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itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator > Class Template Reference
Data Processing Objects » Operators | Group Core » Module ITKCommon

#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:
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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, 2, NeighborhoodAllocator< TPixel > >
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, NeighborhoodAllocator< TPixel > >
 
- Public Types inherited from itk::Neighborhood< TPixel, VDimension, NeighborhoodAllocator< TPixel > >
using AllocatorType = NeighborhoodAllocator< TPixel >
 
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, 2, NeighborhoodAllocator< TPixel > >
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, NeighborhoodAllocator< TPixel > >
NeighborIndexType GetCenterNeighborhoodIndex () const
 
TPixel GetCenterValue () const
 
virtual const char * GetNameOfClass () 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 ()
 
ConstIterator End () const
 
Iterator Begin ()
 
ConstIterator Begin () const
 
TPixel & operator[] (NeighborIndexType i)
 
const TPixel & operator[] (NeighborIndexType i) const
 
TPixel & GetElement (NeighborIndexType i)
 
TPixel & operator[] (const OffsetType &o)
 
const TPixel & operator[] (const OffsetType &o) const
 
void SetRadius (const SizeValueType *rad)
 
AllocatorType & GetBufferReference ()
 
const AllocatorType & GetBufferReference () const
 

Protected Types

using CoefficientVector = typename std::vector< PixelRealType >
 
- Protected Types inherited from itk::NeighborhoodOperator< TPixel, 2, NeighborhoodAllocator< TPixel > >
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, 2, NeighborhoodAllocator< TPixel > >
virtual void Fill (const CoefficientVector &)=0
 
virtual void FillCenteredDirectional (const CoefficientVector &)
 
virtual CoefficientVector GenerateCoefficients ()=0
 
void InitializeToZero ()
 
- Protected Member Functions inherited from itk::Neighborhood< TPixel, VDimension, NeighborhoodAllocator< TPixel > >
virtual void Allocate (NeighborIndexType i)
 
virtual void ComputeNeighborhoodOffsetTable ()
 
virtual void ComputeNeighborhoodStrideTable ()
 
virtual void PrintSelf (std::ostream &, Indent) const
 
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, NeighborhoodAllocator< TPixel > >
static constexpr unsigned int NeighborhoodDimension
 

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, 2, NeighborhoodAllocator< TPixel > >.

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, 2, NeighborhoodAllocator< TPixel > >.

◆ 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, NeighborhoodAllocator< TPixel > >.

◆ 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, NeighborhoodAllocator< TPixel > >.

◆ 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.

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