Why the Perona-Malik filter works
1997
Abstract
Although the widely-used Perona{Malik lter is regarded as ill-posed, straightforward implementations are often surprisingly stable. We give an explanation for this e ect by applying a discrete nonlinear scale-space framework: a spatial discretization on a xed pixel grid gives a well-posed scale-space with many image-simplifying properties, and an explicit time discretization leads to a scheme which does not introduce additional oscillations. This explains why staircasing is essentially the only practically appearing instability.
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