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

Published

Conference Paper

© Springer-Verlag Berlin Heidelberg 1997. 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