#include <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

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

void	SetCoefficients (const CoefficientArrayType &coefficients)

void	SetCoefficients (const ParametersType &coefficients)

virtual	~MultivariateLegendrePolynomial ()

DomainSizeType	m_DomainSize

unsigned int	m_Dimension

unsigned int	m_Degree

unsigned int	m_NumberOfCoefficients

CoefficientArrayType	m_CoefficientArray

CoefficientArrayType	m_CachedXCoef

CoefficientArrayType	m_CachedYCoef

CoefficientArrayType	m_CachedZCoef

DoubleArrayType	m_NormFactor

IndexValueType	m_PrevY

IndexValueType	m_PrevZ

double	Evaluate (IndexType &index)

unsigned int	GetNumberOfCoefficients (unsigned int dimension, unsigned int degree)

void	Print (std::ostream &os) const

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

double	LegendreSum (const double x, int n, const CoefficientArrayType &coef, int offset=0)

void	CalculateXCoef (double norm_y, const CoefficientArrayType &coef)

void	CalculateYCoef (double norm_z, const CoefficientArrayType &coef)

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, (http://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 (http://www.cs.unc.edu/~styner/docs/StynerTR97.pdf)

Definition at line 77 of file itkMultivariateLegendrePolynomial.h.

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

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

◆ CalculateYCoef()

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

protected

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

◆ 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

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

◆ Print()

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

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

◆ PrintSelf()

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

protected

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

◆ 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

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 317 of file itkMultivariateLegendrePolynomial.h.

◆ m_CachedYCoef

CoefficientArrayType itk::MultivariateLegendrePolynomial::m_CachedYCoef

private

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 318 of file itkMultivariateLegendrePolynomial.h.

◆ m_CachedZCoef

CoefficientArrayType itk::MultivariateLegendrePolynomial::m_CachedZCoef

private

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 319 of file itkMultivariateLegendrePolynomial.h.

◆ m_CoefficientArray

CoefficientArrayType itk::MultivariateLegendrePolynomial::m_CoefficientArray

private

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 316 of file itkMultivariateLegendrePolynomial.h.

◆ m_Degree

unsigned int itk::MultivariateLegendrePolynomial::m_Degree

private

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 313 of file itkMultivariateLegendrePolynomial.h.

◆ m_Dimension

unsigned int itk::MultivariateLegendrePolynomial::m_Dimension

private

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 312 of file itkMultivariateLegendrePolynomial.h.

◆ m_DomainSize

DomainSizeType itk::MultivariateLegendrePolynomial::m_DomainSize

private

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 311 of file itkMultivariateLegendrePolynomial.h.

◆ m_NormFactor

DoubleArrayType itk::MultivariateLegendrePolynomial::m_NormFactor

private

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 321 of file itkMultivariateLegendrePolynomial.h.

◆ m_NumberOfCoefficients

unsigned int itk::MultivariateLegendrePolynomial::m_NumberOfCoefficients

private

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 314 of file itkMultivariateLegendrePolynomial.h.

◆ m_PrevY

IndexValueType itk::MultivariateLegendrePolynomial::m_PrevY

private

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 322 of file itkMultivariateLegendrePolynomial.h.

◆ m_PrevZ

IndexValueType itk::MultivariateLegendrePolynomial::m_PrevZ

private

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 323 of file itkMultivariateLegendrePolynomial.h.

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

itkMultivariateLegendrePolynomial.h

Classes

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ CoefficientArrayType

◆ DomainSizeType

◆ DoubleArrayType

◆ IndexType

◆ LongArrayType

◆ ParametersType

◆ Self

◆ ULongArrayType

Constructor & Destructor Documentation

◆ MultivariateLegendrePolynomial()

◆ ~MultivariateLegendrePolynomial()

Member Function Documentation

◆ CalculateXCoef()

◆ CalculateYCoef()

◆ Evaluate()

◆ GetCoefficients()

◆ GetDegree()

◆ GetDimension()

◆ GetDomainSize()

◆ GetNumberOfCoefficients() [1/2]

◆ GetNumberOfCoefficients() [2/2]

◆ LegendreSum()

◆ Print()

◆ PrintSelf()

◆ SetCoefficients() [1/2]

◆ SetCoefficients() [2/2]

Member Data Documentation

◆ m_CachedXCoef

◆ m_CachedYCoef

◆ m_CachedZCoef

◆ m_CoefficientArray

◆ m_Degree

◆ m_Dimension

◆ m_DomainSize

◆ m_NormFactor

◆ m_NumberOfCoefficients

◆ m_PrevY

◆ m_PrevZ