#include <itkGaussianDerivativeOperator.h>

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 (NeighborhoodIterator) 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 error" 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://doi.org/10.54294/mrg5is

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 105 of file 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	PixelRealType = typename NumericTraits< TPixel >::RealType

using	PixelType = TPixel

using	Self = NeighborhoodOperator

using	SizeType = itk::Size< VDimension >

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
double	GetMaximumError ()

const char *	GetNameOfClass () const override

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

void	SetMaximumError (const double maxerror)


void	SetNormalizeAcrossScale (bool flag)

bool	GetNormalizeAcrossScale () const

virtual void	NormalizeAcrossScaleOn ()


void	SetVariance (const double variance)

double	GetVariance () const


void	SetSpacing (const double spacing)

double	GetSpacing () const


void	SetMaximumKernelWidth (unsigned int n)

virtual unsigned int	GetMaximumKernelWidth () const


void	SetOrder (const unsigned int order)

unsigned int	GetOrder () 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

const char *	GetNameOfClass () const override

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

void	ScaleCoefficients (PixelRealType)

void	SetDirection (const unsigned long direction)

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

SizeType	GetSize () const

SizeValueType	GetSize (DimensionValueType n) const

std::slice	GetSlice (unsigned int) const

OffsetValueType	GetStride (DimensionValueType axis) const

	ITK_UNEQUAL_OPERATOR_MEMBER_FUNCTION (Self)

	Neighborhood ()=default

	Neighborhood (const Self &)=default

	Neighborhood (Self &&)=default

Self &	operator= (const Self &)=default

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

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 std::vector< PixelRealType >

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

Protected Member Functions
void	Fill (const CoefficientVector &coeff) override

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 ()

Static Protected Member Functions
static double	ModifiedBesselI (int, double)

static double	ModifiedBesselI0 (double)

static double	ModifiedBesselI1 (double)

Private Member Functions
CoefficientVector	GenerateGaussianCoefficients () const

Private Attributes
double	m_MaximumError { 0.005 }

unsigned int	m_MaximumKernelWidth { 30 }

bool	m_NormalizeAcrossScale { true }

unsigned int	m_Order { 1 }

double	m_Spacing { 1.0 }

double	m_Variance { 1.0 }

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

Member Typedef Documentation

◆ CoefficientVector

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

using itk::NeighborhoodOperator< TPixel, VDimension, TAllocator >::CoefficientVector = typename std::vector<PixelRealType>

protected

Type alias support for coefficient vector type. Necessary to fix bug in the microsoft VC++ compiler.

Definition at line 153 of file itkNeighborhoodOperator.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 120 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 119 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 116 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 110 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 111 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 )

inlineoverrideprotectedvirtual

Arranges coefficients spatially in the memory buffer.

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

Definition at line 242 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

◆ GetMaximumError()

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

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

inline

Definition at line 184 of file itkGaussianDerivativeOperator.h.

◆ GetMaximumKernelWidth()

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

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

virtual

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.

◆ GetNameOfClass()

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

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

overridevirtual

See also: LightObject::GetNameOfClass()

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

◆ GetNormalizeAcrossScale()

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

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

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 136 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

Sets/Get the order of the derivative.

Definition at line 208 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

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

Definition at line 165 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

Set/Get the variance of the Gaussian kernel.

Definition at line 152 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.

◆ NormalizeAcrossScaleOn()

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

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

virtual

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.

◆ PrintSelf()

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

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

overridevirtual

Standard itk object method.

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 176 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 194 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 131 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 203 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 160 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 147 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 261 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 266 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 254 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 269 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 272 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 257 of file itkGaussianDerivativeOperator.h.

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

itkGaussianDerivativeOperator.h

Detailed Description

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

Public Types

Public Member Functions

Protected Types

Protected Member Functions

Static Protected Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Member Typedef Documentation

◆ CoefficientVector

◆ DerivativeOperatorType

◆ GaussianOperatorType

◆ InterpolationModeEnum

◆ Self

◆ Superclass

Member Function Documentation

◆ Fill()

◆ GenerateCoefficients()

◆ GenerateGaussianCoefficients()

◆ GetMaximumError()

◆ GetMaximumKernelWidth()

◆ GetNameOfClass()

◆ GetNormalizeAcrossScale()

◆ GetOrder()

◆ GetSpacing()

◆ GetVariance()

◆ ModifiedBesselI()

◆ ModifiedBesselI0()

◆ ModifiedBesselI1()

◆ 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 >