Functions
std::vector< TooN::Matrix< 3 > >	tag::five_point (const std::tr1::array< std::pair< TooN::Vector< 3 >, TooN::Vector< 3 > >, 5 > &points)

std::vector< TooN::SE3<> >	tag::se3_from_E (const TooN::Matrix< 3 > &E)

TooN::SE3	tag::optimize_epipolar (const std::vector< std::pair< TooN::Vector< 3 >, TooN::Vector< 3 > > > &points, const TooN::SE3<> &initial)

std::pair< double, double >	tag::essential_reprojection_errors_squared (const TooN::Matrix< 3 > &E, const TooN::Vector< 3 > &q, const TooN::Vector< 3 > &p)

std::pair< double, double >	tag::essential_reprojection_errors (const TooN::Matrix< 3 > &E, const TooN::Vector< 3 > &q, const TooN::Vector< 3 > &p)

template<class V , class M >
void	tag::getCrossProductMatrix (const V &vec, M &result)

template<class V >
TooN::Matrix< 3 >	tag::getCrossProductMatrix (const V &vec)

template<class M >
void	tag::getEssentialMatrix (const TooN::SE3<> &transform, M &E)

TooN::Matrix< 3 >	tag::getEssentialMatrix (const TooN::SE3<> &transform)

Detailed Description

various functions dealing with essential matrices including 5 point estimation after Nister, reconstruction of R,t from essential matrix after Horn, and construction of E from R,t.

Function Documentation

std::pair<double, double> tag::essential_reprojection_errors	(	const TooN::Matrix< 3 > &	E,
		const TooN::Vector< 3 > &	q,
		const TooN::Vector< 3 > &	p
	)

Given an essential matrix E and two points p and q, this functions computes the reprojection errors given by the signed distance from p to the line defined by $E\vec{q}$ and the signed distance from q to the line defined by $E^T\vec{p}$ . If E is not an essential matrix then the errors will not be sensible.

Parameters

E	E: essential matrix
q	q: right hand (first) point
p	p: left hand (second) point

Returns: the reprojection errors

std::pair<double, double> tag::essential_reprojection_errors_squared	(	const TooN::Matrix< 3 > &	E,
		const TooN::Vector< 3 > &	q,
		const TooN::Vector< 3 > &	p
	)

Given an essential matrix E and two points p and q, this functions computes the reprojection errors given by the squared distance from p to the line defined by $E\vec{q}$ and the squared distance from q to the line defined by $E^T\vec{p}$ . If E is not an essential matrix then the errors will not be sensible. This function avoids a sqrt compared to tag::essential_reprojection_errors.

Parameters

E	E: essential matrix
q	q: right hand (first) point
p	p: left hand (second) point

Returns: the reprojection errors

std::vector<TooN::Matrix<3> > tag::five_point ( const std::tr1::array< std::pair< TooN::Vector< 3 >, TooN::Vector< 3 > >, 5 > & points )

Computes essential matrices representing the epipolar geometry between correspondences. This function implements Nister's 5 point algorithm. For all of the input points pairs, each out matrix satisfies the condition:

$\ \vec{\text{second}}\ E \ \vec{\text{first}} = 0. \$

Parameters

points	a array of pairs of directions in 3 space containing correspondences
initial	an inital value for the transformation used as starting point of the optimization

Returns: the optimized transformation

template<class V , class M >

void tag::getCrossProductMatrix	(	const V &	vec,
		M &	result
	)

inline

creates a cross product matrix M from a 3 vector v, such that for all vectors w, the following holds: v ^ w = M * w

Parameters

	vec	the 3 vector input
[out]	result	the 3x3 matrix to set to the cross product matrix

Referenced by tag::getCrossProductMatrix(), tag::optimize_epipolar(), and tag::se3_from_E().

template<class V >

TooN::Matrix<3> tag::getCrossProductMatrix ( const V & vec )

inline

creates an returns a cross product matrix M from a 3 vector v, such that for all vectors w, the following holds: v ^ w = M * w

Parameters

vec	the 3 vector input

Returns: the 3x3 matrix to set to the cross product matrix

References tag::getCrossProductMatrix().

template<class M >

void tag::getEssentialMatrix	(	const TooN::SE3<> &	transform,
		M &	E
	)

inline

creates the essential matrix corresponding to a given transformation

Parameters

	transform	the transformation as SE3
[out]	E	the 3x3 matrix set to the essential matrix

Referenced by tag::getEssentialMatrix().

TooN::Matrix<3> tag::getEssentialMatrix ( const TooN::SE3<> & transform )

inline

creates and returns the essential matrix corresponding to a given transformation

Parameters

transform the transformation as SE3

Returns: the 3x3 matrix set to the essential matrix

References tag::getEssentialMatrix().

TooN::SE3 tag::optimize_epipolar	(	const std::vector< std::pair< TooN::Vector< 3 >, TooN::Vector< 3 > > > &	points,
		const TooN::SE3<> &	initial
	)

optimizes a transformation representing the epipolar geometry between correspondences. This function minimizes the algebraic error of the epipolar geometry through non-linear optimization of the rotation and direction of the translation. For all of the input points pairs, each out matrix satisfies the condition:

$\vec{\text{second}}\ E \ \vec{\text{first}} = 0.$

Parameters

points	a vector of pairs of directions in 3 space containing correspondences
initial	an inital value for the transformation used as starting point of the optimization

Returns: the optimized transformation

References tag::getCrossProductMatrix().

std::vector< TooN::SE3<> > tag::se3_from_E ( const TooN::Matrix< 3 > & E )

reconstructs possible R,t from essential matrix E. The implementation follows the algorithm in Recovering Baseline and Orientation from 'Essential' Matrix BKP Horn, Jan 1990

Parameters

E	essential matrix

Returns: vector with 4 SE3s representing the possible transformations

References tag::getCrossProductMatrix().

Functions

Detailed Description

Function Documentation