#include <itkAnisotropicDiffusionFunction.h>

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.

See also: VectorAnisotropicDiffusionFunction; ScalarAnisotropicDiffusionFunction; GradientAnisotropicDiffusionFunction; CurvatureAnisotropicDiffusionFunction; VectorGradientAnisotropicDiffusionFunction

Todo:: Automatically generate the time step value from image dimensionality and order of the equations

Definition at line 139 of file 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	RadiusType = typename ConstNeighborhoodIterator< TImage >::RadiusType

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
virtual void	CalculateAverageGradientMagnitudeSquared (ImageType *)=0

TimeStepType	ComputeGlobalTimeStep (void *) const override

const double &	GetAverageGradientMagnitudeSquared () const

const double &	GetConductanceParameter () const

void *	GetGlobalDataPointer () const override

const char *	GetNameOfClass () const override

const TimeStepType &	GetTimeStep () const

void	ReleaseGlobalDataPointer (void *) const override

void	SetAverageGradientMagnitudeSquared (const double c)

void	SetConductanceParameter (const double c)

void	SetTimeStep (const TimeStepType &t)

Public Member Functions inherited from itk::FiniteDifferenceFunction< TImage >
virtual TimeStepType	ComputeGlobalTimeStep (void *GlobalData) const=0

const NeighborhoodScalesType	ComputeNeighborhoodScales () const

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

virtual void *	GetGlobalDataPointer () const=0

const char *	GetNameOfClass () const override

const RadiusType &	GetRadius () const

void	GetScaleCoefficients (PixelRealType vals[ImageDimension]) const

virtual void	InitializeIteration ()

virtual void	ReleaseGlobalDataPointer (void *GlobalData) const=0

void	SetRadius (const RadiusType &r)

void	SetScaleCoefficients (const PixelRealType vals[ImageDimension])

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

virtual Pointer	CreateAnother () const

virtual void	Delete ()

virtual const char *	GetNameOfClass () const

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

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

virtual	~LightObject ()

Private Attributes
double	m_AverageGradientMagnitudeSquared {}

double	m_ConductanceParameter {}

TimeStepType	m_TimeStep {}

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

static Pointer	New ()

Protected Attributes inherited from itk::FiniteDifferenceFunction< TImage >
RadiusType	m_Radius

PixelRealType	m_ScaleCoefficients [ImageDimension]

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

Member Typedef Documentation

◆ ConstPointer

template<typename TImage >

using itk::AnisotropicDiffusionFunction< TImage >::ConstPointer = SmartPointer<const Self>

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<Self>

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<TImage>

Definition at line 147 of file itkAnisotropicDiffusionFunction.h.

Constructor & Destructor Documentation

◆ 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

◆ CalculateAverageGradientMagnitudeSquared()

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.

Implemented in itk::ScalarAnisotropicDiffusionFunction< TImage >, and itk::VectorAnisotropicDiffusionFunction< TImage >.

◆ 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.

◆ GetAverageGradientMagnitudeSquared()

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 >

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

overridevirtual

See also: LightObject::GetNameOfClass()

Reimplemented from itk::LightObject.

Reimplemented in itk::CurvatureNDAnisotropicDiffusionFunction< TImage >, itk::GradientNDAnisotropicDiffusionFunction< TImage >, itk::ScalarAnisotropicDiffusionFunction< TImage >, itk::VectorAnisotropicDiffusionFunction< TImage >, itk::VectorCurvatureNDAnisotropicDiffusionFunction< TImage >, and itk::VectorGradientNDAnisotropicDiffusionFunction< 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.

Reimplemented in itk::VectorAnisotropicDiffusionFunction< TImage >, and itk::VectorCurvatureNDAnisotropicDiffusionFunction< TImage >.

Definition at line 249 of file itkAnisotropicDiffusionFunction.h.