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Robust anisotropic diffusion

1998

Article

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Relations between anisotropic diffusion and robust statistics are described in this paper. Specifically, 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 an image that has been smoothed with anisotropic diffusion. Additionally, we derive a relationship between anisotropic diffusion and regularization with line processes. Adding constraints on the spatial organization of the line processes allows us to develop new anisotropic diffusion equations that result in a qualitative improvement in the continuity of edges

Author(s): Black, M. J. and Sapiro, G. and Marimont, D. and Heeger, D.
Journal: IEEE Transactions on Image Processing
Volume: 7
Number (issue): 3
Pages: 421-432
Year: 1998
Month: March

Department(s): Perceiving Systems
Bibtex Type: Article (article)
Paper Type: Journal

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BibTex

@article{Black:IEEE:1998:7,
  title = {Robust anisotropic diffusion},
  author = {Black, M. J. and Sapiro, G. and Marimont, D. and Heeger, D.},
  journal = {IEEE Transactions on Image Processing},
  volume = {7},
  number = {3},
  pages = {421-432},
  month = mar,
  year = {1998},
  month_numeric = {3}
}