BIAS::RotationAveraging Class Reference

Computes mean of rotations due to different measures. More...

#include <Geometry/RotationAveraging.hh>

Inheritance diagram for BIAS::RotationAveraging:

Collaboration diagram for BIAS::RotationAveraging:

Public Member Functions
void	AddDebugLevel (const long int lv)
void	AddDebugLevel (const std::string &name)
int	ChordalL2Mean (const std::vector< BIAS::RMatrix > &R, BIAS::RMatrix &meanR)
	Compute chordal L2-mean of rotations. More...
int	ChordalL2Mean (const std::vector< BIAS::Quaternion< double > > &Q, BIAS::Quaternion< double > &meanQ)
	Compute chordal L2-mean of rotations using unit quaternions. More...
bool	DebugLevelIsSet (const long int lv) const
bool	DebugLevelIsSet (const std::string &name) const
int	GeodesicL1Mean (const std::vector< BIAS::RMatrix > &R, BIAS::RMatrix &meanR)
	Compute geodesic L1-mean (geodesic median) of rotations. More...
int	GeodesicL2Mean (const std::vector< BIAS::RMatrix > &R, BIAS::RMatrix &meanR)
	Compute geodesic L2-mean (Karcher/geometric mean) of rotations. More...
int	GetDebugLevel () const
std::ostream &	GetDebugStream () const
void	GetDebugStream (std::ostream &os) const
int	LogarithmicL2Mean (const std::vector< BIAS::RMatrix > &R, BIAS::RMatrix &meanR)
	Compute matrix logarithm L2-mean of rotations. More...
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	QuaternionL2Mean (const std::vector< BIAS::RMatrix > &R, BIAS::RMatrix &meanR)
	Compute quaternion L2-mean of rotations. More...
int	QuaternionL2Mean (const std::vector< BIAS::Quaternion< double > > &Q, BIAS::Quaternion< double > &meanQ)
	Compute quaternion L2-mean of rotations. More...
void	RemoveDebugLevel (const long int lv)
void	RemoveDebugLevel (const std::string &name)
	RotationAveraging ()
void	SetDebugLevel (const long int lv)
void	SetDebugLevel (const std::string &name)
void	SetDebugStream (const std::ostream &os)
void	SetMaxIterations (unsigned int num)
	Set maximal number of iterations for geodesic L1-/L2-mean computation. More...
void	SetTolerance (double epsilon)
	Set threshold for convergence of iterative geodesic L1-/L2-mean computation. More...
void	ShowDebugLevel (std::ostream &os=std::cout) const
	prints all internally known debuglevels More...
	~RotationAveraging ()

Static Public Member Functions
static long int	GetGlobalDebugLevel ()
static void	SetGlobalDebugLevel (long int lev)

Protected Member Functions
long	ConsumeNextFreeDebuglevel_ ()
	returns the next available debuglevel 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

Static Protected Attributes
static std::ostream	_zDebugStream
static long int	GlobalDebugLevel = 0

Detailed Description

Computes mean of rotations due to different measures.

Author

esquivel

Date

09/2011

This tool computes the average rotation of given rotations R_1,...,R_n with respect to different distance measures d: SO(3) x SO(3) -> R on rotations as described in [1]. The L2-mean for a given d is defined by the rotation matrix R from mean(R_1,...,R_n) = {i=1}^N d(R,R_i)^2 while the L1-mean is given by {i=1}^N d(R,R_i).

Implemented so far are:

• geodesic L2-mean (Karcher mean): d_geod(R,S) = |log(RS')| where the rotation matrix logarithm computes the angle-axis representation theta*r for a rotation matrix R, hence d_geod(R,S) returns the rotation angle theta of the matrix RS'
• quaternion L2-mean: d_quat(R,S) = min(|r-s|,|r+s|) where r,s are the unit quaternion representations of rotation matrices R,S, hence d_quat(R,S) returns 2*sin(theta/4)
• chordal L2-mean: d_chor(R,S) = |R-S|_F = 2*sqrt(2)*sin(theta/2)
• geodesic L1-mean (geodesic median): computed via Weiszfeld algorithm [2]
• logarithmic L2-mean: computes R = exp(mean(log(R_1),...,log(R_n)))

While closed form solutions exist for the L2-means (except geodesic mean), iterative algorithms are given for the geodesic L1-/L2-mean.

The solution is in general only optimal under the assumptions that the rotation angles of all R_i are less than 180 degree resp. all rotations cover less than a hemisphere of the space SO(3).

[1] Y. Dai, J. Trumpf, H. Li, N. Barnes & R. Hartley: "Rotation Averaging with Application to Camera-Rig Calibration", 2009. [2] R. Hartley, K. Aftab, J. Trumpf: "L1 Rotation Averaging Using the Weiszfeld Algorithm", 2011.

Definition at line 55 of file RotationAveraging.hh.

Constructor & Destructor Documentation

RotationAveraging::RotationAveraging

(

)

Definition at line 14 of file RotationAveraging.cpp.

References BIAS::Debug::NewDebugLevel().

BIAS::RotationAveraging::~RotationAveraging ( )

inline

Definition at line 61 of file RotationAveraging.hh.

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 RotationAveraging::ChordalL2Mean	(	const std::vector< BIAS::RMatrix > &	R,
		BIAS::RMatrix &	meanR
	)

Compute chordal L2-mean of rotations.

Parameters

[in]	R	Input rotation matrices to compute the average for
[out]	meanR	Output average rotation matrix

Returns

Returns 0 on success, < 0 otherwise.

Definition at line 154 of file RotationAveraging.cpp.

References BIAS::RMatrix::EnforceConstraints(), and BIAS::MatrixZero.

int RotationAveraging::ChordalL2Mean	(	const std::vector< BIAS::Quaternion< double > > &	Q,
		BIAS::Quaternion< double > &	meanQ
	)

Compute chordal L2-mean of rotations using unit quaternions.

Parameters

[in]	Q	Input unit quaternions to compute the average for
[out]	meanQ	Output average rotation as unit quaternion

Returns

Returns 0 on success, < 0 otherwise.

Definition at line 170 of file RotationAveraging.cpp.

References BIAS::Matrix< T >::GetCol(), BIAS::SVD::GetV(), BIAS::MatrixZero, BIAS::Quaternion< T >::Normalize(), and BIAS::Vector4< T >::SetZero().

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 RotationAveraging::GeodesicL1Mean	(	const std::vector< BIAS::RMatrix > &	R,
		BIAS::RMatrix &	meanR
	)

Compute geodesic L1-mean (geodesic median) of rotations.

Parameters

[in]	R	Input rotation matrices to compute the average for
[out]	meanR	Output average rotation matrix

Returns

Returns 0 on success, < 0 otherwise.

Definition at line 21 of file RotationAveraging.cpp.

References BIAS::Equal(), GeodesicL2Mean(), BIAS::RMatrixBase::GetRotationAxisAngle(), BIAS::Vector3< T >::MultiplyIP(), BIAS::Vector3< T >::Normalize(), BIAS::Vector3< T >::NormL2(), BIAS::RMatrixBase::Set(), BIAS::Vector3< T >::SetZero(), and BIAS::Matrix3x3< T >::Transpose().

int RotationAveraging::GeodesicL2Mean	(	const std::vector< BIAS::RMatrix > &	R,
		BIAS::RMatrix &	meanR
	)

Compute geodesic L2-mean (Karcher/geometric mean) of rotations.

Parameters

[in]	R	Input rotation matrices to compute the average for
[out]	meanR	Output average rotation matrix

Returns

Returns 0 on success, < 0 otherwise.

Definition at line 69 of file RotationAveraging.cpp.

References BIAS::RMatrixBase::GetRotationAxisAngle(), BIAS::Vector3< T >::Normalize(), BIAS::Vector3< T >::NormL2(), BIAS::RMatrixBase::Set(), BIAS::Vector3< T >::SetZero(), and BIAS::Matrix3x3< T >::Transpose().

Referenced by GeodesicL1Mean().

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.

int RotationAveraging::LogarithmicL2Mean	(	const std::vector< BIAS::RMatrix > &	R,
		BIAS::RMatrix &	meanR
	)

Compute matrix logarithm L2-mean of rotations.

The matrix logarithm of a rotation matrix is the angle/axis vector phi * r, also known as the modified Rodrigues vector.

Parameters

[in]	R	Input rotation matrices to compute the average for
[out]	meanR	Output average rotation matrix

Returns

Returns 0 on success, < 0 otherwise.

Definition at line 140 of file RotationAveraging.cpp.

References BIAS::Vector3< T >::MultiplyIP(), and BIAS::RMatrixBase::SetFromAxisAngle().

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(), 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 RotationAveraging::QuaternionL2Mean	(	const std::vector< BIAS::RMatrix > &	R,
		BIAS::RMatrix &	meanR
	)

Compute quaternion L2-mean of rotations.

Parameters

[in]	R	Input rotation matrices to compute the average for
[out]	meanR	Output average rotation matrix

Returns

Returns 0 on success, < 0 otherwise.

Definition at line 106 of file RotationAveraging.cpp.

References BIAS::RMatrixBase::SetFromQuaternion().

int RotationAveraging::QuaternionL2Mean	(	const std::vector< BIAS::Quaternion< double > > &	Q,
		BIAS::Quaternion< double > &	meanQ
	)

Compute quaternion L2-mean of rotations.

Parameters

[in]	Q	Input unit quaternions to compute the average for
[out]	meanQ	Output average rotation as unit quaternion

Returns

Returns 0 on success, < 0 otherwise.

Definition at line 123 of file RotationAveraging.cpp.

References BIAS::Vector4< T >::MultiplyIP(), BIAS::Quaternion< T >::Normalize(), and BIAS::Vector4< T >::SetZero().

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

inlineinherited

Examples:

ExampleCamera.cpp, ExampleCamPoseCalib.cpp, ExampleCopy.cpp, ExampleDcam.cpp, ExampleDcamImageConvert.cpp, ExampleDirectToDisk.cpp, ExampleGrabTrippleFromXB3.cpp, ExampleHarrisColor.cpp, ExampleLDA.cpp, ExampleLineMatcher.cpp, ExampleMDCamToShm.cpp, ExampleParabola.cpp, ExamplePMatrix.cpp, ExamplePtGreyHiresColor.cpp, ExampleVideoSource_Shm.cpp, and Scan1394Bus.cpp.

Definition at line 318 of file Debug.hh.

Referenced by BIAS::ShowCamWxVideoSourceFactory::CreateBumbleBee(), BIAS::ShowCamWxVideoSourceFactory::CreateDCAM(), BIAS::VideoSource_MDcam::ScanBus(), BIAS::GLProjectionParametersBase::SetDebugLevel(), BIAS::VideoSource_Disk::VideoSource_Disk(), BIAS::VideoSource_DV2::VideoSource_DV2(), BIAS::VideoSource_DV::VideoSource_DV_Internal_Init_(), and BIAS::VideoSource_V4L::VideoSource_V4L().

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::RotationAveraging::SetMaxIterations ( unsigned int  num )

inline

Set maximal number of iterations for geodesic L1-/L2-mean computation.

Parameters

[in]

num

Maximal number of iterations

Definition at line 71 of file RotationAveraging.hh.

void BIAS::RotationAveraging::SetTolerance ( double  epsilon )

inline

Set threshold for convergence of iterative geodesic L1-/L2-mean computation.

The algorithm stops if the angular update is less.

Parameters

[in]

epsilon

Threshold for convergence in radians

Definition at line 66 of file RotationAveraging.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.

Member Data Documentation

long int BIAS::Debug::_liDebugLevel

protectedinherited

Definition at line 510 of file Debug.hh.

Referenced by BIAS::Debug::operator=(), and BIAS::ImageBase::operator=().

long int BIAS::Debug::_liNextDebugLevel

protectedinherited

new concept, debuglevel are managed here in the debug class

Definition at line 516 of file Debug.hh.

Referenced by BIAS::Debug::operator=().

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

protectedinherited

Definition at line 517 of file Debug.hh.

Referenced by BIAS::Debug::operator=().

std::ostream BIAS::Debug::_zDebugStream

staticprotectedinherited

Definition at line 511 of file Debug.hh.

Referenced by BIAS::Debug::operator=().

long int BIAS::Debug::GlobalDebugLevel = 0

staticprotectedinherited

Definition at line 513 of file Debug.hh.

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

• Geometry/RotationAveraging.hh
• Geometry/RotationAveraging.cpp