ITK
4.3.0
Insight Segmentation and Registration Toolkit
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#include <itkMultivariateLegendrePolynomial.h>
2D and 3D multivariate Legendre Polynomial
In 2D,
where P_i() denoting a Legendre polynomial of degree i and l it the degree of the polynomial
In 3D,
The size of the parameter vector for 2D is , and for 3D is
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.
"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.
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 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 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 |
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) |
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.
typedef std::vector< double > itk::MultivariateLegendrePolynomial::DoubleArrayType |
Definition at line 79 of file itkMultivariateLegendrePolynomial.h.
Definition at line 92 of file itkMultivariateLegendrePolynomial.h.
typedef std::vector< long > itk::MultivariateLegendrePolynomial::LongArrayType |
Definition at line 81 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 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.
itk::MultivariateLegendrePolynomial::MultivariateLegendrePolynomial | ( | unsigned int | dimension, |
unsigned int | degree, | ||
const DomainSizeType & | domainSize | ||
) |
Constructor.
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virtual |
Destructor.
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protected |
In the case which the bias field is 2D, it returns bias value at the point which is specified by the index
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In the case which the bias field is 2D, it returns bias value at the point which is specified by the index
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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.
const CoefficientArrayType& itk::MultivariateLegendrePolynomial::GetCoefficients | ( | void | ) | const |
Gets Legendre polynomials' coefficients.
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Gets the degree (the degree of Legendre polynomials).
Definition at line 107 of file itkMultivariateLegendrePolynomial.h.
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Gets the dimension.
Definition at line 103 of file itkMultivariateLegendrePolynomial.h.
Referenced by itk::MultivariateLegendrePolynomial::SimpleForwardIterator::SimpleForwardIterator().
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Gets each dimesion's size.
Definition at line 120 of file itkMultivariateLegendrePolynomial.h.
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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
Definition at line 116 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.
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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
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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 | ) | throw ( CoefficientVectorSizeMismatch ) |
Sets the Legendre polynomials' parameters.
void itk::MultivariateLegendrePolynomial::SetCoefficients | ( | const ParametersType & | coef | ) | throw ( CoefficientVectorSizeMismatch ) |
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.