Publications [#376577] of Guillermo Sapiro

Papers Published

1. Black, MJ; Sapiro, G; Marimont, D; Heeger, D, Robust anisotropic diffusion: Connections between robust statistics, line processing, and anisotropic diffusion, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1252 (January, 1997), pp. 323-326, ISBN 9783540631675
   (last updated on 2025/02/02)

   Abstract:
   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.