#include <ippe.h>

Public Member Functions
void	generateSquareObjectCorners2D (double squareLength, cv::OutputArray _objectPoints)
	Generates the 4 object points of a square planar object, without including the z-component (which is z=0 for all points). More...

void	generateSquareObjectCorners3D (double squareLength, cv::OutputArray _objectPoints)
	Generates the 4 object points of a square planar object. More...

double	meanSceneDepth (cv::InputArray objectPoints, cv::InputArray rvec, cv::InputArray tvec)
	Computes the average depth of an object given its pose in camera coordinates. More...

	PoseSolver ()
	PoseSolver constructor. More...

void	solveGeneric (cv::InputArray _objectPoints, cv::InputArray _imagePoints, cv::InputArray _cameraMatrix, cv::InputArray _distCoeffs, cv::OutputArray _rvec1, cv::OutputArray _tvec1, float &reprojErr1, cv::OutputArray _rvec2, cv::OutputArray _tvec2, float &reprojErr2)
	Finds the two possible poses of a planar object given a set of correspondences and their respective reprojection errors. The poses are sorted with the first having the lowest reprojection error. More...

void	solveSquare (double squareLength, cv::InputArray _imagePoints, cv::InputArray _cameraMatrix, cv::InputArray _distCoeffs, cv::OutputArray _rvec1, cv::OutputArray _tvec1, float &reprojErr1, cv::OutputArray _rvec2, cv::OutputArray _tvec2, float &reprojErr2)
	Finds the two possible poses of a square planar object and their respective reprojection errors using IPPE. These poses are sorted so that the first one is the one with the lowest reprojection error. More...

	~PoseSolver ()
	PoseSolver destructor. More...

Private Member Functions
bool	computeObjextSpaceR3Pts (cv::InputArray _objectPoints, cv::OutputArray _R)
	Computes the rotation _R that rotates the object points to the plane z=0. This uses the cross-product method with the first three object points. More...

bool	computeObjextSpaceRSvD (cv::InputArray _objectPointsZeroMean, cv::OutputArray _R)
	computeObjextSpaceRSvD Computes the rotation _R that rotates the object points to the plane z=0. This uses the cross-product method with the first three object points. More...

void	computeRotations (double j00, double j01, double j10, double j11, double p, double q, cv::OutputArray _R1, cv::OutputArray _R2)
	Computes the two rotation solutions from the Jacobian of a homography matrix H at a point (ux,uy) on the object plane. For highest accuracy the Jacobian should be computed at the centroid of the point correspondences (see the IPPE paper for the explanation of this). For a point (ux,uy) on the object plane, suppose the homography H maps (ux,uy) to a point (p,q) in the image (in normalized pixel coordinates). The Jacobian matrix [J00, J01; J10,J11] is the Jacobian of the mapping evaluated at (ux,uy). More...

void	computeTranslation (cv::InputArray _objectPoints, cv::InputArray _normalizedImgPoints, cv::InputArray _R, cv::OutputArray _t)
	Computes the translation solution for a given rotation solution. More...

void	evalReprojError (cv::InputArray _objectPoints, cv::InputArray _imagePoints, cv::InputArray _cameraMatrix, cv::InputArray _distCoeffs, cv::InputArray _M, float &err)
	Evaluates the Root Mean Squared (RMS) reprojection error of a pose solution. More...

void	homographyFromSquarePoints (cv::InputArray _targetPoints, double halfLength, cv::OutputArray _H)
	Closed-form solution for the homography mapping with four corner correspondences of a square (it maps source points to target points). The source points are the four corners of a zero-centred squared defined by: point 0: [-squareLength / 2.0, squareLength / 2.0] point 1: [squareLength / 2.0, squareLength / 2.0] point 2: [squareLength / 2.0, -squareLength / 2.0] point 3: [-squareLength / 2.0, -squareLength / 2.0]. More...

void	makeCanonicalObjectPoints (cv::InputArray _objectPoints, cv::OutputArray _canonicalObjectPoints, cv::OutputArray _MobjectPoints2Canonical)
	Takes a set of planar object points and transforms them to 'canonical' object coordinates This is when they have zero mean and are on the plane z=0. More...

void	rot2vec (cv::InputArray _R, cv::OutputArray _r)
	Fast conversion from a rotation matrix to a rotation vector using Rodrigues' formula. More...

void	rotateVec2ZAxis (cv::InputArray _a, cv::OutputArray _Ra)
	Finds the rotation _Ra that rotates a vector _a to the z axis (0,0,1) More...

void	solveCanonicalForm (cv::InputArray _canonicalObjPoints, cv::InputArray _normalizedInputPoints, cv::InputArray _H, cv::OutputArray _Ma, cv::OutputArray _Mb)
	Finds the two possible poses of a planar object in its canonical position, given a set of correspondences in normalized pixel coordinates. These poses are NOT sorted on reprojection error. Note that the returned poses are object-to-camera transforms, and not camera-to-object transforms. More...

void	solveGeneric (cv::InputArray _objectPoints, cv::InputArray _normalizedImagePoints, cv::OutputArray _Ma, cv::OutputArray _Mb)
	Finds the two possible poses of a planar object given a set of correspondences in normalized pixel coordinates. These poses are NOT sorted on reprojection error. Note that the returned poses are object-to-camera transforms, and not camera-to-object transforms. More...

void	sortPosesByReprojError (cv::InputArray _objectPoints, cv::InputArray _imagePoints, cv::InputArray _cameraMatrix, cv::InputArray _distCoeffs, cv::InputArray _Ma, cv::InputArray _Mb, cv::OutputArray _M1, cv::OutputArray _M2, float &err1, float &err2)
	Sorts two pose solutions according to their RMS reprojection error (lowest first). More...

Detailed Description

Definition at line 67 of file ippe.h.

Constructor & Destructor Documentation

◆ PoseSolver()

IPPE::PoseSolver::PoseSolver ( )

PoseSolver constructor.

Definition at line 151 of file ippe.cpp.

◆ ~PoseSolver()

IPPE::PoseSolver::~PoseSolver ( )

PoseSolver destructor.

Definition at line 155 of file ippe.cpp.

Member Function Documentation

◆ computeObjextSpaceR3Pts()

bool IPPE::PoseSolver::computeObjextSpaceR3Pts	(	cv::InputArray	_objectPoints,
		cv::OutputArray	_R
	)

private

Computes the rotation _R that rotates the object points to the plane z=0. This uses the cross-product method with the first three object points.

Parameters

_objectPoints	Array of N>=3 coplanar object points defined in object coordinates. 1xN/Nx1 3-channel (float or double) where N is the number of points
_R	Rotation Mat: 3x3 (double)

Returns: success (true) or failure (false)

Definition at line 1213 of file ippe.cpp.

◆ computeObjextSpaceRSvD()

bool IPPE::PoseSolver::computeObjextSpaceRSvD	(	cv::InputArray	_objectPointsZeroMean,
		cv::OutputArray	_R
	)

private

computeObjextSpaceRSvD Computes the rotation _R that rotates the object points to the plane z=0. This uses the cross-product method with the first three object points.

Parameters

_objectPointsZeroMean	zero-meaned co=planar object points: 3xN matrix (double) where N>=3
_R	Rotation Mat: 3x3 (double)

Returns: success (true) or failure (false)

Definition at line 1275 of file ippe.cpp.

◆ computeRotations()

void IPPE::PoseSolver::computeRotations	(	double	j00,
		double	j01,
		double	j10,
		double	j11,
		double	p,
		double	q,
		cv::OutputArray	_R1,
		cv::OutputArray	_R2
	)

private

Computes the two rotation solutions from the Jacobian of a homography matrix H at a point (ux,uy) on the object plane. For highest accuracy the Jacobian should be computed at the centroid of the point correspondences (see the IPPE paper for the explanation of this). For a point (ux,uy) on the object plane, suppose the homography H maps (ux,uy) to a point (p,q) in the image (in normalized pixel coordinates). The Jacobian matrix [J00, J01; J10,J11] is the Jacobian of the mapping evaluated at (ux,uy).

Parameters

j00	Homography jacobian coefficent at (ux,uy)
j01	Homography jacobian coefficent at (ux,uy)
j10	Homography jacobian coefficent at (ux,uy)
j11	Homography jacobian coefficent at (ux,uy)
p	the x coordinate of point (ux,uy) mapped into the image (undistorted and normalized position)
q	the y coordinate of point (ux,uy) mapped into the image (undistorted and normalized position)

Definition at line 537 of file ippe.cpp.

◆ computeTranslation()

void IPPE::PoseSolver::computeTranslation	(	cv::InputArray	_objectPoints,
		cv::InputArray	_normalizedImgPoints,
		cv::InputArray	_R,
		cv::OutputArray	_t
	)

private

Computes the translation solution for a given rotation solution.

Parameters

_objectPoints	Array of corresponding object points, 1xN/Nx1 3-channel where N is the number of points
_normalizedImagePoints	Array of corresponding image points (undistorted), 1xN/Nx1 2-channel where N is the number of points
_R	Rotation solution (3x1 rotation vector)
_t	Translation solution Translation solution (3x1 rotation vector)

Definition at line 440 of file ippe.cpp.

◆ evalReprojError()

void IPPE::PoseSolver::evalReprojError	(	cv::InputArray	_objectPoints,
		cv::InputArray	_imagePoints,
		cv::InputArray	_cameraMatrix,
		cv::InputArray	_distCoeffs,
		cv::InputArray	_M,
		float &	err
	)

private

Evaluates the Root Mean Squared (RMS) reprojection error of a pose solution.

Parameters

_objectPoints	Array of 4 or more coplanar object points defined in object coordinates. 1xN/Nx1 3-channel (float or double) where N is the number of points
_imagePoints	Array of corresponding image points, 1xN/Nx1 2-channel. This can either be in pixel coordinates or normalized pixel coordinates.
_cameraMatrix	Intrinsic camera matrix (same definition as OpenCV). If _imagePoints is in normalized pixel coordinates you must set _cameraMatrix = cv::noArray().
_distCoeffs	Intrinsic camera distortion vector (same definition as OpenCV). If _imagePoints is in normalized pixel coordinates you must set _cameraMatrix = cv::noArray().
_M	Pose matrix from 3D object to camera coordinates: 4x4 1-channel (double)
err	RMS reprojection error

Definition at line 846 of file ippe.cpp.

◆ generateSquareObjectCorners2D()

void IPPE::PoseSolver::generateSquareObjectCorners2D	(	double	squareLength,
		cv::OutputArray	_objectPoints
	)

Generates the 4 object points of a square planar object, without including the z-component (which is z=0 for all points).

Parameters

squareLength	The square's length (which is also it's width) in object coordinate units (e.g. millimeters, meters, etc.)
_objectPoints	Set of 4 object points (1x4 2-channel double)

Definition at line 366 of file ippe.cpp.

◆ generateSquareObjectCorners3D()

void IPPE::PoseSolver::generateSquareObjectCorners3D	(	double	squareLength,
		cv::OutputArray	_objectPoints
	)

Generates the 4 object points of a square planar object.

Parameters

squareLength	The square's length (which is also it's width) in object coordinate units (e.g. millimeters, meters, etc.)
_objectPoints	Set of 4 object points (1x4 3-channel double)

Definition at line 356 of file ippe.cpp.

◆ homographyFromSquarePoints()

void IPPE::PoseSolver::homographyFromSquarePoints	(	cv::InputArray	_targetPoints,
		double	halfLength,
		cv::OutputArray	_H
	)

private

Closed-form solution for the homography mapping with four corner correspondences of a square (it maps source points to target points). The source points are the four corners of a zero-centred squared defined by: point 0: [-squareLength / 2.0, squareLength / 2.0] point 1: [squareLength / 2.0, squareLength / 2.0] point 2: [squareLength / 2.0, -squareLength / 2.0] point 3: [-squareLength / 2.0, -squareLength / 2.0].

Parameters

_targetPoints	Array of four corresponding target points, 1x4/4x1 2-channel. Note that the points should be ordered to correspond with points 0, 1, 2 and 3.
halfLength	the square's half length (i.e. squareLength/2.0)
_H	Homograhy mapping the source points to the target points, 3x3 single channel

Definition at line 660 of file ippe.cpp.

◆ makeCanonicalObjectPoints()

void IPPE::PoseSolver::makeCanonicalObjectPoints	(	cv::InputArray	_objectPoints,
		cv::OutputArray	_canonicalObjectPoints,
		cv::OutputArray	_MobjectPoints2Canonical
	)

private

Takes a set of planar object points and transforms them to 'canonical' object coordinates This is when they have zero mean and are on the plane z=0.

Parameters

_objectPoints	Array of 4 or more coplanar object points defined in object coordinates. 1xN/Nx1 3-channel (float or double) where N is the number of points
_canonicalObjectPoints	Object points in canonical coordinates 1xN/Nx1 2-channel (double)
_MobjectPoints2Canonical	Transform matrix mapping _objectPoints to _canonicalObjectPoints: 4x4 1-channel (double)

Definition at line 734 of file ippe.cpp.

◆ meanSceneDepth()

double IPPE::PoseSolver::meanSceneDepth	(	cv::InputArray	objectPoints,
		cv::InputArray	rvec,
		cv::InputArray	tvec
	)

Computes the average depth of an object given its pose in camera coordinates.

Parameters

objectPoints	Object points defined in 3D object space
rvec	Rotation component of pose
tvec	Translation component of pose

Returns: : average depth of the object

Definition at line 376 of file ippe.cpp.

◆ rot2vec()

void IPPE::PoseSolver::rot2vec	(	cv::InputArray	_R,
		cv::OutputArray	_r
	)

private

Fast conversion from a rotation matrix to a rotation vector using Rodrigues' formula.

Parameters

_R	Input rotation matrix, 3x3 1-channel (double)
_r	Output rotation vector, 3x1/1x3 1-channel (double)

Definition at line 409 of file ippe.cpp.

◆ rotateVec2ZAxis()

void IPPE::PoseSolver::rotateVec2ZAxis	(	cv::InputArray	_a,
		cv::OutputArray	_Ra
	)

private

Finds the rotation _Ra that rotates a vector _a to the z axis (0,0,1)

Parameters

_a	vector: 3x1 mat (double)
_Ra	Rotation: 3x3 mat (double)

Definition at line 1169 of file ippe.cpp.

◆ solveCanonicalForm()

void IPPE::PoseSolver::solveCanonicalForm	(	cv::InputArray	_canonicalObjPoints,
		cv::InputArray	_normalizedInputPoints,
		cv::InputArray	_H,
		cv::OutputArray	_Ma,
		cv::OutputArray	_Mb
	)

private

Finds the two possible poses of a planar object in its canonical position, given a set of correspondences in normalized pixel coordinates. These poses are NOT sorted on reprojection error. Note that the returned poses are object-to-camera transforms, and not camera-to-object transforms.

Parameters

_canonicalObjPoints	Array of 4 or more coplanar object points defined in object coordinates. 1xN/Nx1 3-channel (double) where N is the number of points
_normalizedInputPoints	Array of corresponding image points in normalized pixel coordinates, 1xN/Nx1 2-channel (double) where N is the number of points
_H	Homography mapping canonicalObjPoints to normalizedInputPoints.
_Ma
_Mb

Definition at line 255 of file ippe.cpp.

◆ solveGeneric() [1/2]

void IPPE::PoseSolver::solveGeneric	(	cv::InputArray	_objectPoints,
		cv::InputArray	_imagePoints,
		cv::InputArray	_cameraMatrix,
		cv::InputArray	_distCoeffs,
		cv::OutputArray	_rvec1,
		cv::OutputArray	_tvec1,
		float &	reprojErr1,
		cv::OutputArray	_rvec2,
		cv::OutputArray	_tvec2,
		float &	reprojErr2
	)

Finds the two possible poses of a planar object given a set of correspondences and their respective reprojection errors. The poses are sorted with the first having the lowest reprojection error.

Parameters

_objectPoints	Array of 4 or more coplanar object points defined in object coordinates. 1xN/Nx1 3-channel (float or double) where N is the number of points
_imagePoints	Array of corresponding image points, 1xN/Nx1 2-channel. This can either be in pixel coordinates or normalized pixel coordinates.
_cameraMatrix	Intrinsic camera matrix (same definition as OpenCV). If _imagePoints is in normalized pixel coordinates you must set _cameraMatrix = cv::noArray()
_distCoeffs	Intrinsic camera distortion vector (same definition as OpenCV). If _imagePoints is in normalized pixel coordinates you must set _cameraMatrix = cv::noArray()
_rvec1	First rotation solution (3x1 rotation vector)
_tvec1	First translation solution (3x1 vector)
reprojErr1	Reprojection error of first solution
_rvec2	Second rotation solution (3x1 rotation vector)
_tvec2	Second translation solution (3x1 vector)
reprojErr2	Reprojection error of second solution

Definition at line 159 of file ippe.cpp.

◆ solveGeneric() [2/2]

void IPPE::PoseSolver::solveGeneric	(	cv::InputArray	_objectPoints,
		cv::InputArray	_normalizedImagePoints,
		cv::OutputArray	_Ma,
		cv::OutputArray	_Mb
	)

private

Finds the two possible poses of a planar object given a set of correspondences in normalized pixel coordinates. These poses are NOT sorted on reprojection error. Note that the returned poses are object-to-camera transforms, and not camera-to-object transforms.

Parameters

_objectPoints	Array of 4 or more coplanar object points defined in object coordinates. 1xN/Nx1 3-channel (float or double).
_normalizedImagePoints	Array of corresponding image points in normalized pixel coordinates, 1xN/Nx1 2-channel (float or double).
_Ma	First pose solution (unsorted)
_Mb	Second pose solution (unsorted)

Definition at line 197 of file ippe.cpp.

◆ solveSquare()

void IPPE::PoseSolver::solveSquare	(	double	squareLength,
		cv::InputArray	_imagePoints,
		cv::InputArray	_cameraMatrix,
		cv::InputArray	_distCoeffs,
		cv::OutputArray	_rvec1,
		cv::OutputArray	_tvec1,
		float &	reprojErr1,
		cv::OutputArray	_rvec2,
		cv::OutputArray	_tvec2,
		float &	reprojErr2
	)

Finds the two possible poses of a square planar object and their respective reprojection errors using IPPE. These poses are sorted so that the first one is the one with the lowest reprojection error.

Parameters

_squareLength	The square's length (which is also it's width) in object coordinate units (e.g. millimeters, meters, etc.)
_imagePoints	Array of corresponding image points, 1xN/Nx1 2-channel. This can either be in pixel coordinates or normalized pixel coordinates.
_cameraMatrix	Intrinsic camera matrix (same definition as OpenCV). If _imagePoints is in normalized pixel coordinates you must set _cameraMatrix = cv::noArray()
_distCoeffs	Intrinsic camera distortion vector (same definition as OpenCV). If _imagePoints is in normalized pixel coordinates you must set _cameraMatrix = cv::noArray()
_rvec1	First rotation solution (3x1 rotation vector)
_tvec1	First translation solution (3x1 vector)
reprojErr1	Reprojection error of first solution
_rvec2	Second rotation solution (3x1 rotation vector)
_tvec2	Second translation solution (3x1 vector)
reprojErr2	Reprojection error of second solution

Definition at line 297 of file ippe.cpp.

◆ sortPosesByReprojError()

void IPPE::PoseSolver::sortPosesByReprojError	(	cv::InputArray	_objectPoints,
		cv::InputArray	_imagePoints,
		cv::InputArray	_cameraMatrix,
		cv::InputArray	_distCoeffs,
		cv::InputArray	_Ma,
		cv::InputArray	_Mb,
		cv::OutputArray	_M1,
		cv::OutputArray	_M2,
		float &	err1,
		float &	err2
	)

private

Sorts two pose solutions according to their RMS reprojection error (lowest first).

Parameters

_objectPoints	Array of 4 or more coplanar object points defined in object coordinates. 1xN/Nx1 3-channel (float or double) where N is the number of points
_imagePoints	Array of corresponding image points, 1xN/Nx1 2-channel. This can either be in pixel coordinates or normalized pixel coordinates.
_cameraMatrix	Intrinsic camera matrix (same definition as OpenCV). If _imagePoints is in normalized pixel coordinates you must set _cameraMatrix = cv::noArray().
_distCoeffs	Intrinsic camera distortion vector (same definition as OpenCV). If _imagePoints is in normalized pixel coordinates you must set _cameraMatrix = cv::noArray().
_Ma	Pose matrix 1: 4x4 1-channel
_Mb	Pose matrix 2: 4x4 1-channel
_M1	Member of (Ma,Mb} with lowest RMS reprojection error. Performs deep copy.
_M2	Member of (Ma,Mb} with highest RMS reprojection error. Performs deep copy.
err1	RMS reprojection error of _M1
err2	RMS reprojection error of _M2

Definition at line 895 of file ippe.cpp.

The documentation for this class was generated from the following files:

Public Member Functions

Private Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ PoseSolver()

◆ ~PoseSolver()

Member Function Documentation

◆ computeObjextSpaceR3Pts()

◆ computeObjextSpaceRSvD()

◆ computeRotations()

◆ computeTranslation()

◆ evalReprojError()

◆ generateSquareObjectCorners2D()

◆ generateSquareObjectCorners3D()

◆ homographyFromSquarePoints()

◆ makeCanonicalObjectPoints()

◆ meanSceneDepth()

◆ rot2vec()

◆ rotateVec2ZAxis()

◆ solveCanonicalForm()

◆ solveGeneric() [1/2]

◆ solveGeneric() [2/2]

◆ solveSquare()

◆ sortPosesByReprojError()