Robust anisotropic diffusion: Connections between robust statistics, line processing, and anisotropic diffusion

Conference Paper

Relations between anisotropic diffusion and robust statistics are described in this paper. 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 biweightrobust 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 the image. Finally, connections between robust estimation and line processing provide a framework to introduce spatial coherence in anisotropic diffusion flows.

Full Text

Duke Authors

Cited Authors

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

Published Date

  • January 1, 1997

Published In

Volume / Issue

  • 1252 /

Start / End Page

  • 323 - 326

Electronic International Standard Serial Number (EISSN)

  • 1611-3349

International Standard Serial Number (ISSN)

  • 0302-9743

International Standard Book Number 10 (ISBN-10)

  • 3540631674

International Standard Book Number 13 (ISBN-13)

  • 9783540631675

Digital Object Identifier (DOI)

  • 10.1007/3-540-63167-4_27

Citation Source

  • Scopus