This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# PeronaMalikFilter

 PeronaMalikFilter[image] applies a Perona-Malik diffusion filter to image. PeronaMalikFilterspecifies the amount of diffusion t to be applied. PeronaMalikFilteruses a conductance parameter k. PeronaMalikFilterapplies a Gaussian regularization of width to the image gradient in the conductance function.
• 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, 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.
Perona-Malik filtering applied to a microscope image:
Perona-Malik filtering applied to a microscope image:
 Out[1]=
 Scope   (3)
Perona-Malik filtering applied to an MRI image:
Specify a large conductance parameter to preserve only strong edges:
Specifying a minimum scale to neglect edges created by noise:
 Applications   (2)
Use Perona-Malik filtering to isolate ovarian follicles in an ultrasound image:
Smooth an ultrasound image to segment an angiomyolipoma:
Normally stronger edges are enhanced and the weaker edges are blurred:
With a lower conductance parameter, blurring diminishes:
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