PeronaMalikFilter

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applies a Perona–Malik diffusion filter to image.

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PeronaMalikFilter[image,t]

specifies the amount of diffusion time t to be applied.

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PeronaMalikFilter[image,t,k]

uses a conductance parameter k.

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PeronaMalikFilter[image,t,k,σ]

applies a Gaussian regularization of width σ to the image gradient in the conductance function.

Details

Perona–Malik filtering is an inhomogeneous diffusion method typically used for smoothing images while preserving edges.
PeronaMalikFilter works on 2D grayscale or multichannel images, operating on each channel separately.
PeronaMalikFilter applies the diffusion equation $partial_tf=del . c_(k)(TemplateBox[{{{del , _, sigma}, f}}, Abs]) del f$ to every image channel .
The function $c_(k)(TemplateBox[{{{del , _, sigma}, f}}, Abs])=ⅇ^(-|del _sigmaf|^2/k^2)$ of the σ-regularized gradient norm $TemplateBox[{{{del , _, sigma}, f}}, Abs]$ 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 $c_(k)(TemplateBox[{{{del , _, sigma}, f}}, Abs])$ 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].