Absolute Orientation

Functions
template<int D>
TooN::Matrix< D >	tag::computeRotation (const std::vector< TooN::Vector< D > > &a, const std::vector< TooN::Vector< D > > &b)
TooN::SO3	tag::computeOrientation (const std::vector< TooN::Vector< 3 > > &a, const std::vector< TooN::Vector< 3 > > &b)
TooN::SO2	tag::computeOrientation (const std::vector< TooN::Vector< 2 > > &a, const std::vector< TooN::Vector< 2 > > &b)
TooN::SO3	tag::computeOrientation (const TooN::Vector< 3 > &a1, const TooN::Vector< 3 > &b1, const TooN::Vector< 3 > &a2, const TooN::Vector< 3 > &b2)
template<int D>
std::pair< TooN::Matrix< D > , TooN::Vector< D > >	tag::computeAbsoluteOrientation (const std::vector< TooN::Vector< D > > &a, const std::vector< TooN::Vector< D > > &b)
TooN::SE3	tag::computeAbsoluteOrientation (const std::vector< TooN::Vector< 3 > > &a, const std::vector< TooN::Vector< 3 > > &b)
TooN::SE2	tag::computeAbsoluteOrientation (const std::vector< TooN::Vector< 2 > > &a, const std::vector< TooN::Vector< 2 > > &b)
template<int D>
std::tr1::tuple< TooN::Matrix < D >, TooN::Vector< D > , TooN::DefaultPrecision >	tag::computeSimilarity (const std::vector< TooN::Vector< D > > &a, const std::vector< TooN::Vector< D > > &b)
TooN::SIM3	tag::computeSimilarity (const std::vector< TooN::Vector< 3 > > &a, const std::vector< TooN::Vector< 3 > > &b)
TooN::SIM2	tag::computeSimilarity (const std::vector< TooN::Vector< 2 > > &a, const std::vector< TooN::Vector< 2 > > &b)
TooN::SO3	tag::computeMeanOrientation (const std::vector< TooN::SO3<> > &r)
TooN::Matrix< 3 >	tag::quaternionToMatrix (const TooN::Vector< 4 > &q)

Detailed Description

contains various functions to calculate rotations and rigid transformations between sets of D-dim correspondences. There are special case functions for 2D and 3D points sets that directly return SO2, SO3, SE2 and SE3 objects.

Function Documentation

template<int D>

std::pair<TooN::Matrix<D>, TooN::Vector<D> > tag::computeAbsoluteOrientation	(	const std::vector< TooN::Vector< D > > &	a,
		const std::vector< TooN::Vector< D > > &	b
	)

computes the rigid transformation between two corresponding D dimensional point sets after Shinji Umeyama, Least-squares estimation of transformation parameters between two point patterns. IEEE PAMI, 13(4):376-380, 1991. The result is a rotation matrix R and a translation vector t that map points from vector a to points from vector b : b[i] = R * a[i] + t

Parameters

[in]	a	vector of D-dim points
[in]	b	vector of D-dim points

Returns

std::pair containing R and t such that b[i] = R * a[i] + t

References tag::Internal::computeOrientationScale().

Referenced by tag::fourPointPose(), and tag::fourPointPoseFromCamera().

TooN::SE3 tag::computeAbsoluteOrientation ( const std::vector< TooN::Vector< 3 > > &  a, const std::vector< TooN::Vector< 3 > > &  b  )

inline

overload of computeAbsoluteOrientation that computes the rigid transformation between two corresponding 3D point sets as an SE3 that maps points from vector a to points from vector b : b[i] = SE3 * a[i]

Parameters

[in]	a	vector of 3D points
[in]	b	vector of 3D points

Returns

TooN::SE3 T containing the transformation such that b = T a

TooN::SE2 tag::computeAbsoluteOrientation ( const std::vector< TooN::Vector< 2 > > &  a, const std::vector< TooN::Vector< 2 > > &  b  )

inline

overload of computeAbsoluteOrientation that computes the rigid transformation between two corresponding 2D point sets as an SE2 that maps points from vector a to points from vector b : b[i] = SE2 * a[i]

Parameters

[in]	a	vector of 2D points
[in]	b	vector of 2D points

Returns

TooN::SE2 T containing the transformation such that b = T a

TooN::SO3 tag::computeMeanOrientation

(

const std::vector< TooN::SO3<> > &

r

)

computes the mean rotation of a set of rotations. This is the rotation R such that R^{-1} * R_i is minimal for all R_i.

Parameters

[in]

r

a vector of rotations

Returns

TooN::SO3 mean rotation of all input rotations

TooN::SO3 tag::computeOrientation ( const std::vector< TooN::Vector< 3 > > &  a, const std::vector< TooN::Vector< 3 > > &  b  )

inline

computes the rotation between two sets of 3D points maximizing b * Ta This function returns only the rotation matrix as an SO3<> computed after Shinji Umeyama, Least-squares estimation of transformation parameters between two point patterns. IEEE PAMI, 13(4):376-380, 1991.

Parameters

[in]	a	vector of 3D points
[in]	b	vector of 3D points

Returns

TooN::SO3 containing the rotation such that b = T a

References tag::Internal::computeOrientationScale().

Referenced by tag::CameraRotation::estimate(), and tag::solveXABX().

TooN::SO2 tag::computeOrientation ( const std::vector< TooN::Vector< 2 > > &  a, const std::vector< TooN::Vector< 2 > > &  b  )

inline

computes the rotation between two sets of 2D points maximizing b * Ta This function returns only the rotation matrix as an SO3<> computed after Shinji Umeyama, Least-squares estimation of transformation parameters between two point patterns. IEEE PAMI, 13(4):376-380, 1991.

Parameters

[in]	a	vector of 2D points
[in]	b	vector of 2D points

Returns

TooN::SO3 containing the rotation such that b = T a

References tag::Internal::computeOrientationScale().

TooN::SO3 tag::computeOrientation	(	const TooN::Vector< 3 > &	a1,
		const TooN::Vector< 3 > &	b1,
		const TooN::Vector< 3 > &	a2,
		const TooN::Vector< 3 > &	b2
	)

directly computes a rotation between two pairs of rays in space maximizing b * T a its about 8x faster then using the general computeOrientation for 2 correspondences.

Parameters

[in]	a1	first input vector
[in]	b1	first output vector
[in]	a2	second input vector
[in]	b2	second output vector

Returns

TooN::SO3 containing the rotation such that b = T a

References tag::canonicalOrientation().

template<int D>

TooN::Matrix<D> tag::computeRotation ( const std::vector< TooN::Vector< D > > &  a, const std::vector< TooN::Vector< D > > &  b  )

inline

computes the rotation between two sets of D-dim points maximizing b * Ta This function returns only the rotation matrix computed after Shinji Umeyama, Least-squares estimation of transformation parameters between two point patterns. IEEE PAMI, 13(4):376-380, 1991.

Parameters

[in]	a	vector of D-dim points
[in]	b	vector of D-dim points

Returns

DxD matrix R describing the rotation such that b = R a

References tag::Internal::computeOrientationScale().

template<int D>

std::tr1::tuple<TooN::Matrix<D>, TooN::Vector<D>, TooN::DefaultPrecision > tag::computeSimilarity	(	const std::vector< TooN::Vector< D > > &	a,
		const std::vector< TooN::Vector< D > > &	b
	)

computes the rigid transformation between two corresponding D dimensional point sets after Shinji Umeyama, Least-squares estimation of transformation parameters between two point patterns. IEEE PAMI, 13(4):376-380, 1991. The result is a rotation matrix R, a scale factor s and a translation vector t that map points from vector a to points from vector b : b[i] = s * R * a[i] + t

Parameters

[in]	a	vector of D-dim points
[in]	b	vector of D-dim points

Returns

std::tuple containing R, t and s such that b[i] = s * R * a[i] + t

References tag::Internal::computeOrientationScale(), and make_tuple.

TooN::SIM3 tag::computeSimilarity ( const std::vector< TooN::Vector< 3 > > &  a, const std::vector< TooN::Vector< 3 > > &  b  )

inline

alternative to computeSimilarity that computes the rigid transformation between two corresponding 3D point sets as an SE3 and a scale S that maps points from vector a to points from vector b : b[i] = SE3 * S * a[i]

Parameters

[in]	a	vector of 3D points
[in]	b	vector of 3D points

Returns

a pair consisting of a TooN::SE3 T and a double S containing the transformation such that b = T * S * a

TooN::SIM2 tag::computeSimilarity ( const std::vector< TooN::Vector< 2 > > &  a, const std::vector< TooN::Vector< 2 > > &  b  )

inline

alternative to computeSimilarity that computes the rigid transformation between two corresponding 2D point sets as an SE2 and a scale S that maps points from vector a to points from vector b : b[i] = SE2 * S * a[i]

Parameters

[in]	a	vector of 2D points
[in]	b	vector of 2D points

Returns

a pair consisting of a TooN::SE2 T and a double S containing the transformation such that b = T * S * a

TooN::Matrix< 3 > tag::quaternionToMatrix

(

const TooN::Vector< 4 > &

q

)

computes a rotation matrix corresponding to a unit quaternion. The quaternion is in the format (q0,qx,qy,qz).

Parameters

[in]

q

a 4-vector containing the coefficients of a unit quaternion as (q0,qx,qy,qz)

Returns

a 3x3 rotation matrix corresponding to the quaternion