OpenWalnut
1.3.1
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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>
Public Member Functions | |
WSymmetricSphericalHarmonic () | |
Default constructor. | |
WSymmetricSphericalHarmonic (const WValue< double > &SHCoefficients) | |
Constructor. | |
virtual | ~WSymmetricSphericalHarmonic () |
Destructor. | |
double | getValue (double theta, double phi) const |
Return the value on the sphere. | |
double | getValue (const WUnitSphereCoordinates &coordinates) const |
Return the value on the sphere. | |
const WValue< double > & | getCoefficients () const |
Returns the used coefficients (stored like in the mentioned 2007 Descoteaux paper). | |
WValue< double > | getCoefficientsSchultz () const |
Returns the coefficients for Schultz' SH base. | |
WValue< std::complex< double > > | getCoefficientsComplex () const |
Returns the coefficients for the complex base. | |
void | applyFunkRadonTransformation (WMatrix< double > const &frtMat) |
Applies the Funk-Radon-Transformation. | |
size_t | getOrder () const |
Return the order of the spherical harmonic. | |
double | calcGFA (std::vector< WUnitSphereCoordinates > const &orientations) const |
Calculate the generalized fractional anisotropy for this ODF. | |
double | calcGFA (WMatrix< double > const &B) const |
Calculate the generalized fractional anisotropy for this ODF. | |
void | normalize () |
Normalize this SH in place. |
Static Public Member Functions | |
static WMatrix< double > | getSHFittingMatrix (const std::vector< WVector3d > &orientations, int order, double lambda, bool withFRT) |
This calculates the transformation/fitting matrix T like in the 2007 Descoteaux paper. | |
static WMatrix< double > | getSHFittingMatrix (const std::vector< WUnitSphereCoordinates > &orientations, int order, double lambda, bool withFRT) |
This calculates the transformation/fitting matrix T like in the 2007 Descoteaux paper. | |
static WMatrix< double > | getSHFittingMatrixForConstantSolidAngle (const std::vector< WVector3d > &orientations, int order, double lambda) |
This calculates the transformation/fitting matrix T like in the 2010 Aganj paper. | |
static WMatrix< double > | getSHFittingMatrixForConstantSolidAngle (const std::vector< WUnitSphereCoordinates > &orientations, int order, double lambda) |
This calculates the transformation/fitting matrix T like in the 2010 Aganj paper. | |
static WMatrix< double > | calcBaseMatrix (const std::vector< WUnitSphereCoordinates > &orientations, int order) |
Calculates the base matrix B like in the dissertation of Descoteaux. | |
static WMatrix< std::complex < double > > | calcComplexBaseMatrix (std::vector< WUnitSphereCoordinates > const &orientations, int order) |
Calculates the base matrix B for the complex spherical harmonics. | |
static WValue< double > | calcEigenvalues (size_t order) |
Calc eigenvalues for SH elements. | |
static WMatrix< double > | calcMatrixWithEigenvalues (size_t order) |
Calc matrix with the eigenvalues of the SH elements on its diagonal. | |
static WMatrix< double > | 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< double > | 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< double > | calcSHToTensorSymMatrix (std::size_t order, const std::vector< WUnitSphereCoordinates > &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< double > | m_SHCoefficients |
coefficients of the spherical harmonic |
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 41 of file WSymmetricSphericalHarmonic.h.
WSymmetricSphericalHarmonic::WSymmetricSphericalHarmonic | ( | ) |
Default constructor.
Definition at line 41 of file WSymmetricSphericalHarmonic.cpp.
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explicit |
Constructor.
SHCoefficients | the initial coefficients (stored like in the mentioned Descoteaux paper). |
Definition at line 47 of file WSymmetricSphericalHarmonic.cpp.
References m_order, m_SHCoefficients, and WValue< T >::size().
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virtual |
Destructor.
Definition at line 56 of file WSymmetricSphericalHarmonic.cpp.
void WSymmetricSphericalHarmonic::applyFunkRadonTransformation | ( | WMatrix< double > const & | frtMat | ) |
Applies the Funk-Radon-Transformation.
This is faster than matrix multiplication. ( O(n) instead of O(n²) )
frtMat | the frt matrix as calculated by calcFRTMatrix() |
Definition at line 243 of file WSymmetricSphericalHarmonic.cpp.
References WMatrix< T >::getNbCols(), WMatrix< T >::getNbRows(), m_SHCoefficients, and WValue< T >::size().
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static |
Calculates the base matrix B like in the dissertation of Descoteaux.
orientations | The vector with the used orientation on the unit sphere (usually the gradients of the HARDI) |
order | The order of the spherical harmonics intended to create |
Definition at line 347 of file WSymmetricSphericalHarmonic.cpp.
Referenced by calcSHToTensorSymMatrix(), getSHFittingMatrix(), and getSHFittingMatrixForConstantSolidAngle().
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static |
Calculates the base matrix B for the complex spherical harmonics.
orientations | The vector with the used orientation on the unit sphere (usually the gradients of the HARDI) |
order | The order of the spherical harmonics intended to create |
Definition at line 382 of file WSymmetricSphericalHarmonic.cpp.
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static |
Calc eigenvalues for SH elements.
order | The order of the spherical harmonic |
Definition at line 411 of file WSymmetricSphericalHarmonic.cpp.
Referenced by calcMatrixWithEigenvalues(), and calcSmoothingMatrix().
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static |
Calculates the Funk-Radon-Transformation-Matrix P from the 2007 Descoteaux Paper "Regularized, Fast, and Robust Analytical Q-Ball Imaging".
order | The order of the spherical harmonic |
Definition at line 449 of file WSymmetricSphericalHarmonic.cpp.
Referenced by getSHFittingMatrix(), getSHFittingMatrixForConstantSolidAngle(), and WSymmetricSphericalHarmonicTest::testCalcFRTMatrix().
double WSymmetricSphericalHarmonic::calcGFA | ( | std::vector< WUnitSphereCoordinates > 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
orientations | A vector of unit sphere coordinates. |
Definition at line 149 of file WSymmetricSphericalHarmonic.cpp.
References getValue().
double WSymmetricSphericalHarmonic::calcGFA | ( | WMatrix< double > 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: David S. Tuch, "Q-Ball Imaging", Magn. Reson. Med. 52, 2004, 1358-1372
B | The matrix of SH base functions. |
Definition at line 192 of file WSymmetricSphericalHarmonic.cpp.
References WMatrix< T >::getNbCols(), WMatrix< T >::getNbRows(), m_SHCoefficients, and WValue< T >::size().
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static |
Calc matrix with the eigenvalues of the SH elements on its diagonal.
order | The order of the spherical harmonic |
Definition at line 427 of file WSymmetricSphericalHarmonic.cpp.
References calcEigenvalues(), and WValue< T >::size().
Referenced by getSHFittingMatrixForConstantSolidAngle().
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static |
Calculates a matrix that converts spherical harmonics to symmetric tensors of equal or lower order.
order | The order of the symmetric tensor. |
orientations | A vector of at least (orderTensor+1) * (orderTensor+2) / 2 orientations. |
Definition at line 467 of file WSymmetricSphericalHarmonic.cpp.
References calcBaseMatrix().
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static |
This calcs the smoothing matrix L from the 2007 Descoteaux Paper "Regularized, Fast, and Robust Analytical Q-Ball Imaging".
order | The order of the spherical harmonic |
Definition at line 438 of file WSymmetricSphericalHarmonic.cpp.
References calcEigenvalues(), and WValue< T >::size().
Referenced by getSHFittingMatrix(), getSHFittingMatrixForConstantSolidAngle(), and WSymmetricSphericalHarmonicTest::testCalcSmoothingMatrix().
const WValue< double > & WSymmetricSphericalHarmonic::getCoefficients | ( | ) | const |
Returns the used coefficients (stored like in the mentioned 2007 Descoteaux paper).
Definition at line 91 of file WSymmetricSphericalHarmonic.cpp.
References m_SHCoefficients.
WValue< std::complex< double > > WSymmetricSphericalHarmonic::getCoefficientsComplex | ( | ) | const |
Returns the coefficients for the complex base.
Definition at line 119 of file WSymmetricSphericalHarmonic.cpp.
References m_order, m_SHCoefficients, and WValue< T >::size().
WValue< double > WSymmetricSphericalHarmonic::getCoefficientsSchultz | ( | ) | const |
Returns the coefficients for Schultz' SH base.
Definition at line 96 of file WSymmetricSphericalHarmonic.cpp.
References m_order, m_SHCoefficients, and WValue< T >::size().
size_t WSymmetricSphericalHarmonic::getOrder | ( | ) | const |
Return the order of the spherical harmonic.
Definition at line 254 of file WSymmetricSphericalHarmonic.cpp.
References m_order.
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static |
This calculates the transformation/fitting matrix T like in the 2007 Descoteaux paper.
The orientations are given as WVector3d.
orientations | The vector with the used orientation on the unit sphere (usually the gradients of the HARDI) |
order | The order of the spherical harmonics intended to create |
lambda | Regularization parameter for smoothing matrix |
withFRT | include the Funk-Radon-Transformation? |
Definition at line 259 of file WSymmetricSphericalHarmonic.cpp.
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static |
This calculates the transformation/fitting matrix T like in the 2007 Descoteaux paper.
The orientations are given as WUnitSphereCoordinates .
orientations | The vector with the used orientation on the unit sphere (usually the gradients of the HARDI) |
order | The order of the spherical harmonics intended to create |
lambda | Regularization parameter for smoothing matrix |
withFRT | include the Funk-Radon-Transformation? |
Definition at line 273 of file WSymmetricSphericalHarmonic.cpp.
References calcBaseMatrix(), calcFRTMatrix(), calcSmoothingMatrix(), and WMatrix< T >::transposed().
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static |
This calculates the transformation/fitting matrix T like in the 2010 Aganj paper.
The orientations are given as WUnitSphereCoordinates .
orientations | The vector with the used orientation on the unit sphere (usually the gradients of the HARDI) |
order | The order of the spherical harmonics intended to create |
lambda | Regularization parameter for smoothing matrix |
Definition at line 296 of file WSymmetricSphericalHarmonic.cpp.
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static |
This calculates the transformation/fitting matrix T like in the 2010 Aganj paper.
The orientations are given as WUnitSphereCoordinates .
orientations | The vector with the used orientation on the unit sphere (usually the gradients of the HARDI) |
order | The order of the spherical harmonics intended to create |
lambda | Regularization parameter for smoothing matrix |
Definition at line 309 of file WSymmetricSphericalHarmonic.cpp.
References calcBaseMatrix(), calcFRTMatrix(), calcMatrixWithEigenvalues(), calcSmoothingMatrix(), wlog::debug(), and WMatrix< T >::transposed().
double WSymmetricSphericalHarmonic::getValue | ( | double | theta, |
double | phi | ||
) | const |
Return the value on the sphere.
theta | angle for the position on the unit sphere |
phi | angle for the position on the unit sphere |
Definition at line 60 of file WSymmetricSphericalHarmonic.cpp.
References m_order, and m_SHCoefficients.
Referenced by calcGFA(), and getValue().
double WSymmetricSphericalHarmonic::getValue | ( | const WUnitSphereCoordinates & | coordinates | ) | const |
Return the value on the sphere.
coordinates | for the position on the unit sphere |
Definition at line 86 of file WSymmetricSphericalHarmonic.cpp.
References WUnitSphereCoordinates::getPhi(), WUnitSphereCoordinates::getTheta(), and getValue().
void WSymmetricSphericalHarmonic::normalize | ( | ) |
Normalize this SH in place.
Definition at line 519 of file WSymmetricSphericalHarmonic.cpp.
References m_SHCoefficients, and WValue< T >::size().
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private |
order of the spherical harmonic
Definition at line 253 of file WSymmetricSphericalHarmonic.h.
Referenced by getCoefficientsComplex(), getCoefficientsSchultz(), getOrder(), getValue(), and WSymmetricSphericalHarmonic().
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private |
coefficients of the spherical harmonic
Definition at line 256 of file WSymmetricSphericalHarmonic.h.
Referenced by applyFunkRadonTransformation(), calcGFA(), getCoefficients(), getCoefficientsComplex(), getCoefficientsSchultz(), getValue(), normalize(), and WSymmetricSphericalHarmonic().