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<typename TPixel, unsigned int VDimension = 2, typename 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
using	PixelRealType = typename Superclass::PixelRealType
using	PixelType = typename Superclass::PixelType
using	Self = HigherOrderAccurateDerivativeOperator
using	Superclass = NeighborhoodOperator< TPixel, VDimension, TAllocator >
Public Types inherited from itk::NeighborhoodOperator< TPixel, VDimension, TAllocator >
using	PixelRealType = typename NumericTraits< TPixel >::RealType
using	PixelType = TPixel
using	Self = NeighborhoodOperator
using	SizeType = typename Superclass::SizeType
using	SliceIteratorType = SliceIterator< TPixel, Self >
using	Superclass = Neighborhood< TPixel, VDimension, TAllocator >
Public Types inherited from itk::Neighborhood< TPixel, VDimension, TAllocator >
using	AllocatorType = TAllocator
using	ConstIterator = typename AllocatorType::const_iterator
using	DimensionValueType = unsigned int
using	Iterator = typename AllocatorType::iterator
using	NeighborIndexType = SizeValueType
using	OffsetType = Offset< VDimension >
using	PixelType = TPixel
using	RadiusType = ::itk::Size< VDimension >
using	Self = Neighborhood
using	SizeType = ::itk::Size< VDimension >
using	SizeValueType = typename SizeType::SizeValueType
using	SliceIteratorType = SliceIterator< TPixel, Self >

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)
Self &	operator= (const Self &other)
void	PrintSelf (std::ostream &os, Indent i) const override
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)
Self &	operator= (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)
	Neighborhood (Self &&)=default
bool	operator!= (const Self &other) const
Self &	operator= (const Self &other)
Self &	operator= (Self &&)=default
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 ()=default
	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)
AllocatorType &	GetBufferReference ()
const AllocatorType &	GetBufferReference () const
TPixel &	operator[] (const OffsetType &o)
const TPixel &	operator[] (const OffsetType &o) const

Protected Types
using	CoefficientVector = typename Superclass::CoefficientVector
Protected Types inherited from itk::NeighborhoodOperator< TPixel, VDimension, TAllocator >
using	CoefficientVector = std::vector< PixelRealType >

Protected Member Functions
CoefficientVector	GenerateCoefficients () override
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) override
CoefficientVector	GenerateFirstOrderCoefficients ()

Additional Inherited Members
Static Public Attributes inherited from itk::Neighborhood< TPixel, VDimension, TAllocator >
static constexpr unsigned int	NeighborhoodDimension = VDimension

Member Typedef Documentation

template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>

using itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::CoefficientVector = typename Superclass::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<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>

using itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::PixelRealType = typename Superclass::PixelRealType

Definition at line 73 of file itkHigherOrderAccurateDerivativeOperator.h.

template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>

using itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::PixelType = typename Superclass::PixelType

Definition at line 72 of file itkHigherOrderAccurateDerivativeOperator.h.

template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>

using itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::Self = HigherOrderAccurateDerivativeOperator

Standard class type alias.

Definition at line 68 of file itkHigherOrderAccurateDerivativeOperator.h.

template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>

using itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::Superclass = NeighborhoodOperator< TPixel, VDimension, TAllocator >

Definition at line 70 of file itkHigherOrderAccurateDerivativeOperator.h.

Constructor & Destructor Documentation

template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>

itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::HigherOrderAccurateDerivativeOperator ( )

inline

Constructor.

Definition at line 79 of file itkHigherOrderAccurateDerivativeOperator.h.

template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>

itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::HigherOrderAccurateDerivativeOperator ( const Self &  other )

inline

Copy constructor.

Definition at line 85 of file itkHigherOrderAccurateDerivativeOperator.h.

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

Member Function Documentation

template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>

void itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::Fill ( const CoefficientVector &  coeff )

inlineoverrideprotectedvirtual

Arranges coefficients spatially in the memory buffer.

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

Definition at line 136 of file itkHigherOrderAccurateDerivativeOperator.h.

References itk::NeighborhoodOperator< TPixel, VDimension, TAllocator >::FillCenteredDirectional().

template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>

CoefficientVector itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::GenerateCoefficients ( )

overrideprotectedvirtual

Calculates operator coefficients.

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

template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>

CoefficientVector itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::GenerateFirstOrderCoefficients ( )

private

Arranges coefficients spatially in the memory buffer.

template<typename TPixel , unsigned int VDimension = 2, typename 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<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>

unsigned int itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::GetOrder ( ) const

inline

Returns the order of the derivative.

Definition at line 105 of file itkHigherOrderAccurateDerivativeOperator.h.

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

template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>

unsigned int itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::GetOrderOfAccuracy ( ) const

inline

Definition at line 115 of file itkHigherOrderAccurateDerivativeOperator.h.

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

template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>

Self& itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::operator= ( const Self &  other )

inline

Assignment operator

Definition at line 90 of file itkHigherOrderAccurateDerivativeOperator.h.

References itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::m_Order, and itk::NeighborhoodOperator< TPixel, VDimension, TAllocator >::operator=().

template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>

void itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::PrintSelf ( std::ostream &  os, Indent  i  ) const

inlineoverridevirtual

Prints some debugging information

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

Definition at line 118 of file itkHigherOrderAccurateDerivativeOperator.h.

References itk::Indent::GetNextIndent(), itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::m_Order, itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::m_OrderOfAccuracy, and itk::NeighborhoodOperator< TPixel, VDimension, TAllocator >::PrintSelf().

template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>

void itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::SetOrder ( const unsigned int &  order )

inline

Sets the order of the derivative.

Definition at line 99 of file itkHigherOrderAccurateDerivativeOperator.h.

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

template<typename TPixel , unsigned int VDimension = 2, typename 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<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>

unsigned int itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::m_Order

private

Order of the derivative.

Definition at line 143 of file itkHigherOrderAccurateDerivativeOperator.h.

Referenced by itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::GetOrder(), itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::HigherOrderAccurateDerivativeOperator(), itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::operator=(), itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::PrintSelf(), and itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::SetOrder().

template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>

unsigned int itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::m_OrderOfAccuracy

private

Order of accuracy.

Definition at line 146 of file itkHigherOrderAccurateDerivativeOperator.h.

Referenced by itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::GetOrderOfAccuracy(), itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::PrintSelf(), and itk::HigherOrderAccurateDerivativeOperator< TPixel, VDimension, TAllocator >::SetOrderOfAccuracy().

---

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

• itkHigherOrderAccurateDerivativeOperator.h