ROBUST ANISOTROPIC DIFFUSION

Relations between anisotropic diffusion and robust statistics are desc ribed in this paper, Specifically, we show that anisotropic diffusion can be seen as a robust estimation procedure that estimates a piecewis e smooth image from a noisy input image, The ''edge-stopping'' functio n in the anisotropic diffusion equation is closely related to the erro r 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 prev ious formulations and improves the automatic stopping of the diffusion . The robust statistical interpretation also provides a means for dete cting the boundaries (edges) between the piecewise smooth regions in a n image that has been smoothed with anisotropic diffusion, Additionall y, we derive a relationship between anisotropic diffusion and regulari zation with Line processes. Adding constraints on the spatial organiza tion of the line processes allows us to develop new anisotropic diffus ion equations that result in a qualitative improvement in the continui ty of edges.