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 the line processes allows us to develop new anisotropic diffusion equations that result in a qualitative improvement in the continuity of edges.

Full Text

Duke Authors

Cited Authors

  • Black, MJ; Sapiro, G; Marimont, DH; Heeger, D

Published Date

  • 1998

Published In

Volume / Issue

  • 7 / 3

Start / End Page

  • 421 - 432

PubMed ID

  • 18276262

International Standard Serial Number (ISSN)

  • 1057-7149

Digital Object Identifier (DOI)

  • 10.1109/83.661192

Language

  • eng

Citation Source

  • PubMed