BUILT-IN MATHEMATICA SYMBOL

# PeronaMalikFilter

PeronaMalikFilter[image]
applies a Perona-Malik diffusion filter to image.

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

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

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

## DetailsDetails

• Perona-Malik 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 -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 is the standard deviation of the Gaussian kernel , with which the image gradient is convolved. The -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)

Perona-Malik filtering applied to a microscope image:

 Out[1]=