ITK  4.8.0
Insight Segmentation and Registration Toolkit
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itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator > Class Template Reference

#include <itkHigherOrderAccurateDerivativeOperator.h>

+ Inheritance diagram for itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >:
+ Collaboration diagram for itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >:

Detailed Description

template<class TPixel, unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
class itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >

A NeighborhoodOperator for calculating an n-th order accurate derivative at a pixel.

Calculate the image derivative from a higher order accurate central-difference derivative kernel.

Based on the work here:

Khan, IR and Ohba, Ryoji. "Closed-form expressions for the finite difference approximations of first and higher derivatives based on Taylor series." Journal of Computational and Applied Mathematics. vol 107. p. 179-193. 1999.

Khan, IR and Ohba, Ryoji. "Taylor series based finite difference approximations of higher-degree derivatives." Journal of Computational and Applied Mathematics. vol 154. p. 115-124. 2003.

To specify the order of accuracy, use SetOrderOfAccuracy(). The approximation will be accurate to two times the OrderOfAccuracy in terms of Taylor series terms.

Todo:
: implement support for higher order derivatives.
See Also
DerivativeOperator
NeighborhoodOperator
Neighborhood
ForwardDifferenceOperator
BackwardDifferenceOperator

Definition at line 62 of file itkHigherOrderAccurateDerivativeOperator.h.

Public Types

typedef Superclass::PixelRealType PixelRealType
 
typedef Superclass::PixelType PixelType
 
typedef
HigherOrderAccurateDerivativeOperator 
Self
 
typedef NeighborhoodOperator
< TPixel, VDimension,
TAllocator > 
Superclass
 
- Public Types inherited from itk::NeighborhoodOperator< TPixel, VDimension, TAllocator >
typedef NumericTraits< TPixel >
::RealType 
PixelRealType
 
typedef TPixel PixelType
 
typedef NeighborhoodOperator Self
 
typedef Superclass::SizeType SizeType
 
typedef SliceIterator< TPixel,
Self
SliceIteratorType
 
typedef Neighborhood< TPixel,
VDimension, TAllocator > 
Superclass
 
- Public Types inherited from itk::Neighborhood< TPixel, VDimension, TAllocator >
typedef TAllocator AllocatorType
 
typedef
AllocatorType::const_iterator 
ConstIterator
 
typedef unsigned int DimensionValueType
 
typedef AllocatorType::iterator Iterator
 
typedef SizeValueType NeighborIndexType
 
typedef Offset< VDimension > OffsetType
 
typedef TPixel PixelType
 
typedef Neighborhood Self
 
typedef SizeType::SizeValueType SizeValueType
 
typedef SliceIterator< TPixel,
Self
SliceIteratorType
 

Public Member Functions

virtual const char * GetNameOfClass () const
 
unsigned int GetOrder () const
 
unsigned int GetOrderOfAccuracy () const
 
 HigherOrderAccurateDerivativeOperator ()
 
 HigherOrderAccurateDerivativeOperator (const Self &other)
 
void SetOrder (const unsigned int &order)
 
void SetOrderOfAccuracy (const unsigned int &order)
 
Selfoperator= (const Self &other)
 
virtual void PrintSelf (std::ostream &os, Indent i) const
 
- Public Member Functions inherited from itk::NeighborhoodOperator< TPixel, VDimension, TAllocator >
virtual void CreateDirectional ()
 
virtual void CreateToRadius (const SizeType &)
 
virtual void CreateToRadius (const SizeValueType)
 
virtual void FlipAxes ()
 
unsigned long GetDirection () const
 
 NeighborhoodOperator ()
 
 NeighborhoodOperator (const Self &orig)
 
void ScaleCoefficients (PixelRealType)
 
void SetDirection (const unsigned long &direction)
 
Selfoperator= (const Self &orig)
 
- Public Member Functions inherited from itk::Neighborhood< TPixel, VDimension, TAllocator >
NeighborIndexType GetCenterNeighborhoodIndex () const
 
TPixel GetCenterValue () const
 
virtual NeighborIndexType GetNeighborhoodIndex (const OffsetType &) const
 
OffsetType GetOffset (NeighborIndexType i) const
 
const SizeType GetRadius () const
 
SizeValueType GetRadius (DimensionValueType n) const
 
SizeValueType GetSize (DimensionValueType n) const
 
SizeType GetSize () const
 
std::slice GetSlice (unsigned int) const
 
OffsetValueType GetStride (DimensionValueType axis) const
 
 itkTypeMacroNoParent (Neighborhood)
 
 Neighborhood (const Self &other)
 
bool operator!= (const Self &other) const
 
Selfoperator= (const Self &other)
 
bool operator== (const Self &other) const
 
void Print (std::ostream &os) const
 
void SetRadius (const SizeType &)
 
void SetRadius (const SizeValueType)
 
NeighborIndexType Size () const
 
virtual ~Neighborhood ()
 
 Neighborhood ()
 
Iterator End ()
 
Iterator Begin ()
 
ConstIterator End () const
 
ConstIterator Begin () const
 
TPixel & operator[] (NeighborIndexType i)
 
const TPixel & operator[] (NeighborIndexType i) const
 
TPixel & GetElement (NeighborIndexType i)
 
void SetRadius (const SizeValueType *rad)
 
AllocatorTypeGetBufferReference ()
 
const AllocatorTypeGetBufferReference () const
 
TPixel & operator[] (const OffsetType &o)
 
const TPixel & operator[] (const OffsetType &o) const
 

Protected Types

typedef
Superclass::CoefficientVector 
CoefficientVector
 
- Protected Types inherited from itk::NeighborhoodOperator< TPixel, VDimension, TAllocator >
typedef std::vector
< PixelRealType
CoefficientVector
 

Protected Member Functions

CoefficientVector GenerateCoefficients ()
 
- Protected Member Functions inherited from itk::NeighborhoodOperator< TPixel, VDimension, TAllocator >
virtual void FillCenteredDirectional (const CoefficientVector &)
 
void InitializeToZero ()
 
- Protected Member Functions inherited from itk::Neighborhood< TPixel, VDimension, TAllocator >
virtual void Allocate (NeighborIndexType i)
 
virtual void ComputeNeighborhoodOffsetTable ()
 
virtual void ComputeNeighborhoodStrideTable ()
 
void SetSize ()
 

Private Attributes

unsigned int m_Order
 
unsigned int m_OrderOfAccuracy
 
void Fill (const CoefficientVector &coeff)
 
CoefficientVector GenerateFirstOrderCoefficients ()
 

Additional Inherited Members

- Public Attributes inherited from itk::Neighborhood< TPixel, VDimension, TAllocator >
typedef::itk::Size< VDimension > RadiusType
 
typedef::itk::Size< VDimension > SizeType
 
- Static Public Attributes inherited from itk::Neighborhood< TPixel, VDimension, TAllocator >
static const unsigned int NeighborhoodDimension = VDimension
 

Member Typedef Documentation

template<class TPixel , unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
typedef Superclass::CoefficientVector itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::CoefficientVector
protected

Typedef support for coefficient vector type. Necessary to work around compiler bug on VC++.

Definition at line 130 of file itkHigherOrderAccurateDerivativeOperator.h.

template<class TPixel , unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
typedef Superclass::PixelRealType itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::PixelRealType

Definition at line 73 of file itkHigherOrderAccurateDerivativeOperator.h.

template<class TPixel , unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
typedef Superclass::PixelType itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::PixelType

Definition at line 72 of file itkHigherOrderAccurateDerivativeOperator.h.

template<class TPixel , unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
typedef HigherOrderAccurateDerivativeOperator itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::Self

Standard class typedefs.

Definition at line 68 of file itkHigherOrderAccurateDerivativeOperator.h.

template<class TPixel , unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
typedef NeighborhoodOperator< TPixel, VDimension, TAllocator > itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::Superclass

Definition at line 70 of file itkHigherOrderAccurateDerivativeOperator.h.

Constructor & Destructor Documentation

template<class TPixel , unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::HigherOrderAccurateDerivativeOperator ( )
inline

Constructor.

Definition at line 79 of file itkHigherOrderAccurateDerivativeOperator.h.

template<class TPixel , unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::HigherOrderAccurateDerivativeOperator ( const Self other)
inline

Member Function Documentation

template<class TPixel , unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
void itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::Fill ( const CoefficientVector coeff)
inlineprotectedvirtual
template<class TPixel , unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
CoefficientVector itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::GenerateCoefficients ( )
protectedvirtual

Calculates operator coefficients.

Implements itk::NeighborhoodOperator< TPixel, VDimension, TAllocator >.

template<class TPixel , unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
CoefficientVector itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::GenerateFirstOrderCoefficients ( )
private

Arranges coefficients spatially in the memory buffer.

template<class TPixel , unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
virtual const char* itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::GetNameOfClass ( ) const
virtual

Run-time type information (and related methods).

Reimplemented from itk::NeighborhoodOperator< TPixel, VDimension, TAllocator >.

template<class TPixel , unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
unsigned int itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::GetOrder ( ) const
inline
template<class TPixel , unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
unsigned int itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::GetOrderOfAccuracy ( ) const
inline
template<class TPixel , unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
Self& itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::operator= ( const Self other)
inline
template<class TPixel , unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
virtual void itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::PrintSelf ( std::ostream &  os,
Indent  i 
) const
inlinevirtual
template<class TPixel , unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
void itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::SetOrder ( const unsigned int &  order)
inline
template<class TPixel , unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
void itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::SetOrderOfAccuracy ( const unsigned int &  order)
inline

Sets the order of accuracy of the derivative. The derivative estimate will be accurate out to two times the given order in terms of Taylor Series terms. The radius of the neighborhood operator is also equal to the given order.

Definition at line 110 of file itkHigherOrderAccurateDerivativeOperator.h.

References itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::m_OrderOfAccuracy.

Member Data Documentation

template<class TPixel , unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
unsigned int itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::m_Order
private
template<class TPixel , unsigned int VDimension = 2, class TAllocator = NeighborhoodAllocator< TPixel >>
unsigned int itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::m_OrderOfAccuracy
private

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