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Summarize PnP pose computation on a single separate page.

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catree
2021-12-23 19:43:27 +01:00
parent 4d9365990a
commit 9c61d80bc4
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modules/3d/include/opencv2/3d.hpp
+25 -254
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@@ -387,7 +387,9 @@ 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
@@ -404,7 +406,7 @@ 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.
@param flags Method for solving a PnP problem: see @ref calib3d_solvePnP_flags
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 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
@@ -967,10 +848,12 @@ a 3D point expressed in the world frame into the camera frame:
CV_EXPORTS_W bool solvePnP( InputArray objectPoints, InputArray imagePoints,
InputArray cameraMatrix, InputArray distCoeffs,
OutputArray rvec, OutputArray tvec,
bool useExtrinsicGuess = false, int flags = 0 );
bool useExtrinsicGuess = false, int flags = SOLVEPNP_ITERATIVE );
/** @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,
@@ -1015,7 +898,7 @@ CV_EXPORTS_W bool solvePnPRansac( InputArray objectPoints, InputArray imagePoint
OutputArray rvec, OutputArray tvec,
bool useExtrinsicGuess = false, int iterationsCount = 100,
float reprojectionError = 8.0, double confidence = 0.99,
OutputArray inliers = noArray(), int flags = 0 );
OutputArray inliers = noArray(), int flags = SOLVEPNP_ITERATIVE );
/*
Finds rotation and translation vector.
@@ -1028,6 +911,8 @@ 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.
@@ -1059,6 +944,8 @@ 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,
@@ -1087,6 +974,8 @@ 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,
@@ -1116,6 +1005,9 @@ 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.
@@ -1143,37 +1035,7 @@ 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
@@ -1182,98 +1044,7 @@ 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
@@ -1309,7 +1080,7 @@ CV_EXPORTS_W int solvePnPGeneric( InputArray objectPoints, InputArray imagePoint
InputArray cameraMatrix, InputArray distCoeffs,
OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs,
bool useExtrinsicGuess = false,
int flags = 0,
int flags = SOLVEPNP_ITERATIVE,
InputArray rvec = noArray(), InputArray tvec = noArray(),
OutputArray reprojectionError = noArray() );