ITK  4.1.0
Insight Segmentation and Registration Toolkit
Public Types | Public Member Functions | Static Public Attributes | Protected Member Functions | Private Member Functions | Private Attributes
itk::AnisotropicDiffusionFunction< TImage > Class Template Reference

#include <itkAnisotropicDiffusionFunction.h>

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

List of all members.

Public Types

typedef SmartPointer< const SelfConstPointer
typedef Superclass::FloatOffsetType FloatOffsetType
typedef Superclass::ImageType ImageType
typedef
Superclass::NeighborhoodType 
NeighborhoodType
typedef Superclass::PixelRealType PixelrealType
typedef Superclass::PixelType PixelType
typedef SmartPointer< SelfPointer
typedef Superclass::RadiusType RadiusType
typedef
AnisotropicDiffusionFunction 
Self
typedef
FiniteDifferenceFunction
< TImage > 
Superclass
typedef Superclass::TimeStepType TimeStepType

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 TimeStepTypeGetTimeStep () const
virtual void ReleaseGlobalDataPointer (void *) const
void SetAverageGradientMagnitudeSquared (const double &c)
void SetConductanceParameter (const double &c)
void SetTimeStep (const TimeStepType &t)

Static Public Attributes

static const unsigned int ImageDimension = Superclass::ImageDimension

Protected Member Functions

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

Private Member Functions

 AnisotropicDiffusionFunction (const Self &)
void operator= (const Self &)

Private Attributes

double m_AverageGradientMagnitudeSquared
double m_ConductanceParameter
TimeStepType m_TimeStep

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 $c$ 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 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. Typical values are less than 0.250. A stable value for most 2 and 3d functions is 0.125. 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 affect 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 Jalhandra 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 138 of file itkAnisotropicDiffusionFunction.h.


Member Typedef Documentation

template<class TImage >
typedef SmartPointer< const Self > itk::AnisotropicDiffusionFunction< TImage >::ConstPointer
template<class TImage >
typedef Superclass::ImageType itk::AnisotropicDiffusionFunction< TImage >::ImageType

Definition at line 155 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >
typedef Superclass::PixelType itk::AnisotropicDiffusionFunction< TImage >::PixelType
template<class TImage >
typedef SmartPointer< Self > itk::AnisotropicDiffusionFunction< TImage >::Pointer
template<class TImage >
typedef Superclass::RadiusType itk::AnisotropicDiffusionFunction< TImage >::RadiusType
template<class TImage >
typedef AnisotropicDiffusionFunction itk::AnisotropicDiffusionFunction< TImage >::Self
template<class TImage >
typedef FiniteDifferenceFunction< TImage > itk::AnisotropicDiffusionFunction< TImage >::Superclass
template<class TImage >
typedef Superclass::TimeStepType itk::AnisotropicDiffusionFunction< TImage >::TimeStepType

Constructor & Destructor Documentation

template<class TImage >
itk::AnisotropicDiffusionFunction< TImage >::AnisotropicDiffusionFunction ( ) [inline, protected]

Definition at line 227 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >
itk::AnisotropicDiffusionFunction< TImage >::~AnisotropicDiffusionFunction ( ) [inline, protected]

Definition at line 234 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 [inline, virtual]

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 208 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 196 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >
const double& itk::AnisotropicDiffusionFunction< TImage >::GetConductanceParameter ( ) const [inline]

Definition at line 190 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >
virtual void* itk::AnisotropicDiffusionFunction< TImage >::GetGlobalDataPointer ( ) const [inline, virtual]

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 215 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >
virtual const char* itk::AnisotropicDiffusionFunction< TImage >::GetNameOfClass ( ) const [virtual]
template<class TImage >
const TimeStepType& itk::AnisotropicDiffusionFunction< TImage >::GetTimeStep ( ) const [inline]

Definition at line 179 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 [inline, protected, virtual]

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::FiniteDifferenceFunction< TImage >.

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

Definition at line 236 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >
virtual void itk::AnisotropicDiffusionFunction< TImage >::ReleaseGlobalDataPointer ( void *  ) const [inline, virtual]

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

Implements itk::FiniteDifferenceFunction< TImage >.

Definition at line 221 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >
void itk::AnisotropicDiffusionFunction< TImage >::SetAverageGradientMagnitudeSquared ( const double &  c) [inline]

Definition at line 201 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >
void itk::AnisotropicDiffusionFunction< TImage >::SetConductanceParameter ( const double &  c) [inline]

Set/Get the conductance parameter. The conductance parameter.

Definition at line 185 of file itkAnisotropicDiffusionFunction.h.

template<class 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 174 of file itkAnisotropicDiffusionFunction.h.


Member Data Documentation

template<class TImage >
const unsigned int itk::AnisotropicDiffusionFunction< TImage >::ImageDimension = Superclass::ImageDimension [static]
template<class TImage >
double itk::AnisotropicDiffusionFunction< TImage >::m_AverageGradientMagnitudeSquared [private]

Definition at line 248 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >
double itk::AnisotropicDiffusionFunction< TImage >::m_ConductanceParameter [private]

Definition at line 249 of file itkAnisotropicDiffusionFunction.h.

template<class TImage >
TimeStepType itk::AnisotropicDiffusionFunction< TImage >::m_TimeStep [private]

Definition at line 250 of file itkAnisotropicDiffusionFunction.h.


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