#include <itkGaussianDerivativeOperator.h>

Inheritance diagram for itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >:

Collaboration diagram for itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >:

Public Types
using	DerivativeOperatorType = DerivativeOperator< TPixel, VDimension, TAllocator >

using	GaussianOperatorType = GaussianOperator< TPixel, VDimension, TAllocator >

using	InterpolationModeEnum = GaussianDerivativeOperatorEnums::InterpolationMode

using	Self = GaussianDerivativeOperator

using	Superclass = NeighborhoodOperator< TPixel, VDimension, TAllocator >

Public Types inherited from itk::NeighborhoodOperator< TPixel, VDimension, TAllocator >
using	PixelType = TPixel

using	Self = NeighborhoodOperator

using	SizeType = typename Superclass::SizeType

using	SliceIteratorType = SliceIterator< TPixel, Self >

using	Superclass = Neighborhood< TPixel, VDimension, TAllocator >

using	PixelRealType = typename NumericTraits< TPixel >::RealType

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 >

using	CoefficientVector = typename Superclass::CoefficientVector

bool	m_NormalizeAcrossScale { true }

double	m_Variance { 1.0 }

double	m_MaximumError { 0.005 }

unsigned int	m_MaximumKernelWidth { 30 }

unsigned int	m_Order { 1 }

double	m_Spacing { 1.0 }

void	SetNormalizeAcrossScale (bool flag)

bool	GetNormalizeAcrossScale () const

virtual void	NormalizeAcrossScaleOn ()

virtual void	NormalizeAcrossScaleOff ()

void	SetVariance (const double variance)

double	GetVariance () const

void	SetSpacing (const double spacing)

double	GetSpacing () const

void	SetMaximumError (const double maxerror)

double	GetMaximumError ()

void	SetMaximumKernelWidth (unsigned int n)

void	SetOrder (const unsigned int order)

unsigned int	GetOrder () const

void	PrintSelf (std::ostream &os, Indent i) const override

static double	ModifiedBesselI0 (double)

static double	ModifiedBesselI1 (double)

static double	ModifiedBesselI (int, double)

CoefficientVector	GenerateCoefficients () override

void	Fill (const CoefficientVector &coeff) override

CoefficientVector	GenerateGaussianCoefficients () const

const char *	GetNameOfClass () const override

Additional Inherited Members
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

void	SetDirection (const unsigned long &direction)

void	PrintSelf (std::ostream &os, Indent i) const override

void	ScaleCoefficients (PixelRealType)

Public Member Functions inherited from itk::Neighborhood< TPixel, VDimension, TAllocator >
	itkTypeMacroNoParent (Neighborhood)

	Neighborhood ()

virtual	~Neighborhood ()=default

	Neighborhood (const Self &other)

	Neighborhood (Self &&)=default

Self &	operator= (const Self &other)

Self &	operator= (Self &&)=default

bool	operator== (const Self &other) const

bool	operator!= (const Self &other) const

const SizeType	GetRadius () const

SizeValueType	GetRadius (DimensionValueType n) const

SizeValueType	GetSize (DimensionValueType n) const

SizeType	GetSize () const

OffsetValueType	GetStride (DimensionValueType axis) const

Iterator	End ()

Iterator	Begin ()

ConstIterator	End () const

ConstIterator	Begin () const

NeighborIndexType	Size () const

TPixel &	operator[] (NeighborIndexType i)

const TPixel &	operator[] (NeighborIndexType i) const

TPixel &	GetElement (NeighborIndexType i)

TPixel	GetCenterValue () const

void	SetRadius (const SizeType &)

void	SetRadius (const SizeValueType *rad)

void	SetRadius (const SizeValueType)

void	Print (std::ostream &os) const

AllocatorType &	GetBufferReference ()

const AllocatorType &	GetBufferReference () const

TPixel &	operator[] (const OffsetType &o)

const TPixel &	operator[] (const OffsetType &o) const

OffsetType	GetOffset (NeighborIndexType i) const

virtual NeighborIndexType	GetNeighborhoodIndex (const OffsetType &) const

NeighborIndexType	GetCenterNeighborhoodIndex () const

std::slice	GetSlice (unsigned int) const

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

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

Protected Member Functions inherited from itk::NeighborhoodOperator< TPixel, VDimension, TAllocator >
virtual void	Fill (const CoefficientVector &)=0

virtual void	FillCenteredDirectional (const CoefficientVector &)

void	InitializeToZero ()

Protected Member Functions inherited from itk::Neighborhood< TPixel, VDimension, TAllocator >
void	SetSize ()

virtual void	Allocate (NeighborIndexType i)

virtual void	ComputeNeighborhoodStrideTable ()

virtual void	ComputeNeighborhoodOffsetTable ()

Detailed Description

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

A NeighborhoodOperator whose coefficients are a one dimensional, discrete derivative Gaussian kernel.

GaussianDerivativeOperator can be used to calculate Gaussian derivatives by taking its inner product with to a Neighborhood (NeighborhooIterator) that is swept across an image region. It is a directional operator. N successive applications oriented along each dimensional direction will calculate separable, efficient, N-D Gaussian derivatives of an image region.

GaussianDerivativeOperator takes three parameters:

(1) The floating-point variance of the desired Gaussian function.

(2) The order of the derivative to be calculated (zero order means it performs only smoothing as a standard itk::GaussianOperator)

(3) The "maximum error" allowed in the discrete Gaussian function. "Maximum errror" is defined as the difference between the area under the discrete Gaussian curve and the area under the continuous Gaussian. Maximum error affects the Gaussian operator size. Care should be taken not to make this value too small relative to the variance lest the operator size become unreasonably large.

References: The Gaussian kernel contained in this operator was described by Tony Lindeberg (Discrete Scale-Space Theory and the Scale-Space Primal Sketch. Dissertation. Royal Institute of Technology, Stockholm, Sweden. May 1991.).

Author: Ivan Macia, Vicomtech, Spain, https://www.vicomtech.org/en

This implementation is derived from the Insight Journal paper: https://www.insight-journal.org/browse/publication/179

Note: GaussianDerivativeOperator does not have any user-declared "special member function", following the C++ Rule of Zero: the compiler will generate them if necessary.

See also: GaussianOperator; NeighborhoodOperator; NeighborhoodIterator; Neighborhood

ITK Sphinx Examples:

All ITK Sphinx Examples

Create Gaussian Derivative Kernel

Examples: SphinxExamples/src/Core/Common/CreateGaussianDerivativeKernel/Code.cxx, and SphinxExamples/src/Core/Common/DemonstrateAllOperators/Code.cxx.

Definition at line 106 of file itkGaussianDerivativeOperator.h.

Member Typedef Documentation

◆ CoefficientVector

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

using itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::CoefficientVector = typename Superclass::CoefficientVector

protected

Normalize derivatives across scale space

Definition at line 215 of file itkGaussianDerivativeOperator.h.

◆ DerivativeOperatorType

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

using itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::DerivativeOperatorType = DerivativeOperator<TPixel, VDimension, TAllocator>

Definition at line 118 of file itkGaussianDerivativeOperator.h.

◆ GaussianOperatorType

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

using itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::GaussianOperatorType = GaussianOperator<TPixel, VDimension, TAllocator>

Neighborhood operator types.

Definition at line 117 of file itkGaussianDerivativeOperator.h.

◆ InterpolationModeEnum

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

using itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::InterpolationModeEnum = GaussianDerivativeOperatorEnums::InterpolationMode

Definition at line 114 of file itkGaussianDerivativeOperator.h.

◆ Self

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

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

Standard class type aliases.

Definition at line 111 of file itkGaussianDerivativeOperator.h.

◆ Superclass

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

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

Definition at line 112 of file itkGaussianDerivativeOperator.h.

Member Function Documentation

◆ Fill()

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

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

inlineoverrideprotected

Arranges coefficients spatially in the memory buffer.

Definition at line 238 of file itkGaussianDerivativeOperator.h.

◆ GenerateCoefficients()

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

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

overrideprotectedvirtual

Calculates operator coefficients.

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

◆ GenerateGaussianCoefficients()

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

CoefficientVector itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::GenerateGaussianCoefficients ( ) const

private

Normalize derivatives across scale space

◆ GetMaximumError()

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

double itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::GetMaximumError ( )

inline

Normalize derivatives across scale space

Definition at line 182 of file itkGaussianDerivativeOperator.h.

◆ GetNameOfClass()

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

const char* itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::GetNameOfClass ( ) const

inlineoverrideprivatevirtual

For compatibility with itkWarningMacro

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

Definition at line 251 of file itkGaussianDerivativeOperator.h.

◆ GetNormalizeAcrossScale()

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

bool itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::GetNormalizeAcrossScale ( ) const

inline

Normalize derivatives across scale space

Definition at line 134 of file itkGaussianDerivativeOperator.h.

◆ GetOrder()

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

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

inline

Normalize derivatives across scale space

Definition at line 204 of file itkGaussianDerivativeOperator.h.

◆ GetSpacing()

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

double itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::GetSpacing ( ) const

inline

Normalize derivatives across scale space

Definition at line 163 of file itkGaussianDerivativeOperator.h.

◆ GetVariance()

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

double itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::GetVariance ( ) const

inline

Normalize derivatives across scale space

Definition at line 150 of file itkGaussianDerivativeOperator.h.

◆ ModifiedBesselI()

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

static double itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::ModifiedBesselI	(	int	,
		double
	)

staticprotected

Returns the value of the modified Bessel function Ik(x) at a point x>=0, where k>=2.

◆ ModifiedBesselI0()

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

static double itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::ModifiedBesselI0 ( double )

staticprotected

Returns the value of the modified Bessel function I0(x) at a point x >= 0.

◆ ModifiedBesselI1()

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

static double itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::ModifiedBesselI1 ( double )

staticprotected

Returns the value of the modified Bessel function I1(x) at a point x, x real.

◆ NormalizeAcrossScaleOff()

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

virtual void itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::NormalizeAcrossScaleOff ( )

virtual

Normalize derivatives across scale space

◆ NormalizeAcrossScaleOn()

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

virtual void itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::NormalizeAcrossScaleOn ( )

virtual

Normalize derivatives across scale space

◆ PrintSelf()

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

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

overridevirtual

Prints member variables

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

◆ SetMaximumError()

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

void itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::SetMaximumError ( const double maxerror )

inline

Set/Get the desired maximum error of the gaussian approximation. Maximum error is the difference between the area under the discrete Gaussian curve and the area under the continuous Gaussian. Maximum error affects the Gaussian operator size. The value is clamped between 0.00001 and 0.99999.

Definition at line 174 of file itkGaussianDerivativeOperator.h.

◆ SetMaximumKernelWidth()

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

void itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::SetMaximumKernelWidth ( unsigned int n )

inline

Sets/Get a limit for growth of the kernel. Small maximum error values with large variances will yield very large kernel sizes. This value can be used to truncate a kernel in such instances. A warning will be given on truncation of the kernel.

Definition at line 192 of file itkGaussianDerivativeOperator.h.

◆ SetNormalizeAcrossScale()

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

void itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::SetNormalizeAcrossScale ( bool flag )

inline

Set/Get the flag for calculating scale-space normalized derivatives.

Normalized derivatives are obtained multiplying by the scale parameter $t^1/order$. This use useful for scale-space selection algorithms such as blob detection. The scaling results in the value of the derivatives being independent of the size of an object.

Definition at line 129 of file itkGaussianDerivativeOperator.h.

◆ SetOrder()

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

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

inline

Sets/Get the order of the derivative.

Definition at line 199 of file itkGaussianDerivativeOperator.h.

◆ SetSpacing()

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

void itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::SetSpacing ( const double spacing )

inline

Set/Get the spacing for the direction of this kernel.

Definition at line 158 of file itkGaussianDerivativeOperator.h.

◆ SetVariance()

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

void itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::SetVariance ( const double variance )

inline

Set/Get the variance of the Gaussian kernel.

Definition at line 145 of file itkGaussianDerivativeOperator.h.

Member Data Documentation

◆ m_MaximumError

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

double itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::m_MaximumError { 0.005 }

private

Difference between the areas under the curves of the continuous and discrete Gaussian functions.

Definition at line 264 of file itkGaussianDerivativeOperator.h.

◆ m_MaximumKernelWidth

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

unsigned int itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::m_MaximumKernelWidth { 30 }

private

Maximum kernel size allowed. This value is used to truncate a kernel that has grown too large. A warning is given when the specified maximum error causes the kernel to exceed this size.

Definition at line 269 of file itkGaussianDerivativeOperator.h.

◆ m_NormalizeAcrossScale

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

bool itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::m_NormalizeAcrossScale { true }

private

Normalize derivatives across scale space

Definition at line 257 of file itkGaussianDerivativeOperator.h.

◆ m_Order

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

unsigned int itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::m_Order { 1 }

private

Order of the derivative.

Definition at line 272 of file itkGaussianDerivativeOperator.h.

◆ m_Spacing

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

double itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::m_Spacing { 1.0 }

private

Spacing in the direction of this kernel.

Definition at line 275 of file itkGaussianDerivativeOperator.h.

◆ m_Variance

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

double itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::m_Variance { 1.0 }

private

Desired variance of the discrete Gaussian function.

Definition at line 260 of file itkGaussianDerivativeOperator.h.

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

itkGaussianDerivativeOperator.h

Public Types

Additional Inherited Members

Detailed Description

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

Member Typedef Documentation

◆ CoefficientVector

◆ DerivativeOperatorType

◆ GaussianOperatorType

◆ InterpolationModeEnum

◆ Self

◆ Superclass

Member Function Documentation

◆ Fill()

◆ GenerateCoefficients()

◆ GenerateGaussianCoefficients()

◆ GetMaximumError()

◆ GetNameOfClass()

◆ GetNormalizeAcrossScale()

◆ GetOrder()

◆ GetSpacing()

◆ GetVariance()

◆ ModifiedBesselI()

◆ ModifiedBesselI0()

◆ ModifiedBesselI1()

◆ NormalizeAcrossScaleOff()

◆ NormalizeAcrossScaleOn()

◆ PrintSelf()

◆ SetMaximumError()

◆ SetMaximumKernelWidth()

◆ SetNormalizeAcrossScale()

◆ SetOrder()

◆ SetSpacing()

◆ SetVariance()

Member Data Documentation

◆ m_MaximumError

◆ m_MaximumKernelWidth

◆ m_NormalizeAcrossScale

◆ m_Order

◆ m_Spacing

◆ m_Variance

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