2,
2010	Size imageSize, InputArray R, InputArray T,
2011	OutputArray R1, OutputArray R2,
2012	OutputArray P1, OutputArray P2,
2013	OutputArray Q, int flags = CALIB_ZERO_DISPARITY,
2014	double alpha = -1, Size newImageSize = Size(),
2015	CV_OUT Rect* validPixROI1 = 0, CV_OUT Rect* validPixROI2 = 0 );
2016
2017	/** @brief Computes a rectification transform for an uncalibrated stereo camera.
2018
2019	@param points1 Array of feature points in the first image.
2020	@param points2 The corresponding points in the second image. The same formats as in
2021	#findFundamentalMat are supported.
2022	@param F Input fundamental matrix. It can be computed from the same set of point pairs using
2023	#findFundamentalMat .
2024	@param imgSize Size of the image.
2025	@param H1 Output rectification homography matrix for the first image.
2026	@param H2 Output rectification homography matrix for the second image.
2027	@param threshold Optional threshold used to filter out the outliers. If the parameter is greater
2028	than zero, all the point pairs that do not comply with the epipolar geometry (that is, the points
2029	for which \f$|\texttt{points2[i]}^T \cdot \texttt{F} \cdot \texttt{points1[i]}|>\texttt{threshold}\f$ )
2030	are rejected prior to computing the homographies. Otherwise, all the points are considered inliers.
2031
2032	The function computes the rectification transformations without knowing intrinsic parameters of the
2033	cameras and their relative position in the space, which explains the suffix "uncalibrated". Another
2034	related difference from #stereoRectify is that the function outputs not the rectification
2035	transformations in the object (3D) space, but the planar perspective transformations encoded by the
2036	homography matrices H1 and H2 . The function implements the algorithm @cite Hartley99 .
2037
2038	@note
2039	While the algorithm does not need to know the intrinsic parameters of the cameras, it heavily
2040	depends on the epipolar geometry. Therefore, if the camera lenses have a significant distortion,
2041	it would be better to correct it before computing the fundamental matrix and calling this
2042	function. For example, distortion coefficients can be estimated for each head of stereo camera
2043	separately by using #calibrateCamera . Then, the images can be corrected using #undistort , or
2044	just the point coordinates can be corrected with #undistortPoints .
2045	*/
2046	CV_EXPORTS_W bool stereoRectifyUncalibrated( InputArray points1, InputArray points2,
2047	InputArray F, Size imgSize,
2048	OutputArray H1, OutputArray H2,
2049	double threshold = 5 );
2050
2051	//! computes the rectification transformations for 3-head camera, where all the heads are on the same line.
2052	CV_EXPORTS_W float rectify3Collinear( InputArray cameraMatrix1, InputArray distCoeffs1,
2053	InputArray cameraMatrix2, InputArray distCoeffs2,
2054	InputArray cameraMatrix3, InputArray distCoeffs3,
2055	InputArrayOfArrays imgpt1, InputArrayOfArrays imgpt3,
2056	Size imageSize, InputArray R12, InputArray T12,
2057	InputArray R13, InputArray T13,
2058	OutputArray R1, OutputArray R2, OutputArray R3,
2059	OutputArray P1, OutputArray P2, OutputArray P3,
2060	OutputArray Q, double alpha, Size newImgSize,
2061	CV_OUT Rect* roi1, CV_OUT Rect* roi2, int flags );
2062
2063	/** @brief Returns the new camera intrinsic matrix based on the free scaling parameter.
2064
2065	@param cameraMatrix Input camera intrinsic matrix.
2066	@param distCoeffs Input vector of distortion coefficients
2067	\f$\distcoeffs\f$. If the vector is NULL/empty, the zero distortion coefficients are
2068	assumed.
2069	@param imageSize Original image size.
2070	@param alpha Free scaling parameter between 0 (when all the pixels in the undistorted image are
2071	valid) and 1 (when all the source image pixels are retained in the undistorted image). See
2072	#stereoRectify for details.
2073	@param newImgSize Image size after rectification. By default, it is set to imageSize .
2074	@param validPixROI Optional output rectangle that outlines all-good-pixels region in the
2075	undistorted image. See roi1, roi2 description in #stereoRectify .
2076	@param centerPrincipalPoint Optional flag that indicates whether in the new camera intrinsic matrix the
2077	principal point should be at the image center or not. By default, the principal point is chosen to
2078	best fit a subset of the source image (determined by alpha) to the corrected image.
2079	@return new_camera_matrix Output new camera intrinsic matrix.
2080
2081	The function computes and returns the optimal new camera intrinsic matrix based on the free scaling parameter.
2082	By varying this parameter, you may retrieve only sensible pixels alpha=0 , keep all the original
2083	image pixels if there is valuable information in the corners alpha=1 , or get something in between.
2084	When alpha\>0 , the undistorted result is likely to have some black pixels corresponding to
2085	"virtual" pixels outside of the captured distorted image. The original camera intrinsic matrix, distortion
2086	coefficients, the computed new camera intrinsic matrix, and newImageSize should be passed to
2087	#initUndistortRectifyMap to produce the maps for #remap .
2088	*/
2089	CV_EXPORTS_W Mat getOptimalNewCameraMatrix( InputArray cameraMatrix, InputArray distCoeffs,
2090	Size imageSize, double alpha, Size newImgSize = Size(),
2091	CV_OUT Rect* validPixROI = 0,
2092	bool centerPrincipalPoint = false);
2093
2094	/** @brief Computes Hand-Eye calibration: \f$_{}^{g}\textrm{T}_c\f$
2095
2096	@param[in] R_gripper2base Rotation part extracted from the homogeneous matrix that transforms a point
2097	expressed in the gripper frame to the robot base frame (\f$_{}^{b}\textrm{T}_g\f$).
2098	This is a vector (`vector<Mat>`) that contains the rotation, `(3x3)` rotation matrices or `(3x1)` rotation vectors,
2099	for all the transformations from gripper frame to robot base frame.
2100	@param[in] t_gripper2base Translation part extracted from the homogeneous matrix that transforms a point
2101	expressed in the gripper frame to the robot base frame (\f$_{}^{b}\textrm{T}_g\f$).
2102	This is a vector (`vector<Mat>`) that contains the `(3x1)` translation vectors for all the transformations
2103	from gripper frame to robot base frame.
2104	@param[in] R_target2cam Rotation part extracted from the homogeneous matrix that transforms a point
2105	expressed in the target frame to the camera frame (\f$_{}^{c}\textrm{T}_t\f$).
2106	This is a vector (`vector<Mat>`) that contains the rotation, `(3x3)` rotation matrices or `(3x1)` rotation vectors,
2107	for all the transformations from calibration target frame to camera frame.
2108	@param[in] t_target2cam Rotation part extracted from the homogeneous matrix that transforms a point
2109	expressed in the target frame to the camera frame (\f$_{}^{c}\textrm{T}_t\f$).
2110	This is a vector (`vector<Mat>`) that contains the `(3x1)` translation vectors for all the transformations
2111	from calibration target frame to camera frame.
2112	@param[out] R_cam2gripper Estimated `(3x3)` rotation part extracted from the homogeneous matrix that transforms a point
2113	expressed in the camera frame to the gripper frame (\f$_{}^{g}\textrm{T}_c\f$).
2114	@param[out] t_cam2gripper Estimated `(3x1)` translation part extracted from the homogeneous matrix that transforms a point
2115	expressed in the camera frame to the gripper frame (\f$_{}^{g}\textrm{T}_c\f$).
2116	@param[in] method One of the implemented Hand-Eye calibration method, see cv::HandEyeCalibrationMethod
2117
2118	The function performs the Hand-Eye calibration using various methods. One approach consists in estimating the
2119	rotation then the translation (separable solutions) and the following methods are implemented:
2120	- R. Tsai, R. Lenz A New Technique for Fully Autonomous and Efficient 3D Robotics Hand/EyeCalibration \cite Tsai89
2121	- F. Park, B. Martin Robot Sensor Calibration: Solving AX = XB on the Euclidean Group \cite Park94
2122	- R. Horaud, F. Dornaika Hand-Eye Calibration \cite Horaud95
2123
2124	Another approach consists in estimating simultaneously the rotation and the translation (simultaneous solutions),
2125	with the following implemented methods:
2126	- N. Andreff, R. Horaud, B. Espiau On-line Hand-Eye Calibration \cite Andreff99
2127	- K. Daniilidis Hand-Eye Calibration Using Dual Quaternions \cite Daniilidis98
2128
2129	The following picture describes the Hand-Eye calibration problem where the transformation between a camera ("eye")
2130	mounted on a robot gripper ("hand") has to be estimated. This configuration is called eye-in-hand.
2131
2132	The eye-to-hand configuration consists in a static camera observing a calibration pattern mounted on the robot
2133	end-effector. The transformation from the camera to the robot base frame can then be estimated by inputting
2134	the suitable transformations to the function, see below.
2135
2136	
2137
2138	The calibration procedure is the following:
2139	- a static calibration pattern is used to estimate the transformation between the target frame
2140	and the camera frame
2141	- the robot gripper is moved in order to acquire several poses
2142	- for each pose, the homogeneous transformation between the gripper frame and the robot base frame is recorded using for
2143	instance the robot kinematics
2144	\f[
2145	\begin{bmatrix}
2146	X_b\\
2147	Y_b\\
2148	Z_b\\
2149	1
2150	\end{bmatrix}
2151	=
2152	\begin{bmatrix}
2153	_{}^{b}\textrm{R}_g & _{}^{b}\textrm{t}_g \\
2154	0_{1 \times 3} & 1
2155	\end{bmatrix}
2156	\begin{bmatrix}
2157	X_g\\
2158	Y_g\\
2159	Z_g\\
2160	1
2161	\end{bmatrix}
2162	\f]
2163	- for each pose, the homogeneous transformation between the calibration target frame and the camera frame is recorded using
2164	for instance a pose estimation method (PnP) from 2D-3D point correspondences
2165	\f[
2166	\begin{bmatrix}
2167	X_c\\
2168	Y_c\\
2169	Z_c\\
2170	1
2171	\end{bmatrix}
2172	=
2173	\begin{bmatrix}
2174	_{}^{c}\textrm{R}_t & _{}^{c}\textrm{t}_t \\
2175	0_{1 \times 3} & 1
2176	\end{bmatrix}
2177	\begin{bmatrix}
2178	X_t\\
2179	Y_t\\
2180	Z_t\\
2181	1
2182	\end{bmatrix}
2183	\f]
2184
2185	The Hand-Eye calibration procedure returns the following homogeneous transformation
2186	\f[
2187	\begin{bmatrix}
2188	X_g\\
2189	Y_g\\
2190	Z_g\\
2191	1
2192	\end{bmatrix}
2193	=
2194	\begin{bmatrix}
2195	_{}^{g}\textrm{R}_c & _{}^{g}\textrm{t}_c \\
2196	0_{1 \times 3} & 1
2197	\end{bmatrix}
2198	\begin{bmatrix}
2199	X_c\\
2200	Y_c\\
2201	Z_c\\
2202	1
2203	\end{bmatrix}
2204	\f]
2205
2206	This problem is also known as solving the \f$\mathbf{A}\mathbf{X}=\mathbf{X}\mathbf{B}\f$ equation:
2207	- for an eye-in-hand configuration
2208	\f[
2209	\begin{align*}
2210	^{b}{\textrm{T}_g}^{(1)} \hspace{0.2em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(1)} &=
2211	\hspace{0.1em} ^{b}{\textrm{T}_g}^{(2)} \hspace{0.2em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} \\
2212
2213	(^{b}{\textrm{T}_g}^{(2)})^{-1} \hspace{0.2em} ^{b}{\textrm{T}_g}^{(1)} \hspace{0.2em} ^{g}\textrm{T}_c &=
2214	\hspace{0.1em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} (^{c}{\textrm{T}_t}^{(1)})^{-1} \\
2215
2216	\textrm{A}_i \textrm{X} &= \textrm{X} \textrm{B}_i \\
2217	\end{align*}
2218	\f]
2219
2220	- for an eye-to-hand configuration
2221	\f[
2222	\begin{align*}
2223	^{g}{\textrm{T}_b}^{(1)} \hspace{0.2em} ^{b}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(1)} &=
2224	\hspace{0.1em} ^{g}{\textrm{T}_b}^{(2)} \hspace{0.2em} ^{b}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} \\
2225
2226	(^{g}{\textrm{T}_b}^{(2)})^{-1} \hspace{0.2em} ^{g}{\textrm{T}_b}^{(1)} \hspace{0.2em} ^{b}\textrm{T}_c &=
2227	\hspace{0.1em} ^{b}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} (^{c}{\textrm{T}_t}^{(1)})^{-1} \\
2228
2229	\textrm{A}_i \textrm{X} &= \textrm{X} \textrm{B}_i \\
2230	\end{align*}
2231	\f]
2232
2233	\note
2234	Additional information can be found on this [website](http://campar.in.tum.de/Chair/HandEyeCalibration).
2235	\note
2236	A minimum of 2 motions with non parallel rotation axes are necessary to determine the hand-eye transformation.
2237	So at least 3 different poses are required, but it is strongly recommended to use many more poses.
2238
2239	*/
2240	CV_EXPORTS_W void calibrateHandEye( InputArrayOfArrays R_gripper2base, InputArrayOfArrays t_gripper2base,
2241	InputArrayOfArrays R_target2cam, InputArrayOfArrays t_target2cam,
2242	OutputArray R_cam2gripper, OutputArray t_cam2gripper,
2243	HandEyeCalibrationMethod method=CALIB_HAND_EYE_TSAI );
2244
2245	/** @brief Computes Robot-World/Hand-Eye calibration: \f$_{}^{w}\textrm{T}_b\f$ and \f$_{}^{c}\textrm{T}_g\f$
2246
2247	@param[in] R_world2cam Rotation part extracted from the homogeneous matrix that transforms a point
2248	expressed in the world frame to the camera frame (\f$_{}^{c}\textrm{T}_w\f$).
2249	This is a vector (`vector<Mat>`) that contains the rotation, `(3x3)` rotation matrices or `(3x1)` rotation vectors,
2250	for all the transformations from world frame to the camera frame.
2251	@param[in] t_world2cam Translation part extracted from the homogeneous matrix that transforms a point
2252	expressed in the world frame to the camera frame (\f$_{}^{c}\textrm{T}_w\f$).
2253	This is a vector (`vector<Mat>`) that contains the `(3x1)` translation vectors for all the transformations
2254	from world frame to the camera frame.
2255	@param[in] R_base2gripper Rotation part extracted from the homogeneous matrix that transforms a point
2256	expressed in the robot base frame to the gripper frame (\f$_{}^{g}\textrm{T}_b\f$).
2257	This is a vector (`vector<Mat>`) that contains the rotation, `(3x3)` rotation matrices or `(3x1)` rotation vectors,
2258	for all the transformations from robot base frame to the gripper frame.
2259	@param[in] t_base2gripper Rotation part extracted from the homogeneous matrix that transforms a point
2260	expressed in the robot base frame to the gripper frame (\f$_{}^{g}\textrm{T}_b\f$).
2261	This is a vector (`vector<Mat>`) that contains the `(3x1)` translation vectors for all the transformations
2262	from robot base frame to the gripper frame.
2263	@param[out] R_base2world Estimated `(3x3)` rotation part extracted from the homogeneous matrix that transforms a point
2264	expressed in the robot base frame to the world frame (\f$_{}^{w}\textrm{T}_b\f$).
2265	@param[out] t_base2world Estimated `(3x1)` translation part extracted from the homogeneous matrix that transforms a point
2266	expressed in the robot base frame to the world frame (\f$_{}^{w}\textrm{T}_b\f$).
2267	@param[out] R_gripper2cam Estimated `(3x3)` rotation part extracted from the homogeneous matrix that transforms a point
2268	expressed in the gripper frame to the camera frame (\f$_{}^{c}\textrm{T}_g\f$).
2269	@param[out] t_gripper2cam Estimated `(3x1)` translation part extracted from the homogeneous matrix that transforms a point
2270	expressed in the gripper frame to the camera frame (\f$_{}^{c}\textrm{T}_g\f$).
2271	@param[in] method One of the implemented Robot-World/Hand-Eye calibration method, see cv::RobotWorldHandEyeCalibrationMethod
2272
2273	The function performs the Robot-World/Hand-Eye calibration using various methods. One approach consists in estimating the
2274	rotation then the translation (separable solutions):
2275	- M. Shah, Solving the robot-world/hand-eye calibration problem using the kronecker product \cite Shah2013SolvingTR
2276
2277	Another approach consists in estimating simultaneously the rotation and the translation (simultaneous solutions),
2278	with the following implemented method:
2279	- A. Li, L. Wang, and D. Wu, Simultaneous robot-world and hand-eye calibration using dual-quaternions and kronecker product \cite Li2010SimultaneousRA
2280
2281	The following picture describes the Robot-World/Hand-Eye calibration problem where the transformations between a robot and a world frame
2282	and between a robot gripper ("hand") and a camera ("eye") mounted at the robot end-effector have to be estimated.
2283
2284	
2285
2286	The calibration procedure is the following:
2287	- a static calibration pattern is used to estimate the transformation between the target frame
2288	and the camera frame
2289	- the robot gripper is moved in order to acquire several poses
2290	- for each pose, the homogeneous transformation between the gripper frame and the robot base frame is recorded using for
2291	instance the robot kinematics
2292	\f[
2293	\begin{bmatrix}
2294	X_g\\
2295	Y_g\\
2296	Z_g\\
2297	1
2298	\end{bmatrix}
2299	=
2300	\begin{bmatrix}
2301	_{}^{g}\textrm{R}_b & _{}^{g}\textrm{t}_b \\
2302	0_{1 \times 3} & 1
2303	\end{bmatrix}
2304	\begin{bmatrix}
2305	X_b\\
2306	Y_b\\
2307	Z_b\\
2308	1
2309	\end{bmatrix}
2310	\f]
2311	- for each pose, the homogeneous transformation between the calibration target frame (the world frame) and the camera frame is recorded using
2312	for instance a pose estimation method (PnP) from 2D-3D point correspondences
2313	\f[
2314	\begin{bmatrix}
2315	X_c\\
2316	Y_c\\
2317	Z_c\\
2318	1
2319	\end{bmatrix}
2320	=
2321	\begin{bmatrix}
2322	_{}^{c}\textrm{R}_w & _{}^{c}\textrm{t}_w \\
2323	0_{1 \times 3} & 1
2324	\end{bmatrix}
2325	\begin{bmatrix}
2326	X_w\\
2327	Y_w\\
2328	Z_w\\
2329	1
2330	\end{bmatrix}
2331	\f]
2332
2333	The Robot-World/Hand-Eye calibration procedure returns the following homogeneous transformations
2334	\f[
2335	\begin{bmatrix}
2336	X_w\\
2337	Y_w\\
2338	Z_w\\
2339	1
2340	\end{bmatrix}
2341	=
2342	\begin{bmatrix}
2343	_{}^{w}\textrm{R}_b & _{}^{w}\textrm{t}_b \\
2344	0_{1 \times 3} & 1
2345	\end{bmatrix}
2346	\begin{bmatrix}
2347	X_b\\
2348	Y_b\\
2349	Z_b\\
2350	1
2351	\end{bmatrix}
2352	\f]
2353	\f[
2354	\begin{bmatrix}
2355	X_c\\
2356	Y_c\\
2357	Z_c\\
2358	1
2359	\end{bmatrix}
2360	=
2361	\begin{bmatrix}
2362	_{}^{c}\textrm{R}_g & _{}^{c}\textrm{t}_g \\
2363	0_{1 \times 3} & 1
2364	\end{bmatrix}
2365	\begin{bmatrix}
2366	X_g\\
2367	Y_g\\
2368	Z_g\\
2369	1
2370	\end{bmatrix}
2371	\f]
2372
2373	This problem is also known as solving the \f$\mathbf{A}\mathbf{X}=\mathbf{Z}\mathbf{B}\f$ equation, with:
2374	- \f$\mathbf{A} \Leftrightarrow \hspace{0.1em} _{}^{c}\textrm{T}_w\f$
2375	- \f$\mathbf{X} \Leftrightarrow \hspace{0.1em} _{}^{w}\textrm{T}_b\f$
2376	- \f$\mathbf{Z} \Leftrightarrow \hspace{0.1em} _{}^{c}\textrm{T}_g\f$
2377	- \f$\mathbf{B} \Leftrightarrow \hspace{0.1em} _{}^{g}\textrm{T}_b\f$
2378
2379	\note
2380	At least 3 measurements are required (input vectors size must be greater or equal to 3).
2381
2382	*/
2383	CV_EXPORTS_W void calibrateRobotWorldHandEye( InputArrayOfArrays R_world2cam, InputArrayOfArrays t_world2cam,
2384	InputArrayOfArrays R_base2gripper, InputArrayOfArrays t_base2gripper,
2385	OutputArray R_base2world, OutputArray t_base2world,
2386	OutputArray R_gripper2cam, OutputArray t_gripper2cam,
2387	RobotWorldHandEyeCalibrationMethod method=CALIB_ROBOT_WORLD_HAND_EYE_SHAH );
2388
2389	/** @brief Converts points from Euclidean to homogeneous space.
2390
2391	@param src Input vector of N-dimensional points.
2392	@param dst Output vector of N+1-dimensional points.
2393
2394	The function converts points from Euclidean to homogeneous space by appending 1's to the tuple of
2395	point coordinates. That is, each point (x1, x2, ..., xn) is converted to (x1, x2, ..., xn, 1).
2396	*/
2397	CV_EXPORTS_W void convertPointsToHomogeneous( InputArray src, OutputArray dst );
2398
2399	/** @brief Converts points from homogeneous to Euclidean space.
2400
2401	@param src Input vector of N-dimensional points.
2402	@param dst Output vector of N-1-dimensional points.
2403
2404	The function converts points homogeneous to Euclidean space using perspective projection. That is,
2405	each point (x1, x2, ... x(n-1), xn) is converted to (x1/xn, x2/xn, ..., x(n-1)/xn). When xn=0, the
2406	output point coordinates will be (0,0,0,...).
2407	*/
2408	CV_EXPORTS_W void convertPointsFromHomogeneous( InputArray src, OutputArray dst );
2409
2410	/** @brief Converts points to/from homogeneous coordinates.
2411
2412	@param src Input array or vector of 2D, 3D, or 4D points.
2413	@param dst Output vector of 2D, 3D, or 4D points.
2414
2415	The function converts 2D or 3D points from/to homogeneous coordinates by calling either
2416	#convertPointsToHomogeneous or #convertPointsFromHomogeneous.
2417
2418	@note The function is obsolete. Use one of the previous two functions instead.
2419	*/
2420	CV_EXPORTS void convertPointsHomogeneous( InputArray src, OutputArray dst );
2421
2422	/** @brief Calculates a fundamental matrix from the corresponding points in two images.
2423
2424	@param points1 Array of N points from the first image. The point coordinates should be
2425	floating-point (single or double precision).
2426	@param points2 Array of the second image points of the same size and format as points1 .
2427	@param method Method for computing a fundamental matrix.
2428	- @ref FM_7POINT for a 7-point algorithm. \f$N = 7\f$
2429	- @ref FM_8POINT for an 8-point algorithm. \f$N \ge 8\f$
2430	- @ref FM_RANSAC for the RANSAC algorithm. \f$N \ge 8\f$
2431	- @ref FM_LMEDS for the LMedS algorithm. \f$N \ge 8\f$
2432	@param ransacReprojThreshold Parameter used only for RANSAC. It is the maximum distance from a point to an epipolar
2433	line in pixels, beyond which the point is considered an outlier and is not used for computing the
2434	final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the
2435	point localization, image resolution, and the image noise.
2436	@param confidence Parameter used for the RANSAC and LMedS methods only. It specifies a desirable level
2437	of confidence (probability) that the estimated matrix is correct.
2438	@param[out] mask optional output mask
2439	@param maxIters The maximum number of robust method iterations.
2440
2441	The epipolar geometry is described by the following equation:
2442
2443	\f[[p_2; 1]^T F [p_1; 1] = 0\f]
2444
2445	where \f$F\f$ is a fundamental matrix, \f$p_1\f$ and \f$p_2\f$ are corresponding points in the first and the
2446	second images, respectively.
2447
2448	The function calculates the fundamental matrix using one of four methods listed above and returns
2449	the found fundamental matrix. Normally just one matrix is found. But in case of the 7-point
2450	algorithm, the function may return up to 3 solutions ( \f$9 \times 3\f$ matrix that stores all 3
2451	matrices sequentially).
2452
2453	The calculated fundamental matrix may be passed further to #computeCorrespondEpilines that finds the
2454	epipolar lines corresponding to the specified points. It can also be passed to
2455	#stereoRectifyUncalibrated to compute the rectification transformation. :
2456	@code
2457	// Example. Estimation of fundamental matrix using the RANSAC algorithm
2458	int point_count = 100;
2459	vector<Point2f> points1(point_count);
2460	vector<Point2f> points2(point_count);
2461
2462	// initialize the points here ...
2463	for( int i = 0; i < point_count; i++ )
2464	{
2465	points1[i] = ...;
2466	points2[i] = ...;
2467	}
2468
2469	Mat fundamental_matrix =
2470	findFundamentalMat(points1, points2, FM_RANSAC, 3, 0.99);
2471	@endcode
2472	*/
2473	CV_EXPORTS_W Mat findFundamentalMat( InputArray points1, InputArray points2,
2474	int method, double ransacReprojThreshold, double confidence,
2475	int maxIters, OutputArray mask = noArray() );
2476
2477	/** @overload */
2478	CV_EXPORTS_W Mat findFundamentalMat( InputArray points1, InputArray points2,
2479	int method = FM_RANSAC,
2480	double ransacReprojThreshold = 3., double confidence = 0.99,
2481	OutputArray mask = noArray() );
2482
2483	/** @overload */
2484	CV_EXPORTS Mat findFundamentalMat( InputArray points1, InputArray points2,
2485	OutputArray mask, int method = FM_RANSAC,
2486	double ransacReprojThreshold = 3., double confidence = 0.99 );
2487
2488
2489	CV_EXPORTS_W Mat findFundamentalMat( InputArray points1, InputArray points2,
2490	OutputArray mask, const UsacParams &params);
2491
2492	/** @brief Calculates an essential matrix from the corresponding points in two images.
2493
2494	@param points1 Array of N (N \>= 5) 2D points from the first image. The point coordinates should
2495	be floating-point (single or double precision).
2496	@param points2 Array of the second image points of the same size and format as points1.
2497	@param cameraMatrix Camera intrinsic matrix \f$\cameramatrix{A}\f$ .
2498	Note that this function assumes that points1 and points2 are feature points from cameras with the
2499	same camera intrinsic matrix. If this assumption does not hold for your use case, use another
2500	function overload or #undistortPoints with `P = cv::NoArray()` for both cameras to transform image
2501	points to normalized image coordinates, which are valid for the identity camera intrinsic matrix.
2502	When passing these coordinates, pass the identity matrix for this parameter.
2503	@param method Method for computing an essential matrix.
2504	- @ref RANSAC for the RANSAC algorithm.
2505	- @ref LMEDS for the LMedS algorithm.
2506	@param prob Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of
2507	confidence (probability) that the estimated matrix is correct.
2508	@param threshold Parameter used for RANSAC. It is the maximum distance from a point to an epipolar
2509	line in pixels, beyond which the point is considered an outlier and is not used for computing the
2510	final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the
2511	point localization, image resolution, and the image noise.
2512	@param mask Output array of N elements, every element of which is set to 0 for outliers and to 1
2513	for the other points. The array is computed only in the RANSAC and LMedS methods.
2514	@param maxIters The maximum number of robust method iterations.
2515
2516	This function estimates essential matrix based on the five-point algorithm solver in @cite Nister03 .
2517	@cite SteweniusCFS is also a related. The epipolar geometry is described by the following equation:
2518
2519	\f[[p_2; 1]^T K^{-T} E K^{-1} [p_1; 1] = 0\f]
2520
2521	where \f$E\f$ is an essential matrix, \f$p_1\f$ and \f$p_2\f$ are corresponding points in the first and the
2522	second images, respectively. The result of this function may be passed further to
2523	#decomposeEssentialMat or #recoverPose to recover the relative pose between cameras.
2524	*/
2525	CV_EXPORTS_W
2526	Mat findEssentialMat(
2527	InputArray points1, InputArray points2,
2528	InputArray cameraMatrix, int method = RANSAC,
2529	double prob = 0.999, double threshold = 1.0,
2530	int maxIters = 1000, OutputArray mask = noArray()
2531	);
2532
2533	/** @overload */
2534	CV_EXPORTS
2535	Mat findEssentialMat(
2536	InputArray points1, InputArray points2,
2537	InputArray cameraMatrix, int method,
2538	double prob, double threshold,
2539	OutputArray mask
2540	); // TODO remove from OpenCV 5.0
2541
2542	/** @overload
2543	@param points1 Array of N (N \>= 5) 2D points from the first image. The point coordinates should
2544	be floating-point (single or double precision).
2545	@param points2 Array of the second image points of the same size and format as points1 .
2546	@param focal focal length of the camera. Note that this function assumes that points1 and points2
2547	are feature points from cameras with same focal length and principal point.
2548	@param pp principal point of the camera.
2549	@param method Method for computing a fundamental matrix.
2550	- @ref RANSAC for the RANSAC algorithm.
2551	- @ref LMEDS for the LMedS algorithm.
2552	@param threshold Parameter used for RANSAC. It is the maximum distance from a point to an epipolar
2553	line in pixels, beyond which the point is considered an outlier and is not used for computing the
2554	final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the
2555	point localization, image resolution, and the image noise.
2556	@param prob Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of
2557	confidence (probability) that the estimated matrix is correct.
2558	@param mask Output array of N elements, every element of which is set to 0 for outliers and to 1
2559	for the other points. The array is computed only in the RANSAC and LMedS methods.
2560	@param maxIters The maximum number of robust method iterations.
2561
2562	This function differs from the one above that it computes camera intrinsic matrix from focal length and
2563	principal point:
2564
2565	\f[A =
2566	\begin{bmatrix}
2567	f & 0 & x_{pp} \\
2568	0 & f & y_{pp} \\
2569	0 & 0 & 1
2570	\end{bmatrix}\f]
2571	*/
2572	CV_EXPORTS_W
2573	Mat findEssentialMat(
2574	InputArray points1, InputArray points2,
2575	double focal = 1.0, Point2d pp = Point2d(0, 0),
2576	int method = RANSAC, double prob = 0.999,
2577	double threshold = 1.0, int maxIters = 1000,
2578	OutputArray mask = noArray()
2579	);
2580
2581	/** @overload */
2582	CV_EXPORTS
2583	Mat findEssentialMat(
2584	InputArray points1, InputArray points2,
2585	double focal, Point2d pp,
2586	int method, double prob,
2587	double threshold, OutputArray mask
2588	); // TODO remove from OpenCV 5.0
2589
2590	/** @brief Calculates an essential matrix from the corresponding points in two images from potentially two different cameras.
2591
2592	@param points1 Array of N (N \>= 5) 2D points from the first image. The point coordinates should
2593	be floating-point (single or double precision).
2594	@param points2 Array of the second image points of the same size and format as points1.
2595	@param cameraMatrix1 Camera matrix for the first camera \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
2596	@param cameraMatrix2 Camera matrix for the second camera \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
2597	@param distCoeffs1 Input vector of distortion coefficients for the first camera
2598	\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
2599	of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
2600	@param distCoeffs2 Input vector of distortion coefficients for the second camera
2601	\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
2602	of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
2603	@param method Method for computing an essential matrix.
2604	- @ref RANSAC for the RANSAC algorithm.
2605	- @ref LMEDS for the LMedS algorithm.
2606	@param prob Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of
2607	confidence (probability) that the estimated matrix is correct.
2608	@param threshold Parameter used for RANSAC. It is the maximum distance from a point to an epipolar
2609	line in pixels, beyond which the point is considered an outlier and is not used for computing the
2610	final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the
2611	point localization, image resolution, and the image noise.
2612	@param mask Output array of N elements, every element of which is set to 0 for outliers and to 1
2613	for the other points. The array is computed only in the RANSAC and LMedS methods.
2614
2615	This function estimates essential matrix based on the five-point algorithm solver in @cite Nister03 .
2616	@cite SteweniusCFS is also a related. The epipolar geometry is described by the following equation:
2617
2618	\f[[p_2; 1]^T K^{-T} E K^{-1} [p_1; 1] = 0\f]
2619
2620	where \f$E\f$ is an essential matrix, \f$p_1\f$ and \f$p_2\f$ are corresponding points in the first and the
2621	second images, respectively. The result of this function may be passed further to
2622	#decomposeEssentialMat or #recoverPose to recover the relative pose between cameras.
2623	*/
2624	CV_EXPORTS_W Mat findEssentialMat( InputArray points1, InputArray points2,
2625	InputArray cameraMatrix1, InputArray distCoeffs1,
2626	InputArray cameraMatrix2, InputArray distCoeffs2,
2627	int method = RANSAC,
2628	double prob = 0.999, double threshold = 1.0,
2629	OutputArray mask = noArray() );
2630
2631
2632	CV_EXPORTS_W Mat findEssentialMat( InputArray points1, InputArray points2,
2633	InputArray cameraMatrix1, InputArray cameraMatrix2,
2634	InputArray dist_coeff1, InputArray dist_coeff2, OutputArray mask,
2635	const UsacParams &params);
2636
2637	/** @brief Decompose an essential matrix to possible rotations and translation.
2638
2639	@param E The input essential matrix.
2640	@param R1 One possible rotation matrix.
2641	@param R2 Another possible rotation matrix.
2642	@param t One possible translation.
2643
2644	This function decomposes the essential matrix E using svd decomposition @cite HartleyZ00. In
2645	general, four possible poses exist for the decomposition of E. They are \f$[R_1, t]\f$,
2646	\f$[R_1, -t]\f$, \f$[R_2, t]\f$, \f$[R_2, -t]\f$.
2647
2648	If E gives the epipolar constraint \f$[p_2; 1]^T A^{-T} E A^{-1} [p_1; 1] = 0\f$ between the image
2649	points \f$p_1\f$ in the first image and \f$p_2\f$ in second image, then any of the tuples
2650	\f$[R_1, t]\f$, \f$[R_1, -t]\f$, \f$[R_2, t]\f$, \f$[R_2, -t]\f$ is a change of basis from the first
2651	camera's coordinate system to the second camera's coordinate system. However, by decomposing E, one
2652	can only get the direction of the translation. For this reason, the translation t is returned with
2653	unit length.
2654	*/
2655	CV_EXPORTS_W void decomposeEssentialMat( InputArray E, OutputArray R1, OutputArray R2, OutputArray t );
2656
2657	/** @brief Recovers the relative camera rotation and the translation from corresponding points in two images from two different cameras, using cheirality check. Returns the number of
2658	inliers that pass the check.
2659
2660	@param points1 Array of N 2D points from the first image. The point coordinates should be
2661	floating-point (single or double precision).
2662	@param points2 Array of the second image points of the same size and format as points1 .
2663	@param cameraMatrix1 Input/output camera matrix for the first camera, the same as in
2664	@ref calibrateCamera. Furthermore, for the stereo case, additional flags may be used, see below.
2665	@param distCoeffs1 Input/output vector of distortion coefficients, the same as in
2666	@ref calibrateCamera.
2667	@param cameraMatrix2 Input/output camera matrix for the first camera, the same as in
2668	@ref calibrateCamera. Furthermore, for the stereo case, additional flags may be used, see below.
2669	@param distCoeffs2 Input/output vector of distortion coefficients, the same as in
2670	@ref calibrateCamera.
2671	@param E The output essential matrix.
2672	@param R Output rotation matrix. Together with the translation vector, this matrix makes up a tuple
2673	that performs a change of basis from the first camera's coordinate system to the second camera's
2674	coordinate system. Note that, in general, t can not be used for this tuple, see the parameter
2675	described below.
2676	@param t Output translation vector. This vector is obtained by @ref decomposeEssentialMat and
2677	therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit
2678	length.
2679	@param method Method for computing an essential matrix.
2680	- @ref RANSAC for the RANSAC algorithm.
2681	- @ref LMEDS for the LMedS algorithm.
2682	@param prob Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of
2683	confidence (probability) that the estimated matrix is correct.
2684	@param threshold Parameter used for RANSAC. It is the maximum distance from a point to an epipolar
2685	line in pixels, beyond which the point is considered an outlier and is not used for computing the
2686	final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the
2687	point localization, image resolution, and the image noise.
2688	@param mask Input/output mask for inliers in points1 and points2. If it is not empty, then it marks
2689	inliers in points1 and points2 for then given essential matrix E. Only these inliers will be used to
2690	recover pose. In the output mask only inliers which pass the cheirality check.
2691
2692	This function decomposes an essential matrix using @ref decomposeEssentialMat and then verifies
2693	possible pose hypotheses by doing cheirality check. The cheirality check means that the
2694	triangulated 3D points should have positive depth. Some details can be found in @cite Nister03.
2695
2696	This function can be used to process the output E and mask from @ref findEssentialMat. In this
2697	scenario, points1 and points2 are the same input for findEssentialMat.:
2698	@code
2699	// Example. Estimation of fundamental matrix using the RANSAC algorithm
2700	int point_count = 100;
2701	vector<Point2f> points1(point_count);
2702	vector<Point2f> points2(point_count);
2703
2704	// initialize the points here ...
2705	for( int i = 0; i < point_count; i++ )
2706	{
2707	points1[i] = ...;
2708	points2[i] = ...;
2709	}
2710
2711	// Input: camera calibration of both cameras, for example using intrinsic chessboard calibration.
2712	Mat cameraMatrix1, distCoeffs1, cameraMatrix2, distCoeffs2;
2713
2714	// Output: Essential matrix, relative rotation and relative translation.
2715	Mat E, R, t, mask;
2716
2717	recoverPose(points1, points2, cameraMatrix1, distCoeffs1, cameraMatrix2, distCoeffs2, E, R, t, mask);
2718	@endcode
2719	*/
2720	CV_EXPORTS_W int recoverPose( InputArray points1, InputArray points2,
2721	InputArray cameraMatrix1, InputArray distCoeffs1,
2722	InputArray cameraMatrix2, InputArray distCoeffs2,
2723	OutputArray E, OutputArray R, OutputArray t,
2724	int method = cv::RANSAC, double prob = 0.999, double threshold = 1.0,
2725	InputOutputArray mask = noArray());
2726
2727	/** @brief Recovers the relative camera rotation and the translation from an estimated essential
2728	matrix and the corresponding points in two images, using chirality check. Returns the number of
2729	inliers that pass the check.
2730
2731	@param E The input essential matrix.
2732	@param points1 Array of N 2D points from the first image. The point coordinates should be
2733	floating-point (single or double precision).
2734	@param points2 Array of the second image points of the same size and format as points1 .
2735	@param cameraMatrix Camera intrinsic matrix \f$\cameramatrix{A}\f$ .
2736	Note that this function assumes that points1 and points2 are feature points from cameras with the
2737	same camera intrinsic matrix.
2738	@param R Output rotation matrix. Together with the translation vector, this matrix makes up a tuple
2739	that performs a change of basis from the first camera's coordinate system to the second camera's
2740	coordinate system. Note that, in general, t can not be used for this tuple, see the parameter
2741	described below.
2742	@param t Output translation vector. This vector is obtained by @ref decomposeEssentialMat and
2743	therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit
2744	length.
2745	@param mask Input/output mask for inliers in points1 and points2. If it is not empty, then it marks
2746	inliers in points1 and points2 for the given essential matrix E. Only these inliers will be used to
2747	recover pose. In the output mask only inliers which pass the chirality check.
2748
2749	This function decomposes an essential matrix using @ref decomposeEssentialMat and then verifies
2750	possible pose hypotheses by doing chirality check. The chirality check means that the
2751	triangulated 3D points should have positive depth. Some details can be found in @cite Nister03.
2752
2753	This function can be used to process the output E and mask from @ref findEssentialMat. In this
2754	scenario, points1 and points2 are the same input for #findEssentialMat :
2755	@code
2756	// Example. Estimation of fundamental matrix using the RANSAC algorithm
2757	int point_count = 100;
2758	vector<Point2f> points1(point_count);
2759	vector<Point2f> points2(point_count);
2760
2761	// initialize the points here ...
2762	for( int i = 0; i < point_count; i++ )
2763	{
2764	points1[i] = ...;
2765	points2[i] = ...;
2766	}
2767
2768	// cametra matrix with both focal lengths = 1, and principal point = (0, 0)
2769	Mat cameraMatrix = Mat::eye(3, 3, CV_64F);
2770
2771	Mat E, R, t, mask;
2772
2773	E = findEssentialMat(points1, points2, cameraMatrix, RANSAC, 0.999, 1.0, mask);
2774	recoverPose(E, points1, points2, cameraMatrix, R, t, mask);
2775	@endcode
2776	*/
2777	CV_EXPORTS_W int recoverPose( InputArray E, InputArray points1, InputArray points2,
2778	InputArray cameraMatrix, OutputArray R, OutputArray t,
2779	InputOutputArray mask = noArray() );
2780
2781	/** @overload
2782	@param E The input essential matrix.
2783	@param points1 Array of N 2D points from the first image. The point coordinates should be
2784	floating-point (single or double precision).
2785	@param points2 Array of the second image points of the same size and format as points1 .
2786	@param R Output rotation matrix. Together with the translation vector, this matrix makes up a tuple
2787	that performs a change of basis from the first camera's coordinate system to the second camera's
2788	coordinate system. Note that, in general, t can not be used for this tuple, see the parameter
2789	description below.
2790	@param t Output translation vector. This vector is obtained by @ref decomposeEssentialMat and
2791	therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit
2792	length.
2793	@param focal Focal length of the camera. Note that this function assumes that points1 and points2
2794	are feature points from cameras with same focal length and principal point.
2795	@param pp principal point of the camera.
2796	@param mask Input/output mask for inliers in points1 and points2. If it is not empty, then it marks
2797	inliers in points1 and points2 for the given essential matrix E. Only these inliers will be used to
2798	recover pose. In the output mask only inliers which pass the chirality check.
2799
2800	This function differs from the one above that it computes camera intrinsic matrix from focal length and
2801	principal point:
2802
2803	\f[A =
2804	\begin{bmatrix}
2805	f & 0 & x_{pp} \\
2806	0 & f & y_{pp} \\
2807	0 & 0 & 1
2808	\end{bmatrix}\f]
2809	*/
2810	CV_EXPORTS_W int recoverPose( InputArray E, InputArray points1, InputArray points2,
2811	OutputArray R, OutputArray t,
2812	double focal = 1.0, Point2d pp = Point2d(0, 0),
2813	InputOutputArray mask = noArray() );
2814
2815	/** @overload
2816	@param E The input essential matrix.
2817	@param points1 Array of N 2D points from the first image. The point coordinates should be
2818	floating-point (single or double precision).
2819	@param points2 Array of the second image points of the same size and format as points1.
2820	@param cameraMatrix Camera intrinsic matrix \f$\cameramatrix{A}\f$ .
2821	Note that this function assumes that points1 and points2 are feature points from cameras with the
2822	same camera intrinsic matrix.
2823	@param R Output rotation matrix. Together with the translation vector, this matrix makes up a tuple
2824	that performs a change of basis from the first camera's coordinate system to the second camera's
2825	coordinate system. Note that, in general, t can not be used for this tuple, see the parameter
2826	description below.
2827	@param t Output translation vector. This vector is obtained by @ref decomposeEssentialMat and
2828	therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit
2829	length.
2830	@param distanceThresh threshold distance which is used to filter out far away points (i.e. infinite
2831	points).
2832	@param mask Input/output mask for inliers in points1 and points2. If it is not empty, then it marks
2833	inliers in points1 and points2 for the given essential matrix E. Only these inliers will be used to
2834	recover pose. In the output mask only inliers which pass the chirality check.
2835	@param triangulatedPoints 3D points which were reconstructed by triangulation.
2836
2837	This function differs from the one above that it outputs the triangulated 3D point that are used for
2838	the chirality check.
2839	*/
2840	CV_EXPORTS_W int recoverPose( InputArray E, InputArray points1, InputArray points2,
2841	InputArray cameraMatrix, OutputArray R, OutputArray t, double distanceThresh, InputOutputArray mask = noArray(),
2842	OutputArray triangulatedPoints = noArray());
2843
2844	/** @brief For points in an image of a stereo pair, computes the corresponding epilines in the other image.
2845
2846	@param points Input points. \f$N \times 1\f$ or \f$1 \times N\f$ matrix of type CV_32FC2 or
2847	vector\<Point2f\> .
2848	@param whichImage Index of the image (1 or 2) that contains the points .
2849	@param F Fundamental matrix that can be estimated using #findFundamentalMat or #stereoRectify .
2850	@param lines Output vector of the epipolar lines corresponding to the points in the other image.
2851	Each line \f$ax + by + c=0\f$ is encoded by 3 numbers \f$(a, b, c)\f$ .
2852
2853	For every point in one of the two images of a stereo pair, the function finds the equation of the
2854	corresponding epipolar line in the other image.
2855
2856	From the fundamental matrix definition (see #findFundamentalMat ), line \f$l^{(2)}_i\f$ in the second
2857	image for the point \f$p^{(1)}_i\f$ in the first image (when whichImage=1 ) is computed as:
2858
2859	\f[l^{(2)}_i = F p^{(1)}_i\f]
2860
2861	And vice versa, when whichImage=2, \f$l^{(1)}_i\f$ is computed from \f$p^{(2)}_i\f$ as:
2862
2863	\f[l^{(1)}_i = F^T p^{(2)}_i\f]
2864
2865	Line coefficients are defined up to a scale. They are normalized so that \f$a_i^2+b_i^2=1\f$ .
2866	*/
2867	CV_EXPORTS_W void computeCorrespondEpilines( InputArray points, int whichImage,
2868	InputArray F, OutputArray lines );
2869
2870	/** @brief This function reconstructs 3-dimensional points (in homogeneous coordinates) by using
2871	their observations with a stereo camera.
2872
2873	@param projMatr1 3x4 projection matrix of the first camera, i.e. this matrix projects 3D points
2874	given in the world's coordinate system into the first image.
2875	@param projMatr2 3x4 projection matrix of the second camera, i.e. this matrix projects 3D points
2876	given in the world's coordinate system into the second image.
2877	@param projPoints1 2xN array of feature points in the first image. In the case of the c++ version,
2878	it can be also a vector of feature points or two-channel matrix of size 1xN or Nx1.
2879	@param projPoints2 2xN array of corresponding points in the second image. In the case of the c++
2880	version, it can be also a vector of feature points or two-channel matrix of size 1xN or Nx1.
2881	@param points4D 4xN array of reconstructed points in homogeneous coordinates. These points are
2882	returned in the world's coordinate system.
2883
2884	@note
2885	Keep in mind that all input data should be of float type in order for this function to work.
2886
2887	@note
2888	If the projection matrices from @ref stereoRectify are used, then the returned points are
2889	represented in the first camera's rectified coordinate system.
2890
2891	@sa
2892	reprojectImageTo3D
2893	*/
2894	CV_EXPORTS_W void triangulatePoints( InputArray projMatr1, InputArray projMatr2,
2895	InputArray projPoints1, InputArray projPoints2,
2896	OutputArray points4D );
2897
2898	/** @brief Refines coordinates of corresponding points.
2899
2900	@param F 3x3 fundamental matrix.
2901	@param points1 1xN array containing the first set of points.
2902	@param points2 1xN array containing the second set of points.
2903	@param newPoints1 The optimized points1.
2904	@param newPoints2 The optimized points2.
2905
2906	The function implements the Optimal Triangulation Method (see Multiple View Geometry @cite HartleyZ00 for details).
2907	For each given point correspondence points1[i] \<-\> points2[i], and a fundamental matrix F, it
2908	computes the corrected correspondences newPoints1[i] \<-\> newPoints2[i] that minimize the geometric
2909	error \f$d(points1[i], newPoints1[i])^2 + d(points2[i],newPoints2[i])^2\f$ (where \f$d(a,b)\f$ is the
2910	geometric distance between points \f$a\f$ and \f$b\f$ ) subject to the epipolar constraint
2911	\f$newPoints2^T \cdot F \cdot newPoints1 = 0\f$ .
2912	*/
2913	CV_EXPORTS_W void correctMatches( InputArray F, InputArray points1, InputArray points2,
2914	OutputArray newPoints1, OutputArray newPoints2 );
2915
2916	/** @brief Filters off small noise blobs (speckles) in the disparity map
2917
2918	@param img The input 16-bit signed disparity image
2919	@param newVal The disparity value used to paint-off the speckles
2920	@param maxSpeckleSize The maximum speckle size to consider it a speckle. Larger blobs are not
2921	affected by the algorithm
2922	@param maxDiff Maximum difference between neighbor disparity pixels to put them into the same
2923	blob. Note that since StereoBM, StereoSGBM and may be other algorithms return a fixed-point
2924	disparity map, where disparity values are multiplied by 16, this scale factor should be taken into
2925	account when specifying this parameter value.
2926	@param buf The optional temporary buffer to avoid memory allocation within the function.
2927	*/
2928	CV_EXPORTS_W void filterSpeckles( InputOutputArray img, double newVal,
2929	int maxSpeckleSize, double maxDiff,
2930	InputOutputArray buf = noArray() );
2931
2932	//! computes valid disparity ROI from the valid ROIs of the rectified images (that are returned by #stereoRectify)
2933	CV_EXPORTS_W Rect getValidDisparityROI( Rect roi1, Rect roi2,
2934	int minDisparity, int numberOfDisparities,
2935	int blockSize );
2936
2937	//! validates disparity using the left-right check. The matrix "cost" should be computed by the stereo correspondence algorithm
2938	CV_EXPORTS_W void validateDisparity( InputOutputArray disparity, InputArray cost,
2939	int minDisparity, int numberOfDisparities,
2940	int disp12MaxDisp = 1 );
2941
2942	/** @brief Reprojects a disparity image to 3D space.
2943
2944	@param disparity Input single-channel 8-bit unsigned, 16-bit signed, 32-bit signed or 32-bit
2945	floating-point disparity image. The values of 8-bit / 16-bit signed formats are assumed to have no
2946	fractional bits. If the disparity is 16-bit signed format, as computed by @ref StereoBM or
2947	@ref StereoSGBM and maybe other algorithms, it should be divided by 16 (and scaled to float) before
2948	being used here.
2949	@param _3dImage Output 3-channel floating-point image of the same size as disparity. Each element of
2950	_3dImage(x,y) contains 3D coordinates of the point (x,y) computed from the disparity map. If one
2951	uses Q obtained by @ref stereoRectify, then the returned points are represented in the first
2952	camera's rectified coordinate system.
2953	@param Q \f$4 \times 4\f$ perspective transformation matrix that can be obtained with
2954	@ref stereoRectify.
2955	@param handleMissingValues Indicates, whether the function should handle missing values (i.e.
2956	points where the disparity was not computed). If handleMissingValues=true, then pixels with the
2957	minimal disparity that corresponds to the outliers (see StereoMatcher::compute ) are transformed
2958	to 3D points with a very large Z value (currently set to 10000).
2959	@param ddepth The optional output array depth. If it is -1, the output image will have CV_32F
2960	depth. ddepth can also be set to CV_16S, CV_32S or CV_32F.
2961
2962	The function transforms a single-channel disparity map to a 3-channel image representing a 3D
2963	surface. That is, for each pixel (x,y) and the corresponding disparity d=disparity(x,y) , it
2964	computes:
2965
2966	\f[\begin{bmatrix}
2967	X \\
2968	Y \\
2969	Z \\
2970	W
2971	\end{bmatrix} = Q \begin{bmatrix}
2972	x \\
2973	y \\
2974	\texttt{disparity} (x,y) \\
2975	1
2976	\end{bmatrix}.\f]
2977
2978	@sa
2979	To reproject a sparse set of points {(x,y,d),...} to 3D space, use perspectiveTransform.
2980	*/
2981	CV_EXPORTS_W void reprojectImageTo3D( InputArray disparity,
2982	OutputArray _3dImage, InputArray Q,
2983	bool handleMissingValues = false,
2984	int ddepth = -1 );
2985
2986	/** @brief Calculates the Sampson Distance between two points.
2987
2988	The function cv::sampsonDistance calculates and returns the first order approximation of the geometric error as:
2989	\f[
2990	sd( \texttt{pt1} , \texttt{pt2} )=
2991	\frac{(\texttt{pt2}^t \cdot \texttt{F} \cdot \texttt{pt1})^2}
2992	{((\texttt{F} \cdot \texttt{pt1})(0))^2 +
2993	((\texttt{F} \cdot \texttt{pt1})(1))^2 +
2994	((\texttt{F}^t \cdot \texttt{pt2})(0))^2 +
2995	((\texttt{F}^t \cdot \texttt{pt2})(1))^2}
2996	\f]
2997	The fundamental matrix may be calculated using the #findFundamentalMat function. See @cite HartleyZ00 11.4.3 for details.
2998	@param pt1 first homogeneous 2d point
2999	@param pt2 second homogeneous 2d point
3000	@param F fundamental matrix
3001	@return The computed Sampson distance.
3002	*/
3003	CV_EXPORTS_W double sampsonDistance(InputArray pt1, InputArray pt2, InputArray F);
3004
3005	/** @brief Computes an optimal affine transformation between two 3D point sets.
3006
3007	It computes
3008	\f[
3009	\begin{bmatrix}
3010	x\\
3011	y\\
3012	z\\
3013	\end{bmatrix}
3014	=
3015	\begin{bmatrix}
3016	a_{11} & a_{12} & a_{13}\\
3017	a_{21} & a_{22} & a_{23}\\
3018	a_{31} & a_{32} & a_{33}\\
3019	\end{bmatrix}
3020	\begin{bmatrix}
3021	X\\
3022	Y\\
3023	Z\\
3024	\end{bmatrix}
3025	+
3026	\begin{bmatrix}
3027	b_1\\
3028	b_2\\
3029	b_3\\
3030	\end{bmatrix}
3031	\f]
3032
3033	@param src First input 3D point set containing \f$(X,Y,Z)\f$.
3034	@param dst Second input 3D point set containing \f$(x,y,z)\f$.
3035	@param out Output 3D affine transformation matrix \f$3 \times 4\f$ of the form
3036	\f[
3037	\begin{bmatrix}
3038	a_{11} & a_{12} & a_{13} & b_1\\
3039	a_{21} & a_{22} & a_{23} & b_2\\
3040	a_{31} & a_{32} & a_{33} & b_3\\
3041	\end{bmatrix}
3042	\f]
3043	@param inliers Output vector indicating which points are inliers (1-inlier, 0-outlier).
3044	@param ransacThreshold Maximum reprojection error in the RANSAC algorithm to consider a point as
3045	an inlier.
3046	@param confidence Confidence level, between 0 and 1, for the estimated transformation. Anything
3047	between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation
3048	significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation.
3049
3050	The function estimates an optimal 3D affine transformation between two 3D point sets using the
3051	RANSAC algorithm.
3052	*/
3053	CV_EXPORTS_W int estimateAffine3D(InputArray src, InputArray dst,
3054	OutputArray out, OutputArray inliers,
3055	double ransacThreshold = 3, double confidence = 0.99);
3056
3057	/** @brief Computes an optimal affine transformation between two 3D point sets.
3058
3059	It computes \f$R,s,t\f$ minimizing \f$\sum{i} dst_i - c \cdot R \cdot src_i \f$
3060	where \f$R\f$ is a 3x3 rotation matrix, \f$t\f$ is a 3x1 translation vector and \f$s\f$ is a
3061	scalar size value. This is an implementation of the algorithm by Umeyama \cite umeyama1991least .
3062	The estimated affine transform has a homogeneous scale which is a subclass of affine
3063	transformations with 7 degrees of freedom. The paired point sets need to comprise at least 3
3064	points each.
3065
3066	@param src First input 3D point set.
3067	@param dst Second input 3D point set.
3068	@param scale If null is passed, the scale parameter c will be assumed to be 1.0.
3069	Else the pointed-to variable will be set to the optimal scale.
3070	@param force_rotation If true, the returned rotation will never be a reflection.
3071	This might be unwanted, e.g. when optimizing a transform between a right- and a
3072	left-handed coordinate system.
3073	@return 3D affine transformation matrix \f$3 \times 4\f$ of the form
3074	\f[T =
3075	\begin{bmatrix}
3076	R & t\\
3077	\end{bmatrix}
3078	\f]
3079
3080	*/
3081	CV_EXPORTS_W cv::Mat estimateAffine3D(InputArray src, InputArray dst,
3082	CV_OUT double* scale = nullptr, bool force_rotation = true);
3083
3084	/** @brief Computes an optimal translation between two 3D point sets.
3085	*
3086	* It computes
3087	* \f[
3088	* \begin{bmatrix}
3089	* x\\
3090	* y\\
3091	* z\\
3092	* \end{bmatrix}
3093	* =
3094	* \begin{bmatrix}
3095	* X\\
3096	* Y\\
3097	* Z\\
3098	* \end{bmatrix}
3099	* +
3100	* \begin{bmatrix}
3101	* b_1\\
3102	* b_2\\
3103	* b_3\\
3104	* \end{bmatrix}
3105	* \f]
3106	*
3107	* @param src First input 3D point set containing \f$(X,Y,Z)\f$.
3108	* @param dst Second input 3D point set containing \f$(x,y,z)\f$.
3109	* @param out Output 3D translation vector \f$3 \times 1\f$ of the form
3110	* \f[
3111	* \begin{bmatrix}
3112	* b_1 \\
3113	* b_2 \\
3114	* b_3 \\
3115	* \end{bmatrix}
3116	* \f]
3117	* @param inliers Output vector indicating which points are inliers (1-inlier, 0-outlier).
3118	* @param ransacThreshold Maximum reprojection error in the RANSAC algorithm to consider a point as
3119	* an inlier.
3120	* @param confidence Confidence level, between 0 and 1, for the estimated transformation. Anything
3121	* between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation
3122	* significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation.
3123	*
3124	* The function estimates an optimal 3D translation between two 3D point sets using the
3125	* RANSAC algorithm.
3126	* */
3127	CV_EXPORTS_W int estimateTranslation3D(InputArray src, InputArray dst,
3128	OutputArray out, OutputArray inliers,
3129	double ransacThreshold = 3, double confidence = 0.99);
3130
3131	/** @brief Computes an optimal affine transformation between two 2D point sets.
3132
3133	It computes
3134	\f[
3135	\begin{bmatrix}
3136	x\\
3137	y\\
3138	\end{bmatrix}
3139	=
3140	\begin{bmatrix}
3141	a_{11} & a_{12}\\
3142	a_{21} & a_{22}\\
3143	\end{bmatrix}
3144	\begin{bmatrix}
3145	X\\
3146	Y\\
3147	\end{bmatrix}
3148	+
3149	\begin{bmatrix}
3150	b_1\\
3151	b_2\\
3152	\end{bmatrix}
3153	\f]
3154
3155	@param from First input 2D point set containing \f$(X,Y)\f$.
3156	@param to Second input 2D point set containing \f$(x,y)\f$.
3157	@param inliers Output vector indicating which points are inliers (1-inlier, 0-outlier).
3158	@param method Robust method used to compute transformation. The following methods are possible:
3159	- @ref RANSAC - RANSAC-based robust method
3160	- @ref LMEDS - Least-Median robust method
3161	RANSAC is the default method.
3162	@param ransacReprojThreshold Maximum reprojection error in the RANSAC algorithm to consider
3163	a point as an inlier. Applies only to RANSAC.
3164	@param maxIters The maximum number of robust method iterations.
3165	@param confidence Confidence level, between 0 and 1, for the estimated transformation. Anything
3166	between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation
3167	significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation.
3168	@param refineIters Maximum number of iterations of refining algorithm (Levenberg-Marquardt).
3169	Passing 0 will disable refining, so the output matrix will be output of robust method.
3170
3171	@return Output 2D affine transformation matrix \f$2 \times 3\f$ or empty matrix if transformation
3172	could not be estimated. The returned matrix has the following form:
3173	\f[
3174	\begin{bmatrix}
3175	a_{11} & a_{12} & b_1\\
3176	a_{21} & a_{22} & b_2\\
3177	\end{bmatrix}
3178	\f]
3179
3180	The function estimates an optimal 2D affine transformation between two 2D point sets using the
3181	selected robust algorithm.
3182
3183	The computed transformation is then refined further (using only inliers) with the
3184	Levenberg-Marquardt method to reduce the re-projection error even more.
3185
3186	@note
3187	The RANSAC method can handle practically any ratio of outliers but needs a threshold to
3188	distinguish inliers from outliers. The method LMeDS does not need any threshold but it works
3189	correctly only when there are more than 50% of inliers.
3190
3191	@sa estimateAffinePartial2D, getAffineTransform
3192	*/
3193	CV_EXPORTS_W cv::Mat estimateAffine2D(InputArray from, InputArray to, OutputArray inliers = noArray(),
3194	int method = RANSAC, double ransacReprojThreshold = 3,
3195	size_t maxIters = 2000, double confidence = 0.99,
3196	size_t refineIters = 10);
3197
3198
3199	CV_EXPORTS_W cv::Mat estimateAffine2D(InputArray pts1, InputArray pts2, OutputArray inliers,
3200	const UsacParams &params);
3201
3202	/** @brief Computes an optimal limited affine transformation with 4 degrees of freedom between
3203	two 2D point sets.
3204
3205	@param from First input 2D point set.
3206	@param to Second input 2D point set.
3207	@param inliers Output vector indicating which points are inliers.
3208	@param method Robust method used to compute transformation. The following methods are possible:
3209	- @ref RANSAC - RANSAC-based robust method
3210	- @ref LMEDS - Least-Median robust method
3211	RANSAC is the default method.
3212	@param ransacReprojThreshold Maximum reprojection error in the RANSAC algorithm to consider
3213	a point as an inlier. Applies only to RANSAC.
3214	@param maxIters The maximum number of robust method iterations.
3215	@param confidence Confidence level, between 0 and 1, for the estimated transformation. Anything
3216	between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation
3217	significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation.
3218	@param refineIters Maximum number of iterations of refining algorithm (Levenberg-Marquardt).
3219	Passing 0 will disable refining, so the output matrix will be output of robust method.
3220
3221	@return Output 2D affine transformation (4 degrees of freedom) matrix \f$2 \times 3\f$ or
3222	empty matrix if transformation could not be estimated.
3223
3224	The function estimates an optimal 2D affine transformation with 4 degrees of freedom limited to
3225	combinations of translation, rotation, and uniform scaling. Uses the selected algorithm for robust
3226	estimation.
3227
3228	The computed transformation is then refined further (using only inliers) with the
3229	Levenberg-Marquardt method to reduce the re-projection error even more.
3230
3231	Estimated transformation matrix is:
3232	\f[ \begin{bmatrix} \cos(\theta) \cdot s & -\sin(\theta) \cdot s & t_x \\
3233	\sin(\theta) \cdot s & \cos(\theta) \cdot s & t_y
3234	\end{bmatrix} \f]
3235	Where \f$ \theta \f$ is the rotation angle, \f$ s \f$ the scaling factor and \f$ t_x, t_y \f$ are
3236	translations in \f$ x, y \f$ axes respectively.
3237
3238	@note
3239	The RANSAC method can handle practically any ratio of outliers but need a threshold to
3240	distinguish inliers from outliers. The method LMeDS does not need any threshold but it works
3241	correctly only when there are more than 50% of inliers.
3242
3243	@sa estimateAffine2D, getAffineTransform
3244	*/
3245	CV_EXPORTS_W cv::Mat estimateAffinePartial2D(InputArray from, InputArray to, OutputArray inliers = noArray(),
3246	int method = RANSAC, double ransacReprojThreshold = 3,
3247	size_t maxIters = 2000, double confidence = 0.99,
3248	size_t refineIters = 10);
3249
3250	/** @example samples/cpp/tutorial_code/features2D/Homography/decompose_homography.cpp
3251	An example program with homography decomposition.
3252
3253	Check @ref tutorial_homography "the corresponding tutorial" for more details.
3254	*/
3255
3256	/** @brief Decompose a homography matrix to rotation(s), translation(s) and plane normal(s).
3257
3258	@param H The input homography matrix between two images.
3259	@param K The input camera intrinsic matrix.
3260	@param rotations Array of rotation matrices.
3261	@param translations Array of translation matrices.
3262	@param normals Array of plane normal matrices.
3263
3264	This function extracts relative camera motion between two views of a planar object and returns up to
3265	four mathematical solution tuples of rotation, translation, and plane normal. The decomposition of
3266	the homography matrix H is described in detail in @cite Malis2007.
3267
3268	If the homography H, induced by the plane, gives the constraint
3269	\f[s_i \vecthree{x'_i}{y'_i}{1} \sim H \vecthree{x_i}{y_i}{1}\f] on the source image points
3270	\f$p_i\f$ and the destination image points \f$p'_i\f$, then the tuple of rotations[k] and
3271	translations[k] is a change of basis from the source camera's coordinate system to the destination
3272	camera's coordinate system. However, by decomposing H, one can only get the translation normalized
3273	by the (typically unknown) depth of the scene, i.e. its direction but with normalized length.
3274
3275	If point correspondences are available, at least two solutions may further be invalidated, by
3276	applying positive depth constraint, i.e. all points must be in front of the camera.
3277	*/
3278	CV_EXPORTS_W int decomposeHomographyMat(InputArray H,
3279	InputArray K,
3280	OutputArrayOfArrays rotations,
3281	OutputArrayOfArrays translations,
3282	OutputArrayOfArrays normals);
3283
3284	/** @brief Filters homography decompositions based on additional information.
3285
3286	@param rotations Vector of rotation matrices.
3287	@param normals Vector of plane normal matrices.
3288	@param beforePoints Vector of (rectified) visible reference points before the homography is applied
3289	@param afterPoints Vector of (rectified) visible reference points after the homography is applied
3290	@param possibleSolutions Vector of int indices representing the viable solution set after filtering
3291	@param pointsMask optional Mat/Vector of 8u type representing the mask for the inliers as given by the #findHomography function
3292
3293	This function is intended to filter the output of the #decomposeHomographyMat based on additional
3294	information as described in @cite Malis2007 . The summary of the method: the #decomposeHomographyMat function
3295	returns 2 unique solutions and their "opposites" for a total of 4 solutions. If we have access to the
3296	sets of points visible in the camera frame before and after the homography transformation is applied,
3297	we can determine which are the true potential solutions and which are the opposites by verifying which
3298	homographies are consistent with all visible reference points being in front of the camera. The inputs
3299	are left unchanged; the filtered solution set is returned as indices into the existing one.
3300
3301	*/
3302	CV_EXPORTS_W void filterHomographyDecompByVisibleRefpoints(InputArrayOfArrays rotations,
3303	InputArrayOfArrays normals,
3304	InputArray beforePoints,
3305	InputArray afterPoints,
3306	OutputArray possibleSolutions,
3307	InputArray pointsMask = noArray());
3308
3309	/** @brief The base class for stereo correspondence algorithms.
3310	*/
3311	class CV_EXPORTS_W StereoMatcher : public Algorithm
3312	{
3313	public:
3314	enum { DISP_SHIFT = 4,
3315	DISP_SCALE = (1 << DISP_SHIFT)
3316	};
3317
3318	/** @brief Computes disparity map for the specified stereo pair
3319
3320	@param left Left 8-bit single-channel image.
3321	@param right Right image of the same size and the same type as the left one.
3322	@param disparity Output disparity map. It has the same size as the input images. Some algorithms,
3323	like StereoBM or StereoSGBM compute 16-bit fixed-point disparity map (where each disparity value
3324	has 4 fractional bits), whereas other algorithms output 32-bit floating-point disparity map.
3325	*/
3326	CV_WRAP virtual void compute( InputArray left, InputArray right,
3327	OutputArray disparity ) = 0;
3328
3329	CV_WRAP virtual int getMinDisparity() const = 0;
3330	CV_WRAP virtual void setMinDisparity(int minDisparity) = 0;
3331
3332	CV_WRAP virtual int getNumDisparities() const = 0;
3333	CV_WRAP virtual void setNumDisparities(int numDisparities) = 0;
3334
3335	CV_WRAP virtual int getBlockSize() const = 0;
3336	CV_WRAP virtual void setBlockSize(int blockSize) = 0;
3337
3338	CV_WRAP virtual int getSpeckleWindowSize() const = 0;
3339	CV_WRAP virtual void setSpeckleWindowSize(int speckleWindowSize) = 0;
3340
3341	CV_WRAP virtual int getSpeckleRange() const = 0;
3342	CV_WRAP virtual void setSpeckleRange(int speckleRange) = 0;
3343
3344	CV_WRAP virtual int getDisp12MaxDiff() const = 0;
3345	CV_WRAP virtual void setDisp12MaxDiff(int disp12MaxDiff) = 0;
3346	};
3347
3348
3349	/** @brief Class for computing stereo correspondence using the block matching algorithm, introduced and
3350	contributed to OpenCV by K. Konolige.
3351	*/
3352	class CV_EXPORTS_W StereoBM : public StereoMatcher
3353	{
3354	public:
3355	enum { PREFILTER_NORMALIZED_RESPONSE = 0,
3356	PREFILTER_XSOBEL = 1
3357	};
3358
3359	CV_WRAP virtual int getPreFilterType() const = 0;
3360	CV_WRAP virtual void setPreFilterType(int preFilterType) = 0;
3361
3362	CV_WRAP virtual int getPreFilterSize() const = 0;
3363	CV_WRAP virtual void setPreFilterSize(int preFilterSize) = 0;
3364
3365	CV_WRAP virtual int getPreFilterCap() const = 0;
3366	CV_WRAP virtual void setPreFilterCap(int preFilterCap) = 0;
3367
3368	CV_WRAP virtual int getTextureThreshold() const = 0;
3369	CV_WRAP virtual void setTextureThreshold(int textureThreshold) = 0;
3370
3371	CV_WRAP virtual int getUniquenessRatio() const = 0;
3372	CV_WRAP virtual void setUniquenessRatio(int uniquenessRatio) = 0;
3373
3374	CV_WRAP virtual int getSmallerBlockSize() const = 0;
3375	CV_WRAP virtual void setSmallerBlockSize(int blockSize) = 0;
3376
3377	CV_WRAP virtual Rect getROI1() const = 0;
3378	CV_WRAP virtual void setROI1(Rect roi1) = 0;
3379
3380	CV_WRAP virtual Rect getROI2() const = 0;
3381	CV_WRAP virtual void setROI2(Rect roi2) = 0;
3382
3383	/** @brief Creates StereoBM object
3384
3385	@param numDisparities the disparity search range. For each pixel algorithm will find the best
3386	disparity from 0 (default minimum disparity) to numDisparities. The search range can then be
3387	shifted by changing the minimum disparity.
3388	@param blockSize the linear size of the blocks compared by the algorithm. The size should be odd
3389	(as the block is centered at the current pixel). Larger block size implies smoother, though less
3390	accurate disparity map. Smaller block size gives more detailed disparity map, but there is higher
3391	chance for algorithm to find a wrong correspondence.
3392
3393	The function create StereoBM object. You can then call StereoBM::compute() to compute disparity for
3394	a specific stereo pair.
3395	*/
3396	CV_WRAP static Ptr<StereoBM> create(int numDisparities = 0, int blockSize = 21);
3397	};
3398
3399	/** @brief The class implements the modified H. Hirschmuller algorithm @cite HH08 that differs from the original
3400	one as follows:
3401
3402	- By default, the algorithm is single-pass, which means that you consider only 5 directions
3403	instead of 8. Set mode=StereoSGBM::MODE_HH in createStereoSGBM to run the full variant of the
3404	algorithm but beware that it may consume a lot of memory.
3405	- The algorithm matches blocks, not individual pixels. Though, setting blockSize=1 reduces the
3406	blocks to single pixels.
3407	- Mutual information cost function is not implemented. Instead, a simpler Birchfield-Tomasi
3408	sub-pixel metric from @cite BT98 is used. Though, the color images are supported as well.
3409	- Some pre- and post- processing steps from K. Konolige algorithm StereoBM are included, for
3410	example: pre-filtering (StereoBM::PREFILTER_XSOBEL type) and post-filtering (uniqueness
3411	check, quadratic interpolation and speckle filtering).
3412
3413	@note
3414	- (Python) An example illustrating the use of the StereoSGBM matching algorithm can be found
3415	at opencv_source_code/samples/python/stereo_match.py
3416	*/
3417	class CV_EXPORTS_W StereoSGBM : public StereoMatcher
3418	{
3419	public:
3420	enum
3421	{
3422	MODE_SGBM = 0,
3423	MODE_HH = 1,
3424	MODE_SGBM_3WAY = 2,
3425	MODE_HH4 = 3
3426	};
3427
3428	CV_WRAP virtual int getPreFilterCap() const = 0;
3429	CV_WRAP virtual void setPreFilterCap(int preFilterCap) = 0;
3430
3431	CV_WRAP virtual int getUniquenessRatio() const = 0;
3432	CV_WRAP virtual void setUniquenessRatio(int uniquenessRatio) = 0;
3433
3434	CV_WRAP virtual int getP1() const = 0;
3435	CV_WRAP virtual void setP1(int P1) = 0;
3436
3437	CV_WRAP virtual int getP2() const = 0;
3438	CV_WRAP virtual void setP2(int P2) = 0;
3439
3440	CV_WRAP virtual int getMode() const = 0;
3441	CV_WRAP virtual void setMode(int mode) = 0;
3442
3443	/** @brief Creates StereoSGBM object
3444
3445	@param minDisparity Minimum possible disparity value. Normally, it is zero but sometimes
3446	rectification algorithms can shift images, so this parameter needs to be adjusted accordingly.
3447	@param numDisparities Maximum disparity minus minimum disparity. The value is always greater than
3448	zero. In the current implementation, this parameter must be divisible by 16.
3449	@param blockSize Matched block size. It must be an odd number \>=1 . Normally, it should be
3450	somewhere in the 3..11 range.
3451	@param P1 The first parameter controlling the disparity smoothness. See below.
3452	@param P2 The second parameter controlling the disparity smoothness. The larger the values are,
3453	the smoother the disparity is. P1 is the penalty on the disparity change by plus or minus 1
3454	between neighbor pixels. P2 is the penalty on the disparity change by more than 1 between neighbor
3455	pixels. The algorithm requires P2 \> P1 . See stereo_match.cpp sample where some reasonably good
3456	P1 and P2 values are shown (like 8\*number_of_image_channels\*blockSize\*blockSize and
3457	32\*number_of_image_channels\*blockSize\*blockSize , respectively).
3458	@param disp12MaxDiff Maximum allowed difference (in integer pixel units) in the left-right
3459	disparity check. Set it to a non-positive value to disable the check.
3460	@param preFilterCap Truncation value for the prefiltered image pixels. The algorithm first
3461	computes x-derivative at each pixel and clips its value by [-preFilterCap, preFilterCap] interval.
3462	The result values are passed to the Birchfield-Tomasi pixel cost function.
3463	@param uniquenessRatio Margin in percentage by which the best (minimum) computed cost function
3464	value should "win" the second best value to consider the found match correct. Normally, a value
3465	within the 5-15 range is good enough.
3466	@param speckleWindowSize Maximum size of smooth disparity regions to consider their noise speckles
3467	and invalidate. Set it to 0 to disable speckle filtering. Otherwise, set it somewhere in the
3468	50-200 range.
3469	@param speckleRange Maximum disparity variation within each connected component. If you do speckle
3470	filtering, set the parameter to a positive value, it will be implicitly multiplied by 16.
3471	Normally, 1 or 2 is good enough.
3472	@param mode Set it to StereoSGBM::MODE_HH to run the full-scale two-pass dynamic programming
3473	algorithm. It will consume O(W\*H\*numDisparities) bytes, which is large for 640x480 stereo and
3474	huge for HD-size pictures. By default, it is set to false .
3475
3476	The first constructor initializes StereoSGBM with all the default parameters. So, you only have to
3477	set StereoSGBM::numDisparities at minimum. The second constructor enables you to set each parameter
3478	to a custom value.
3479	*/
3480	CV_WRAP static Ptr<StereoSGBM> create(int minDisparity = 0, int numDisparities = 16, int blockSize = 3,
3481	int P1 = 0, int P2 = 0, int disp12MaxDiff = 0,
3482	int preFilterCap = 0, int uniquenessRatio = 0,
3483	int speckleWindowSize = 0, int speckleRange = 0,
3484	int mode = StereoSGBM::MODE_SGBM);
3485	};
3486
3487
3488	//! cv::undistort mode
3489	enum UndistortTypes
3490	{
3491	PROJ_SPHERICAL_ORTHO = 0,
3492	PROJ_SPHERICAL_EQRECT = 1
3493	};
3494
3495	/** @brief Transforms an image to compensate for lens distortion.
3496
3497	The function transforms an image to compensate radial and tangential lens distortion.
3498
3499	The function is simply a combination of #initUndistortRectifyMap (with unity R ) and #remap
3500	(with bilinear interpolation). See the former function for details of the transformation being
3501	performed.
3502
3503	Those pixels in the destination image, for which there is no correspondent pixels in the source
3504	image, are filled with zeros (black color).
3505
3506	A particular subset of the source image that will be visible in the corrected image can be regulated
3507	by newCameraMatrix. You can use #getOptimalNewCameraMatrix to compute the appropriate
3508	newCameraMatrix depending on your requirements.
3509
3510	The camera matrix and the distortion parameters can be determined using #calibrateCamera. If
3511	the resolution of images is different from the resolution used at the calibration stage, \f$f_x,
3512	f_y, c_x\f$ and \f$c_y\f$ need to be scaled accordingly, while the distortion coefficients remain
3513	the same.
3514
3515	@param src Input (distorted) image.
3516	@param dst Output (corrected) image that has the same size and type as src .
3517	@param cameraMatrix Input camera matrix \f$A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
3518	@param distCoeffs Input vector of distortion coefficients
3519	\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
3520	of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
3521	@param newCameraMatrix Camera matrix of the distorted image. By default, it is the same as
3522	cameraMatrix but you may additionally scale and shift the result by using a different matrix.
3523	*/
3524	CV_EXPORTS_W void undistort( InputArray src, OutputArray dst,
3525	InputArray cameraMatrix,
3526	InputArray distCoeffs,
3527	InputArray newCameraMatrix = noArray() );
3528
3529	/** @brief Computes the undistortion and rectification transformation map.
3530
3531	The function computes the joint undistortion and rectification transformation and represents the
3532	result in the form of maps for #remap. The undistorted image looks like original, as if it is
3533	captured with a camera using the camera matrix =newCameraMatrix and zero distortion. In case of a
3534	monocular camera, newCameraMatrix is usually equal to cameraMatrix, or it can be computed by
3535	#getOptimalNewCameraMatrix for a better control over scaling. In case of a stereo camera,
3536	newCameraMatrix is normally set to P1 or P2 computed by #stereoRectify .
3537
3538	Also, this new camera is oriented differently in the coordinate space, according to R. That, for
3539	example, helps to align two heads of a stereo camera so that the epipolar lines on both images
3540	become horizontal and have the same y- coordinate (in case of a horizontally aligned stereo camera).
3541
3542	The function actually builds the maps for the inverse mapping algorithm that is used by #remap. That
3543	is, for each pixel \f$(u, v)\f$ in the destination (corrected and rectified) image, the function
3544	computes the corresponding coordinates in the source image (that is, in the original image from
3545	camera). The following process is applied:
3546	\f[
3547	\begin{array}{l}
3548	x \leftarrow (u - {c'}_x)/{f'}_x \\
3549	y \leftarrow (v - {c'}_y)/{f'}_y \\
3550	{[X\,Y\,W]} ^T \leftarrow R^{-1}*[x \, y \, 1]^T \\
3551	x' \leftarrow X/W \\
3552	y' \leftarrow Y/W \\
3553	r^2 \leftarrow x'^2 + y'^2 \\
3554	x'' \leftarrow x' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6}
3555	+ 2p_1 x' y' + p_2(r^2 + 2 x'^2) + s_1 r^2 + s_2 r^4\\
3556	y'' \leftarrow y' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6}
3557	+ p_1 (r^2 + 2 y'^2) + 2 p_2 x' y' + s_3 r^2 + s_4 r^4 \\
3558	s\vecthree{x'''}{y'''}{1} =
3559	\vecthreethree{R_{33}(\tau_x, \tau_y)}{0}{-R_{13}((\tau_x, \tau_y)}
3560	{0}{R_{33}(\tau_x, \tau_y)}{-R_{23}(\tau_x, \tau_y)}
3561	{0}{0}{1} R(\tau_x, \tau_y) \vecthree{x''}{y''}{1}\\
3562	map_x(u,v) \leftarrow x''' f_x + c_x \\
3563	map_y(u,v) \leftarrow y''' f_y + c_y
3564	\end{array}
3565	\f]
3566	where \f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
3567	are the distortion coefficients.
3568
3569	In case of a stereo camera, this function is called twice: once for each camera head, after
3570	#stereoRectify, which in its turn is called after #stereoCalibrate. But if the stereo camera
3571	was not calibrated, it is still possible to compute the rectification transformations directly from
3572	the fundamental matrix using #stereoRectifyUncalibrated. For each camera, the function computes
3573	homography H as the rectification transformation in a pixel domain, not a rotation matrix R in 3D
3574	space. R can be computed from H as
3575	\f[\texttt{R} = \texttt{cameraMatrix} ^{-1} \cdot \texttt{H} \cdot \texttt{cameraMatrix}\f]
3576	where cameraMatrix can be chosen arbitrarily.
3577
3578	@param cameraMatrix Input camera matrix \f$A=\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
3579	@param distCoeffs Input vector of distortion coefficients
3580	\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
3581	of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
3582	@param R Optional rectification transformation in the object space (3x3 matrix). R1 or R2 ,
3583	computed by #stereoRectify can be passed here. If the matrix is empty, the identity transformation
3584	is assumed. In #initUndistortRectifyMap R assumed to be an identity matrix.
3585	@param newCameraMatrix New camera matrix \f$A'=\vecthreethree{f_x'}{0}{c_x'}{0}{f_y'}{c_y'}{0}{0}{1}\f$.
3586	@param size Undistorted image size.
3587	@param m1type Type of the first output map that can be CV_32FC1, CV_32FC2 or CV_16SC2, see #convertMaps
3588	@param map1 The first output map.
3589	@param map2 The second output map.
3590	*/
3591	CV_EXPORTS_W
3592	void initUndistortRectifyMap(InputArray cameraMatrix, InputArray distCoeffs,
3593	InputArray R, InputArray newCameraMatrix,
3594	Size size, int m1type, OutputArray map1, OutputArray map2);
3595
3596	/** @brief Computes the projection and inverse-rectification transformation map. In essense, this is the inverse of
3597	#initUndistortRectifyMap to accomodate stereo-rectification of projectors ('inverse-cameras') in projector-camera pairs.
3598
3599	The function computes the joint projection and inverse rectification transformation and represents the
3600	result in the form of maps for #remap. The projected image looks like a distorted version of the original which,
3601	once projected by a projector, should visually match the original. In case of a monocular camera, newCameraMatrix
3602	is usually equal to cameraMatrix, or it can be computed by
3603	#getOptimalNewCameraMatrix for a better control over scaling. In case of a projector-camera pair,
3604	newCameraMatrix is normally set to P1 or P2 computed by #stereoRectify .
3605
3606	The projector is oriented differently in the coordinate space, according to R. In case of projector-camera pairs,
3607	this helps align the projector (in the same manner as #initUndistortRectifyMap for the camera) to create a stereo-rectified pair. This
3608	allows epipolar lines on both images to become horizontal and have the same y-coordinate (in case of a horizontally aligned projector-camera pair).
3609
3610	The function builds the maps for the inverse mapping algorithm that is used by #remap. That
3611	is, for each pixel \f$(u, v)\f$ in the destination (projected and inverse-rectified) image, the function
3612	computes the corresponding coordinates in the source image (that is, in the original digital image). The following process is applied:
3613
3614	\f[
3615	\begin{array}{l}
3616	\text{newCameraMatrix}\\
3617	x \leftarrow (u - {c'}_x)/{f'}_x \\
3618	y \leftarrow (v - {c'}_y)/{f'}_y \\
3619
3620	\\\text{Undistortion}
3621	\\\scriptsize{\textit{though equation shown is for radial undistortion, function implements cv::undistortPoints()}}\\
3622	r^2 \leftarrow x^2 + y^2 \\
3623	\theta \leftarrow \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6}\\
3624	x' \leftarrow \frac{x}{\theta} \\
3625	y' \leftarrow \frac{y}{\theta} \\
3626
3627	\\\text{Rectification}\\
3628	{[X\,Y\,W]} ^T \leftarrow R*[x' \, y' \, 1]^T \\
3629	x'' \leftarrow X/W \\
3630	y'' \leftarrow Y/W \\
3631
3632	\\\text{cameraMatrix}\\
3633	map_x(u,v) \leftarrow x'' f_x + c_x \\
3634	map_y(u,v) \leftarrow y'' f_y + c_y
3635	\end{array}
3636	\f]
3637	where \f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
3638	are the distortion coefficients vector distCoeffs.
3639
3640	In case of a stereo-rectified projector-camera pair, this function is called for the projector while #initUndistortRectifyMap is called for the camera head.
3641	This is done after #stereoRectify, which in turn is called after #stereoCalibrate. If the projector-camera pair
3642	is not calibrated, it is still possible to compute the rectification transformations directly from
3643	the fundamental matrix using #stereoRectifyUncalibrated. For the projector and camera, the function computes
3644	homography H as the rectification transformation in a pixel domain, not a rotation matrix R in 3D
3645	space. R can be computed from H as
3646	\f[\texttt{R} = \texttt{cameraMatrix} ^{-1} \cdot \texttt{H} \cdot \texttt{cameraMatrix}\f]
3647	where cameraMatrix can be chosen arbitrarily.
3648
3649	@param cameraMatrix Input camera matrix \f$A=\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
3650	@param distCoeffs Input vector of distortion coefficients
3651	\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
3652	of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
3653	@param R Optional rectification transformation in the object space (3x3 matrix). R1 or R2,
3654	computed by #stereoRectify can be passed here. If the matrix is empty, the identity transformation
3655	is assumed.
3656	@param newCameraMatrix New camera matrix \f$A'=\vecthreethree{f_x'}{0}{c_x'}{0}{f_y'}{c_y'}{0}{0}{1}\f$.
3657	@param size Distorted image size.
3658	@param m1type Type of the first output map. Can be CV_32FC1, CV_32FC2 or CV_16SC2, see #convertMaps
3659	@param map1 The first output map for #remap.
3660	@param map2 The second output map for #remap.
3661	*/
3662	CV_EXPORTS_W
3663	void initInverseRectificationMap( InputArray cameraMatrix, InputArray distCoeffs,
3664	InputArray R, InputArray newCameraMatrix,
3665	const Size& size, int m1type, OutputArray map1, OutputArray map2 );
3666
3667	//! initializes maps for #remap for wide-angle
3668	CV_EXPORTS
3669	float initWideAngleProjMap(InputArray cameraMatrix, InputArray distCoeffs,
3670	Size imageSize, int destImageWidth,
3671	int m1type, OutputArray map1, OutputArray map2,
3672	enum UndistortTypes projType = PROJ_SPHERICAL_EQRECT, double alpha = 0);
3673	static inline
3674	float initWideAngleProjMap(InputArray cameraMatrix, InputArray distCoeffs,
3675	Size imageSize, int destImageWidth,
3676	int m1type, OutputArray map1, OutputArray map2,
3677	int projType, double alpha = 0)
3678	{
3679	return initWideAngleProjMap(cameraMatrix, distCoeffs, imageSize, destImageWidth,
3680	m1type, map1, map2, projType: (UndistortTypes)projType, alpha);
3681	}
3682
3683	/** @brief Returns the default new camera matrix.
3684
3685	The function returns the camera matrix that is either an exact copy of the input cameraMatrix (when
3686	centerPrinicipalPoint=false ), or the modified one (when centerPrincipalPoint=true).
3687
3688	In the latter case, the new camera matrix will be:
3689
3690	\f[\begin{bmatrix} f_x && 0 && ( \texttt{imgSize.width} -1)*0.5 \\ 0 && f_y && ( \texttt{imgSize.height} -1)*0.5 \\ 0 && 0 && 1 \end{bmatrix} ,\f]
3691
3692	where \f$f_x\f$ and \f$f_y\f$ are \f$(0,0)\f$ and \f$(1,1)\f$ elements of cameraMatrix, respectively.
3693
3694	By default, the undistortion functions in OpenCV (see #initUndistortRectifyMap, #undistort) do not
3695	move the principal point. However, when you work with stereo, it is important to move the principal
3696	points in both views to the same y-coordinate (which is required by most of stereo correspondence
3697	algorithms), and may be to the same x-coordinate too. So, you can form the new camera matrix for
3698	each view where the principal points are located at the center.
3699
3700	@param cameraMatrix Input camera matrix.
3701	@param imgsize Camera view image size in pixels.
3702	@param centerPrincipalPoint Location of the principal point in the new camera matrix. The
3703	parameter indicates whether this location should be at the image center or not.
3704	*/
3705	CV_EXPORTS_W
3706	Mat getDefaultNewCameraMatrix(InputArray cameraMatrix, Size imgsize = Size(),
3707	bool centerPrincipalPoint = false);
3708
3709	/** @brief Computes the ideal point coordinates from the observed point coordinates.
3710
3711	The function is similar to #undistort and #initUndistortRectifyMap but it operates on a
3712	sparse set of points instead of a raster image. Also the function performs a reverse transformation
3713	to #projectPoints. In case of a 3D object, it does not reconstruct its 3D coordinates, but for a
3714	planar object, it does, up to a translation vector, if the proper R is specified.
3715
3716	For each observed point coordinate \f$(u, v)\f$ the function computes:
3717	\f[
3718	\begin{array}{l}
3719	x^{"} \leftarrow (u - c_x)/f_x \\
3720	y^{"} \leftarrow (v - c_y)/f_y \\
3721	(x',y') = undistort(x^{"},y^{"}, \texttt{distCoeffs}) \\
3722	{[X\,Y\,W]} ^T \leftarrow R*[x' \, y' \, 1]^T \\
3723	x \leftarrow X/W \\
3724	y \leftarrow Y/W \\
3725	\text{only performed if P is specified:} \\
3726	u' \leftarrow x {f'}_x + {c'}_x \\
3727	v' \leftarrow y {f'}_y + {c'}_y
3728	\end{array}
3729	\f]
3730
3731	where *undistort* is an approximate iterative algorithm that estimates the normalized original
3732	point coordinates out of the normalized distorted point coordinates ("normalized" means that the
3733	coordinates do not depend on the camera matrix).
3734
3735	The function can be used for both a stereo camera head or a monocular camera (when R is empty).
3736	@param src Observed point coordinates, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel (CV_32FC2 or CV_64FC2) (or
3737	vector\<Point2f\> ).
3738	@param dst Output ideal point coordinates (1xN/Nx1 2-channel or vector\<Point2f\> ) after undistortion and reverse perspective
3739	transformation. If matrix P is identity or omitted, dst will contain normalized point coordinates.
3740	@param cameraMatrix Camera matrix \f$\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
3741	@param distCoeffs Input vector of distortion coefficients
3742	\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
3743	of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
3744	@param R Rectification transformation in the object space (3x3 matrix). R1 or R2 computed by
3745	#stereoRectify can be passed here. If the matrix is empty, the identity transformation is used.
3746	@param P New camera matrix (3x3) or new projection matrix (3x4) \f$\begin{bmatrix} {f'}_x & 0 & {c'}_x & t_x \\ 0 & {f'}_y & {c'}_y & t_y \\ 0 & 0 & 1 & t_z \end{bmatrix}\f$. P1 or P2 computed by
3747	#stereoRectify can be passed here. If the matrix is empty, the identity new camera matrix is used.
3748	*/
3749	CV_EXPORTS_W
3750	void undistortPoints(InputArray src, OutputArray dst,
3751	InputArray cameraMatrix, InputArray distCoeffs,
3752	InputArray R = noArray(), InputArray P = noArray());
3753	/** @overload
3754	@note Default version of #undistortPoints does 5 iterations to compute undistorted points.
3755	*/
3756	CV_EXPORTS_AS(undistortPointsIter)
3757	void undistortPoints(InputArray src, OutputArray dst,
3758	InputArray cameraMatrix, InputArray distCoeffs,
3759	InputArray R, InputArray P, TermCriteria criteria);
3760
3761	/**
3762	* @brief Compute undistorted image points position
3763	*
3764	* @param src Observed points position, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel (CV_32FC2 or
3765	CV_64FC2) (or vector\<Point2f\> ).
3766	* @param dst Output undistorted points position (1xN/Nx1 2-channel or vector\<Point2f\> ).
3767	* @param cameraMatrix Camera matrix \f$\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
3768	* @param distCoeffs Distortion coefficients
3769	*/
3770	CV_EXPORTS_W
3771	void undistortImagePoints(InputArray src, OutputArray dst, InputArray cameraMatrix,
3772	InputArray distCoeffs,
3773	TermCriteria = TermCriteria(TermCriteria::MAX_ITER + TermCriteria::EPS, 5,
3774	0.01));
3775
3776	//! @} calib3d
3777
3778	/** @brief The methods in this namespace use a so-called fisheye camera model.
3779	@ingroup calib3d_fisheye
3780	*/
3781	namespace fisheye
3782	{
3783	//! @addtogroup calib3d_fisheye
3784	//! @{
3785
3786	enum{
3787	CALIB_USE_INTRINSIC_GUESS = 1 << 0,
3788	CALIB_RECOMPUTE_EXTRINSIC = 1 << 1,
3789	CALIB_CHECK_COND = 1 << 2,
3790	CALIB_FIX_SKEW = 1 << 3,
3791	CALIB_FIX_K1 = 1 << 4,
3792	CALIB_FIX_K2 = 1 << 5,
3793	CALIB_FIX_K3 = 1 << 6,
3794	CALIB_FIX_K4 = 1 << 7,
3795	CALIB_FIX_INTRINSIC = 1 << 8,
3796	CALIB_FIX_PRINCIPAL_POINT = 1 << 9,
3797	CALIB_ZERO_DISPARITY = 1 << 10,
3798	CALIB_FIX_FOCAL_LENGTH = 1 << 11
3799	};
3800
3801	/** @brief Projects points using fisheye model
3802
3803	@param objectPoints Array of object points, 1xN/Nx1 3-channel (or vector\<Point3f\> ), where N is
3804	the number of points in the view.
3805	@param imagePoints Output array of image points, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel, or
3806	vector\<Point2f\>.
3807	@param affine
3808	@param K Camera intrinsic matrix \f$\cameramatrix{K}\f$.
3809	@param D Input vector of distortion coefficients \f$\distcoeffsfisheye\f$.
3810	@param alpha The skew coefficient.
3811	@param jacobian Optional output 2Nx15 jacobian matrix of derivatives of image points with respect
3812	to components of the focal lengths, coordinates of the principal point, distortion coefficients,
3813	rotation vector, translation vector, and the skew. In the old interface different components of
3814	the jacobian are returned via different output parameters.
3815
3816	The function computes projections of 3D points to the image plane given intrinsic and extrinsic
3817	camera parameters. Optionally, the function computes Jacobians - matrices of partial derivatives of
3818	image points coordinates (as functions of all the input parameters) with respect to the particular
3819	parameters, intrinsic and/or extrinsic.
3820	*/
3821	CV_EXPORTS void projectPoints(InputArray objectPoints, OutputArray imagePoints, const Affine3d& affine,
3822	InputArray K, InputArray D, double alpha = 0, OutputArray jacobian = noArray());
3823
3824	/** @overload */
3825	CV_EXPORTS_W void projectPoints(InputArray objectPoints, OutputArray imagePoints, InputArray rvec, InputArray tvec,
3826	InputArray K, InputArray D, double alpha = 0, OutputArray jacobian = noArray());
3827
3828	/** @brief Distorts 2D points using fisheye model.
3829
3830	@param undistorted Array of object points, 1xN/Nx1 2-channel (or vector\<Point2f\> ), where N is
3831	the number of points in the view.
3832	@param K Camera intrinsic matrix \f$\cameramatrix{K}\f$.
3833	@param D Input vector of distortion coefficients \f$\distcoeffsfisheye\f$.
3834	@param alpha The skew coefficient.
3835	@param distorted Output array of image points, 1xN/Nx1 2-channel, or vector\<Point2f\> .
3836
3837	Note that the function assumes the camera intrinsic matrix of the undistorted points to be identity.
3838	This means if you want to distort image points you have to multiply them with \f$K^{-1}\f$ or
3839	use another function overload.
3840	*/
3841	CV_EXPORTS_W void distortPoints(InputArray undistorted, OutputArray distorted, InputArray K, InputArray D, double alpha = 0);
3842
3843	/** @overload
3844	Overload of distortPoints function to handle cases when undistorted points are obtained with non-identity
3845	camera matrix, e.g. output of #estimateNewCameraMatrixForUndistortRectify.
3846	@param undistorted Array of object points, 1xN/Nx1 2-channel (or vector\<Point2f\> ), where N is
3847	the number of points in the view.
3848	@param Kundistorted Camera intrinsic matrix used as new camera matrix for undistortion.
3849	@param K Camera intrinsic matrix \f$\cameramatrix{K}\f$.
3850	@param D Input vector of distortion coefficients \f$\distcoeffsfisheye\f$.
3851	@param alpha The skew coefficient.
3852	@param distorted Output array of image points, 1xN/Nx1 2-channel, or vector\<Point2f\> .
3853	@sa estimateNewCameraMatrixForUndistortRectify
3854	*/
3855	CV_EXPORTS_W void distortPoints(InputArray undistorted, OutputArray distorted, InputArray Kundistorted, InputArray K, InputArray D, double alpha = 0);
3856
3857	/** @brief Undistorts 2D points using fisheye model
3858
3859	@param distorted Array of object points, 1xN/Nx1 2-channel (or vector\<Point2f\> ), where N is the
3860	number of points in the view.
3861	@param K Camera intrinsic matrix \f$\cameramatrix{K}\f$.
3862	@param D Input vector of distortion coefficients \f$\distcoeffsfisheye\f$.
3863	@param R Rectification transformation in the object space: 3x3 1-channel, or vector: 3x1/1x3
3864	1-channel or 1x1 3-channel
3865	@param P New camera intrinsic matrix (3x3) or new projection matrix (3x4)
3866	@param criteria Termination criteria
3867	@param undistorted Output array of image points, 1xN/Nx1 2-channel, or vector\<Point2f\> .
3868	*/
3869	CV_EXPORTS_W void undistortPoints(InputArray distorted, OutputArray undistorted,
3870	InputArray K, InputArray D, InputArray R = noArray(), InputArray P = noArray(),
3871	TermCriteria criteria = TermCriteria(TermCriteria::MAX_ITER + TermCriteria::EPS, 10, 1e-8));
3872
3873	/** @brief Computes undistortion and rectification maps for image transform by #remap. If D is empty zero
3874	distortion is used, if R or P is empty identity matrixes are used.
3875
3876	@param K Camera intrinsic matrix \f$\cameramatrix{K}\f$.
3877	@param D Input vector of distortion coefficients \f$\distcoeffsfisheye\f$.
3878	@param R Rectification transformation in the object space: 3x3 1-channel, or vector: 3x1/1x3
3879	1-channel or 1x1 3-channel
3880	@param P New camera intrinsic matrix (3x3) or new projection matrix (3x4)
3881	@param size Undistorted image size.
3882	@param m1type Type of the first output map that can be CV_32FC1 or CV_16SC2 . See #convertMaps
3883	for details.
3884	@param map1 The first output map.
3885	@param map2 The second output map.
3886	*/
3887	CV_EXPORTS_W void initUndistortRectifyMap(InputArray K, InputArray D, InputArray R, InputArray P,
3888	const cv::Size& size, int m1type, OutputArray map1, OutputArray map2);
3889
3890	/** @brief Transforms an image to compensate for fisheye lens distortion.
3891
3892	@param distorted image with fisheye lens distortion.
3893	@param undistorted Output image with compensated fisheye lens distortion.
3894	@param K Camera intrinsic matrix \f$\cameramatrix{K}\f$.
3895	@param D Input vector of distortion coefficients \f$\distcoeffsfisheye\f$.
3896	@param Knew Camera intrinsic matrix of the distorted image. By default, it is the identity matrix but you
3897	may additionally scale and shift the result by using a different matrix.
3898	@param new_size the new size
3899
3900	The function transforms an image to compensate radial and tangential lens distortion.
3901
3902	The function is simply a combination of #fisheye::initUndistortRectifyMap (with unity R ) and #remap
3903	(with bilinear interpolation). See the former function for details of the transformation being
3904	performed.
3905
3906	See below the results of undistortImage.
3907	- a\) result of undistort of perspective camera model (all possible coefficients (k_1, k_2, k_3,
3908	k_4, k_5, k_6) of distortion were optimized under calibration)
3909	- b\) result of #fisheye::undistortImage of fisheye camera model (all possible coefficients (k_1, k_2,
3910	k_3, k_4) of fisheye distortion were optimized under calibration)
3911	- c\) original image was captured with fisheye lens
3912
3913	Pictures a) and b) almost the same. But if we consider points of image located far from the center
3914	of image, we can notice that on image a) these points are distorted.
3915
3916	
3917	*/
3918	CV_EXPORTS_W void undistortImage(InputArray distorted, OutputArray undistorted,
3919	InputArray K, InputArray D, InputArray Knew = cv::noArray(), const Size& new_size = Size());
3920
3921	/** @brief Estimates new camera intrinsic matrix for undistortion or rectification.
3922
3923	@param K Camera intrinsic matrix \f$\cameramatrix{K}\f$.
3924	@param image_size Size of the image
3925	@param D Input vector of distortion coefficients \f$\distcoeffsfisheye\f$.
3926	@param R Rectification transformation in the object space: 3x3 1-channel, or vector: 3x1/1x3
3927	1-channel or 1x1 3-channel
3928	@param P New camera intrinsic matrix (3x3) or new projection matrix (3x4)
3929	@param balance Sets the new focal length in range between the min focal length and the max focal
3930	length. Balance is in range of [0, 1].
3931	@param new_size the new size
3932	@param fov_scale Divisor for new focal length.
3933	*/
3934	CV_EXPORTS_W void estimateNewCameraMatrixForUndistortRectify(InputArray K, InputArray D, const Size &image_size, InputArray R,
3935	OutputArray P, double balance = 0.0, const Size& new_size = Size(), double fov_scale = 1.0);
3936
3937	/** @brief Performs camera calibration
3938
3939	@param objectPoints vector of vectors of calibration pattern points in the calibration pattern
3940	coordinate space.
3941	@param imagePoints vector of vectors of the projections of calibration pattern points.
3942	imagePoints.size() and objectPoints.size() and imagePoints[i].size() must be equal to
3943	objectPoints[i].size() for each i.
3944	@param image_size Size of the image used only to initialize the camera intrinsic matrix.
3945	@param K Output 3x3 floating-point camera intrinsic matrix
3946	\f$\cameramatrix{A}\f$ . If
3947	@ref fisheye::CALIB_USE_INTRINSIC_GUESS is specified, some or all of fx, fy, cx, cy must be
3948	initialized before calling the function.
3949	@param D Output vector of distortion coefficients \f$\distcoeffsfisheye\f$.
3950	@param rvecs Output vector of rotation vectors (see @ref Rodrigues ) estimated for each pattern view.
3951	That is, each k-th rotation vector together with the corresponding k-th translation vector (see
3952	the next output parameter description) brings the calibration pattern from the model coordinate
3953	space (in which object points are specified) to the world coordinate space, that is, a real
3954	position of the calibration pattern in the k-th pattern view (k=0.. *M* -1).
3955	@param tvecs Output vector of translation vectors estimated for each pattern view.
3956	@param flags Different flags that may be zero or a combination of the following values:
3957	- @ref fisheye::CALIB_USE_INTRINSIC_GUESS cameraMatrix contains valid initial values of
3958	fx, fy, cx, cy that are optimized further. Otherwise, (cx, cy) is initially set to the image
3959	center ( imageSize is used), and focal distances are computed in a least-squares fashion.
3960	- @ref fisheye::CALIB_RECOMPUTE_EXTRINSIC Extrinsic will be recomputed after each iteration
3961	of intrinsic optimization.
3962	- @ref fisheye::CALIB_CHECK_COND The functions will check validity of condition number.
3963	- @ref fisheye::CALIB_FIX_SKEW Skew coefficient (alpha) is set to zero and stay zero.
3964	- @ref fisheye::CALIB_FIX_K1,..., @ref fisheye::CALIB_FIX_K4 Selected distortion coefficients
3965	are set to zeros and stay zero.
3966	- @ref fisheye::CALIB_FIX_PRINCIPAL_POINT The principal point is not changed during the global
3967	optimization. It stays at the center or at a different location specified when @ref fisheye::CALIB_USE_INTRINSIC_GUESS is set too.
3968	- @ref fisheye::CALIB_FIX_FOCAL_LENGTH The focal length is not changed during the global
3969	optimization. It is the \f$max(width,height)/\pi\f$ or the provided \f$f_x\f$, \f$f_y\f$ when @ref fisheye::CALIB_USE_INTRINSIC_GUESS is set too.
3970	@param criteria Termination criteria for the iterative optimization algorithm.
3971	*/
3972	CV_EXPORTS_W double calibrate(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints, const Size& image_size,
3973	InputOutputArray K, InputOutputArray D, OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs, int flags = 0,
3974	TermCriteria criteria = TermCriteria(TermCriteria::COUNT + TermCriteria::EPS, 100, DBL_EPSILON));
3975
3976	/** @brief Stereo rectification for fisheye camera model
3977
3978	@param K1 First camera intrinsic matrix.
3979	@param D1 First camera distortion parameters.
3980	@param K2 Second camera intrinsic matrix.
3981	@param D2 Second camera distortion parameters.
3982	@param imageSize Size of the image used for stereo calibration.
3983	@param R Rotation matrix between the coordinate systems of the first and the second
3984	cameras.
3985	@param tvec Translation vector between coordinate systems of the cameras.
3986	@param R1 Output 3x3 rectification transform (rotation matrix) for the first camera.
3987	@param R2 Output 3x3 rectification transform (rotation matrix) for the second camera.
3988	@param P1 Output 3x4 projection matrix in the new (rectified) coordinate systems for the first
3989	camera.
3990	@param P2 Output 3x4 projection matrix in the new (rectified) coordinate systems for the second
3991	camera.
3992	@param Q Output \f$4 \times 4\f$ disparity-to-depth mapping matrix (see #reprojectImageTo3D ).
3993	@param flags Operation flags that may be zero or @ref fisheye::CALIB_ZERO_DISPARITY . If the flag is set,
3994	the function makes the principal points of each camera have the same pixel coordinates in the
3995	rectified views. And if the flag is not set, the function may still shift the images in the
3996	horizontal or vertical direction (depending on the orientation of epipolar lines) to maximize the
3997	useful image area.
3998	@param newImageSize New image resolution after rectification. The same size should be passed to
3999	#initUndistortRectifyMap (see the stereo_calib.cpp sample in OpenCV samples directory). When (0,0)
4000	is passed (default), it is set to the original imageSize . Setting it to larger value can help you
4001	preserve details in the original image, especially when there is a big radial distortion.
4002	@param balance Sets the new focal length in range between the min focal length and the max focal
4003	length. Balance is in range of [0, 1].
4004	@param fov_scale Divisor for new focal length.
4005	*/
4006	CV_EXPORTS_W void stereoRectify(InputArray K1, InputArray D1, InputArray K2, InputArray D2, const Size &imageSize, InputArray R, InputArray tvec,
4007	OutputArray R1, OutputArray R2, OutputArray P1, OutputArray P2, OutputArray Q, int flags, const Size &newImageSize = Size(),
4008	double balance = 0.0, double fov_scale = 1.0);
4009
4010	/** @brief Performs stereo calibration
4011
4012	@param objectPoints Vector of vectors of the calibration pattern points.
4013	@param imagePoints1 Vector of vectors of the projections of the calibration pattern points,
4014	observed by the first camera.
4015	@param imagePoints2 Vector of vectors of the projections of the calibration pattern points,
4016	observed by the second camera.
4017	@param K1 Input/output first camera intrinsic matrix:
4018	\f$\vecthreethree{f_x^{(j)}}{0}{c_x^{(j)}}{0}{f_y^{(j)}}{c_y^{(j)}}{0}{0}{1}\f$ , \f$j = 0,\, 1\f$ . If
4019	any of @ref fisheye::CALIB_USE_INTRINSIC_GUESS , @ref fisheye::CALIB_FIX_INTRINSIC are specified,
4020	some or all of the matrix components must be initialized.
4021	@param D1 Input/output vector of distortion coefficients \f$\distcoeffsfisheye\f$ of 4 elements.
4022	@param K2 Input/output second camera intrinsic matrix. The parameter is similar to K1 .
4023	@param D2 Input/output lens distortion coefficients for the second camera. The parameter is
4024	similar to D1 .
4025	@param imageSize Size of the image used only to initialize camera intrinsic matrix.
4026	@param R Output rotation matrix between the 1st and the 2nd camera coordinate systems.
4027	@param T Output translation vector between the coordinate systems of the cameras.
4028	@param rvecs Output vector of rotation vectors ( @ref Rodrigues ) estimated for each pattern view in the
4029	coordinate system of the first camera of the stereo pair (e.g. std::vector<cv::Mat>). More in detail, each
4030	i-th rotation vector together with the corresponding i-th translation vector (see the next output parameter
4031	description) brings the calibration pattern from the object coordinate space (in which object points are
4032	specified) to the camera coordinate space of the first camera of the stereo pair. In more technical terms,
4033	the tuple of the i-th rotation and translation vector performs a change of basis from object coordinate space
4034	to camera coordinate space of the first camera of the stereo pair.
4035	@param tvecs Output vector of translation vectors estimated for each pattern view, see parameter description
4036	of previous output parameter ( rvecs ).
4037	@param flags Different flags that may be zero or a combination of the following values:
4038	- @ref fisheye::CALIB_FIX_INTRINSIC Fix K1, K2? and D1, D2? so that only R, T matrices
4039	are estimated.
4040	- @ref fisheye::CALIB_USE_INTRINSIC_GUESS K1, K2 contains valid initial values of
4041	fx, fy, cx, cy that are optimized further. Otherwise, (cx, cy) is initially set to the image
4042	center (imageSize is used), and focal distances are computed in a least-squares fashion.
4043	- @ref fisheye::CALIB_RECOMPUTE_EXTRINSIC Extrinsic will be recomputed after each iteration
4044	of intrinsic optimization.
4045	- @ref fisheye::CALIB_CHECK_COND The functions will check validity of condition number.
4046	- @ref fisheye::CALIB_FIX_SKEW Skew coefficient (alpha) is set to zero and stay zero.
4047	- @ref fisheye::CALIB_FIX_K1,..., @ref fisheye::CALIB_FIX_K4 Selected distortion coefficients are set to zeros and stay
4048	zero.
4049	@param criteria Termination criteria for the iterative optimization algorithm.
4050	*/
4051	CV_EXPORTS_W double stereoCalibrate(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2,
4052	InputOutputArray K1, InputOutputArray D1, InputOutputArray K2, InputOutputArray D2, Size imageSize,
4053	OutputArray R, OutputArray T, OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs, int flags = fisheye::CALIB_FIX_INTRINSIC,
4054	TermCriteria criteria = TermCriteria(TermCriteria::COUNT + TermCriteria::EPS, 100, DBL_EPSILON));
4055
4056	/// @overload
4057	CV_EXPORTS_W double stereoCalibrate(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2,
4058	InputOutputArray K1, InputOutputArray D1, InputOutputArray K2, InputOutputArray D2, Size imageSize,
4059	OutputArray R, OutputArray T, int flags = fisheye::CALIB_FIX_INTRINSIC,
4060	TermCriteria criteria = TermCriteria(TermCriteria::COUNT + TermCriteria::EPS, 100, DBL_EPSILON));
4061
4062	/**
4063	@brief Finds an object pose from 3D-2D point correspondences for fisheye camera moodel.
4064
4065	@param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or
4066	1xN/Nx1 3-channel, where N is the number of points. vector\<Point3d\> can be also passed here.
4067	@param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
4068	where N is the number of points. vector\<Point2d\> can be also passed here.
4069	@param cameraMatrix Input camera intrinsic matrix \f$\cameramatrix{A}\f$ .
4070	@param distCoeffs Input vector of distortion coefficients (4x1/1x4).
4071	@param rvec Output rotation vector (see @ref Rodrigues ) that, together with tvec, brings points from
4072	the model coordinate system to the camera coordinate system.
4073	@param tvec Output translation vector.
4074	@param useExtrinsicGuess Parameter used for #SOLVEPNP_ITERATIVE. If true (1), the function uses
4075	the provided rvec and tvec values as initial approximations of the rotation and translation
4076	vectors, respectively, and further optimizes them.
4077	@param flags Method for solving a PnP problem: see @ref calib3d_solvePnP_flags
4078	This function returns the rotation and the translation vectors that transform a 3D point expressed in the object
4079	coordinate frame to the camera coordinate frame, using different methods:
4080	- P3P methods (@ref SOLVEPNP_P3P, @ref SOLVEPNP_AP3P): need 4 input points to return a unique solution.
4081	- @ref SOLVEPNP_IPPE Input points must be >= 4 and object points must be coplanar.
4082	- @ref SOLVEPNP_IPPE_SQUARE Special case suitable for marker pose estimation.
4083	Number of input points must be 4. Object points must be defined in the following order:
4084	- point 0: [-squareLength / 2, squareLength / 2, 0]
4085	- point 1: [ squareLength / 2, squareLength / 2, 0]
4086	- point 2: [ squareLength / 2, -squareLength / 2, 0]
4087	- point 3: [-squareLength / 2, -squareLength / 2, 0]
4088	- for all the other flags, number of input points must be >= 4 and object points can be in any configuration.
4089	@param criteria Termination criteria for internal undistortPoints call.
4090	The function interally undistorts points with @ref undistortPoints and call @ref cv::solvePnP,
4091	thus the input are very similar. More information about Perspective-n-Points is described in @ref calib3d_solvePnP
4092	for more information.
4093	*/
4094	CV_EXPORTS_W bool solvePnP( InputArray objectPoints, InputArray imagePoints,
4095	InputArray cameraMatrix, InputArray distCoeffs,
4096	OutputArray rvec, OutputArray tvec,
4097	bool useExtrinsicGuess = false, int flags = SOLVEPNP_ITERATIVE,
4098	TermCriteria criteria = TermCriteria(TermCriteria::MAX_ITER + TermCriteria::EPS, 10, 1e-8)
4099	);
4100
4101	//! @} calib3d_fisheye
4102	} // end namespace fisheye
4103
4104	} //end namespace cv
4105
4106	#if 0 //def __cplusplus
4107	//////////////////////////////////////////////////////////////////////////////////////////
4108	class CV_EXPORTS CvLevMarq
4109	{
4110	public:
4111	CvLevMarq();
4112	CvLevMarq( int nparams, int nerrs, CvTermCriteria criteria=
4113	cvTermCriteria(CV_TERMCRIT_EPS+CV_TERMCRIT_ITER,30,DBL_EPSILON),
4114	bool completeSymmFlag=false );
4115	~CvLevMarq();
4116	void init( int nparams, int nerrs, CvTermCriteria criteria=
4117	cvTermCriteria(CV_TERMCRIT_EPS+CV_TERMCRIT_ITER,30,DBL_EPSILON),
4118	bool completeSymmFlag=false );
4119	bool update( const CvMat*& param, CvMat*& J, CvMat*& err );
4120	bool updateAlt( const CvMat*& param, CvMat*& JtJ, CvMat*& JtErr, double*& errNorm );
4121
4122	void clear();
4123	void step();
4124	enum { DONE=0, STARTED=1, CALC_J=2, CHECK_ERR=3 };
4125
4126	cv::Ptr<CvMat> mask;
4127	cv::Ptr<CvMat> prevParam;
4128	cv::Ptr<CvMat> param;
4129	cv::Ptr<CvMat> J;
4130	cv::Ptr<CvMat> err;
4131	cv::Ptr<CvMat> JtJ;
4132	cv::Ptr<CvMat> JtJN;
4133	cv::Ptr<CvMat> JtErr;
4134	cv::Ptr<CvMat> JtJV;
4135	cv::Ptr<CvMat> JtJW;
4136	double prevErrNorm, errNorm;
4137	int lambdaLg10;
4138	CvTermCriteria criteria;
4139	int state;
4140	int iters;
4141	bool completeSymmFlag;
4142	int solveMethod;
4143	};
4144	#endif
4145
4146	#endif
4147