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

M. J. Black, G. Sapiro, D. Marimont, D. Heeger

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish (US)
Title of host publicationScale-Space Theory in Computer Vision - 1st International Conference, Scale-Space 1997, Proceedings
EditorsBart ter Haar Romeny, Max Viergever, Luc Florack, Jan Koenderink
PublisherSpringer Verlag
Pages323-326
Number of pages4
ISBN (Print)3540631674, 9783540631675
DOIs
StatePublished - Jan 1 1997
Event1st International Conference on Scale-Space Theory in Computer Vision, Scale-Space 1997 - Utrecht, Netherlands
Duration: Jul 2 1997Jul 4 1997

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1252
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other1st International Conference on Scale-Space Theory in Computer Vision, Scale-Space 1997
CountryNetherlands
CityUtrecht
Period7/2/977/4/97

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Black, M. J., Sapiro, G., Marimont, D., & Heeger, D. (1997). Robust anisotropic diffusion: Connections between robust statistics, line processing, and anisotropic diffusion. In B. ter Haar Romeny, M. Viergever, L. Florack, & J. Koenderink (Eds.), Scale-Space Theory in Computer Vision - 1st International Conference, Scale-Space 1997, Proceedings (pp. 323-326). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1252). Springer Verlag. https://doi.org/10.1007/3-540-63167-4_27