Robust anisotropic diffusion

—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 t...

• Type: Journal
• Year: 1998
• Where: TIP
• Authors: Michael J. Black, Guillermo Sapiro, David H. Marimont, David Heeger
• Keywords: Anisotropic Diffusion, Anisotropic Diffusion Equations, Robust, TIP 1998