# Wolfram Language & System 10.0 (2014)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# PeronaMalikFilter

PeronaMalikFilter[image]
applies a PeronaMalik diffusion filter to image.

PeronaMalikFilter[image,t]
specifies the amount of diffusion time t to be applied.

PeronaMalikFilter[image,t,k]
uses a conductance parameter k.

PeronaMalikFilter[image,t,k,σ]
applies a Gaussian regularization of width σ to the image gradient in the conductance function.

## DetailsDetails

• PeronaMalik filtering is an inhomogeneous diffusion method typically used for smoothing images while preserving edges.
• PeronaMalikFilter works on arbitrary grayscale or multichannel images, operating on each channel separately.
• applies the diffusion equation to every image channel .
• The function of the σ-regularized gradient norm defines the conductance of the diffusion current. At edges where the gradient norm is large in comparison to k, diffusion is suppressed, thereby preserving edges.
• In PeronaMalikFilter[image,t], t parameterizes the evolution of the diffusion and thereby the spatial range of the filter.
• The conductance parameter k can take any positive value. The default value of k is Automatic, which assigns to k the 50% quantile of the gradient norm of image. If more than one channel is present, the gradient norm of the channel average is taken into account.
• The regularization parameter σ is the standard deviation of the Gaussian kernel , with which the image gradient is convolved. The σ-regularization makes the conductance term less susceptible to noise. If , a finite difference scheme is used to determine the gradient.
• PeronaMalikFilter[image] is equivalent to PeronaMalikFilter[image,1,Automatic,0].

## ExamplesExamplesopen allclose all

### Basic Examples  (1)Basic Examples  (1)

PeronaMalik filtering applied to a microscope image:

 Out[2]=