#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 [113] and [112].

Definition at line 69 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 79 of file itkMultivariateLegendrePolynomial.h.

◆ DomainSizeType

using itk::MultivariateLegendrePolynomial::DomainSizeType = ULongArrayType

The size of the domain.

Definition at line 86 of file itkMultivariateLegendrePolynomial.h.

◆ DoubleArrayType

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

Definition at line 74 of file itkMultivariateLegendrePolynomial.h.

◆ IndexType

using itk::MultivariateLegendrePolynomial::IndexType = LongArrayType

Definition at line 87 of file itkMultivariateLegendrePolynomial.h.

◆ LongArrayType

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

Definition at line 76 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 83 of file itkMultivariateLegendrePolynomial.h.

◆ Self

using itk::MultivariateLegendrePolynomial::Self = MultivariateLegendrePolynomial

Definition at line 72 of file itkMultivariateLegendrePolynomial.h.

◆ ULongArrayType

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

Definition at line 75 of file itkMultivariateLegendrePolynomial.h.

Constructor & Destructor Documentation

◆ MultivariateLegendrePolynomial()

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

Constructor.

Referenced by itk::MultivariateLegendrePolynomial::SimpleForwardIterator::SimpleForwardIterator().

◆ ~MultivariateLegendrePolynomial()

virtual itk::MultivariateLegendrePolynomial::~MultivariateLegendrePolynomial ( )

virtual

Destructor.

Member Function Documentation

◆ CalculateXCoef()

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

protected

Referenced by Evaluate().

◆ CalculateYCoef()

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

protected

Referenced by Evaluate().

◆ 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 162 of file itkMultivariateLegendrePolynomial.h.

References CalculateXCoef(), CalculateYCoef(), LegendreSum(), m_CachedXCoef, m_CachedYCoef, m_CoefficientArray, m_Degree, m_Dimension, m_NormFactor, m_PrevY, and m_PrevZ.

◆ 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 104 of file itkMultivariateLegendrePolynomial.h.

References m_Degree.

◆ GetDimension()

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

inline

Gets the dimension.

Definition at line 97 of file itkMultivariateLegendrePolynomial.h.

References m_Dimension.

Referenced by itk::MultivariateLegendrePolynomial::SimpleForwardIterator::SimpleForwardIterator().

◆ GetDomainSize()

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

inline

Gets each dimension's size.

Definition at line 123 of file itkMultivariateLegendrePolynomial.h.

References m_DomainSize.

Referenced by itk::MultivariateLegendrePolynomial::SimpleForwardIterator::SimpleForwardIterator().

◆ 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