ITK  5.0.0 Insight Segmentation and Registration Toolkit
itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator > Class Template Reference

`#include <itkGaussianDerivativeOperator.h>`

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

## 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.).

This implementation is derived from the Insight Journal paper: https://hdl.handle.net/1926/1290

GaussianOperator
NeighborhoodOperator
NeighborhoodIterator
Neighborhood
Wiki Examples:
Examples:
WikiExamples/Operators/GaussianDerivativeOperator.cxx.

Definition at line 79 of file itkGaussianDerivativeOperator.h.

## Public Types

using DerivativeOperatorType = DerivativeOperator< TPixel, VDimension, TAllocator >

using GaussianOperatorType = GaussianOperator< TPixel, VDimension, TAllocator >

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 = 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

GaussianDerivativeOperator ()=default

GaussianDerivativeOperator (const Self &other)

double GetMaximumError ()

Selfoperator= (const Self &other)

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

void SetMaximumError (const double maxerror)

void SetMaximumKernelWidth (unsigned int n)

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 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 FlipAxes ()

unsigned long GetDirection () const

NeighborhoodOperator ()

NeighborhoodOperator (const Self &orig)

void ScaleCoefficients (PixelRealType)

void SetDirection (const unsigned long &direction)

Selfoperator= (const Self &orig)

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

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

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

Selfoperator= (const Self &other)

Selfoperator= (Self &&)=default

bool operator== (const Self &other) const

void Print (std::ostream &os) const

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)

AllocatorTypeGetBufferReference ()

const AllocatorTypeGetBufferReference () 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

void Fill (const CoefficientVector &coeff) override

CoefficientVector GenerateCoefficients () override

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 >
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

const char * GetNameOfClass () const override

## 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}

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

Definition at line 159 of file itkGaussianDerivativeOperator.h.

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 90 of file itkGaussianDerivativeOperator.h.

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 89 of file itkGaussianDerivativeOperator.h.

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 85 of file itkGaussianDerivativeOperator.h.

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 86 of file itkGaussianDerivativeOperator.h.

## Constructor & Destructor Documentation

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

Constructor.

template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>
 itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::GaussianDerivativeOperator ( const Self & other )

Copy constructor

## Member Function Documentation

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 177 of file itkGaussianDerivativeOperator.h.

template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>
 CoefficientVector itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::GenerateCoefficients ( )
overrideprotectedvirtual

Calculates operator coefficients.

template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>
 CoefficientVector itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::GenerateGaussianCoefficients ( ) const
private
template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>
 double itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::GetMaximumError ( )
inline

Definition at line 138 of file itkGaussianDerivativeOperator.h.

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 187 of file itkGaussianDerivativeOperator.h.

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 111 of file itkGaussianDerivativeOperator.h.

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 151 of file itkGaussianDerivativeOperator.h.

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 124 of file itkGaussianDerivativeOperator.h.

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 119 of file itkGaussianDerivativeOperator.h.

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.

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.

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.

template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>
 virtual void itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::NormalizeAcrossScaleOff ( )
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.

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.

template<typename TPixel , unsigned int VDimension = 2, typename TAllocator = NeighborhoodAllocator< TPixel >>
 Self& itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::operator= ( const Self & other )

Assignment operator

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 >.

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 131 of file itkGaussianDerivativeOperator.h.

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 144 of file itkGaussianDerivativeOperator.h.

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 110 of file itkGaussianDerivativeOperator.h.

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 150 of file itkGaussianDerivativeOperator.h.

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 123 of file itkGaussianDerivativeOperator.h.

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 118 of file itkGaussianDerivativeOperator.h.

## Member Data Documentation

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 200 of file itkGaussianDerivativeOperator.h.

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 205 of file itkGaussianDerivativeOperator.h.

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 193 of file itkGaussianDerivativeOperator.h.

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 208 of file itkGaussianDerivativeOperator.h.

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 211 of file itkGaussianDerivativeOperator.h.

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 196 of file itkGaussianDerivativeOperator.h.

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