title: Robust anisotropic diffusion.
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.
authors.affiliation: Xerox Palo Alto Res. Center, CA 94304, USA.
authors.forename: M J
authors.initials: MJ
authors.lastname: Black
authors.forename: G
authors.initials: G
authors.lastname: Sapiro
authors.forename: D H
authors.initials: DH
authors.lastname: Marimont
authors.forename: D
authors.initials: D
authors.lastname: Heeger