Projection

Functions
double	cv::sfm::depth (InputArray R, InputArray t, InputArray X)
	Returns the depth of a point transformed by a rigid transform.
void	cv::sfm::euclideanToHomogeneous (InputArray src, OutputArray dst)
	Converts points from Euclidean to homogeneous space. E.g., ((x,y)->(x,y,1))
void	cv::sfm::homogeneousToEuclidean (InputArray src, OutputArray dst)
	Converts point coordinates from homogeneous to euclidean pixel coordinates. E.g., ((x,y,z)->(x/z, y/z))
void	cv::sfm::KRtFromProjection (InputArray P, OutputArray K, OutputArray R, OutputArray t)
	Get K, R and t from projection matrix P, decompose using the RQ decomposition.
void	cv::sfm::projectionFromKRt (InputArray K, InputArray R, InputArray t, OutputArray P)
	Get projection matrix P from K, R and t.

Detailed Description

Function Documentation

double cv::sfm::depth	(	InputArray	R,
		InputArray	t,
		InputArray	X
	)

Returns the depth of a point transformed by a rigid transform.

Parameters

R	Input 3x3 rotation matrix.
t	Input 3x1 translation vector.
X	Input 3x1 or 4x1 vector with the 3d point.

void cv::sfm::euclideanToHomogeneous	(	InputArray	src,
		OutputArray	dst
	)

Converts points from Euclidean to homogeneous space. E.g., ((x,y)->(x,y,1))

Parameters

src	Input vector of N-dimensional points.
dst	Output vector of N+1-dimensional points.

void cv::sfm::homogeneousToEuclidean	(	InputArray	src,
		OutputArray	dst
	)

Converts point coordinates from homogeneous to euclidean pixel coordinates. E.g., ((x,y,z)->(x/z, y/z))

Parameters

src	Input vector of N-dimensional points.
dst	Output vector of N-1-dimensional points.

void cv::sfm::KRtFromProjection	(	InputArray	P,
		OutputArray	K,
		OutputArray	R,
		OutputArray	t
	)

Get K, R and t from projection matrix P, decompose using the RQ decomposition.

Parameters

P	Input 3x4 projection matrix.
K	Output 3x3 camera matrix \(K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\).
R	Output 3x3 rotation matrix.
t	Output 3x1 translation vector.

Reference:HartleyZ00 A4.1.1 pag.579

void cv::sfm::projectionFromKRt	(	InputArray	K,
		InputArray	R,
		InputArray	t,
		OutputArray	P
	)

Get projection matrix P from K, R and t.

Parameters

K	Input 3x3 camera matrix \(K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\).
R	Input 3x3 rotation matrix.
t	Input 3x1 translation vector.
P	Output 3x4 projection matrix.

This function estimate the projection matrix by solving the following equation: \(P = K * [R|t]\)