ITK  4.1.0
Insight Segmentation and Registration Toolkit
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itk::MultivariateLegendrePolynomial Class Reference

#include <itkMultivariateLegendrePolynomial.h>

+ Collaboration diagram for itk::MultivariateLegendrePolynomial:

List of all members.

Classes

class  CoefficientVectorSizeMismatch
 Exception object. More...
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 CoefficientArrayTypeGetCoefficients (void) const
unsigned int GetDegree (void) const
unsigned int GetDimension (void) const
const DomainSizeTypeGetDomainSize (void) const
unsigned int GetNumberOfCoefficients (void) const
 MultivariateLegendrePolynomial (unsigned int dimension, unsigned int degree, const DomainSizeType &domainSize)
void SetCoefficients (const CoefficientArrayType &coef) throw ( CoefficientVectorSizeMismatch )
void SetCoefficients (const ParametersType &coef) throw ( CoefficientVectorSizeMismatch )
virtual ~MultivariateLegendrePolynomial ()
DomainSizeType m_DomainSize
unsigned int m_Dimension
unsigned int m_Degree
unsigned int m_NumberOfCoefficients
bool m_MultiplicativeBias
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)

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.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 74 of file itkMultivariateLegendrePolynomial.h.


Member Typedef Documentation

Internal coefficient storage type.

Definition at line 84 of file itkMultivariateLegendrePolynomial.h.

The size of the domain.

Definition at line 91 of file itkMultivariateLegendrePolynomial.h.

Definition at line 79 of file itkMultivariateLegendrePolynomial.h.

Definition at line 92 of file itkMultivariateLegendrePolynomial.h.

Definition at line 81 of file itkMultivariateLegendrePolynomial.h.

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

Definition at line 88 of file itkMultivariateLegendrePolynomial.h.

Definition at line 77 of file itkMultivariateLegendrePolynomial.h.

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

Definition at line 80 of file itkMultivariateLegendrePolynomial.h.


Constructor & Destructor Documentation

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

Constructor.

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

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 155 of file itkMultivariateLegendrePolynomial.h.

Gets Legendre polynomials' coefficients.

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

Gets the degree (the degree of Legendre polynomials).

Definition at line 107 of file itkMultivariateLegendrePolynomial.h.

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

Gets each dimesion's size.

Definition at line 120 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 116 of file itkMultivariateLegendrePolynomial.h.

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

Sets the Legendre polynomials' parameters.

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

Member Data Documentation

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.

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.

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.

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.

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.

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.

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 288 of file itkMultivariateLegendrePolynomial.h.

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.

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.

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.

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.

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: