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Publications [#264834] of Guillermo Sapiro

Papers Published

  1. Black, MJ; Sapiro, G; Marimont, DH; Heeger, D, Robust Anisotropic Diffusion: Connections Between Robust Statistics, Line Processing, and Anisotropic Diffusion., edited by Romeny, BMTH; Florack, L; Koenderink, JJ; Viergever, MA, Scale-Space, vol. 1252 (1997), pp. 323-326, SPRINGER, ISBN 3-540-63167-4 [html], [doi]
    (last updated on 2018/07/17)

    © Springer-Verlag Berlin Heidelberg 1997. Relations between anisotropic diffusion and robust statistics are described in this paper. 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 on Tukey's biweightrobust 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 the image. Finally, connections between robust estimation and line processing provide a framework to introduce spatial coherence in anisotropic diffusion flows.
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