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itk::MultivariateLegendrePolynomial Class Reference
Module ITKPolynomials

#include <itkMultivariateLegendrePolynomial.h>

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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

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 &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

using itk::MultivariateLegendrePolynomial::CoefficientArrayType = DoubleArrayType

Internal coefficient storage type.

Definition at line 85 of file itkMultivariateLegendrePolynomial.h.

using itk::MultivariateLegendrePolynomial::DomainSizeType = ULongArrayType

The size of the domain.

Definition at line 92 of file itkMultivariateLegendrePolynomial.h.

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

Definition at line 80 of file itkMultivariateLegendrePolynomial.h.

using itk::MultivariateLegendrePolynomial::IndexType = LongArrayType

Definition at line 93 of file itkMultivariateLegendrePolynomial.h.

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

Definition at line 82 of file itkMultivariateLegendrePolynomial.h.

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

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

Definition at line 89 of file itkMultivariateLegendrePolynomial.h.

using itk::MultivariateLegendrePolynomial::Self = MultivariateLegendrePolynomial

Definition at line 78 of file itkMultivariateLegendrePolynomial.h.

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

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 ( ) const
inline

Gets the degree (the degree of Legendre polynomials).

Definition at line 108 of file itkMultivariateLegendrePolynomial.h.

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

Gets the dimension.

Definition at line 104 of file itkMultivariateLegendrePolynomial.h.

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

Gets each dimesion's size.

Definition at line 121 of file itkMultivariateLegendrePolynomial.h.

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 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.

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