#include <itkMultivariateLegendrePolynomial.h>

Collaboration diagram for itk::MultivariateLegendrePolynomial:

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 75 of file itkMultivariateLegendrePolynomial.h.

Classes
class	CoefficientVectorSizeMismatch

class	SimpleForwardIterator

Public Types
typedef DoubleArrayType	CoefficientArrayType

typedef ULongArrayType	DomainSizeType

typedef std::vector< double >	DoubleArrayType

typedef LongArrayType	IndexType

typedef std::vector< long >	LongArrayType

typedef Array< double >	ParametersType

typedef MultivariateLegendrePolynomial	Self

typedef std::vector< unsigned long >	ULongArrayType

Public Member Functions
const CoefficientArrayType &	GetCoefficients () const

unsigned int	GetDegree (void) const

unsigned int	GetDimension (void) const

const DomainSizeType &	GetDomainSize (void) const

unsigned int	GetNumberOfCoefficients (void) const

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

void	SetCoefficients (const CoefficientArrayType &coef)

void	SetCoefficients (const ParametersType &coef)

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	GetNumberOfCoefficients (unsigned int dimension, unsigned int degree)

void	Print (std::ostream &os)

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

typedef DoubleArrayType itk::MultivariateLegendrePolynomial::CoefficientArrayType

Internal coefficient storage type.

Definition at line 85 of file itkMultivariateLegendrePolynomial.h.

typedef ULongArrayType itk::MultivariateLegendrePolynomial::DomainSizeType

The size of the domain.

Definition at line 92 of file itkMultivariateLegendrePolynomial.h.

typedef std::vector< double > itk::MultivariateLegendrePolynomial::DoubleArrayType

Definition at line 80 of file itkMultivariateLegendrePolynomial.h.

typedef LongArrayType itk::MultivariateLegendrePolynomial::IndexType

Definition at line 93 of file itkMultivariateLegendrePolynomial.h.

typedef std::vector< long > itk::MultivariateLegendrePolynomial::LongArrayType

Definition at line 82 of file itkMultivariateLegendrePolynomial.h.

typedef Array< double > itk::MultivariateLegendrePolynomial::ParametersType

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

Definition at line 89 of file itkMultivariateLegendrePolynomial.h.

typedef MultivariateLegendrePolynomial itk::MultivariateLegendrePolynomial::Self

Definition at line 78 of file itkMultivariateLegendrePolynomial.h.

typedef std::vector< unsigned long > itk::MultivariateLegendrePolynomial::ULongArrayType

Definition at line 81 of file itkMultivariateLegendrePolynomial.h.

Constructor & Destructor Documentation

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

Constructor.

virtual itk::MultivariateLegendrePolynomial::~MultivariateLegendrePolynomial ( )

virtual

Destructor.

Member Function Documentation

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

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

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 154 of file itkMultivariateLegendrePolynomial.h.

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

Gets Legendre polynomials' coefficients.

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

inline

Gets the degree (the degree of Legendre polynomials).

Definition at line 108 of file itkMultivariateLegendrePolynomial.h.

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

inline

Gets the dimension.

Definition at line 104 of file itkMultivariateLegendrePolynomial.h.

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

inline

Gets each dimesion's size.

Definition at line 121 of file itkMultivariateLegendrePolynomial.h.

unsigned int itk::MultivariateLegendrePolynomial::GetNumberOfCoefficients ( void ) 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 117 of file itkMultivariateLegendrePolynomial.h.

unsigned int itk::MultivariateLegendrePolynomial::GetNumberOfCoefficients ( )

Gets the number of coefficients.

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

Gets the number of coefficients.

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

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

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

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

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

Sets the Legendre polynomials' parameters.

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

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

Member Data Documentation

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 295 of file itkMultivariateLegendrePolynomial.h.

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 296 of file itkMultivariateLegendrePolynomial.h.

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 297 of file itkMultivariateLegendrePolynomial.h.

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 294 of file itkMultivariateLegendrePolynomial.h.

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 291 of file itkMultivariateLegendrePolynomial.h.

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 290 of file itkMultivariateLegendrePolynomial.h.

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 289 of file itkMultivariateLegendrePolynomial.h.

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 299 of file itkMultivariateLegendrePolynomial.h.

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 292 of file itkMultivariateLegendrePolynomial.h.

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 300 of file itkMultivariateLegendrePolynomial.h.

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 301 of file itkMultivariateLegendrePolynomial.h.

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

itkMultivariateLegendrePolynomial.h

Detailed Description

Classes

Public Types

Public Member Functions

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation