itk::MultivariateLegendrePolynomial Class Reference

#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	SetCoefficients (const CoefficientArrayType &coefficients)
void	SetCoefficients (const ParametersType &coefficients)
virtual	~MultivariateLegendrePolynomial ()
double	Evaluate (IndexType &index)
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 {}
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)

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 317 of file itkMultivariateLegendrePolynomial.h.

m_CachedYCoef

CoefficientArrayType itk::MultivariateLegendrePolynomial::m_CachedYCoef {}

private

Definition at line 318 of file itkMultivariateLegendrePolynomial.h.

m_CachedZCoef

CoefficientArrayType itk::MultivariateLegendrePolynomial::m_CachedZCoef {}

private

Definition at line 319 of file itkMultivariateLegendrePolynomial.h.

m_CoefficientArray

CoefficientArrayType itk::MultivariateLegendrePolynomial::m_CoefficientArray {}

private

Definition at line 316 of file itkMultivariateLegendrePolynomial.h.

m_Degree

unsigned int itk::MultivariateLegendrePolynomial::m_Degree {}

private

Definition at line 313 of file itkMultivariateLegendrePolynomial.h.

m_Dimension

unsigned int itk::MultivariateLegendrePolynomial::m_Dimension {}

private

Definition at line 312 of file itkMultivariateLegendrePolynomial.h.

m_DomainSize

DomainSizeType itk::MultivariateLegendrePolynomial::m_DomainSize {}

private

Definition at line 311 of file itkMultivariateLegendrePolynomial.h.

m_NormFactor

DoubleArrayType itk::MultivariateLegendrePolynomial::m_NormFactor {}

private

Definition at line 321 of file itkMultivariateLegendrePolynomial.h.

m_NumberOfCoefficients

unsigned int itk::MultivariateLegendrePolynomial::m_NumberOfCoefficients {}

private

Definition at line 314 of file itkMultivariateLegendrePolynomial.h.

m_PrevY

IndexValueType itk::MultivariateLegendrePolynomial::m_PrevY {}

private

Definition at line 322 of file itkMultivariateLegendrePolynomial.h.

m_PrevZ

IndexValueType itk::MultivariateLegendrePolynomial::m_PrevZ {}

private

Definition at line 323 of file itkMultivariateLegendrePolynomial.h.

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

• itkMultivariateLegendrePolynomial.h