ITK  5.3.0 Insight Toolkit
itk::AnisotropicDiffusionFunction< TImage > Class Template Referenceabstract

#include <itkAnisotropicDiffusionFunction.h>

Inheritance diagram for itk::AnisotropicDiffusionFunction< TImage >:
Collaboration diagram for itk::AnisotropicDiffusionFunction< TImage >:

## Public Types

using ConstPointer = SmartPointer< const Self >

using PixelrealType = typename Superclass::PixelRealType

using Pointer = SmartPointer< Self >

using Self = AnisotropicDiffusionFunction

using Superclass = FiniteDifferenceFunction< TImage >

Public Types inherited from itk::FiniteDifferenceFunction< TImage >
using ConstPointer = SmartPointer< const Self >

using DefaultBoundaryConditionType = ZeroFluxNeumannBoundaryCondition< ImageType >

using FloatOffsetType = Vector< float, Self::ImageDimension >

using ImageType = TImage

using NeighborhoodScalesType = Vector< PixelRealType, Self::ImageDimension >

using NeighborhoodType = ConstNeighborhoodIterator< TImage, DefaultBoundaryConditionType >

using PixelRealType = double

using PixelType = typename ImageType::PixelType

using Pointer = SmartPointer< Self >

using Self = FiniteDifferenceFunction

using Superclass = LightObject

using TimeStepType = double

Public Types inherited from itk::LightObject
using ConstPointer = SmartPointer< const Self >

using Pointer = SmartPointer< Self >

using Self = LightObject

## Public Member Functions

TimeStepType ComputeGlobalTimeStep (void *) const override

const double & GetAverageGradientMagnitudeSquared () const

const double & GetConductanceParameter () const

void * GetGlobalDataPointer () const override

virtual const char * GetNameOfClass () const

const TimeStepTypeGetTimeStep () const

void ReleaseGlobalDataPointer (void *) const override

void SetConductanceParameter (const double c)

void SetTimeStep (const TimeStepType &t)

Public Member Functions inherited from itk::FiniteDifferenceFunction< TImage >
const NeighborhoodScalesType ComputeNeighborhoodScales () const

virtual PixelType ComputeUpdate (const NeighborhoodType &neighborhood, void *globalData, const FloatOffsetType &offset=FloatOffsetType(0.0))=0

void GetScaleCoefficients (PixelRealType vals[ImageDimension]) const

virtual void InitializeIteration ()

void SetScaleCoefficients (const PixelRealType vals[ImageDimension])

Public Member Functions inherited from itk::LightObject
Pointer Clone () const

virtual Pointer CreateAnother () const

virtual void Delete ()

virtual int GetReferenceCount () const

void Print (std::ostream &os, Indent indent=0) const

virtual void Register () const

virtual void SetReferenceCount (int)

virtual void UnRegister () const noexcept

## Static Public Attributes

static constexpr unsigned int ImageDimension = Superclass::ImageDimension

Static Public Attributes inherited from itk::FiniteDifferenceFunction< TImage >
static constexpr unsigned int ImageDimension

## Protected Member Functions

AnisotropicDiffusionFunction ()

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

~AnisotropicDiffusionFunction () override=default

Protected Member Functions inherited from itk::FiniteDifferenceFunction< TImage >
FiniteDifferenceFunction ()

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

~FiniteDifferenceFunction () override=default

Protected Member Functions inherited from itk::LightObject
virtual LightObject::Pointer InternalClone () const

LightObject ()

virtual void PrintHeader (std::ostream &os, Indent indent) const

virtual void PrintTrailer (std::ostream &os, Indent indent) const

virtual ~LightObject ()

## Private Attributes

double m_ConductanceParameter

TimeStepType m_TimeStep

Static Public Member Functions inherited from itk::LightObject
static void BreakOnError ()

static Pointer New ()

Protected Attributes inherited from itk::FiniteDifferenceFunction< TImage >

PixelRealType m_ScaleCoefficients [ImageDimension]

Protected Attributes inherited from itk::LightObject
std::atomic< int > m_ReferenceCount

## Detailed Description

### template<typename TImage> class itk::AnisotropicDiffusionFunction< TImage >

This class is a virtual base for anisotropic diffusion function objects. It is a component object in the finite difference solver hierarchy (see itkFiniteDifferenceImageFilter for an overview). AnisotropicDiffusionFunction objects are used by AnisotropicDiffusionImageFilter objects to perform non-linear diffusion on itk::Images.

Overview of anisotropic diffusion

Anisotropic diffusion methods are formulated to reduce noise (or unwanted detail) in images while preserving specific image features. For many applications, there is an assumption that light-dark transitions (edges) are interesting. Standard isotropic diffusion methods move and blur light-dark boundaries. Anisotropic diffusion methods are formulated to specifically preserve edges.

Anisotropic diffusion methods can be thought of as tools for calculating multi-scale descriptions of images. Embed an image $$U(\mathbf{x})$$ in a higher dimensional function of derived images, $$U(\mathbf{x}, t)$$. This higher dimensional function represents the solution of the heat diffusion equation,

$\frac{d U(\mathbf{x})}{d t} = \nabla \cdot c \nabla U(\mathbf{x})$

with constant $$c$$ and initial condition $$U(\mathbf{x}, 0) = U_0(\mathbf{x})$$, the original image.
Extending to the case where $$c$$ is not a constant, but a function of $$\mathbf{x}$$, gives

$\frac{d U(\mathbf{x})}{d t} = C(\mathbf{x})\Delta U(\mathbf{x}) + \nabla C(\mathbf{x}) \nabla U(\mathbf{x})$

Our choice of $$C$$ now varies the strength of diffusion anisotropically. Typically, $$C$$ is chosen as some function of image features to selectively preserve or remove those features. For example, edges tend to be preserved over smoother regions where $$C$$ is inversely scaled according to gradient magnitude as in

$C(\mathbf{x}) = e^{-(\frac{\parallel \nabla U(\mathbf{x}) \parallel}{K})^2}$

.
Several variations on the scheme presented above are implemented in Itk as subclasses of this equation. The equations are solved using an iterative, finite forward difference technique (see the FiniteDifferenceImageFilter class).
How to use this class
This class must be subclassed to provide the CalculateUpdate() methods of FiniteDifferenceFunction and the function CalculateAverageGradientMagnitudeSquared(), which is called before each iteration to recalibrate the conductance term.
Parameters
The parameters defined in this class apply to the basic anisotropic diffusion equation described in AnisotropicDiffusionFunction. Variations on the basic equation will be more or less sensitive to these parameters. For example, functions that perform higher-order derivative calculations may require smaller time-steps than those that only do first-derivative calculations. Wherever possible, reasonable parameters settings are suggested in the documentation of a specific equation implementation.
TimeStep
In the anisotropic diffusion filter hierarchy, the time step is set explicitly by the user. The time step referred to here corresponds exactly to $$\Delta t$$ in the finite difference update equation described in FiniteDifferenceImageFilter (see itkFiniteDifferenceImageFilter for more information). Appropriate time steps for solving this type of p.d.e. depend on the dimensionality of the image and the order of the equation. Stable values for most 2D and 3D functions are 0.125 and 0.0625, respectively, when the pixel spacing is unity or is turned off. In general, you should keep the time step below $$(PixelSpacing)/2^{N+1}$$, where $$N$$ is the number of image dimensions. A filter will automatically attempt to constrain its time step to a stable value and generate a run-time warning if the time step is set too high.
Conductance Parameter
The conductance parameter controls the sensitivity of the conductance term in the basic anisotropic diffusion equation. It affects the conductance term in different ways depending on the particular variation on the basic equation. As a general rule, the lower the value, the more strongly the diffusion equation preserves image features (such as high gradients or curvature). A high value for conductance will cause the filter to diffuse image features more readily. Typical values range from 0.5 to 2.0 for data like the Visible Human color data, but the correct value for your application is wholly dependent on the results you want from a specific data set and the number or iterations you perform.
References
Pietro Perona and Jitendra Malik, `‘Scale-space and edge detection using anisotropic diffusion,’' IEEE Transactions on Pattern Analysis Machine Intelligence, vol. 12, pp. 629-639, 1990.
VectorAnisotropicDiffusionFunction
ScalarAnisotropicDiffusionFunction
CurvatureAnisotropicDiffusionFunction
Todo:
Automatically generate the time step value from image dimensionality and order of the equations

Definition at line 139 of file itkAnisotropicDiffusionFunction.h.

## ◆ ConstPointer

template<typename TImage >
 using itk::AnisotropicDiffusionFunction< TImage >::ConstPointer = SmartPointer

Definition at line 149 of file itkAnisotropicDiffusionFunction.h.

## ◆ PixelrealType

template<typename TImage >
 using itk::AnisotropicDiffusionFunction< TImage >::PixelrealType = typename Superclass::PixelRealType

Definition at line 157 of file itkAnisotropicDiffusionFunction.h.

## ◆ Pointer

template<typename TImage >
 using itk::AnisotropicDiffusionFunction< TImage >::Pointer = SmartPointer

Definition at line 148 of file itkAnisotropicDiffusionFunction.h.

## ◆ Self

template<typename TImage >
 using itk::AnisotropicDiffusionFunction< TImage >::Self = AnisotropicDiffusionFunction

Standard class type aliases.

Definition at line 146 of file itkAnisotropicDiffusionFunction.h.

## ◆ Superclass

template<typename TImage >
 using itk::AnisotropicDiffusionFunction< TImage >::Superclass = FiniteDifferenceFunction

Definition at line 147 of file itkAnisotropicDiffusionFunction.h.

## ◆ AnisotropicDiffusionFunction()

template<typename TImage >
 itk::AnisotropicDiffusionFunction< TImage >::AnisotropicDiffusionFunction ( )
inlineprotected

Definition at line 239 of file itkAnisotropicDiffusionFunction.h.

## ◆ ~AnisotropicDiffusionFunction()

template<typename TImage >
 itk::AnisotropicDiffusionFunction< TImage >::~AnisotropicDiffusionFunction ( )
overrideprotecteddefault

## Member Function Documentation

template<typename TImage >
 virtual void itk::AnisotropicDiffusionFunction< TImage >::CalculateAverageGradientMagnitudeSquared ( ImageType * )
pure virtual

This method is called before each iteration. It calculates a scalar value that is the average of the gradient magnitude squared at each pixel in the output image (intermediate solution). The average gradient magnitude value is typically used in the anisotropic diffusion equations to calibrate the conductance term.

## ◆ ComputeGlobalTimeStep()

template<typename TImage >
 TimeStepType itk::AnisotropicDiffusionFunction< TImage >::ComputeGlobalTimeStep ( void * ) const
inlineoverridevirtual

Returns the time step supplied by the user. We don't need to use the global data supplied since we are returning a fixed value.

Implements itk::FiniteDifferenceFunction< TImage >.

Definition at line 218 of file itkAnisotropicDiffusionFunction.h.

template<typename TImage >
 const double& itk::AnisotropicDiffusionFunction< TImage >::GetAverageGradientMagnitudeSquared ( ) const
inline

Set/Get the average gradient magnitude squared.

Definition at line 204 of file itkAnisotropicDiffusionFunction.h.

## ◆ GetConductanceParameter()

template<typename TImage >
 const double& itk::AnisotropicDiffusionFunction< TImage >::GetConductanceParameter ( ) const
inline

Definition at line 197 of file itkAnisotropicDiffusionFunction.h.

## ◆ GetGlobalDataPointer()

template<typename TImage >
 void* itk::AnisotropicDiffusionFunction< TImage >::GetGlobalDataPointer ( ) const
inlineoverridevirtual

The anisotropic diffusion classes don't use this particular parameter so it's safe to return a null value.

Implements itk::FiniteDifferenceFunction< TImage >.

Definition at line 226 of file itkAnisotropicDiffusionFunction.h.

## ◆ GetNameOfClass()

template<typename TImage >
 virtual const char* itk::AnisotropicDiffusionFunction< TImage >::GetNameOfClass ( ) const
virtual

Run-time type information (and related methods)

Reimplemented from itk::FiniteDifferenceFunction< TImage >.

## ◆ GetTimeStep()

template<typename TImage >
 const TimeStepType& itk::AnisotropicDiffusionFunction< TImage >::GetTimeStep ( ) const
inline

Definition at line 184 of file itkAnisotropicDiffusionFunction.h.

## ◆ PrintSelf()

template<typename TImage >
 void itk::AnisotropicDiffusionFunction< TImage >::PrintSelf ( std::ostream & os, Indent indent ) const
inlineoverrideprotectedvirtual

Methods invoked by Print() to print information about the object including superclasses. Typically not called by the user (use Print() instead) but used in the hierarchical print process to combine the output of several classes.

Reimplemented from itk::LightObject.

Definition at line 249 of file itkAnisotropicDiffusionFunction.h.

## ◆ ReleaseGlobalDataPointer()

template<typename TImage >
 void itk::AnisotropicDiffusionFunction< TImage >::ReleaseGlobalDataPointer ( void * ) const
inlineoverridevirtual

Does nothing. No global data is used in this class of equations.

Implements itk::FiniteDifferenceFunction< TImage >.

Definition at line 233 of file itkAnisotropicDiffusionFunction.h.

template<typename TImage >
 void itk::AnisotropicDiffusionFunction< TImage >::SetAverageGradientMagnitudeSquared ( const double c )
inline

Definition at line 210 of file itkAnisotropicDiffusionFunction.h.

## ◆ SetConductanceParameter()

template<typename TImage >
 void itk::AnisotropicDiffusionFunction< TImage >::SetConductanceParameter ( const double c )
inline

Set/Get the conductance parameter. The conductance parameter.

Definition at line 191 of file itkAnisotropicDiffusionFunction.h.

## ◆ SetTimeStep()

template<typename TImage >
 void itk::AnisotropicDiffusionFunction< TImage >::SetTimeStep ( const TimeStepType & t )
inline

Set/Get the time step. For this class of anisotropic diffusion filters, the time-step is supplied by the user and remains fixed for all updates.

Definition at line 178 of file itkAnisotropicDiffusionFunction.h.

## ◆ ImageDimension

template<typename TImage >
 constexpr unsigned int itk::AnisotropicDiffusionFunction< TImage >::ImageDimension = Superclass::ImageDimension
staticconstexpr

Inherit some parameters from the superclass type

Definition at line 164 of file itkAnisotropicDiffusionFunction.h.

template<typename TImage >
private

Definition at line 257 of file itkAnisotropicDiffusionFunction.h.

## ◆ m_ConductanceParameter

template<typename TImage >
 double itk::AnisotropicDiffusionFunction< TImage >::m_ConductanceParameter
private

Definition at line 258 of file itkAnisotropicDiffusionFunction.h.

## ◆ m_TimeStep

template<typename TImage >
 TimeStepType itk::AnisotropicDiffusionFunction< TImage >::m_TimeStep
private

Definition at line 259 of file itkAnisotropicDiffusionFunction.h.

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