Edge-preserving smoothing is an image processing technique that smooths away textures whilst retaining sharp edges. Examples are the median filter, the bilateral filter, the guided filter and anisotropic diffusion.
When we need to preserve edge information and at the same time preserve the edges. Even when uniform smoothing does not remove the boundaries, it does distort them. This is not acceptable in the context of, for example, medical imaging.
An alternative to linear filtering, called anisotropic diffusion, was introduced by Perona and Malik. It is related to earlier work by Grossberg who used a similar nonlinear diffusion processes to model human vision. The motivation for anisotropic diffusion (also called nonuniform or variable conductance diffusion) is that a Gaussian smoothed image is a single time slice of the solution to the heat equation, that has the original image as its initial conditions.
Anisotropic diffusion includes a variable conductance term that, in turn, depends on the differential structure of the image. Thus, the variable conductance can be formulated to limit the smoothing at “edges” in images, as measured by high gradient magnitude, for example.
(source: ITK manual)
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