Estimate 3x3 matrix relating image coordinates with each other, i.e. More...

#include <Geometry/HMatrixEstimation.hh>

Collaboration diagram for BIAS::HMatrixEstimation:

Public Member Functions
int	Compute (const std::vector< BIAS::HomgPoint2D > &fromPoints, const std::vector< BIAS::HomgPoint2D > &toPoints, HMatrix &H)
	Calculate homography between 2d points using the DLT. More...

int	Compute (const std::vector< BIAS::Vector2< double > > &fromPoints, const std::vector< BIAS::Vector2< double > > &toPoints, HMatrix &H)
	Calculate homography between 2d points using the DLT. More...

int	ComputeAffine (const std::vector< BIAS::HomgPoint2D > &fromPoints, const std::vector< BIAS::HomgPoint2D > &toPoints, HMatrix &H)
	Compute affine transformation between 2d points, i.e. More...

double	GetError () const
	Returns the average squared error of the estimation applying the estimated homography matrix to all correspondences. More...

	HMatrixEstimation (bool normalizeHartley=true)
	Create homography estimation instance. More...

int	Optimize (BIAS::HMatrix &H, const std::vector< BIAS::HomgPoint2D > &p1, const std::vector< BIAS::HomgPoint2D > &p2)
	Optimize a given homography matrix from 2d point correspondences. More...

void	SetNormalizeHartley (bool normalize)
	Decide whether to normalize input vector as proposed by Hartley (strongly recommended) or use the DLT on raw data. More...

	~HMatrixEstimation ()

Static Protected Member Functions
static int	HErrorFunction_ (void p, int m, int n, const double x, double *fvec, int iflag)
	Objective function for Levenberg-Marquardt optimization. More...

Protected Attributes
HMatrix	H_
	Stores the estimated homography matrix (used in GetError) More...

Normalization	normalization_
	The normalization algorithm instance. More...

bool	normalizeHartley_
	Flag indicating whether we should normalize the given points before and denormalize the homography matrix after computation, so that it refers to the original points. More...

std::vector< BIAS::HomgPoint2D >	pointsFrom_
	Stores the points in image 1 (used in Optimize and GetError) More...

std::vector< BIAS::HomgPoint2D >	pointsTo_
	Stores the points in image 2 (used in Optimize and GetError) More...

Detailed Description

Estimate 3x3 matrix relating image coordinates with each other, i.e.

a homography or affine transformation.

Author: koeser 12/2005

Examples:: ExampleHMatrixEstimation.cpp, and HMatrixTest.cpp.

Definition at line 48 of file HMatrixEstimation.hh.

Constructor & Destructor Documentation

BIAS::HMatrixEstimation::HMatrixEstimation ( bool normalizeHartley = true )

inlineexplicit

Create homography estimation instance.

Parameters

normalizeHartley Use normalization of input vectors proposed by Hartley (strongly recommended) or use the DLT on raw data

Definition at line 56 of file HMatrixEstimation.hh.

BIAS::HMatrixEstimation::~HMatrixEstimation ( )

inline

Definition at line 59 of file HMatrixEstimation.hh.

Member Function Documentation

int HMatrixEstimation::Compute	(	const std::vector< BIAS::HomgPoint2D > &	fromPoints,
		const std::vector< BIAS::HomgPoint2D > &	toPoints,
		HMatrix &	H
	)

Calculate homography between 2d points using the DLT.

The direct linear transformation algorithm (see Hartley & Zisserman: "Multiple View Geometry", p.73) solves the equation system (p' x (H * p) = 0 in order to solve p' ~ H * p where p, p' are 2d image coordinates in homogeneous coordinates. Each correspondence provides 3 equation, but the linear equation system has but rank 2, so we take only the first two rows. The resulting equation system A*h = 0 s.t. |h| = 1 is solved via SVD where h is vector representation of matrix H.

Parameters

fromPoints	Homogenized points in image 1
toPoints	Corresponding homogenized points in image 2
H	Returns estimated homography matrix

Author: woelk/frahm

Examples:: ExampleHMatrixEstimation.cpp.

Definition at line 92 of file HMatrixEstimation.cpp.

References General_singular_value_decomposition(), BIAS::Matrix3x3< T >::GetData(), BIAS::KMatrix::Invert(), and BIAS::Matrix3x3< T >::SetZero().

int HMatrixEstimation::Compute	(	const std::vector< BIAS::Vector2< double > > &	fromPoints,
		const std::vector< BIAS::Vector2< double > > &	toPoints,
		HMatrix &	H
	)

Calculate homography between 2d points using the DLT.

Parameters

fromPoints	Homogenized points in image 1
toPoints	Corresponding homogenized points in image 2
H	Returns estimated homography matrix

Author: woelk/frahm

Definition at line 228 of file HMatrixEstimation.cpp.

int HMatrixEstimation::ComputeAffine	(	const std::vector< BIAS::HomgPoint2D > &	fromPoints,
		const std::vector< BIAS::HomgPoint2D > &	toPoints,
		HMatrix &	H
	)

Compute affine transformation between 2d points, i.e.

rotation and translation. This method is not using the DLT!

Parameters

fromPoints	Homogenized points in image 1
toPoints	Corresponding homogenized points in image 2
H	Returns estimated affine transformation matrix

Author: koeser 12/2005

Examples:: HMatrixTest.cpp.

Definition at line 162 of file HMatrixEstimation.cpp.

References General_singular_value_decomposition(), BIAS::Matrix3x3< T >::GetData(), BIAS::KMatrix::Invert(), BIAS::MatrixZero, and BIAS::Matrix3x3< T >::SetIdentity().

double HMatrixEstimation::GetError ( ) const

Returns the average squared error of the estimation applying the estimated homography matrix to all correspondences.

Definition at line 245 of file HMatrixEstimation.cpp.

References BIAS::HomgPoint2D::Homogenize(), and BIAS::Vector3< T >::size().

int HMatrixEstimation::HErrorFunction_	(	void *	p,
		int	m,
		int	n,
		const double *	x,
		double *	fvec,
		int	iflag
	)

staticprotected

Objective function for Levenberg-Marquardt optimization.

Definition at line 13 of file HMatrixEstimation.cpp.

References BIAS::Matrix3x3< T >::GetInverse(), BIAS::HomgPoint2D::Homogenize(), BIAS::Parametrization::ParamsToHMatrix(), pointsFrom_, and pointsTo_.

int HMatrixEstimation::Optimize	(	BIAS::HMatrix &	H,
		const std::vector< BIAS::HomgPoint2D > &	p1,
		const std::vector< BIAS::HomgPoint2D > &	p2
	)

Optimize a given homography matrix from 2d point correspondences.

Minimize an error function on the homography matrix using iterative nonlinear optimization techniques such as Levenberg-Marquardt.

Attention: Susceptible to local minima, provide good starting point!

Parameters

H	Homography matrix to optimize, provides starting point
p1	Homogenized points in image 1
p2	Corresponding homogenized points in image 2

Returns: Return 0 on success, <0 for errors

Author: koeser 06/2006

Definition at line 52 of file HMatrixEstimation.cpp.

References BIAS::Parametrization::HMatrixToParams(), BIAS::LevenbergMarquardt(), and BIAS::Parametrization::ParamsToHMatrix().

void BIAS::HMatrixEstimation::SetNormalizeHartley ( bool normalize )

inline

Decide whether to normalize input vector as proposed by Hartley (strongly recommended) or use the DLT on raw data.

Definition at line 116 of file HMatrixEstimation.hh.

Member Data Documentation

HMatrix BIAS::HMatrixEstimation::H_

protected

Stores the estimated homography matrix (used in GetError)

Definition at line 139 of file HMatrixEstimation.hh.

Normalization BIAS::HMatrixEstimation::normalization_

protected

The normalization algorithm instance.

Definition at line 136 of file HMatrixEstimation.hh.

bool BIAS::HMatrixEstimation::normalizeHartley_

protected

Flag indicating whether we should normalize the given points before and denormalize the homography matrix after computation, so that it refers to the original points.

Definition at line 133 of file HMatrixEstimation.hh.

std::vector<BIAS::HomgPoint2D> BIAS::HMatrixEstimation::pointsFrom_

protected

Stores the points in image 1 (used in Optimize and GetError)

Definition at line 142 of file HMatrixEstimation.hh.

Referenced by HErrorFunction_().

std::vector<BIAS::HomgPoint2D> BIAS::HMatrixEstimation::pointsTo_

protected

Stores the points in image 2 (used in Optimize and GetError)

Definition at line 145 of file HMatrixEstimation.hh.

Referenced by HErrorFunction_().

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