Publications [#264898] of Guillermo Sapiro

Papers Published

1. Black, M; Sapiro, G; Marimont, D; Heeger, D, Robust anisotropic diffusion and sharpening of scalar and vector images, IEEE International Conference on Image Processing, vol. 1 (December, 1997), pp. 263-266, IEEE Comput. Soc [doi]
   (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 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 the image. We extend the framework to vector-valued images and show applications to robust image sharpening.