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Commit 214b4d93 authored by Sebastian Eichelbaum's avatar Sebastian Eichelbaum
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src/core/common/math/WSymmetricSphericalHarmonic.cpp
View file @ 214b4d93
......@@ -22,531 +22,5 @@
//
//---------------------------------------------------------------------------
#include <stdint.h>
#include <cmath>
#include <vector>
#include <boost/math/special_functions/spherical_harmonic.hpp>
#include "core/common/WLogger.h"
#include "core/common/math/WGeometryFunctions.h"
#include "../exceptions/WPreconditionNotMet.h"
#include "linearAlgebra/WLinearAlgebra.h"
#include "WLinearAlgebraFunctions.h"
#include "WMatrix.h"
#include "WTensorSym.h"
#include "WUnitSphereCoordinates.h"
#include "WSymmetricSphericalHarmonic.h"
WSymmetricSphericalHarmonic::WSymmetricSphericalHarmonic() :
m_order( 0 ),
m_SHCoefficients( 0 )
{
}
WSymmetricSphericalHarmonic::WSymmetricSphericalHarmonic( const WValue<double>& SHCoefficients ) :
m_SHCoefficients( SHCoefficients )
{
// calculate order from SHCoefficients.size:
// - this is done by reversing the R=(l+1)*(l+2)/2 formula from the Descoteaux paper
double q = std::sqrt( 0.25 + 2.0 * static_cast<double>( m_SHCoefficients.size() ) ) - 1.5;
m_order = static_cast<size_t>( q );
}
WSymmetricSphericalHarmonic::~WSymmetricSphericalHarmonic()
{
}
double WSymmetricSphericalHarmonic::getValue( double theta, double phi ) const
{
double result = 0.0;
int j = 0;
const double rootOf2 = std::sqrt( 2.0 );
for( int k = 0; k <= static_cast<int>( m_order ); k+=2 )
{
// m = 1 .. k
for( int m = 1; m <= k; m++ )
{
j = ( k*k+k+2 ) / 2 + m;
result += m_SHCoefficients[ j-1 ] * rootOf2 *
static_cast<double>( std::pow( -1.0, m+1 ) ) * boost::math::spherical_harmonic_i( k, m, theta, phi );
}
// m = 0
result += m_SHCoefficients[ ( k*k+k+2 ) / 2 - 1 ] * boost::math::spherical_harmonic_r( k, 0, theta, phi );
// m = -k .. -1
for( int m = -k; m < 0; m++ )
{
j = ( k*k+k+2 ) / 2 + m;
result += m_SHCoefficients[ j-1 ] * rootOf2 * boost::math::spherical_harmonic_r( k, -m, theta, phi );
}
}
return result;
}
double WSymmetricSphericalHarmonic::getValue( const WUnitSphereCoordinates& coordinates ) const
{
return getValue( coordinates.getTheta(), coordinates.getPhi() );
}
const WValue<double>& WSymmetricSphericalHarmonic::getCoefficients() const
{
return m_SHCoefficients;
}
WValue< double > WSymmetricSphericalHarmonic::getCoefficientsSchultz() const
{
WValue< double > res( m_SHCoefficients.size() );
size_t k = 0;
for( int l = 0; l <= static_cast< int >( m_order ); l += 2 )
{
for( int m = -l; m <= l; ++m )
{
res[ k ] = m_SHCoefficients[ k ];
if( m < 0 && ( ( -m ) % 2 == 1 ) )
{
res[ k ] *= -1.0;
}
else if( m > 0 && ( m % 2 == 0 ) )
{
res[ k ] *= -1.0;
}
++k;
}
}
return res;
}
WValue< std::complex< double > > WSymmetricSphericalHarmonic::getCoefficientsComplex() const
{
WValue< std::complex< double > > res( m_SHCoefficients.size() );
size_t k = 0;
double r = 1.0 / sqrt( 2.0 );
std::complex< double > i( 0.0, -1.0 );
for( int l = 0; l <= static_cast< int >( m_order ); l += 2 )
{
for( int m = -l; m <= l; ++m )
{
if( m == 0 )
{
res[ k ] = m_SHCoefficients[ k ];
}
else if( m < 0 )
{
res[ k ] += i * r * m_SHCoefficients[ k - 2 * m ];
res[ k ] += ( -m % 2 == 1 ? -r : r ) * m_SHCoefficients[ k ];
}
else if( m > 0 )
{
res[ k ] += i * ( -m % 2 == 0 ? -r : r ) * m_SHCoefficients[ k ];
res[ k ] += r * m_SHCoefficients[ k - 2 * m ];
}
++k;
}
}
return res;
}
double WSymmetricSphericalHarmonic::calcGFA( std::vector< WUnitSphereCoordinates > const& orientations ) const
{
double n = static_cast< double >( orientations.size() );
double d = 0.0;
double gfa = 0.0;
double mean = 0.0;
std::vector< double > v( orientations.size() );
for( std::size_t i = 0; i < orientations.size(); ++i )
{
v[ i ] = getValue( orientations[ i ] );
mean += v[ i ];
}
mean /= n;
for( std::size_t i = 0; i < orientations.size(); ++i )
{
double f = v[ i ];
// we use gfa as a temporary here
gfa += f * f;
f -= mean;
d += f * f;
}
if( gfa == 0.0 || n <= 1.0 )
{
return 0.0;
}
// this is the real gfa
gfa = sqrt( ( n * d ) / ( ( n - 1.0 ) * gfa ) );
WAssert( gfa >= -0.01 && gfa <= 1.01, "" );
if( gfa < 0.0 )
{
return 0.0;
}
else if( gfa > 1.0 )
{
return 1.0;
}
return gfa;
}
double WSymmetricSphericalHarmonic::calcGFA( WMatrix< double > const& B ) const
{
// sh coeffs
WMatrix< double > s( B.getNbCols(), 1 );
WAssert( B.getNbCols() == m_SHCoefficients.size(), "" );
for( std::size_t k = 0; k < B.getNbCols(); ++k )
{
s( k, 0 ) = m_SHCoefficients[ k ];
}
s = B * s;
WAssert( s.getNbRows() == B.getNbRows(), "" );
WAssert( s.getNbCols() == 1u, "" );
double n = static_cast< double >( s.getNbRows() );
double d = 0.0;
double gfa = 0.0;
double mean = 0.0;
for( std::size_t i = 0; i < s.getNbRows(); ++i )
{
mean += s( i, 0 );
}
mean /= n;
for( std::size_t i = 0; i < s.getNbRows(); ++i )
{
double f = s( i, 0 );
// we use gfa as a temporary here
gfa += f * f;
f -= mean;
d += f * f;
}
if( gfa == 0.0 || n <= 1.0 )
{
return 0.0;
}
// this is the real gfa
gfa = sqrt( ( n * d ) / ( ( n - 1.0 ) * gfa ) );
WAssert( gfa >= -0.01 && gfa <= 1.01, "" );
if( gfa < 0.0 )
{
return 0.0;
}
else if( gfa > 1.0 )
{
return 1.0;
}
return gfa;
}
void WSymmetricSphericalHarmonic::applyFunkRadonTransformation( WMatrix< double > const& frtMat )
{
WAssert( frtMat.getNbCols() == m_SHCoefficients.size(), "" );
WAssert( frtMat.getNbRows() == m_SHCoefficients.size(), "" );
// Funk-Radon-Transformation as in Descoteaux's thesis
for( size_t j = 0; j < m_SHCoefficients.size(); j++ )
{
m_SHCoefficients[ j ] *= frtMat( j, j );
}
}
size_t WSymmetricSphericalHarmonic::getOrder() const
{
return m_order;
}
WMatrix<double> WSymmetricSphericalHarmonic::getSHFittingMatrix( const std::vector< WVector3d >& orientations,
int order,
double lambda,
bool withFRT )
{
// convert euclid 3d orientations/gradients to sphere coordinates
std::vector< WUnitSphereCoordinates > sphereCoordinates;
for( std::vector< WVector3d >::const_iterator it = orientations.begin(); it != orientations.end(); it++ )
{
sphereCoordinates.push_back( WUnitSphereCoordinates( *it ) );
}
return WSymmetricSphericalHarmonic::getSHFittingMatrix( sphereCoordinates, order, lambda, withFRT );
}
WMatrix<double> WSymmetricSphericalHarmonic::getSHFittingMatrix( const std::vector< WUnitSphereCoordinates >& orientations,
int order,
double lambda,
bool withFRT )
{
WMatrix<double> B( WSymmetricSphericalHarmonic::calcBaseMatrix( orientations, order ) );
WMatrix<double> Bt( B.transposed() );
WMatrix<double> result( Bt*B );
if( lambda != 0.0 )
{
WMatrix<double> L( WSymmetricSphericalHarmonic::calcSmoothingMatrix( order ) );
result += lambda*L;
}
result = pseudoInverse( result )*Bt;
if( withFRT )
{
WMatrix<double> P( WSymmetricSphericalHarmonic::calcFRTMatrix( order ) );
return ( P * result );
}
return result;
}
WMatrix<double> WSymmetricSphericalHarmonic::getSHFittingMatrixForConstantSolidAngle( const std::vector< WVector3d >& orientations,
int order,
double lambda )
{
// convert euclid 3d orientations/gradients to sphere coordinates
std::vector< WUnitSphereCoordinates > sphereCoordinates;
for( std::vector< WVector3d >::const_iterator it = orientations.begin(); it != orientations.end(); it++ )
{
sphereCoordinates.push_back( WUnitSphereCoordinates( *it ) );
}
return WSymmetricSphericalHarmonic::getSHFittingMatrixForConstantSolidAngle( sphereCoordinates, order, lambda );
}
WMatrix<double> WSymmetricSphericalHarmonic::getSHFittingMatrixForConstantSolidAngle(
const std::vector< WUnitSphereCoordinates >& orientations,
int order,
double lambda )
{
WMatrix<double> B( WSymmetricSphericalHarmonic::calcBaseMatrix( orientations, order ) );
WMatrix<double> Bt( B.transposed() );
WMatrix<double> result( Bt*B );
// regularisation
if( lambda != 0.0 )
{
WMatrix<double> L( WSymmetricSphericalHarmonic::calcSmoothingMatrix( order ) );
result += lambda*L;
}
result = pseudoInverse( result )*Bt;
// multiply with eigenvalues of coefficients / Laplace-Beltrami operator
WMatrix<double> LB( WSymmetricSphericalHarmonic::calcMatrixWithEigenvalues( order ) );
wlog::debug( "" ) << "LB: " << LB;
result = LB*result;
wlog::debug( "" ) << "LB*result: " << result;
// apply FRT
WMatrix<double> P( WSymmetricSphericalHarmonic::calcFRTMatrix( order ) );
result = P * result;
wlog::debug( "" ) << "P: " << P;
wlog::debug( "" ) << "P*result: " << result;
// correction factor
double correctionFactor = 1.0 / ( 16.0 * std::pow( piDouble, 2 ) );
result *= correctionFactor;
return result;
}
WMatrix<double> WSymmetricSphericalHarmonic::calcBaseMatrix( const std::vector< WUnitSphereCoordinates >& orientations,
int order )
{
WMatrix<double> B( orientations.size(), ( ( order + 1 ) * ( order + 2 ) ) / 2 );
// calc B Matrix like in the 2007 Descoteaux paper ("Regularized, Fast, and Robust Analytical Q-Ball Imaging")
int j = 0;
const double rootOf2 = std::sqrt( 2.0 );
for(uint32_t row = 0; row < orientations.size(); row++ )
{
const double theta = orientations[row].getTheta();
const double phi = orientations[row].getPhi();
for( int k = 0; k <= order; k+=2 )
{
// m = 1 .. k
for( int m = 1; m <= k; m++ )
{
j = ( k * k + k + 2 ) / 2 + m;
B( row, j-1 ) = rootOf2 * static_cast<double>( std::pow( static_cast<double>( -1 ), m + 1 ) )
* boost::math::spherical_harmonic_i( k, m, theta, phi );
}
// m = 0
B( row, ( k * k + k + 2 ) / 2 - 1 ) = boost::math::spherical_harmonic_r( k, 0, theta, phi );
// m = -k .. -1
for( int m = -k; m < 0; m++ )
{
j = ( k * k + k + 2 ) / 2 + m;
B( row, j-1 ) = rootOf2*boost::math::spherical_harmonic_r( k, -m, theta, phi );
}
}
}
return B;
}
WMatrix< std::complex< double > >
WSymmetricSphericalHarmonic::calcComplexBaseMatrix( std::vector< WUnitSphereCoordinates > const& orientations, int order )
{
WMatrix< std::complex< double > > B( orientations.size(), ( ( order + 1 ) * ( order + 2 ) ) / 2 );
for( std::size_t row = 0; row < orientations.size(); row++ )
{
const double theta = orientations[ row ].getTheta();
const double phi = orientations[ row ].getPhi();
int j = 0;
for( int k = 0; k <= order; k += 2 )
{
for( int m = -k; m < 0; m++ )
{
B( row, j ) = boost::math::spherical_harmonic( k, m, theta, phi );
++j;
}
B( row, j ) = boost::math::spherical_harmonic( k, 0, theta, phi );
++j;
for( int m = 1; m <= k; m++ )
{
B( row, j ) = boost::math::spherical_harmonic( k, m, theta, phi );
++j;
}
}
}
return B;
}
WValue<double> WSymmetricSphericalHarmonic::calcEigenvalues( size_t order )
{
size_t R = ( ( order + 1 ) * ( order + 2 ) ) / 2;
std::size_t i = 0;
WValue<double> result( R );
for( size_t k = 0; k <= order; k += 2 )
{
for( int m = -static_cast< int >( k ); m <= static_cast< int >( k ); ++m )
{
result[ i ] = -static_cast< double > ( k * ( k + 1 ) );
++i;
}
}
return result;
}
WMatrix<double> WSymmetricSphericalHarmonic::calcMatrixWithEigenvalues( size_t order )
{
WValue<double> eigenvalues( WSymmetricSphericalHarmonic::calcEigenvalues( order ) );
WMatrix<double> L( eigenvalues.size(), eigenvalues.size() );
for( std::size_t i = 0; i < eigenvalues.size(); ++i )
{
L( i, i ) = eigenvalues[ i ];
}
return L;
}
WMatrix<double> WSymmetricSphericalHarmonic::calcSmoothingMatrix( size_t order )
{
WValue<double> eigenvalues( WSymmetricSphericalHarmonic::calcEigenvalues( order ) );
WMatrix<double> L( eigenvalues.size(), eigenvalues.size() );
for( std::size_t i = 0; i < eigenvalues.size(); ++i )
{
L( i, i ) = std::pow( eigenvalues[ i ], 2 );
}
return L;
}
WMatrix<double> WSymmetricSphericalHarmonic::calcFRTMatrix( size_t order )
{
size_t R = ( ( order + 1 ) * ( order + 2 ) ) / 2;
std::size_t i = 0;
WMatrix< double > result( R, R );
for( size_t k = 0; k <= order; k += 2 )
{
double h = 2.0 * piDouble * static_cast< double >( std::pow( static_cast< double >( -1 ), static_cast< double >( k / 2 ) ) ) *
static_cast< double >( oddFactorial( ( k <= 1 ) ? 1 : k - 1 ) ) / static_cast<double>( evenFactorial( k ) );
for( int m = -static_cast< int >( k ); m <= static_cast< int >( k ); ++m )
{
result( i, i ) = h;
++i;
}
}
return result;
}
WMatrix< double > WSymmetricSphericalHarmonic::calcSHToTensorSymMatrix( std::size_t order )
{
std::vector< WVector3d > vertices;
std::vector< unsigned int > triangles;
// calc necessary tesselation level
int level = static_cast< int >( log( static_cast< float >( ( order + 1 ) * ( order + 2 ) ) ) / 2.0f + 1.0f );
tesselateIcosahedron( &vertices, &triangles, level );
std::vector< WUnitSphereCoordinates > orientations;
for( std::vector< WVector3d >::const_iterator cit = vertices.begin(); cit != vertices.end(); cit++ )
{
// avoid linear dependent orientations
if( ( *cit )[ 0 ] >= 0.0001 )
{
orientations.push_back( WUnitSphereCoordinates( *cit ) );
}
}
return WSymmetricSphericalHarmonic::calcSHToTensorSymMatrix( order, orientations );
}
WMatrix< double > WSymmetricSphericalHarmonic::calcSHToTensorSymMatrix( std::size_t order,
const std::vector< WUnitSphereCoordinates >& orientations )
{
std::size_t numElements = ( order + 1 ) * ( order + 2 ) / 2;
WPrecondEquals( order % 2, 0u );
WPrecondLess( numElements, orientations.size() + 1 );
// store first numElements orientations as 3d-vectors
std::vector< WVector3d > directions( numElements );
for( std::size_t i = 0; i < numElements; ++i )
{
directions[ i ] = orientations[ i ].getEuclidean();
}
// initialize an index array
std::vector< std::size_t > indices( order, 0 );
// calc tensor evaluation matrix
WMatrix< double > TEMat( numElements, numElements );
for( std::size_t j = 0; j < numElements; ++j ) // j is the 'permutation index'
{
// stores how often each value is represented in the index array
std::size_t amount[ 3 ] = { 0, 0, 0 };
for( std::size_t k = 0; k < order; ++k )
{
++amount[ indices[ k ] ];
}
// from WTensorSym.h
std::size_t multiplicity = calcSupersymmetricTensorMultiplicity( order, amount[ 0 ], amount[ 1 ], amount[ 2 ] );
for( std::size_t i = 0; i < numElements; ++i ) // i is the 'direction index'
{
TEMat( i, j ) = multiplicity;
for( std::size_t k = 0; k < order; ++k )
{
TEMat( i, j ) *= directions[ i ][ indices[ k ] ];
}
}
// from TensorBase.h
positionIterateSortedOneStep( order, 3, indices );
}
directions.clear();
// we do not want more orientations than nessessary
std::vector< WUnitSphereCoordinates > ori2( orientations.begin(), orientations.begin() + numElements );
WMatrix< double > p = pseudoInverse( TEMat );
WAssert( ( TEMat*p ).isIdentity( 1e-3 ), "Test of inverse matrix failed. Are the given orientations linear independent?" );
return p * calcBaseMatrix( ori2, order );
}
void WSymmetricSphericalHarmonic::normalize()
{
double scale = 0.0;
if( m_SHCoefficients.size() > 0 )
scale = std::sqrt( 4.0 * piDouble ) * m_SHCoefficients[0];
for( size_t i = 0; i < m_SHCoefficients.size(); i++ )
{
m_SHCoefficients[ i ] /= scale;
}
}
// NOLINT
src/core/common/math/WUnitSphereCoordinates.cpp
View file @ 214b4d93
......@@ -22,55 +22,4 @@
//
//---------------------------------------------------------------------------
#include <cmath>
#include "WUnitSphereCoordinates.h"
WUnitSphereCoordinates::WUnitSphereCoordinates()
: m_theta( 0.0 ),
m_phi( 0.0 )
{
}
WUnitSphereCoordinates::WUnitSphereCoordinates( double theta, double phi )
: m_theta( theta ),
m_phi( phi )
{
}
WUnitSphereCoordinates::WUnitSphereCoordinates( WVector3d vector )
{
vector = normalize( vector );
// calculate angles
m_theta = std::acos( vector[2] );
m_phi = std::atan2( vector[1], vector[0] );
}
WUnitSphereCoordinates::~WUnitSphereCoordinates()
{
}
double WUnitSphereCoordinates::getTheta() const
{
return m_theta;
}
double WUnitSphereCoordinates::getPhi() const
{
return m_phi;
}
void WUnitSphereCoordinates::setTheta( double theta )
{