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Public Member Functions | Static Public Member Functions | Private Attributes
WSymmetricSphericalHarmonic< T > Class Template Reference

Class for symmetric spherical harmonics The index scheme of the coefficients/basis values is like in the Descoteaux paper "Regularized, Fast, and Robust Analytical Q-Ball Imaging". More...

#include <WSymmetricSphericalHarmonic.h>

List of all members.

Public Member Functions

 WSymmetricSphericalHarmonic ()
 Default constructor.
 WSymmetricSphericalHarmonic (const WValue< T > &SHCoefficients)
 Constructor.
virtual ~WSymmetricSphericalHarmonic ()
 Destructor.
getValue (T theta, T phi) const
 Return the value on the sphere.
getValue (const WUnitSphereCoordinates< T > &coordinates) const
 Return the value on the sphere.
const WValue< T > & getCoefficients () const
 Returns the used coefficients (stored like in the mentioned 2007 Descoteaux paper).
WValue< T > getCoefficientsSchultz () const
 Returns the coefficients for Schultz' SH base.
WValue< std::complex< T > > getCoefficientsComplex () const
 Returns the coefficients for the complex base.
void applyFunkRadonTransformation (WMatrix< T > const &frtMat)
 Applies the Funk-Radon-Transformation.
size_t getOrder () const
 Return the order of the spherical harmonic.
calcGFA (std::vector< WUnitSphereCoordinates< T > > const &orientations) const
 Calculate the generalized fractional anisotropy for this ODF.
calcGFA (WMatrix< T > const &B) const
 Calculate the generalized fractional anisotropy for this ODF.
void normalize ()
 Normalize this SH in place.

Static Public Member Functions

static WMatrix< T > getSHFittingMatrix (const std::vector< WMatrixFixed< T, 3, 1 > > &orientations, int order, T lambda, bool withFRT)
 This calculates the transformation/fitting matrix T like in the 2007 Descoteaux paper.
static WMatrix< T > getSHFittingMatrix (const std::vector< WUnitSphereCoordinates< T > > &orientations, int order, T lambda, bool withFRT)
 This calculates the transformation/fitting matrix T like in the 2007 Descoteaux paper.
static WMatrix< T > getSHFittingMatrixForConstantSolidAngle (const std::vector< WMatrixFixed< T, 3, 1 > > &orientations, int order, T lambda)
 This calculates the transformation/fitting matrix T like in the 2010 Aganj paper.
static WMatrix< T > getSHFittingMatrixForConstantSolidAngle (const std::vector< WUnitSphereCoordinates< T > > &orientations, int order, T lambda)
 This calculates the transformation/fitting matrix T like in the 2010 Aganj paper.
static WMatrix< T > calcBaseMatrix (const std::vector< WUnitSphereCoordinates< T > > &orientations, int order)
 Calculates the base matrix B like in the dissertation of Descoteaux.
static WMatrix< std::complex< T > > calcComplexBaseMatrix (std::vector< WUnitSphereCoordinates< T > > const &orientations, int order)
 Calculates the base matrix B for the complex spherical harmonics.
static WValue< T > calcEigenvalues (size_t order)
 Calc eigenvalues for SH elements.
static WMatrix< T > calcMatrixWithEigenvalues (size_t order)
 Calc matrix with the eigenvalues of the SH elements on its diagonal.
static WMatrix< T > calcSmoothingMatrix (size_t order)
 This calcs the smoothing matrix L from the 2007 Descoteaux Paper "Regularized, Fast, and Robust Analytical Q-Ball Imaging".
static WMatrix< T > calcFRTMatrix (size_t order)
 Calculates the Funk-Radon-Transformation-Matrix P from the 2007 Descoteaux Paper "Regularized, Fast, and Robust Analytical Q-Ball Imaging".
static WMatrix< T > calcSHToTensorSymMatrix (std::size_t order)
 Calculates a matrix that converts spherical harmonics to symmetric tensors of equal or lower order.
static WMatrix< T > calcSHToTensorSymMatrix (std::size_t order, const std::vector< WUnitSphereCoordinates< T > > &orientations)
 Calculates a matrix that converts spherical harmonics to symmetric tensors of equal or lower order.

Private Attributes

size_t m_order
 order of the spherical harmonic
WValue< T > m_SHCoefficients
 coefficients of the spherical harmonic

Detailed Description

template<typename T>
class WSymmetricSphericalHarmonic< T >

Class for symmetric spherical harmonics The index scheme of the coefficients/basis values is like in the Descoteaux paper "Regularized, Fast, and Robust Analytical Q-Ball Imaging".

Definition at line 51 of file WSymmetricSphericalHarmonic.h.


Constructor & Destructor Documentation

Default constructor.

Definition at line 279 of file WSymmetricSphericalHarmonic.h.

template<typename T >
WSymmetricSphericalHarmonic< T >::WSymmetricSphericalHarmonic ( const WValue< T > &  SHCoefficients) [explicit]

Constructor.

Parameters:
SHCoefficientsthe initial coefficients (stored like in the mentioned Descoteaux paper).

Definition at line 286 of file WSymmetricSphericalHarmonic.h.

References WSymmetricSphericalHarmonic< T >::m_order, and WSymmetricSphericalHarmonic< T >::m_SHCoefficients.

template<typename T >
WSymmetricSphericalHarmonic< T >::~WSymmetricSphericalHarmonic ( ) [virtual]

Destructor.

Definition at line 296 of file WSymmetricSphericalHarmonic.h.


Member Function Documentation

template<typename T >
void WSymmetricSphericalHarmonic< T >::applyFunkRadonTransformation ( WMatrix< T > const &  frtMat)

Applies the Funk-Radon-Transformation.

This is faster than matrix multiplication. ( O(n) instead of O(n²) )

Parameters:
frtMatthe frt matrix as calculated by calcFRTMatrix()

Definition at line 491 of file WSymmetricSphericalHarmonic.h.

References WMatrix< T >::getNbCols(), and WMatrix< T >::getNbRows().

template<typename T >
WMatrix< T > WSymmetricSphericalHarmonic< T >::calcBaseMatrix ( const std::vector< WUnitSphereCoordinates< T > > &  orientations,
int  order 
) [static]

Calculates the base matrix B like in the dissertation of Descoteaux.

Parameters:
orientationsThe vector with the used orientation on the unit sphere (usually the gradients of the HARDI)
orderThe order of the spherical harmonics intended to create
Returns:
The base Matrix B

Definition at line 601 of file WSymmetricSphericalHarmonic.h.

template<typename T >
WMatrix< std::complex< T > > WSymmetricSphericalHarmonic< T >::calcComplexBaseMatrix ( std::vector< WUnitSphereCoordinates< T > > const &  orientations,
int  order 
) [static]

Calculates the base matrix B for the complex spherical harmonics.

Parameters:
orientationsThe vector with the used orientation on the unit sphere (usually the gradients of the HARDI)
orderThe order of the spherical harmonics intended to create
Returns:
The base Matrix B

Definition at line 637 of file WSymmetricSphericalHarmonic.h.

template<typename T >
WValue< T > WSymmetricSphericalHarmonic< T >::calcEigenvalues ( size_t  order) [static]

Calc eigenvalues for SH elements.

Parameters:
orderThe order of the spherical harmonic
Returns:
The eigenvalues of the coefficients

Definition at line 667 of file WSymmetricSphericalHarmonic.h.

template<typename T >
WMatrix< T > WSymmetricSphericalHarmonic< T >::calcFRTMatrix ( size_t  order) [static]

Calculates the Funk-Radon-Transformation-Matrix P from the 2007 Descoteaux Paper "Regularized, Fast, and Robust Analytical Q-Ball Imaging".

Parameters:
orderThe order of the spherical harmonic
Returns:
The Funk-Radon-Matrix P

Definition at line 708 of file WSymmetricSphericalHarmonic.h.

template<typename T >
T WSymmetricSphericalHarmonic< T >::calcGFA ( std::vector< WUnitSphereCoordinates< T > > const &  orientations) const

Calculate the generalized fractional anisotropy for this ODF.

See: David S. Tuch, "Q-Ball Imaging", Magn. Reson. Med. 52, 2004, 1358-1372

Notes:
this only makes sense if this is an ODF, meaning funk-radon-transform was applied etc.
Parameters:
orientationsA vector of unit sphere coordinates.
Returns:
The generalized fractional anisotropy.

Definition at line 395 of file WSymmetricSphericalHarmonic.h.

template<typename T >
T WSymmetricSphericalHarmonic< T >::calcGFA ( WMatrix< T > const &  B) const

Calculate the generalized fractional anisotropy for this ODF.

This version of the function uses precomputed base functions (because calculating the base function values is rather expensive). Use this version if you want to compute the GFA for multiple ODFs with the same base functions. The base function Matrix can be computed using

See also:
calcBMatrix().

See: David S. Tuch, "Q-Ball Imaging", Magn. Reson. Med. 52, 2004, 1358-1372

Notes:
this only makes sense if this is an ODF, meaning funk-radon-transform was applied etc.
Parameters:
BThe matrix of SH base functions.
Returns:
The generalized fractional anisotropy.

Definition at line 439 of file WSymmetricSphericalHarmonic.h.

References WMatrix< T >::getNbCols(), and WMatrix< T >::getNbRows().

template<typename T >
WMatrix< T > WSymmetricSphericalHarmonic< T >::calcMatrixWithEigenvalues ( size_t  order) [static]

Calc matrix with the eigenvalues of the SH elements on its diagonal.

Parameters:
orderThe order of the spherical harmonic
Returns:
The matrix with the eigenvalues of the coefficients

Definition at line 684 of file WSymmetricSphericalHarmonic.h.

References WValue< T >::size().

template<typename T >
WMatrix< T > WSymmetricSphericalHarmonic< T >::calcSHToTensorSymMatrix ( std::size_t  order) [static]

Calculates a matrix that converts spherical harmonics to symmetric tensors of equal or lower order.

Parameters:
orderThe order of the symmetric tensor.
Returns:
the conversion matrix

Definition at line 727 of file WSymmetricSphericalHarmonic.h.

template<typename T >
WMatrix< T > WSymmetricSphericalHarmonic< T >::calcSHToTensorSymMatrix ( std::size_t  order,
const std::vector< WUnitSphereCoordinates< T > > &  orientations 
) [static]

Calculates a matrix that converts spherical harmonics to symmetric tensors of equal or lower order.

Parameters:
orderThe order of the symmetric tensor.
orientationsA vector of at least (orderTensor+1) * (orderTensor+2) / 2 orientations.
Returns:
the conversion matrix

Definition at line 747 of file WSymmetricSphericalHarmonic.h.

template<typename T >
WMatrix< T > WSymmetricSphericalHarmonic< T >::calcSmoothingMatrix ( size_t  order) [static]

This calcs the smoothing matrix L from the 2007 Descoteaux Paper "Regularized, Fast, and Robust Analytical Q-Ball Imaging".

Parameters:
orderThe order of the spherical harmonic
Returns:
The smoothing matrix L

Definition at line 696 of file WSymmetricSphericalHarmonic.h.

References WValue< T >::size().

template<typename T >
const WValue< T > & WSymmetricSphericalHarmonic< T >::getCoefficients ( ) const

Returns the used coefficients (stored like in the mentioned 2007 Descoteaux paper).

Returns:
coefficient list

Definition at line 334 of file WSymmetricSphericalHarmonic.h.

template<typename T >
WValue< std::complex< T > > WSymmetricSphericalHarmonic< T >::getCoefficientsComplex ( ) const

Returns the coefficients for the complex base.

Returns:
coefficiend list

Definition at line 364 of file WSymmetricSphericalHarmonic.h.

template<typename T >
WValue< T > WSymmetricSphericalHarmonic< T >::getCoefficientsSchultz ( ) const

Returns the coefficients for Schultz' SH base.

Returns:
coefficient list

Definition at line 340 of file WSymmetricSphericalHarmonic.h.

template<typename T >
size_t WSymmetricSphericalHarmonic< T >::getOrder ( ) const

Return the order of the spherical harmonic.

Returns:
order of SH

Definition at line 503 of file WSymmetricSphericalHarmonic.h.

template<typename T >
WMatrix< T > WSymmetricSphericalHarmonic< T >::getSHFittingMatrix ( const std::vector< WMatrixFixed< T, 3, 1 > > &  orientations,
int  order,
lambda,
bool  withFRT 
) [static]

This calculates the transformation/fitting matrix T like in the 2007 Descoteaux paper.

The orientations are given as WMatrixFixed< T, 3, 1 >.

Parameters:
orientationsThe vector with the used orientation on the unit sphere (usually the gradients of the HARDI)
orderThe order of the spherical harmonics intended to create
lambdaRegularization parameter for smoothing matrix
withFRTinclude the Funk-Radon-Transformation?
Returns:
Transformation matrix

Definition at line 509 of file WSymmetricSphericalHarmonic.h.

template<typename T >
WMatrix< T > WSymmetricSphericalHarmonic< T >::getSHFittingMatrix ( const std::vector< WUnitSphereCoordinates< T > > &  orientations,
int  order,
lambda,
bool  withFRT 
) [static]

This calculates the transformation/fitting matrix T like in the 2007 Descoteaux paper.

The orientations are given as WUnitSphereCoordinates< T >.

Parameters:
orientationsThe vector with the used orientation on the unit sphere (usually the gradients of the HARDI)
orderThe order of the spherical harmonics intended to create
lambdaRegularization parameter for smoothing matrix
withFRTinclude the Funk-Radon-Transformation?
Returns:
Transformation matrix

Definition at line 524 of file WSymmetricSphericalHarmonic.h.

References WMatrix< T >::transposed().

template<typename T >
WMatrix< T > WSymmetricSphericalHarmonic< T >::getSHFittingMatrixForConstantSolidAngle ( const std::vector< WMatrixFixed< T, 3, 1 > > &  orientations,
int  order,
lambda 
) [static]

This calculates the transformation/fitting matrix T like in the 2010 Aganj paper.

The orientations are given as WUnitSphereCoordinates< T >.

Parameters:
orientationsThe vector with the used orientation on the unit sphere (usually the gradients of the HARDI)
orderThe order of the spherical harmonics intended to create
lambdaRegularization parameter for smoothing matrix
Returns:
Transformation matrix

Definition at line 548 of file WSymmetricSphericalHarmonic.h.

template<typename T >
WMatrix< T > WSymmetricSphericalHarmonic< T >::getSHFittingMatrixForConstantSolidAngle ( const std::vector< WUnitSphereCoordinates< T > > &  orientations,
int  order,
lambda 
) [static]

This calculates the transformation/fitting matrix T like in the 2010 Aganj paper.

The orientations are given as WUnitSphereCoordinates< T >.

Parameters:
orientationsThe vector with the used orientation on the unit sphere (usually the gradients of the HARDI)
orderThe order of the spherical harmonics intended to create
lambdaRegularization parameter for smoothing matrix
Returns:
Transformation matrix

Definition at line 562 of file WSymmetricSphericalHarmonic.h.

References wlog::debug(), and WMatrix< T >::transposed().

template<typename T >
T WSymmetricSphericalHarmonic< T >::getValue ( theta,
phi 
) const

Return the value on the sphere.

Parameters:
thetaangle for the position on the unit sphere
phiangle for the position on the unit sphere
Returns:
value on sphere

Definition at line 301 of file WSymmetricSphericalHarmonic.h.

template<typename T >
T WSymmetricSphericalHarmonic< T >::getValue ( const WUnitSphereCoordinates< T > &  coordinates) const

Return the value on the sphere.

Parameters:
coordinatesfor the position on the unit sphere
Returns:
value on sphere

Definition at line 328 of file WSymmetricSphericalHarmonic.h.

References WUnitSphereCoordinates< T >::getPhi(), and WUnitSphereCoordinates< T >::getTheta().

template<typename T >
void WSymmetricSphericalHarmonic< T >::normalize ( )

Normalize this SH in place.

Definition at line 802 of file WSymmetricSphericalHarmonic.h.


Member Data Documentation

template<typename T>
size_t WSymmetricSphericalHarmonic< T >::m_order [private]

order of the spherical harmonic

Definition at line 272 of file WSymmetricSphericalHarmonic.h.

Referenced by WSymmetricSphericalHarmonic< T >::WSymmetricSphericalHarmonic().

template<typename T>
WValue< T > WSymmetricSphericalHarmonic< T >::m_SHCoefficients [private]

coefficients of the spherical harmonic

Definition at line 275 of file WSymmetricSphericalHarmonic.h.

Referenced by WSymmetricSphericalHarmonic< T >::WSymmetricSphericalHarmonic().


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