Conditioning

Functions
void	cv::sfm::applyTransformationToPoints (InputArray points, InputArray T, OutputArray transformed_points)
	Apply Transformation to points. More...
void	cv::sfm::isotropicPreconditionerFromPoints (InputArray points, OutputArray T)
	Point conditioning (isotropic). More...
void	cv::sfm::normalizeIsotropicPoints (InputArray points, OutputArray normalized_points, OutputArray T)
	This function normalizes points. (isotropic). More...
void	cv::sfm::normalizePoints (InputArray points, OutputArray normalized_points, OutputArray T)
	This function normalizes points (non isotropic). More...
void	cv::sfm::preconditionerFromPoints (InputArray points, OutputArray T)

Detailed Description

Function Documentation

applyTransformationToPoints()

void cv::sfm::applyTransformationToPoints	(	InputArray	points,
		InputArray	T,
		OutputArray	transformed_points
	)

Apply Transformation to points.

Parameters

points	Input vector of N-dimensional points.
T	Input 3x3 transformation matrix such that \(x = T*X\), where \(X\) are the points to transform and \(x\) the transformed points.
transformed_points	Output vector of N-dimensional transformed points.

isotropicPreconditionerFromPoints()

void cv::sfm::isotropicPreconditionerFromPoints	(	InputArray	points,
		OutputArray	T
	)

Point conditioning (isotropic).

Parameters

points	Input vector of N-dimensional points.
T	Output 3x3 transformation matrix.

Computes the transformation matrix such that each coordinate direction will be scaled equally, bringing the centroid to the origin with an average centroid \((1,1,1)^T\).
Reference: [81] 4.4.4 pag.107.

normalizeIsotropicPoints()

void cv::sfm::normalizeIsotropicPoints	(	InputArray	points,
		OutputArray	normalized_points,
		OutputArray	T
	)

This function normalizes points. (isotropic).

Parameters

points	Input vector of N-dimensional points.
normalized_points	Output vector of the same N-dimensional points but with mean 0 and average norm \(\sqrt{2}\).
T	Output 3x3 transform matrix such that \(x = T*X\), where \(X\) are the points to normalize and \(x\) the normalized points.

Internally calls preconditionerFromPoints in order to get the scaling matrix before applying applyTransformationToPoints. This operation is an essential step before applying the DLT algorithm in order to consider the result as optimal.
Reference: [81] 4.4.4 pag.107.

normalizePoints()

void cv::sfm::normalizePoints	(	InputArray	points,
		OutputArray	normalized_points,
		OutputArray	T
	)

This function normalizes points (non isotropic).

Parameters

points	Input vector of N-dimensional points.
normalized_points	Output vector of the same N-dimensional points but with mean 0 and average norm \(\sqrt{2}\).
T	Output 3x3 transform matrix such that \(x = T*X\), where \(X\) are the points to normalize and \(x\) the normalized points.

Internally calls preconditionerFromPoints in order to get the scaling matrix before applying applyTransformationToPoints. This operation is an essential step before applying the DLT algorithm in order to consider the result as optimal.
Reference: [81] 4.4.4 pag.109

preconditionerFromPoints()

void cv::sfm::preconditionerFromPoints	(	InputArray	points,
		OutputArray	T
	)

Point conditioning (non isotropic).

Parameters

points	Input vector of N-dimensional points.
T	Output 3x3 transformation matrix.

Computes the transformation matrix such that the two principal moments of the set of points are equal to unity, forming an approximately symmetric circular cloud of points of radius 1 about the origin.
Reference: [81] 4.4.4 pag.109