Publications [#264909] of Guillermo Sapiro

Papers Published

1. Black, MJ; Sapiro, G; Marimont, DH; Heeger, D, Robust anisotropic diffusion., IEEE transactions on image processing : a publication of the IEEE Signal Processing Society, vol. 7 no. 3 (January, 1998), pp. 421-432, ISSN 1057-7149 [18276262], [doi]
   (last updated on 2025/12/31)

   Abstract:
   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 on 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.