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 >:

List of all members.

Public Types
typedef DerivativeOperator < TPixel, VDimension, TAllocator >	DerivativeOperatorType
typedef GaussianOperator < TPixel, VDimension, TAllocator >	GaussianOperatorType
typedef GaussianDerivativeOperator	Self
typedef NeighborhoodOperator < TPixel, VDimension, TAllocator >	Superclass
Public Types inherited from itk::NeighborhoodOperator< TPixel, VDimension, TAllocator >
typedef NumericTraits< TPixel > ::RealType	PixelRealType
typedef TPixel	PixelType
typedef Superclass::SizeType	SizeType
typedef SliceIterator< TPixel, Self >	SliceIteratorType
Public Types inherited from itk::Neighborhood< TPixel, VDimension, TAllocator >
typedef TAllocator	AllocatorType
typedef AllocatorType::const_iterator	ConstIterator
typedef unsigned int	DimensionValueType
typedef AllocatorType::iterator	Iterator
typedef SizeValueType	NeighborIndexType
typedef Offset< VDimension >	OffsetType
typedef SizeType::SizeValueType	SizeValueType

Public Member Functions
	GaussianDerivativeOperator ()
	GaussianDerivativeOperator (const Self &other)
double	GetMaximumError ()
Self &	operator= (const Self &other)
virtual void	PrintSelf (std::ostream &os, Indent i) const
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	CreateToRadius (const SizeValueType)
virtual void	FlipAxes ()
unsigned long	GetDirection () const
	NeighborhoodOperator ()
	NeighborhoodOperator (const Self &orig)
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
SizeValueType	GetSize (DimensionValueType n) const
SizeType	GetSize () const
std::slice	GetSlice (unsigned int) const
OffsetValueType	GetStride (DimensionValueType axis) const
	Neighborhood (const Self &other)
bool	operator!= (const Self &other) const
bool	operator== (const Self &other) const
void	Print (std::ostream &os) const
void	SetRadius (const SizeType &)
void	SetRadius (const SizeValueType *rad)
void	SetRadius (const SizeValueType)
NeighborIndexType	Size () const
virtual	~Neighborhood ()
	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)
AllocatorType &	GetBufferReference ()
const AllocatorType &	GetBufferReference () const
TPixel &	operator[] (const OffsetType &o)
const TPixel &	operator[] (const OffsetType &o) const

Protected Types
typedef Superclass::CoefficientVector	CoefficientVector
Protected Types inherited from itk::NeighborhoodOperator< TPixel, VDimension, TAllocator >

Protected Member Functions
void	Fill (const CoefficientVector &coeff)
CoefficientVector	GenerateCoefficients ()
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
const char *	GetNameOfClass () const

Private Attributes
double	m_MaximumError
unsigned int	m_MaximumKernelWidth
bool	m_NormalizeAcrossScale
unsigned int	m_Order
double	m_Spacing
double	m_Variance

---

Detailed Description

template<class TPixel, unsigned int VDimension = 2, class 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, http://www.vicomtech.es

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

See also:

GaussianOperator

NeighborhoodOperator

NeighborhoodIterator

Neighborhood

Wiki Examples:

• All Examples

• Create a Gaussian derivative kernel

Definition at line 77 of file itkGaussianDerivativeOperator.h.

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Member Typedef Documentation

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

typedef Superclass::CoefficientVector itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::CoefficientVector

protected

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

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

Definition at line 157 of file itkGaussianDerivativeOperator.h.

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

typedef DerivativeOperator< TPixel, VDimension, TAllocator > itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::DerivativeOperatorType

Definition at line 88 of file itkGaussianDerivativeOperator.h.

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

typedef GaussianOperator< TPixel, VDimension, TAllocator > itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::GaussianOperatorType

Neighborhood operator types.

Definition at line 87 of file itkGaussianDerivativeOperator.h.

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

typedef GaussianDerivativeOperator itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::Self

Standard class typedefs.

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

Definition at line 83 of file itkGaussianDerivativeOperator.h.

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

typedef NeighborhoodOperator< TPixel, VDimension, TAllocator > itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::Superclass

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

Definition at line 84 of file itkGaussianDerivativeOperator.h.

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Constructor & Destructor Documentation

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

itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::GaussianDerivativeOperator

(

)

Constructor.

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

itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::GaussianDerivativeOperator

(

const Self &

other

)

Copy constructor

---

Member Function Documentation

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

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

inlineprotectedvirtual

Arranges coefficients spatially in the memory buffer.

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

Definition at line 175 of file itkGaussianDerivativeOperator.h.

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

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

protectedvirtual

Calculates operator coefficients.

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

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

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

private

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

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

inline

Definition at line 136 of file itkGaussianDerivativeOperator.h.

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

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

inlineprivate

For compatibility with itkWarningMacro

Definition at line 184 of file itkGaussianDerivativeOperator.h.

template<class TPixel , unsigned int VDimension = 2, class 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 109 of file itkGaussianDerivativeOperator.h.

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

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

inline

Sets/Get the order of the derivative.

Definition at line 149 of file itkGaussianDerivativeOperator.h.

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

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

inline

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

Definition at line 122 of file itkGaussianDerivativeOperator.h.

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

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

inline

Set/Get the variance of the Gaussian kernel.

Definition at line 117 of file itkGaussianDerivativeOperator.h.

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

Self& itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::operator=

(

const Self &

other

)

Assignment operator

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

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

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

virtual

Prints member variables

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

template<class TPixel , unsigned int VDimension = 2, class 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 129 of file itkGaussianDerivativeOperator.h.

template<class TPixel , unsigned int VDimension = 2, class 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 142 of file itkGaussianDerivativeOperator.h.

template<class TPixel , unsigned int VDimension = 2, class 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 108 of file itkGaussianDerivativeOperator.h.

template<class TPixel , unsigned int VDimension = 2, class 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 148 of file itkGaussianDerivativeOperator.h.

template<class TPixel , unsigned int VDimension = 2, class 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 121 of file itkGaussianDerivativeOperator.h.

template<class TPixel , unsigned int VDimension = 2, class 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 116 of file itkGaussianDerivativeOperator.h.

---

Member Data Documentation

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

double itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::m_MaximumError

private

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

Definition at line 197 of file itkGaussianDerivativeOperator.h.

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

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

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 202 of file itkGaussianDerivativeOperator.h.

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

bool itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::m_NormalizeAcrossScale

private

Normalize derivatives across scale space

Definition at line 190 of file itkGaussianDerivativeOperator.h.

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

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

private

Order of the derivative.

Definition at line 205 of file itkGaussianDerivativeOperator.h.

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

double itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::m_Spacing

private

Spacing in the direction of this kernel.

Definition at line 208 of file itkGaussianDerivativeOperator.h.

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

double itk::GaussianDerivativeOperator< TPixel, VDimension, TAllocator >::m_Variance

private

Desired variance of the discrete Gaussian function.

Definition at line 193 of file itkGaussianDerivativeOperator.h.

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

• itkGaussianDerivativeOperator.h