Robust anisotropic diffusion

Relations between anisotropic diffusion and robust statistics are described in this paper, Specifically, we show that anisotropic diffusion can be seen as a robust estimation procedure that estimates a piecewise smooth image from a noisy input image, The "edge-stopping" function in the anisotropic diffusion equation is closely related to the error norm and influence function in the robust estimation framework, This connection leads to a new "edge-stopping" function based an Tukey's biweight robust estimator that preserves sharper boundaries than previous formulations and improves the automatic stopping of the diffusion. The robust statistical interpretation also provides a means for detecting the boundaries (edges) between the piecewise smooth regions in an image that has been smoothed with anisotropic diffusion, Additionally, we derive a relationship between anisotropic diffusion and regularization with Line processes. Adding constraints on the spatial organization of the line processes allows us to develop new anisotropic diffusion equations that result in a qualitative improvement in the continuity of edges.