Robust anisotropic diffusion

Connections between robust statistics, line processing, and anisotropic diffusion

M. J. Black, G. Sapiro, D. Marimont, David 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
PublisherSpringer Verlag
Pages323-326
Number of pages4
Volume1252
ISBN (Print)3540631674, 9783540631675
DOIs
StatePublished - 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)03029743
ISSN (Electronic)16113349

Other

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

Fingerprint

Robust Statistics
Anisotropic Diffusion
Robust Estimation
Statistics
Line
Processing
Influence Function
Diffusion equation
Estimator
Norm
Formulation
Estimate
Framework

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

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 Scale-Space Theory in Computer Vision - 1st International Conference, Scale-Space 1997, Proceedings (Vol. 1252, 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

Robust anisotropic diffusion : Connections between robust statistics, line processing, and anisotropic diffusion. / Black, M. J.; Sapiro, G.; Marimont, D.; Heeger, David.

Scale-Space Theory in Computer Vision - 1st International Conference, Scale-Space 1997, Proceedings. Vol. 1252 Springer Verlag, 1997. p. 323-326 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1252).

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

Black, MJ, Sapiro, G, Marimont, D & Heeger, D 1997, Robust anisotropic diffusion: Connections between robust statistics, line processing, and anisotropic diffusion. in Scale-Space Theory in Computer Vision - 1st International Conference, Scale-Space 1997, Proceedings. vol. 1252, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1252, Springer Verlag, pp. 323-326, 1st International Conference on Scale-Space Theory in Computer Vision, Scale-Space 1997, Utrecht, Netherlands, 7/2/97. https://doi.org/10.1007/3-540-63167-4_27
Black MJ, Sapiro G, Marimont D, Heeger D. Robust anisotropic diffusion: Connections between robust statistics, line processing, and anisotropic diffusion. In Scale-Space Theory in Computer Vision - 1st International Conference, Scale-Space 1997, Proceedings. Vol. 1252. Springer Verlag. 1997. p. 323-326. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-63167-4_27
Black, M. J. ; Sapiro, G. ; Marimont, D. ; Heeger, David. / Robust anisotropic diffusion : Connections between robust statistics, line processing, and anisotropic diffusion. Scale-Space Theory in Computer Vision - 1st International Conference, Scale-Space 1997, Proceedings. Vol. 1252 Springer Verlag, 1997. pp. 323-326 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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