Robust anisotropic diffusion and sharpening of scalar and vector images

Michael Black, Guillermo Sapiro, David 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 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 the image. We extend the framework to vector-valued images and show applications to robust image sharpening.

Original languageEnglish (US)
Title of host publicationIEEE International Conference on Image Processing
PublisherIEEE Comp Soc
Pages263-266
Number of pages4
Volume1
StatePublished - 1997
EventProceedings of the 1997 International Conference on Image Processing. Part 2 (of 3) - Santa Barbara, CA, USA
Duration: Oct 26 1997Oct 29 1997

Other

OtherProceedings of the 1997 International Conference on Image Processing. Part 2 (of 3)
CitySanta Barbara, CA, USA
Period10/26/9710/29/97

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Statistics

ASJC Scopus subject areas

  • Computer Vision and Pattern Recognition
  • Hardware and Architecture
  • Electrical and Electronic Engineering

Cite this

Black, M., Sapiro, G., Marimont, D., & Heeger, D. (1997). Robust anisotropic diffusion and sharpening of scalar and vector images. In IEEE International Conference on Image Processing (Vol. 1, pp. 263-266). IEEE Comp Soc.

Robust anisotropic diffusion and sharpening of scalar and vector images. / Black, Michael; Sapiro, Guillermo; Marimont, David; Heeger, David.

IEEE International Conference on Image Processing. Vol. 1 IEEE Comp Soc, 1997. p. 263-266.

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

Black, M, Sapiro, G, Marimont, D & Heeger, D 1997, Robust anisotropic diffusion and sharpening of scalar and vector images. in IEEE International Conference on Image Processing. vol. 1, IEEE Comp Soc, pp. 263-266, Proceedings of the 1997 International Conference on Image Processing. Part 2 (of 3), Santa Barbara, CA, USA, 10/26/97.
Black M, Sapiro G, Marimont D, Heeger D. Robust anisotropic diffusion and sharpening of scalar and vector images. In IEEE International Conference on Image Processing. Vol. 1. IEEE Comp Soc. 1997. p. 263-266
Black, Michael ; Sapiro, Guillermo ; Marimont, David ; Heeger, David. / Robust anisotropic diffusion and sharpening of scalar and vector images. IEEE International Conference on Image Processing. Vol. 1 IEEE Comp Soc, 1997. pp. 263-266
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