Summarize PnP pose computation on a single separate page.

doc/opencv.bib

@@ -240,7 +240,7 @@
   hal_id = {inria-00350283},
   hal_version = {v1},
 }
-@article{Collins14
+@article{Collins14,
   year = {2014},
   issn = {0920-5691},
   journal = {International Journal of Computer Vision},
@@ -1271,6 +1271,12 @@
   number={2},
   pages={117-135},
 }
+@inproceedings{Zuliani2014RANSACFD,
+  title={RANSAC for Dummies With examples using the RANSAC toolbox for Matlab \& Octave and more...},
+  author={Marco Zuliani},
+  year={2014},
+  url = {https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.475.1243&rep=rep1&type=pdf}
+}
 @inproceedings{forstner1987fast,
   title={A fast operator for detection and precise location of distincs points, corners and center of circular features},
   author={FORSTNER, W},

modules/calib3d/doc/calib3d.bib

@@ -40,10 +40,11 @@
   publisher={IEEE}
 }
 
-@inproceedings{Terzakis20,
-  author = {Terzakis, George and Lourakis, Manolis},
-  year = {2020},
-  month = {09},
-  pages = {},
-  title = {A Consistently Fast and Globally Optimal Solution to the Perspective-n-Point Problem}
+@inproceedings{Terzakis2020SQPnP,
+  title={A Consistently Fast and Globally Optimal Solution to the Perspective-n-Point Problem},
+  author={George Terzakis and Manolis Lourakis},
+  booktitle={European Conference on Computer Vision},
+  pages={478--494},
+  year={2020},
+  publisher={Springer International Publishing}
 }

modules/calib3d/doc/solvePnP.markdown

+# Perspective-n-Point (PnP) pose computation {#calib3d_solvePnP}
+
+## Pose computation overview
+
+The pose computation problem @cite Marchand16 consists in solving for the rotation and translation that minimizes the reprojection error from 3D-2D point correspondences.
+
+The `solvePnP` and related functions estimate the object pose given a set of object points, their corresponding image projections, as well as the camera intrinsic matrix and the distortion coefficients, see the figure below (more precisely, the X-axis of the camera frame is pointing to the right, the Y-axis downward and the Z-axis forward).
+
+![](pnp.jpg)
+
+Points expressed in the world frame \f$ \bf{X}_w \f$ are projected into the image plane \f$ \left[ u, v \right] \f$
+using the perspective projection model \f$ \Pi \f$ and the camera intrinsic parameters matrix \f$ \bf{A} \f$ (also denoted \f$ \bf{K} \f$ in the literature):
+
+\f[
+  \begin{align*}
+  \begin{bmatrix}
+  u \\
+  v \\
+  1
+  \end{bmatrix} &=
+  \bf{A} \hspace{0.1em} \Pi \hspace{0.2em} ^{c}\bf{T}_w
+  \begin{bmatrix}
+  X_{w} \\
+  Y_{w} \\
+  Z_{w} \\
+  1
+  \end{bmatrix} \\
+  \begin{bmatrix}
+  u \\
+  v \\
+  1
+  \end{bmatrix} &=
+  \begin{bmatrix}
+  f_x & 0 & c_x \\
+  0 & f_y & c_y \\
+  0 & 0 & 1
+  \end{bmatrix}
+  \begin{bmatrix}
+  1 & 0 & 0 & 0 \\
+  0 & 1 & 0 & 0 \\
+  0 & 0 & 1 & 0
+  \end{bmatrix}
+  \begin{bmatrix}
+  r_{11} & r_{12} & r_{13} & t_x \\
+  r_{21} & r_{22} & r_{23} & t_y \\
+  r_{31} & r_{32} & r_{33} & t_z \\
+  0 & 0 & 0 & 1
+  \end{bmatrix}
+  \begin{bmatrix}
+  X_{w} \\
+  Y_{w} \\
+  Z_{w} \\
+  1
+  \end{bmatrix}
+  \end{align*}
+\f]
+
+The estimated pose is thus the rotation (`rvec`) and the translation (`tvec`) vectors that allow transforming
+a 3D point expressed in the world frame into the camera frame:
+
+\f[
+  \begin{align*}
+  \begin{bmatrix}
+  X_c \\
+  Y_c \\
+  Z_c \\
+  1
+  \end{bmatrix} &=
+  \hspace{0.2em} ^{c}\bf{T}_w
+  \begin{bmatrix}
+  X_{w} \\
+  Y_{w} \\
+  Z_{w} \\
+  1
+  \end{bmatrix} \\
+  \begin{bmatrix}
+  X_c \\
+  Y_c \\
+  Z_c \\
+  1
+  \end{bmatrix} &=
+  \begin{bmatrix}
+  r_{11} & r_{12} & r_{13} & t_x \\
+  r_{21} & r_{22} & r_{23} & t_y \\
+  r_{31} & r_{32} & r_{33} & t_z \\
+  0 & 0 & 0 & 1
+  \end{bmatrix}
+  \begin{bmatrix}
+  X_{w} \\
+  Y_{w} \\
+  Z_{w} \\
+  1
+  \end{bmatrix}
+  \end{align*}
+\f]
+
+## Pose computation methods
+@anchor calib3d_solvePnP_flags
+
+Refer to the cv::SolvePnPMethod enum documentation for the list of possible values. Some details about each method are described below:
+
+-   cv::SOLVEPNP_ITERATIVE Iterative method is based on a Levenberg-Marquardt optimization. In
+this case the function finds such a pose that minimizes reprojection error, that is the sum
+of squared distances between the observed projections "imagePoints" and the projected (using
+cv::projectPoints ) "objectPoints". Initial solution for non-planar "objectPoints" needs at least 6 points and uses the DLT algorithm.
+Initial solution for planar "objectPoints" needs at least 4 points and uses pose from homography decomposition.
+-   cv::SOLVEPNP_P3P Method is based on the paper of X.S. Gao, X.-R. Hou, J. Tang, H.-F. Chang
+"Complete Solution Classification for the Perspective-Three-Point Problem" (@cite gao2003complete).
+In this case the function requires exactly four object and image points.
+-   cv::SOLVEPNP_AP3P Method is based on the paper of T. Ke, S. Roumeliotis
+"An Efficient Algebraic Solution to the Perspective-Three-Point Problem" (@cite Ke17).
+In this case the function requires exactly four object and image points.
+-   cv::SOLVEPNP_EPNP Method has been introduced by F. Moreno-Noguer, V. Lepetit and P. Fua in the
+paper "EPnP: Efficient Perspective-n-Point Camera Pose Estimation" (@cite lepetit2009epnp).
+-   cv::SOLVEPNP_DLS **Broken implementation. Using this flag will fallback to EPnP.** \n
+Method is based on the paper of J. Hesch and S. Roumeliotis.
+"A Direct Least-Squares (DLS) Method for PnP" (@cite hesch2011direct).
+-   cv::SOLVEPNP_UPNP **Broken implementation. Using this flag will fallback to EPnP.** \n
+Method is based on the paper of A. Penate-Sanchez, J. Andrade-Cetto,
+F. Moreno-Noguer. "Exhaustive Linearization for Robust Camera Pose and Focal Length
+Estimation" (@cite penate2013exhaustive). In this case the function also estimates the parameters \f$f_x\f$ and \f$f_y\f$
+assuming that both have the same value. Then the cameraMatrix is updated with the estimated
+focal length.
+-   cv::SOLVEPNP_IPPE Method is based on the paper of T. Collins and A. Bartoli.
+"Infinitesimal Plane-Based Pose Estimation" (@cite Collins14). This method requires coplanar object points.
+-   cv::SOLVEPNP_IPPE_SQUARE Method is based on the paper of Toby Collins and Adrien Bartoli.
+"Infinitesimal Plane-Based Pose Estimation" (@cite Collins14). This method is suitable for marker pose estimation.
+It requires 4 coplanar object points defined in the following order:
+  - point 0: [-squareLength / 2,  squareLength / 2, 0]
+  - point 1: [ squareLength / 2,  squareLength / 2, 0]
+  - point 2: [ squareLength / 2, -squareLength / 2, 0]
+  - point 3: [-squareLength / 2, -squareLength / 2, 0]
+-   cv::SOLVEPNP_SQPNP Method is based on the paper "A Consistently Fast and Globally Optimal Solution to the
+Perspective-n-Point Problem" by G. Terzakis and M.Lourakis (@cite Terzakis2020SQPnP). It requires 3 or more points.
+
+## P3P
+
+The cv::solveP3P() computes an object pose from exactly 3 3D-2D point correspondences. A P3P problem has up to 4 solutions.
+
+@note The solutions are sorted by reprojection errors (lowest to highest).
+
+## PnP
+
+The cv::solvePnP() returns the rotation and the translation vectors that transform a 3D point expressed in the object
+coordinate frame to the camera coordinate frame, using different methods:
+- P3P methods (cv::SOLVEPNP_P3P, cv::SOLVEPNP_AP3P): need 4 input points to return a unique solution.
+- cv::SOLVEPNP_IPPE Input points must be >= 4 and object points must be coplanar.
+- cv::SOLVEPNP_IPPE_SQUARE Special case suitable for marker pose estimation.
+Number of input points must be 4. Object points must be defined in the following order:
+  - point 0: [-squareLength / 2,  squareLength / 2, 0]
+  - point 1: [ squareLength / 2,  squareLength / 2, 0]
+  - point 2: [ squareLength / 2, -squareLength / 2, 0]
+  - point 3: [-squareLength / 2, -squareLength / 2, 0]
+- for all the other flags, number of input points must be >= 4 and object points can be in any configuration.
+
+## Generic PnP
+
+The cv::solvePnPGeneric() allows retrieving all the possible solutions.
+
+Currently, only cv::SOLVEPNP_P3P, cv::SOLVEPNP_AP3P, cv::SOLVEPNP_IPPE, cv::SOLVEPNP_IPPE_SQUARE, cv::SOLVEPNP_SQPNP can return multiple solutions.
+
+## RANSAC PnP
+
+The cv::solvePnPRansac() computes the object pose wrt. the camera frame using a RANSAC scheme to deal with outliers.
+
+More information can be found in @cite Zuliani2014RANSACFD
+
+## Pose refinement
+
+Pose refinement consists in estimating the rotation and translation that minimizes the reprojection error using a non-linear minimization method and starting from an initial estimate of the solution. OpenCV proposes cv::solvePnPRefineLM() and cv::solvePnPRefineVVS() for this problem.
+
+cv::solvePnPRefineLM() uses a non-linear Levenberg-Marquardt minimization scheme @cite Madsen04 @cite Eade13 and the current implementation computes the rotation update as a perturbation and not on SO(3).
+
+cv::solvePnPRefineVVS() uses a Gauss-Newton non-linear minimization scheme @cite Marchand16 and with an update of the rotation part computed using the exponential map.
+
+@note at least three 3D-2D point correspondences are necessary.

modules/calib3d/include/opencv2/calib3d.hpp

@@ -447,7 +447,9 @@ enum { LMEDS  = 4, //!< least-median of squares algorithm
      };
 
 enum SolvePnPMethod {
-    SOLVEPNP_ITERATIVE   = 0,
+    SOLVEPNP_ITERATIVE   = 0, //!< Pose refinement using non-linear Levenberg-Marquardt minimization scheme @cite Madsen04 @cite Eade13 \n
+                              //!< Initial solution for non-planar "objectPoints" needs at least 6 points and uses the DLT algorithm. \n
+                              //!< Initial solution for planar "objectPoints" needs at least 4 points and uses pose from homography decomposition.
     SOLVEPNP_EPNP        = 1, //!< EPnP: Efficient Perspective-n-Point Camera Pose Estimation @cite lepetit2009epnp
     SOLVEPNP_P3P         = 2, //!< Complete Solution Classification for the Perspective-Three-Point Problem @cite gao2003complete
     SOLVEPNP_DLS         = 3, //!< **Broken implementation. Using this flag will fallback to EPnP.** \n
@@ -464,7 +466,7 @@ enum SolvePnPMethod {
                               //!<   - point 1: [ squareLength / 2,  squareLength / 2, 0]
                               //!<   - point 2: [ squareLength / 2, -squareLength / 2, 0]
                               //!<   - point 3: [-squareLength / 2, -squareLength / 2, 0]
-    SOLVEPNP_SQPNP       = 8, //!< SQPnP: A Consistently Fast and Globally OptimalSolution to the Perspective-n-Point Problem @cite Terzakis20
+    SOLVEPNP_SQPNP       = 8, //!< SQPnP: A Consistently Fast and Globally OptimalSolution to the Perspective-n-Point Problem @cite Terzakis2020SQPnP
 #ifndef CV_DOXYGEN
     SOLVEPNP_MAX_COUNT        //!< Used for count
 #endif
@@ -779,6 +781,9 @@ Check @ref tutorial_homography "the corresponding tutorial" for more details
 */
 
 /** @brief Finds an object pose from 3D-2D point correspondences.
+
+@see @ref calib3d_solvePnP
+
 This function returns the rotation and the translation vectors that transform a 3D point expressed in the object
 coordinate frame to the camera coordinate frame, using different methods:
 - P3P methods (@ref SOLVEPNP_P3P, @ref SOLVEPNP_AP3P): need 4 input points to return a unique solution.
@@ -805,133 +810,9 @@ the model coordinate system to the camera coordinate system.
 @param useExtrinsicGuess Parameter used for #SOLVEPNP_ITERATIVE. If true (1), the function uses
 the provided rvec and tvec values as initial approximations of the rotation and translation
 vectors, respectively, and further optimizes them.
-@param flags Method for solving a PnP problem:
--   @ref SOLVEPNP_ITERATIVE Iterative method is based on a Levenberg-Marquardt optimization. In
-this case the function finds such a pose that minimizes reprojection error, that is the sum
-of squared distances between the observed projections imagePoints and the projected (using
-@ref projectPoints ) objectPoints .
--   @ref SOLVEPNP_P3P Method is based on the paper of X.S. Gao, X.-R. Hou, J. Tang, H.-F. Chang
-"Complete Solution Classification for the Perspective-Three-Point Problem" (@cite gao2003complete).
-In this case the function requires exactly four object and image points.
--   @ref SOLVEPNP_AP3P Method is based on the paper of T. Ke, S. Roumeliotis
-"An Efficient Algebraic Solution to the Perspective-Three-Point Problem" (@cite Ke17).
-In this case the function requires exactly four object and image points.
--   @ref SOLVEPNP_EPNP Method has been introduced by F. Moreno-Noguer, V. Lepetit and P. Fua in the
-paper "EPnP: Efficient Perspective-n-Point Camera Pose Estimation" (@cite lepetit2009epnp).
--   @ref SOLVEPNP_DLS **Broken implementation. Using this flag will fallback to EPnP.** \n
-Method is based on the paper of J. Hesch and S. Roumeliotis.
-"A Direct Least-Squares (DLS) Method for PnP" (@cite hesch2011direct).
--   @ref SOLVEPNP_UPNP **Broken implementation. Using this flag will fallback to EPnP.** \n
-Method is based on the paper of A. Penate-Sanchez, J. Andrade-Cetto,
-F. Moreno-Noguer. "Exhaustive Linearization for Robust Camera Pose and Focal Length
-Estimation" (@cite penate2013exhaustive). In this case the function also estimates the parameters \f$f_x\f$ and \f$f_y\f$
-assuming that both have the same value. Then the cameraMatrix is updated with the estimated
-focal length.
--   @ref SOLVEPNP_IPPE Method is based on the paper of T. Collins and A. Bartoli.
-"Infinitesimal Plane-Based Pose Estimation" (@cite Collins14). This method requires coplanar object points.
--   @ref SOLVEPNP_IPPE_SQUARE Method is based on the paper of Toby Collins and Adrien Bartoli.
-"Infinitesimal Plane-Based Pose Estimation" (@cite Collins14). This method is suitable for marker pose estimation.
-It requires 4 coplanar object points defined in the following order:
-  - point 0: [-squareLength / 2,  squareLength / 2, 0]
-  - point 1: [ squareLength / 2,  squareLength / 2, 0]
-  - point 2: [ squareLength / 2, -squareLength / 2, 0]
-  - point 3: [-squareLength / 2, -squareLength / 2, 0]
--   @ref SOLVEPNP_SQPNP Method is based on the paper "A Consistently Fast and Globally Optimal Solution to the
-Perspective-n-Point Problem" by G. Terzakis and M.Lourakis (@cite Terzakis20). It requires 3 or more points.
-
-
-The function estimates the object pose given a set of object points, their corresponding image
-projections, as well as the camera intrinsic matrix and the distortion coefficients, see the figure below
-(more precisely, the X-axis of the camera frame is pointing to the right, the Y-axis downward
-and the Z-axis forward).
+@param flags Method for solving a PnP problem: see @ref calib3d_solvePnP_flags
 
-![](pnp.jpg)
-
-Points expressed in the world frame \f$ \bf{X}_w \f$ are projected into the image plane \f$ \left[ u, v \right] \f$
-using the perspective projection model \f$ \Pi \f$ and the camera intrinsic parameters matrix \f$ \bf{A} \f$:
-
-\f[
-  \begin{align*}
-  \begin{bmatrix}
-  u \\
-  v \\
-  1
-  \end{bmatrix} &=
-  \bf{A} \hspace{0.1em} \Pi \hspace{0.2em} ^{c}\bf{T}_w
-  \begin{bmatrix}
-  X_{w} \\
-  Y_{w} \\
-  Z_{w} \\
-  1
-  \end{bmatrix} \\
-  \begin{bmatrix}
-  u \\
-  v \\
-  1
-  \end{bmatrix} &=
-  \begin{bmatrix}
-  f_x & 0 & c_x \\
-  0 & f_y & c_y \\
-  0 & 0 & 1
-  \end{bmatrix}
-  \begin{bmatrix}
-  1 & 0 & 0 & 0 \\
-  0 & 1 & 0 & 0 \\
-  0 & 0 & 1 & 0
-  \end{bmatrix}
-  \begin{bmatrix}
-  r_{11} & r_{12} & r_{13} & t_x \\
-  r_{21} & r_{22} & r_{23} & t_y \\
-  r_{31} & r_{32} & r_{33} & t_z \\
-  0 & 0 & 0 & 1
-  \end{bmatrix}
-  \begin{bmatrix}
-  X_{w} \\
-  Y_{w} \\
-  Z_{w} \\
-  1
-  \end{bmatrix}
-  \end{align*}
-\f]
-
-The estimated pose is thus the rotation (`rvec`) and the translation (`tvec`) vectors that allow transforming
-a 3D point expressed in the world frame into the camera frame:
-
-\f[
-  \begin{align*}
-  \begin{bmatrix}
-  X_c \\
-  Y_c \\
-  Z_c \\
-  1
-  \end{bmatrix} &=
-  \hspace{0.2em} ^{c}\bf{T}_w
-  \begin{bmatrix}
-  X_{w} \\
-  Y_{w} \\
-  Z_{w} \\
-  1
-  \end{bmatrix} \\
-  \begin{bmatrix}
-  X_c \\
-  Y_c \\
-  Z_c \\
-  1
-  \end{bmatrix} &=
-  \begin{bmatrix}
-  r_{11} & r_{12} & r_{13} & t_x \\
-  r_{21} & r_{22} & r_{23} & t_y \\
-  r_{31} & r_{32} & r_{33} & t_z \\
-  0 & 0 & 0 & 1
-  \end{bmatrix}
-  \begin{bmatrix}
-  X_{w} \\
-  Y_{w} \\
-  Z_{w} \\
-  1
-  \end{bmatrix}
-  \end{align*}
-\f]
+More information about Perspective-n-Points is described in @ref calib3d_solvePnP
 
 @note
    -   An example of how to use solvePnP for planar augmented reality can be found at
@@ -971,6 +852,8 @@ CV_EXPORTS_W bool solvePnP( InputArray objectPoints, InputArray imagePoints,
 
 /** @brief Finds an object pose from 3D-2D point correspondences using the RANSAC scheme.
 
+@see @ref calib3d_solvePnP
+
 @param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or
 1xN/Nx1 3-channel, where N is the number of points. vector\<Point3d\> can be also passed here.
 @param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
@@ -1019,6 +902,8 @@ CV_EXPORTS_W bool solvePnPRansac( InputArray objectPoints, InputArray imagePoint
 
 /** @brief Finds an object pose from 3 3D-2D point correspondences.
 
+@see @ref calib3d_solvePnP
+
 @param objectPoints Array of object points in the object coordinate space, 3x3 1-channel or
 1x3/3x1 3-channel. vector\<Point3f\> can be also passed here.
 @param imagePoints Array of corresponding image points, 3x2 1-channel or 1x3/3x1 2-channel.
@@ -1050,6 +935,8 @@ CV_EXPORTS_W int solveP3P( InputArray objectPoints, InputArray imagePoints,
 /** @brief Refine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame
 to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution.
 
+@see @ref calib3d_solvePnP
+
 @param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel,
 where N is the number of points. vector\<Point3d\> can also be passed here.
 @param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
@@ -1077,6 +964,8 @@ CV_EXPORTS_W void solvePnPRefineLM( InputArray objectPoints, InputArray imagePoi
 /** @brief Refine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame
 to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution.
 
+@see @ref calib3d_solvePnP
+
 @param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel,
 where N is the number of points. vector\<Point3d\> can also be passed here.
 @param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
@@ -1105,6 +994,9 @@ CV_EXPORTS_W void solvePnPRefineVVS( InputArray objectPoints, InputArray imagePo
                                      double VVSlambda = 1);
 
 /** @brief Finds an object pose from 3D-2D point correspondences.
+
+@see @ref calib3d_solvePnP
+
 This function returns a list of all the possible solutions (a solution is a <rotation vector, translation vector>
 couple), depending on the number of input points and the chosen method:
 - 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.
@@ -1132,37 +1024,7 @@ the model coordinate system to the camera coordinate system.
 @param useExtrinsicGuess Parameter used for #SOLVEPNP_ITERATIVE. If true (1), the function uses
 the provided rvec and tvec values as initial approximations of the rotation and translation
 vectors, respectively, and further optimizes them.
-@param flags Method for solving a PnP problem:
--   @ref SOLVEPNP_ITERATIVE Iterative method is based on a Levenberg-Marquardt optimization. In
-this case the function finds such a pose that minimizes reprojection error, that is the sum
-of squared distances between the observed projections imagePoints and the projected (using
-projectPoints ) objectPoints .
--   @ref SOLVEPNP_P3P Method is based on the paper of X.S. Gao, X.-R. Hou, J. Tang, H.-F. Chang
-"Complete Solution Classification for the Perspective-Three-Point Problem" (@cite gao2003complete).
-In this case the function requires exactly four object and image points.
--   @ref SOLVEPNP_AP3P Method is based on the paper of T. Ke, S. Roumeliotis
-"An Efficient Algebraic Solution to the Perspective-Three-Point Problem" (@cite Ke17).
-In this case the function requires exactly four object and image points.
--   @ref SOLVEPNP_EPNP Method has been introduced by F.Moreno-Noguer, V.Lepetit and P.Fua in the
-paper "EPnP: Efficient Perspective-n-Point Camera Pose Estimation" (@cite lepetit2009epnp).
--   @ref SOLVEPNP_DLS **Broken implementation. Using this flag will fallback to EPnP.** \n
-Method is based on the paper of Joel A. Hesch and Stergios I. Roumeliotis.
-"A Direct Least-Squares (DLS) Method for PnP" (@cite hesch2011direct).
--   @ref SOLVEPNP_UPNP **Broken implementation. Using this flag will fallback to EPnP.** \n
-Method is based on the paper of A.Penate-Sanchez, J.Andrade-Cetto,
-F.Moreno-Noguer. "Exhaustive Linearization for Robust Camera Pose and Focal Length
-Estimation" (@cite penate2013exhaustive). In this case the function also estimates the parameters \f$f_x\f$ and \f$f_y\f$
-assuming that both have the same value. Then the cameraMatrix is updated with the estimated
-focal length.
--   @ref SOLVEPNP_IPPE Method is based on the paper of T. Collins and A. Bartoli.
-"Infinitesimal Plane-Based Pose Estimation" (@cite Collins14). This method requires coplanar object points.
--   @ref SOLVEPNP_IPPE_SQUARE Method is based on the paper of Toby Collins and Adrien Bartoli.
-"Infinitesimal Plane-Based Pose Estimation" (@cite Collins14). This method is suitable for marker pose estimation.
-It requires 4 coplanar object points defined in the following order:
-  - point 0: [-squareLength / 2,  squareLength / 2, 0]
-  - point 1: [ squareLength / 2,  squareLength / 2, 0]
-  - point 2: [ squareLength / 2, -squareLength / 2, 0]
-  - point 3: [-squareLength / 2, -squareLength / 2, 0]
+@param flags Method for solving a PnP problem: see @ref calib3d_solvePnP_flags
 @param rvec Rotation vector used to initialize an iterative PnP refinement algorithm, when flag is @ref SOLVEPNP_ITERATIVE
 and useExtrinsicGuess is set to true.
 @param tvec Translation vector used to initialize an iterative PnP refinement algorithm, when flag is @ref SOLVEPNP_ITERATIVE
@@ -1171,98 +1033,7 @@ and useExtrinsicGuess is set to true.
 (\f$ \text{RMSE} = \sqrt{\frac{\sum_{i}^{N} \left ( \hat{y_i} - y_i \right )^2}{N}} \f$) between the input image points
 and the 3D object points projected with the estimated pose.
 
-The function estimates the object pose given a set of object points, their corresponding image
-projections, as well as the camera intrinsic matrix and the distortion coefficients, see the figure below
-(more precisely, the X-axis of the camera frame is pointing to the right, the Y-axis downward
-and the Z-axis forward).
-
-![](pnp.jpg)
-
-Points expressed in the world frame \f$ \bf{X}_w \f$ are projected into the image plane \f$ \left[ u, v \right] \f$
-using the perspective projection model \f$ \Pi \f$ and the camera intrinsic parameters matrix \f$ \bf{A} \f$:
-
-\f[
-  \begin{align*}
-  \begin{bmatrix}
-  u \\
-  v \\
-  1
-  \end{bmatrix} &=
-  \bf{A} \hspace{0.1em} \Pi \hspace{0.2em} ^{c}\bf{T}_w
-  \begin{bmatrix}
-  X_{w} \\
-  Y_{w} \\
-  Z_{w} \\
-  1
-  \end{bmatrix} \\
-  \begin{bmatrix}
-  u \\
-  v \\
-  1
-  \end{bmatrix} &=
-  \begin{bmatrix}
-  f_x & 0 & c_x \\
-  0 & f_y & c_y \\
-  0 & 0 & 1
-  \end{bmatrix}
-  \begin{bmatrix}
-  1 & 0 & 0 & 0 \\
-  0 & 1 & 0 & 0 \\
-  0 & 0 & 1 & 0
-  \end{bmatrix}
-  \begin{bmatrix}
-  r_{11} & r_{12} & r_{13} & t_x \\
-  r_{21} & r_{22} & r_{23} & t_y \\
-  r_{31} & r_{32} & r_{33} & t_z \\
-  0 & 0 & 0 & 1
-  \end{bmatrix}
-  \begin{bmatrix}
-  X_{w} \\
-  Y_{w} \\
-  Z_{w} \\
-  1
-  \end{bmatrix}
-  \end{align*}
-\f]
-
-The estimated pose is thus the rotation (`rvec`) and the translation (`tvec`) vectors that allow transforming
-a 3D point expressed in the world frame into the camera frame:
-
-\f[
-  \begin{align*}
-  \begin{bmatrix}
-  X_c \\
-  Y_c \\
-  Z_c \\
-  1
-  \end{bmatrix} &=
-  \hspace{0.2em} ^{c}\bf{T}_w
-  \begin{bmatrix}
-  X_{w} \\
-  Y_{w} \\
-  Z_{w} \\
-  1
-  \end{bmatrix} \\
-  \begin{bmatrix}
-  X_c \\
-  Y_c \\
-  Z_c \\
-  1
-  \end{bmatrix} &=
-  \begin{bmatrix}
-  r_{11} & r_{12} & r_{13} & t_x \\
-  r_{21} & r_{22} & r_{23} & t_y \\
-  r_{31} & r_{32} & r_{33} & t_z \\
-  0 & 0 & 0 & 1
-  \end{bmatrix}
-  \begin{bmatrix}
-  X_{w} \\
-  Y_{w} \\
-  Z_{w} \\
-  1
-  \end{bmatrix}
-  \end{align*}
-\f]
+More information is described in @ref calib3d_solvePnP
 
 @note
    -   An example of how to use solvePnP for planar augmented reality can be found at