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itk::MultivariateLegendrePolynomial Class Reference
Group Numerics » Module ITKPolynomials

#include <itkMultivariateLegendrePolynomial.h>

Detailed Description

2D and 3D multivariate Legendre Polynomial

In 2D,

\[ f(x_{vector}, parameter_{vector}) = \sum_i^l \left( \sum_j^{l-i} \left( parameter_ {ij} * P_i(x) *P_j(y)) \right) \right) \]

where P_i() denoting a Legendre polynomial of degree i and l it the degree of the polynomial

In 3D,

\[ f(x_{vector}, parameter_{vector}) = \sum_i^l \left( \sum_j^{l-i} \left( \sum_k^{l-i-j} \left( parameter_{ijk} * P_i(x) * P_j(y) * P_k(z) \right) \right) \right) \]

The size of the parameter vector for 2D is \(\frac{(l+1)\cdot(1+2)}{2}\), and for 3D is \(\frac{(l+1)*(l+2)*(l+3)}{3!}\)

To get the size of the parameter vector, users can use one of the two GetNumberOfCoefficients() member functions

To get function result, users can use the operator() or its SimpleForwardIterator's Get() method.

This is a part of the bias correction methods and implementations that was initially developed and implemented by Martin Styner, Univ. of North Carolina at Chapel Hill, and his colleagues.

Note
For more details. refer to the following articles. "Parametric estimate of intensity inhomogeneities applied to MRI" Martin Styner, G. Gerig, Christian Brechbuehler, Gabor Szekely, IEEE TRANSACTIONS ON MEDICAL IMAGING; 19(3), pp. 153-165, 2000, (https://www.cs.unc.edu/~styner/docs/tmi99.pdf)

"Evaluation of 2D/3D bias correction with 1+1ES-optimization" Martin Styner, Prof. Dr. G. Gerig (IKT, BIWI, ETH Zuerich), TR-197 (https://www.cs.unc.edu/~styner/docs/StynerTR97.pdf)

Definition at line 77 of file itkMultivariateLegendrePolynomial.h.

+ Collaboration diagram for itk::MultivariateLegendrePolynomial:

Classes

class  CoefficientVectorSizeMismatch
 
class  SimpleForwardIterator
 

Public Types

using CoefficientArrayType = DoubleArrayType
 
using DomainSizeType = ULongArrayType
 
using DoubleArrayType = std::vector< double >
 
using IndexType = LongArrayType
 
using LongArrayType = std::vector< long >
 
using ParametersType = Array< double >
 
using Self = MultivariateLegendrePolynomial
 
using ULongArrayType = std::vector< unsigned long >
 

Public Member Functions

const CoefficientArrayType & GetCoefficients () const
 
unsigned int GetDegree () const
 
unsigned int GetDimension () const
 
const DomainSizeType & GetDomainSize () const
 
unsigned int GetNumberOfCoefficients () const
 
unsigned int GetNumberOfCoefficients (unsigned int dimension, unsigned int degree)
 
 MultivariateLegendrePolynomial (unsigned int dimension, unsigned int degree, const DomainSizeType &domainSize)
 
void Print (std::ostream &os) const
 
void SetCoefficients (const CoefficientArrayType &coefficients)
 
void SetCoefficients (const ParametersType &coefficients)
 
virtual ~MultivariateLegendrePolynomial ()
 
double Evaluate (IndexType &index)
 

Protected Member Functions

void CalculateXCoef (double norm_y, const CoefficientArrayType &coef)
 
void CalculateYCoef (double norm_z, const CoefficientArrayType &coef)
 
double LegendreSum (const double x, int n, const CoefficientArrayType &coef, int offset=0)
 
void PrintSelf (std::ostream &os, Indent indent) const
 

Private Attributes

CoefficientArrayType m_CachedXCoef {}
 
CoefficientArrayType m_CachedYCoef {}
 
CoefficientArrayType m_CachedZCoef {}
 
CoefficientArrayType m_CoefficientArray {}
 
unsigned int m_Degree {}
 
unsigned int m_Dimension {}
 
DomainSizeType m_DomainSize {}
 
DoubleArrayType m_NormFactor {}
 
unsigned int m_NumberOfCoefficients {}
 
IndexValueType m_PrevY {}
 
IndexValueType m_PrevZ {}
 

Member Typedef Documentation

◆ CoefficientArrayType

using itk::MultivariateLegendrePolynomial::CoefficientArrayType = DoubleArrayType

Internal coefficient storage type.

Definition at line 87 of file itkMultivariateLegendrePolynomial.h.

◆ DomainSizeType

using itk::MultivariateLegendrePolynomial::DomainSizeType = ULongArrayType

The size of the domain.

Definition at line 94 of file itkMultivariateLegendrePolynomial.h.

◆ DoubleArrayType

using itk::MultivariateLegendrePolynomial::DoubleArrayType = std::vector<double>

Definition at line 82 of file itkMultivariateLegendrePolynomial.h.

◆ IndexType

using itk::MultivariateLegendrePolynomial::IndexType = LongArrayType

Definition at line 95 of file itkMultivariateLegendrePolynomial.h.

◆ LongArrayType

using itk::MultivariateLegendrePolynomial::LongArrayType = std::vector<long>

Definition at line 84 of file itkMultivariateLegendrePolynomial.h.

◆ ParametersType

using itk::MultivariateLegendrePolynomial::ParametersType = Array<double>

Same as CoefficientArray This type definition will be used by EnergyFunction object.

Definition at line 91 of file itkMultivariateLegendrePolynomial.h.

◆ Self

using itk::MultivariateLegendrePolynomial::Self = MultivariateLegendrePolynomial

Definition at line 80 of file itkMultivariateLegendrePolynomial.h.

◆ ULongArrayType

using itk::MultivariateLegendrePolynomial::ULongArrayType = std::vector<unsigned long>

Definition at line 83 of file itkMultivariateLegendrePolynomial.h.

Constructor & Destructor Documentation

◆ MultivariateLegendrePolynomial()

itk::MultivariateLegendrePolynomial::MultivariateLegendrePolynomial ( unsigned int  dimension,
unsigned int  degree,
const DomainSizeType &  domainSize 
)

Constructor.

◆ ~MultivariateLegendrePolynomial()

virtual itk::MultivariateLegendrePolynomial::~MultivariateLegendrePolynomial ( )
virtual

Destructor.

Member Function Documentation

◆ CalculateXCoef()

void itk::MultivariateLegendrePolynomial::CalculateXCoef ( double  norm_y,
const CoefficientArrayType &  coef 
)
protected

◆ CalculateYCoef()

void itk::MultivariateLegendrePolynomial::CalculateYCoef ( double  norm_z,
const CoefficientArrayType &  coef 
)
protected

◆ Evaluate()

double itk::MultivariateLegendrePolynomial::Evaluate ( IndexType &  index)
inline

In the case which the bias field is 2D, it returns bias value at the point which is specified by the index

Definition at line 170 of file itkMultivariateLegendrePolynomial.h.

◆ GetCoefficients()

const CoefficientArrayType& itk::MultivariateLegendrePolynomial::GetCoefficients ( ) const

Gets Legendre polynomials' coefficients.

◆ GetDegree()

unsigned int itk::MultivariateLegendrePolynomial::GetDegree ( ) const
inline

Gets the degree (the degree of Legendre polynomials).

Definition at line 112 of file itkMultivariateLegendrePolynomial.h.

◆ GetDimension()

unsigned int itk::MultivariateLegendrePolynomial::GetDimension ( ) const
inline

Gets the dimension.

Definition at line 105 of file itkMultivariateLegendrePolynomial.h.

◆ GetDomainSize()

const DomainSizeType& itk::MultivariateLegendrePolynomial::GetDomainSize ( ) const
inline

Gets each dimension's size.

Definition at line 131 of file itkMultivariateLegendrePolynomial.h.

◆ GetNumberOfCoefficients() [1/2]

unsigned int itk::MultivariateLegendrePolynomial::GetNumberOfCoefficients ( ) const
inline

Returns the number of coefficients of the polynomial This number is computed from the degree of the polynomial the SetCoefficients() method expects an array of this size, an exception is thrown otherwise

See also
SetCoefficients

Definition at line 124 of file itkMultivariateLegendrePolynomial.h.

◆ GetNumberOfCoefficients() [2/2]

unsigned int itk::MultivariateLegendrePolynomial::GetNumberOfCoefficients ( unsigned int  dimension,
unsigned int  degree 
)

Gets the number of coefficients.

◆ LegendreSum()

double itk::MultivariateLegendrePolynomial::LegendreSum ( const double  x,
int  n,
const CoefficientArrayType &  coef,
int  offset = 0 
)
protected

◆ Print()

void itk::MultivariateLegendrePolynomial::Print ( std::ostream &  os) const

◆ PrintSelf()

void itk::MultivariateLegendrePolynomial::PrintSelf ( std::ostream &  os,
Indent  indent 
) const
protected

◆ SetCoefficients() [1/2]

void itk::MultivariateLegendrePolynomial::SetCoefficients ( const CoefficientArrayType &  coefficients)

Sets the Legendre polynomials' parameters.

Warning
The number of coefficients provided should match the number returned by GetNumberOfCoefficients() otherwise an exception is thrown.

◆ SetCoefficients() [2/2]

void itk::MultivariateLegendrePolynomial::SetCoefficients ( const ParametersType &  coefficients)

Member Data Documentation

◆ m_CachedXCoef

CoefficientArrayType itk::MultivariateLegendrePolynomial::m_CachedXCoef {}
private

Definition at line 316 of file itkMultivariateLegendrePolynomial.h.

◆ m_CachedYCoef

CoefficientArrayType itk::MultivariateLegendrePolynomial::m_CachedYCoef {}
private

Definition at line 317 of file itkMultivariateLegendrePolynomial.h.

◆ m_CachedZCoef

CoefficientArrayType itk::MultivariateLegendrePolynomial::m_CachedZCoef {}
private

Definition at line 318 of file itkMultivariateLegendrePolynomial.h.

◆ m_CoefficientArray

CoefficientArrayType itk::MultivariateLegendrePolynomial::m_CoefficientArray {}
private

Definition at line 315 of file itkMultivariateLegendrePolynomial.h.

◆ m_Degree

unsigned int itk::MultivariateLegendrePolynomial::m_Degree {}
private

Definition at line 312 of file itkMultivariateLegendrePolynomial.h.

◆ m_Dimension

unsigned int itk::MultivariateLegendrePolynomial::m_Dimension {}
private

Definition at line 311 of file itkMultivariateLegendrePolynomial.h.

◆ m_DomainSize

DomainSizeType itk::MultivariateLegendrePolynomial::m_DomainSize {}
private

Definition at line 310 of file itkMultivariateLegendrePolynomial.h.

◆ m_NormFactor

DoubleArrayType itk::MultivariateLegendrePolynomial::m_NormFactor {}
private

Definition at line 320 of file itkMultivariateLegendrePolynomial.h.

◆ m_NumberOfCoefficients

unsigned int itk::MultivariateLegendrePolynomial::m_NumberOfCoefficients {}
private

Definition at line 313 of file itkMultivariateLegendrePolynomial.h.

◆ m_PrevY

IndexValueType itk::MultivariateLegendrePolynomial::m_PrevY {}
private

Definition at line 321 of file itkMultivariateLegendrePolynomial.h.

◆ m_PrevZ

IndexValueType itk::MultivariateLegendrePolynomial::m_PrevZ {}
private

Definition at line 322 of file itkMultivariateLegendrePolynomial.h.

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