#include <itkAnisotropicDiffusionFunction.h>

Inheritance diagram for itk::AnisotropicDiffusionFunction< TImage >:

Collaboration diagram for itk::AnisotropicDiffusionFunction< TImage >:

Detailed Description

template<class 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 and initial condition $U(\mathbf{x}, 0) = U_0(\mathbf{x})$ , the original image.

: Extending to the case where 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 now varies the strength of diffusion anisotropically. Typically, 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 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 possibe, 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 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.

Public Types
typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::FloatOffsetType	FloatOffsetType

typedef Superclass::ImageType	ImageType

typedef Superclass::NeighborhoodType	NeighborhoodType

typedef Superclass::PixelRealType	PixelrealType

typedef Superclass::PixelType	PixelType

typedef SmartPointer< Self >	Pointer

typedef Superclass::RadiusType	RadiusType

typedef AnisotropicDiffusionFunction	Self

typedef FiniteDifferenceFunction < TImage >	Superclass

typedef Superclass::TimeStepType	TimeStepType

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

typedef ZeroFluxNeumannBoundaryCondition < ImageType >	DefaultBoundaryConditionType

typedef Vector< float, itkGetStaticConstMacro(ImageDimension) >	FloatOffsetType

typedef TImage	ImageType

typedef Vector< PixelRealType, itkGetStaticConstMacro(ImageDimension) >	NeighborhoodScalesType

typedef ConstNeighborhoodIterator < TImage, DefaultBoundaryConditionType >	NeighborhoodType

typedef double	PixelRealType

typedef ImageType::PixelType	PixelType

typedef SmartPointer< Self >	Pointer

typedef ConstNeighborhoodIterator < TImage >::RadiusType	RadiusType

typedef FiniteDifferenceFunction	Self

typedef LightObject	Superclass

typedef double	TimeStepType

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

typedef SmartPointer< Self >	Pointer

typedef LightObject	Self

Public Member Functions
virtual void	CalculateAverageGradientMagnitudeSquared (ImageType *)=0

virtual TimeStepType	ComputeGlobalTimeStep (void *) const

const double &	GetAverageGradientMagnitudeSquared () const

const double &	GetConductanceParameter () const

virtual void *	GetGlobalDataPointer () const

virtual const char *	GetNameOfClass () const

const TimeStepType &	GetTimeStep () const

virtual void	ReleaseGlobalDataPointer (void *) const

void	SetAverageGradientMagnitudeSquared (const double &c)

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

const RadiusType &	GetRadius () const

void	GetScaleCoefficients (PixelRealType vals[ImageDimension]) const

virtual void	InitializeIteration ()

void	SetRadius (const RadiusType &r)

void	SetScaleCoefficients (PixelRealType vals[ImageDimension])

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

virtual void	Delete ()

virtual int	GetReferenceCount () const

	itkCloneMacro (Self)

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

virtual void	Register () const

virtual void	SetReferenceCount (int)

virtual void	UnRegister () const

Static Public Attributes
static const unsigned int	ImageDimension = Superclass::ImageDimension

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

Protected Member Functions
	AnisotropicDiffusionFunction ()

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

	~AnisotropicDiffusionFunction ()

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

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

	~FiniteDifferenceFunction ()

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 Member Functions
	AnisotropicDiffusionFunction (const Self &)

void	operator= (const Self &)

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 Types inherited from itk::LightObject
typedef int	InternalReferenceCountType

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

PixelRealType	m_ScaleCoefficients [ImageDimension]

Member Typedef Documentation

template<class TImage >

typedef SmartPointer< const Self > itk::AnisotropicDiffusionFunction< TImage >::ConstPointer

Definition at line 148 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >

typedef Superclass::FloatOffsetType itk::AnisotropicDiffusionFunction< TImage >::FloatOffsetType

Definition at line 160 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >

typedef Superclass::ImageType itk::AnisotropicDiffusionFunction< TImage >::ImageType

Inherit some parameters from the superclass type

Definition at line 151 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >

typedef Superclass::NeighborhoodType itk::AnisotropicDiffusionFunction< TImage >::NeighborhoodType

Definition at line 158 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >

typedef Superclass::PixelRealType itk::AnisotropicDiffusionFunction< TImage >::PixelrealType

Definition at line 156 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >

typedef Superclass::PixelType itk::AnisotropicDiffusionFunction< TImage >::PixelType

Definition at line 155 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >

typedef SmartPointer< Self > itk::AnisotropicDiffusionFunction< TImage >::Pointer

Definition at line 147 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >

typedef Superclass::RadiusType itk::AnisotropicDiffusionFunction< TImage >::RadiusType

Definition at line 157 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >

typedef AnisotropicDiffusionFunction itk::AnisotropicDiffusionFunction< TImage >::Self

Standard class typedefs.

Definition at line 145 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >

typedef FiniteDifferenceFunction< TImage > itk::AnisotropicDiffusionFunction< TImage >::Superclass

Definition at line 146 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >

typedef Superclass::TimeStepType itk::AnisotropicDiffusionFunction< TImage >::TimeStepType

Definition at line 159 of file itkAnisotropicDiffusionFunction.h.

Constructor & Destructor Documentation

template<class TImage >

itk::AnisotropicDiffusionFunction< TImage >::AnisotropicDiffusionFunction ( )

inlineprotected

Definition at line 228 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >

itk::AnisotropicDiffusionFunction< TImage >::~AnisotropicDiffusionFunction ( )

inlineprotected

Definition at line 235 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >

itk::AnisotropicDiffusionFunction< TImage >::AnisotropicDiffusionFunction ( const Self & )

private

Member Function Documentation

template<class 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::VectorAnisotropicDiffusionFunction< TImage >, and itk::ScalarAnisotropicDiffusionFunction< TImage >.

template<class TImage >

virtual TimeStepType itk::AnisotropicDiffusionFunction< TImage >::ComputeGlobalTimeStep ( void * ) const

inlinevirtual

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 209 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >

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

inline

Set/Get the average gradient magnitude squared.

Definition at line 197 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >

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

inline

Definition at line 191 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >

virtual void* itk::AnisotropicDiffusionFunction< TImage >::GetGlobalDataPointer ( ) const

inlinevirtual

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 216 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >

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

virtual

Run-time type information (and related methods)

Reimplemented from itk::FiniteDifferenceFunction< TImage >.

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

template<class TImage >

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

inline

Definition at line 180 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >

void itk::AnisotropicDiffusionFunction< TImage >::operator= ( const Self & )

private

template<class TImage >

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

inlineprotectedvirtual

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

Definition at line 237 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >

virtual void itk::AnisotropicDiffusionFunction< TImage >::ReleaseGlobalDataPointer ( void * ) const

inlinevirtual

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

Implements itk::FiniteDifferenceFunction< TImage >.

Definition at line 222 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >

void itk::AnisotropicDiffusionFunction< TImage >::SetAverageGradientMagnitudeSquared ( const double & c )

inline