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itk::MultivariateLegendrePolynomial

itk::MultivariateLegendrePolynomial Class Reference

2D and 3D multivariate Legendre Polynomial More...

#include <itkMultivariateLegendrePolynomial.h>

List of all members.

Classes

class  CoefficientVectorSizeMismatch
class  SimpleForwardIterator
 Iterator which only supports forward iteration and Begin(), IsAtEnd(), and Get() method which work just like as SimpleImageRegionIterator. More...

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 (void) 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 ParametersType &coef) throw (CoefficientVectorSizeMismatch)
void SetCoefficients (const CoefficientArrayType &coef) throw (CoefficientVectorSizeMismatch)
virtual ~MultivariateLegendrePolynomial ()



double Evaluate (IndexType &index)
unsigned int GetNumberOfCoefficients (unsigned int dimension, unsigned int degree)
unsigned int GetNumberOfCoefficients ()
void Print (std::ostream &os)
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

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 implemenations 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.ia.unc.edu/~styner/docs/tmi00.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.ia.unc.edu/~styner/docs/StynerTR97.pdf)

Definition at line 71 of file itkMultivariateLegendrePolynomial.h.

Member Typedef Documentation

typedef DoubleArrayType itk::MultivariateLegendrePolynomial::CoefficientArrayType

Internal coefficient storage type.

Definition at line 81 of file itkMultivariateLegendrePolynomial.h.

typedef ULongArrayType itk::MultivariateLegendrePolynomial::DomainSizeType

The size of the domain.

Definition at line 88 of file itkMultivariateLegendrePolynomial.h.

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

Definition at line 76 of file itkMultivariateLegendrePolynomial.h.

typedef LongArrayType itk::MultivariateLegendrePolynomial::IndexType

Definition at line 89 of file itkMultivariateLegendrePolynomial.h.

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

Definition at line 78 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 85 of file itkMultivariateLegendrePolynomial.h.

typedef MultivariateLegendrePolynomial itk::MultivariateLegendrePolynomial::Self

Definition at line 74 of file itkMultivariateLegendrePolynomial.h.

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

Definition at line 77 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 149 of file itkMultivariateLegendrePolynomial.h.

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

Gets Legendre polynomials' coefficients.

unsigned int itk::MultivariateLegendrePolynomial::GetDegree ( void   )  const [inline]

Gets the degree (the degree of Legendre polynomials).

Definition at line 104 of file itkMultivariateLegendrePolynomial.h.

unsigned int itk::MultivariateLegendrePolynomial::GetDimension ( void   )  const [inline]

Gets the dimension.

Definition at line 100 of file itkMultivariateLegendrePolynomial.h.

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

const DomainSizeType& itk::MultivariateLegendrePolynomial::GetDomainSize ( void   )  const [inline]

Gets each dimesion's size.

Definition at line 117 of file itkMultivariateLegendrePolynomial.h.

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

Gets the number of coefficients.

unsigned int itk::MultivariateLegendrePolynomial::GetNumberOfCoefficients (  ) 

Gets the number of coefficients.

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 113 of file itkMultivariateLegendrePolynomial.h.

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 ParametersType &  coef  )  throw (CoefficientVectorSizeMismatch)
void itk::MultivariateLegendrePolynomial::SetCoefficients ( const CoefficientArrayType &  coef  )  throw (CoefficientVectorSizeMismatch)

Sets the Legendre polynomials' parameters.

Warning:
The number of coefficients provided should match the number returned by GetNumberOfCoefficients() otherwise an exception is thrown.
The documentation for this class was generated from the following file:
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