Projection of 3D points with uncertainties covariances into the 2d image plane taking the camera pose uncertainty into account. More...

#include <Geometry/Covariance3Dto2D.hh>

Inheritance diagram for BIAS::Covariance3Dto2D:

Collaboration diagram for BIAS::Covariance3Dto2D:

Public Member Functions
void	AddDebugLevel (const long int lv)

void	AddDebugLevel (const std::string &name)

	Covariance3Dto2D (BIAS::KMatrix &K, enum BIAS::PMatrixBase::E_ParametrizationType par)

bool	DebugLevelIsSet (const long int lv) const

bool	DebugLevelIsSet (const std::string &name) const

int	GetDebugLevel () const

std::ostream &	GetDebugStream () const

void	GetDebugStream (std::ostream &os) const

long int	Name2DebugLevel (const std::string &name) const
	looks up a debuglevel in the internal map, returns 0 if not found More...

long int	NewDebugLevel (const std::string &name)
	creates a new debuglevel More...

void	PrintDebugLevel (std::ostream &os=std::cout) const

int	Project (const BIAS::Vector< double > &Pose, const BIAS::Matrix< double > &Cov_Pose, const BIAS::Vector3< double > &X, const BIAS::Matrix3x3< double > &Cov_X, BIAS::Vector2< double > &x, BIAS::Matrix2x2< double > &Cov_x) const
	project covariance onto w=1 plane in camera coordinate system More...

void	RemoveDebugLevel (const long int lv)

void	RemoveDebugLevel (const std::string &name)

void	SetAlpha (const double alpha)
	Sets the alpha parameter. More...

void	SetBeta (const double beta)
	Sets the beta parameter. More...

void	SetDebugLevel (const long int lv)

void	SetDebugLevel (const std::string &name)

void	SetDebugStream (const std::ostream &os)

void	SetK (const BIAS::KMatrix &K)

void	SetUseSVD (const bool use_svd)

void	ShowDebugLevel (std::ostream &os=std::cout) const
	prints all internally known debuglevels More...

int	Transform (const Vector< double > &src_mean, const Matrix< double > &src_cov, Vector< double > &dst_mean, Matrix< double > &dst_cov) const
	computes the second order approximation of the transformations of the mean and the associated covariance for the point transformation Transform_(). More...

	~Covariance3Dto2D ()

Static Public Member Functions
static long int	GetGlobalDebugLevel ()

static void	SetGlobalDebugLevel (long int lev)

Protected Member Functions
int	ComputeSigmaPoints_ (const Vector< double > &src_mean, const Matrix< double > &src_cov, std::vector< WeightedSigmaPoint > &sigma_points) const
	The covariance of a n-dimensional vector is approximated using 2n+1 so called sigma points with associated weights. More...

long	ConsumeNextFreeDebuglevel_ ()
	returns the next available debuglevel More...

virtual int	Transform_ (const BIAS::Vector< double > &src, BIAS::Vector< double > &dst) const
	src is a vector consisting of [ 3d point, camera center, orientation ] The orientation must be represented using one case from E_Parametrization dst is the projection into the image More...

Protected Attributes
long int	_liDebugLevel

long int	_liNextDebugLevel
	new concept, debuglevel are managed here in the debug class More...

std::map< std::string, long int >	_String2Debuglevel

double	Alpha_
	the alpha parameter determines the spread of the sigma points More...

double	Beta_
	beta is used to incorporate prior knowledge of the distribution of x. More...

BIAS::KMatrix	K_

double	Kappa_
	kappa is a secondary scaling parameter. More...

enum BIAS::PMatrixBase::E_ParametrizationType	Parametrization_

bool	UseSVD_

Static Protected Attributes
static std::ostream	_zDebugStream

static long int	GlobalDebugLevel = 0

Detailed Description

Projection of 3D points with uncertainties covariances into the 2d image plane taking the camera pose uncertainty into account.

Given a point in 3D with uncertainty represented/approximated by a multivariate normal distribution (i.e. 3x3 covariance matrix). Given further a camera pose (camer center and orientation).

The algorithm computes the projection of the 3D point into the image taking the camera pose uncertainty into account. The probabilty distribution function in the image is represented by a 2D normal distribution (i.e. a 2D covariance matrix).

The resulting 2D covariance matrix is approximated using the unscented transform. See UnscentedTransform for details.

To use it instantiate this class with the appropriate parametrization of the camera orientation. Currently Euler angles, axis (norm 1) and angle, axis times angle and quaternion are supported.

See Example/ExampleCovariance3Dto2D for exemplary usage.

TODO: implement for point normalization instead of homogenization

Author: woelk 02/2006

Definition at line 41 of file Covariance3Dto2D.hh.

Constructor & Destructor Documentation

Covariance3Dto2D::Covariance3Dto2D	(	BIAS::KMatrix &	K,
		enum BIAS::PMatrixBase::E_ParametrizationType	par
	)

Definition at line 12 of file Covariance3Dto2D.cpp.

Covariance3Dto2D::~Covariance3Dto2D ( )

Definition at line 19 of file Covariance3Dto2D.cpp.

Member Function Documentation

void BIAS::Debug::AddDebugLevel ( const long int lv )

inlineinherited

Examples:: EvaluateAlignment.cpp, ExampleAlignment.cpp, ExampleMinMax.cpp, ExampleRANSAC_double.cpp, ExampleRANSACPlane.cpp, and ExampleTriangulateOptimal.cpp.

Definition at line 355 of file Debug.hh.

Referenced by BIAS::GLProjectionParametersBase::AddDebugLevel(), BIAS::Triangulation::CorrectCorrespondences(), BIAS::FilterBase< InputStorageType, OutputStorageType >::FilterBase(), BIAS::ShowCamWxVideoSourceFactory::OpenDevice(), and BIAS::SceneOpenSceneGraph::SceneOpenSceneGraph().

void BIAS::Debug::AddDebugLevel ( const std::string & name )

inlineinherited

Definition at line 362 of file Debug.hh.

int UnscentedTransform::ComputeSigmaPoints_	(	const Vector< double > &	src_mean,
		const Matrix< double > &	src_cov,
		std::vector< WeightedSigmaPoint > &	sigma_points
	)		const

protectedinherited

The covariance of a n-dimensional vector is approximated using 2n+1 so called sigma points with associated weights.

The points and weights are computed in this function

Returns: 0=ok, <0 on error (bad cov, ...)

Definition at line 138 of file UnscentedTransform.cpp.

References BIAS::UnscentedTransform::Alpha_, BIAS::UnscentedTransform::Beta_, BIAS::Debug::DebugLevelIsSet(), BIAS::Matrix< T >::GetCol(), BIAS::Matrix< T >::GetCols(), BIAS::UnscentedTransform::Kappa_, Lapack_Cholesky_SymmetricPositiveDefinit(), BIAS::Less(), TNT::Matrix< T >::num_cols(), TNT::Matrix< T >::num_rows(), BIAS::Vector< T >::Size(), BIAS::SVD::SqrtT(), and BIAS::UnscentedTransform::UseSVD_.

Referenced by BIAS::UnscentedTransform::Transform().

long BIAS::Debug::ConsumeNextFreeDebuglevel_ ( )

inlineprotectedinherited

returns the next available debuglevel

Author: woelk 09/2006

Definition at line 521 of file Debug.hh.

bool BIAS::Debug::DebugLevelIsSet ( const long int lv ) const

inlineinherited

Examples:: ExampleTriangulateOptimal.cpp.

Definition at line 341 of file Debug.hh.

Referenced by BIAS::GenSynthMatches::_AddUniformDistributedOutliers(), BIAS::GenSynthMatches::_CreateCamMovement(), BIAS::GenSynthMatches::_CreateStatic2DPoints(), BIAS::UnscentedTransform::ComputeSigmaPoints_(), BIAS::Triangulation::CorrectCorrespondences(), BIAS::GenSynthMatches::GetGTNormalizedF(), BIAS::MonteCarloTransform::GetSamples_(), and BIAS::MonteCarloTransform::Transform().

bool BIAS::Debug::DebugLevelIsSet ( const std::string & name ) const

inlineinherited

Definition at line 350 of file Debug.hh.

int BIAS::Debug::GetDebugLevel ( ) const

inlineinherited

Examples:: ExampleCamera.cpp, ExampleCamPoseCalib.cpp, ExampleCopy.cpp, and ExampleParabola.cpp.

Definition at line 332 of file Debug.hh.

Referenced by BIAS::listenthread(), BIAS::Image< StorageType >::operator=(), and BIAS::ImageBase::operator=().

std::ostream& BIAS::Debug::GetDebugStream ( ) const

inlineinherited

Definition at line 405 of file Debug.hh.

void BIAS::Debug::GetDebugStream ( std::ostream & os ) const

inlineinherited

Definition at line 414 of file Debug.hh.

static long int BIAS::Debug::GetGlobalDebugLevel ( )

inlinestaticinherited

Definition at line 431 of file Debug.hh.

long int BIAS::Debug::Name2DebugLevel ( const std::string & name ) const

inlineinherited

looks up a debuglevel in the internal map, returns 0 if not found

Author: woelk 09/2006

Definition at line 454 of file Debug.hh.

long int BIAS::Debug::NewDebugLevel ( const std::string & name )

inlineinherited

creates a new debuglevel

Author: woelk 09/2006

Definition at line 474 of file Debug.hh.

Referenced by BIAS::COSAC< SolutionType >::COSAC(), BIAS::ProjectionParametersPerspectiveDepth::Init(), BIAS::MonteCarloTransform::MonteCarloTransform(), BIAS::PMatrixEstimation::PMatrixEstimation(), BIAS::PreemptiveRANSAC< SolutionType >::PreemptiveRANSAC(), BIAS::RANSACPreKnowledge< SolutionType >::RANSACPreKnowledge(), BIAS::ROI::ROI(), BIAS::RotationAveraging::RotationAveraging(), BIAS::SceneOpenSceneGraph::SceneOpenSceneGraph(), BIAS::ThreeDOutOpenSceneGraph::ThreeDOutOpenSceneGraph(), BIAS::Triangulation::Triangulation(), and BIAS::UnscentedTransform::UnscentedTransform().

void BIAS::Debug::PrintDebugLevel ( std::ostream & os = std::cout ) const

inlineinherited

Definition at line 383 of file Debug.hh.

int Covariance3Dto2D::Project	(	const BIAS::Vector< double > &	Pose,
		const BIAS::Matrix< double > &	Cov_Pose,
		const BIAS::Vector3< double > &	X,
		const BIAS::Matrix3x3< double > &	Cov_X,
		BIAS::Vector2< double > &	x,
		BIAS::Matrix2x2< double > &	Cov_x
	)		const

project covariance onto w=1 plane in camera coordinate system

Returns: 0: ok, -1 if ray behind/parallel to that plane

Definition at line 23 of file Covariance3Dto2D.cpp.

References TNT::Vector< T >::newsize(), TNT::Matrix< T >::newsize(), BIAS::Matrix< T >::SetZero(), BIAS::Vector< T >::Size(), and BIAS::UnscentedTransform::Transform().

void BIAS::Debug::RemoveDebugLevel ( const long int lv )

inlineinherited

Definition at line 369 of file Debug.hh.

void BIAS::Debug::RemoveDebugLevel ( const std::string & name )

inlineinherited

Definition at line 376 of file Debug.hh.

void BIAS::UnscentedTransform::SetAlpha ( const double alpha )

inlineinherited

Sets the alpha parameter.

The alpha parameter determines the spread of the sigma points

Definition at line 80 of file UnscentedTransform.hh.

void BIAS::UnscentedTransform::SetBeta ( const double beta )

inlineinherited

Sets the beta parameter.

beta is used to incorporate prior knowledge of the distribution of x. For Gaussian distributions beta = 2.0 is optiomal

Definition at line 86 of file UnscentedTransform.hh.

void BIAS::Debug::SetDebugLevel ( const long int lv )

inlineinherited

void BIAS::Debug::SetDebugLevel ( const std::string & name )

inlineinherited

Definition at line 325 of file Debug.hh.

void BIAS::Debug::SetDebugStream ( const std::ostream & os )

inlineinherited

Definition at line 398 of file Debug.hh.

static void BIAS::Debug::SetGlobalDebugLevel ( long int lev )

inlinestaticinherited

Definition at line 424 of file Debug.hh.

void BIAS::Covariance3Dto2D::SetK ( const BIAS::KMatrix & K )

inline

Definition at line 59 of file Covariance3Dto2D.hh.

void BIAS::UnscentedTransform::SetUseSVD ( const bool use_svd )

inlineinherited

Definition at line 89 of file UnscentedTransform.hh.

void BIAS::Debug::ShowDebugLevel ( std::ostream & os = std::cout ) const

inlineinherited

prints all internally known debuglevels

Author: woelk 09/2006

Definition at line 496 of file Debug.hh.

int UnscentedTransform::Transform	(	const Vector< double > &	src_mean,
		const Matrix< double > &	src_cov,
		Vector< double > &	dst_mean,
		Matrix< double > &	dst_cov
	)		const

virtualinherited

computes the second order approximation of the transformations of the mean and the associated covariance for the point transformation Transform_().

Returns: 0 on success -1 when transformation of mean failed +1 when transfromation of sigma point failed

Implements BIAS::UncertaintyTransformBase.

Definition at line 52 of file UnscentedTransform.cpp.

References BIAS::UnscentedTransform::ComputeSigmaPoints_(), TNT::Matrix< T >::newsize(), TNT::Matrix< T >::num_cols(), TNT::Matrix< T >::num_rows(), BIAS::Vector< T >::OuterProduct(), BIAS::Vector< T >::SetZero(), BIAS::Matrix< T >::SetZero(), BIAS::Vector< T >::Size(), TNT::Vector< T >::size(), BIAS::Matrix< T >::Trace(), and BIAS::UnscentedTransform::Transform_().

Referenced by BIAS::EssentialPoint2Line::Compute(), BIAS::CovEuler2Quaternion::CTransform(), Project(), BIAS::Covariance3Dto2DHomg::Project(), and BIAS::Cov3Dto2DPoseCertain::Transform().

int Covariance3Dto2D::Transform_	(	const BIAS::Vector< double > &	src,
		BIAS::Vector< double > &	dst
	)		const

protectedvirtual

src is a vector consisting of [ 3d point, camera center, orientation ] The orientation must be represented using one case from E_Parametrization dst is the projection into the image

Implements BIAS::UnscentedTransform.

Definition at line 65 of file Covariance3Dto2D.cpp.

References BIAS::PMatrixBase::Compose(), BIAS::HomgPoint2D::Homogenize(), K_, TNT::Vector< T >::newsize(), BIAS::Vector3< T >::NormL2(), Parametrization_, BIAS::HomgPoint3D::Set(), and BIAS::Vector< T >::Size().