Edges as Outliers: Anisotropic Smoothing Using Local Image Statistics

Edges are viewed as statistical outliers with respect to local image gradient magnitudes. Within local image regions we compute a robust statistical measure of the gradient variation and use this in an anisotropic diffusion framework to determine a spatially varying "edge-stopping" parameter σ. We show how to determine this parameter for two edge-stopping functions described in the literature (Perona-Malik and the Tukey biweight). Smoothing of the image is related the local texture and in regions of low texture, small gradient values may be treated as edges whereas in regions of high texture, large gradient magnitudes are necessary before an edge is preserved. Intuitively these results have similarities with human perceptual phenomena such as masking and "popout". Results are shown on a variety of standard images.