Robust Anisotropic Diiusion: Connections between Robust Statistics, Line Processing, and Anisotropic Diiusion

Relations between anisotropic diiusion and robust statistics are described in this paper. We show that anisotropic diiusion 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 diiusion equation is closely related to the error norm and innuence 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 diiusion. 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 diiusion ows.