Robust anisotropic diffusion

Michael J. Black, Guillermo Sapiro, David H. Marimont, David Heeger

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)421-432
Number of pages12
JournalIEEE Transactions on Image Processing
Volume7
Issue number3
DOIs
StatePublished - 1998

Keywords

  • Anisotropic diffusion
  • Line processes
  • Robust statistics

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design

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