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
in a higher dimensional function of derived images,
. This higher dimensional function represents the solution of the heat diffusion equation,
- with constant
and initial condition
, the original image.
- Extending to the case where
is not a constant, but a function of
, gives
- 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
.
- 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
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
, 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.