Computes similarity transformation between 3D point sets. More...

#include <Geometry/AbsoluteOrientation.hh>

Public Types
enum	RotationEstimationMethod { HORN_ALGORITHM, KABSCH_ALGORITHM }
	Methods for rotation estimation. More...

Public Member Functions
	AbsoluteOrientation ()

int	Compute (const std::vector< Vector3< double > > &X, const std::vector< Vector3< double > > &Y, RMatrix &dR, Vector3< double > &dt, double &ds, const std::vector< double > &w=std::vector< double >(0))
	Computes rotation dR, translation dt and isometric scale ds between coordinate systems from corresponding 3D point sets X and Y. More...

int	Compute (const std::vector< Vector3< double > > &X, const std::vector< Vector3< double > > &Y, RMatrix &dR, Vector3< double > &dt, const std::vector< double > &w=std::vector< double >(0))
	Computes rotation dR and translation dt between coordinate systems from corresponding 3D point sets X and Y. More...

int	ComputeRotation (const std::vector< Vector3< double > > &X, const std::vector< Vector3< double > > &Y, RMatrix &dR, const std::vector< double > &w=std::vector< double >(0))
	Computes rotation dR between corresponding 3D ray sets X and Y using the currently set algorithm. More...

double	GetResidualErrors (std::vector< double > &errors, const std::vector< Vector3< double > > &X, const std::vector< Vector3< double > > &Y, const RMatrix &dR, const Vector3< double > &dt, const double &ds=1.0, const std::vector< double > &w=std::vector< double >(0))
	Computes residual errors of 3D point sets X and Y with respect to given rotation dR, translation dt and isometric scale ds. More...

double	GetResidualErrors (std::vector< double > &errors, const std::vector< Vector3< double > > &X, const std::vector< Vector3< double > > &Y, const std::vector< Matrix3x3< double > > &CovX, const std::vector< Matrix3x3< double > > &CovY, const RMatrix &dR, const Vector3< double > &dt, const double &ds=1.0)
	Computes residual errors of 3D point sets X and Y with covariances CovX, CovY with respect to given rotation dR, translation dt and isometric scale ds. More...

double	GetResidualErrors (std::vector< double > &errors, const std::vector< Vector3< double > > &X, const std::vector< Vector3< double > > &Y, const RMatrix &dR, const std::vector< double > &w=std::vector< double >(0))
	Computes residual errors of 3D point sets X and Y with respect to given rotation dR. More...

double	GetResidualErrors (std::vector< double > &errors, const std::vector< Vector3< double > > &X, const std::vector< Vector3< double > > &Y, const std::vector< Matrix3x3< double > > &CovX, const std::vector< Matrix3x3< double > > &CovY, const RMatrix &dR)
	Computes residual errors of 3D point sets X and Y with covariances CovX, CovY with respect to given rotation dR. More...

void	SetRotationAlgorithm (RotationEstimationMethod algorithm)
	Set algorithm used for rotation estimation. More...

	~AbsoluteOrientation ()

Static Public Attributes
static const unsigned int	MIN_CORRESPONDENCES = 3

Friends
class	AbsoluteOrientationRANSAC

Detailed Description

Computes similarity transformation between 3D point sets.

Estimates the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of 3D points in both systems. A SVD-based solution to the least-squares problem for at least three points is used based on an approach proposed in:

[1] B. Horn: Closed-form Solution of Absolute Orientation Using Unit Quaternions, 1987.

Another SVD-based solution estimating a rotation matrix directly instead of using unit quaternions is given by Kabsch's algorithm:

[2] W. Kabsch: A Solution for the Best Rotation to Relate Two Sets of Vectors, 1976.

Note: The transformation between the coordinate systems is given as rotation dR, translation dt, and isometric scale ds, such that points X in the first coordinate system are related to points Y in the second coordinate system by Y = ds*dR*X + dt.

Todo:: Implement Horn's closed-form solution and compare with our SVD-based approach!

Author: esquivel

Date: 12/2008

Examples:: ExampleAbsoluteOrientation.cpp.

Definition at line 64 of file AbsoluteOrientation.hh.

Member Enumeration Documentation

enum BIAS::AbsoluteOrientation::RotationEstimationMethod

Methods for rotation estimation.

Enumerator
HORN_ALGORITHM
KABSCH_ALGORITHM

Examples:: ExampleAbsoluteOrientation.cpp.

Definition at line 72 of file AbsoluteOrientation.hh.

Constructor & Destructor Documentation

AbsoluteOrientation::AbsoluteOrientation ( )

Definition at line 15 of file AbsoluteOrientation.cpp.

AbsoluteOrientation::~AbsoluteOrientation ( )

Definition at line 20 of file AbsoluteOrientation.cpp.

Member Function Documentation

int BIAS::AbsoluteOrientation::Compute	(	const std::vector< Vector3< double > > &	X,
		const std::vector< Vector3< double > > &	Y,
		RMatrix &	dR,
		Vector3< double > &	dt,
		double &	ds,
		const std::vector< double > &	w = `std::vector<double>(0)`
	)

inline

Computes rotation dR, translation dt and isometric scale ds between coordinate systems from corresponding 3D point sets X and Y.

Returns: -1 if computation failed, else 0.

Examples:: ExampleAbsoluteOrientation.cpp.

Definition at line 84 of file AbsoluteOrientation.hh.

int BIAS::AbsoluteOrientation::Compute	(	const std::vector< Vector3< double > > &	X,
		const std::vector< Vector3< double > > &	Y,
		RMatrix &	dR,
		Vector3< double > &	dt,
		const std::vector< double > &	w = `std::vector<double>(0)`
	)

inline

Computes rotation dR and translation dt between coordinate systems from corresponding 3D point sets X and Y.

Returns: -1 if computation failed, else 0.

Definition at line 95 of file AbsoluteOrientation.hh.

int AbsoluteOrientation::ComputeRotation	(	const std::vector< Vector3< double > > &	X,
		const std::vector< Vector3< double > > &	Y,
		BIAS::RMatrix &	dR,
		const std::vector< double > &	w = `std::vector<double>(0)`
	)

Computes rotation dR between corresponding 3D ray sets X and Y using the currently set algorithm.

Returns: -1 if computation failed, else 0.

Definition at line 117 of file AbsoluteOrientation.cpp.

References HORN_ALGORITHM, and KABSCH_ALGORITHM.

double AbsoluteOrientation::GetResidualErrors	(	std::vector< double > &	errors,
		const std::vector< Vector3< double > > &	X,
		const std::vector< Vector3< double > > &	Y,
		const RMatrix &	dR,
		const Vector3< double > &	dt,
		const double &	ds = `1.0`,
		const std::vector< double > &	w = `std::vector<double>(0)`
	)

Computes residual errors of 3D point sets X and Y with respect to given rotation dR, translation dt and isometric scale ds.

Note: Each error is given by (weighted) Euclidean distance dist(X',Y) with X' = ds*dR*X - dt for corresponding 3D points X and Y.

Returns: Sum of squared errors dist(X',Y) with X' = ds*dR*X - dt and residual error for each single correspondence.

Examples:: ExampleAbsoluteOrientation.cpp.

Definition at line 243 of file AbsoluteOrientation.cpp.

References BIAS::Vector3< T >::ScalarProduct().

Referenced by GetResidualErrors(), and BIAS::AbsoluteOrientationRANSAC::GetResidualErrors().

double AbsoluteOrientation::GetResidualErrors	(	std::vector< double > &	errors,
		const std::vector< Vector3< double > > &	X,
		const std::vector< Vector3< double > > &	Y,
		const std::vector< Matrix3x3< double > > &	CovX,
		const std::vector< Matrix3x3< double > > &	CovY,
		const RMatrix &	dR,
		const Vector3< double > &	dt,
		const double &	ds = `1.0`
	)

Computes residual errors of 3D point sets X and Y with covariances CovX, CovY with respect to given rotation dR, translation dt and isometric scale ds.

Note: Computes Mahalanobis distances instead of Euclidean distances!

Returns: Sum of squared errors mahalanobis(X',Y) with X' = ds*dR*X - dt as well as residual error for each single correspondence.

Definition at line 276 of file AbsoluteOrientation.cpp.

References BIAS::Matrix3x3< T >::GetInverse(), BIAS::Matrix3x3< T >::Mult(), BIAS::Vector3< T >::ScalarProduct(), and BIAS::Matrix3x3< T >::Transpose().

double AbsoluteOrientation::GetResidualErrors	(	std::vector< double > &	errors,
		const std::vector< Vector3< double > > &	X,
		const std::vector< Vector3< double > > &	Y,
		const RMatrix &	dR,
		const std::vector< double > &	w = `std::vector<double>(0)`
	)

Computes residual errors of 3D point sets X and Y with respect to given rotation dR.

Note: Each error is given by (weighted) Euclidean distance dist(X',Y) with X' = dR*X for corresponding 3D points X and Y.

Returns: Sum of squared errors dist(X',Y) with X' = dR*X and residual error for each single correspondence.

Definition at line 308 of file AbsoluteOrientation.cpp.

References GetResidualErrors().

double AbsoluteOrientation::GetResidualErrors	(	std::vector< double > &	errors,
		const std::vector< Vector3< double > > &	X,
		const std::vector< Vector3< double > > &	Y,
		const std::vector< Matrix3x3< double > > &	CovX,
		const std::vector< Matrix3x3< double > > &	CovY,
		const RMatrix &	dR
	)