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Robust anisotropic diffusion

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4 Author(s)
Black, M.J. ; Xerox Palo Alto Res. Center, CA, USA ; Sapiro, G. ; Marimont, D.H. ; Heeger, D.

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

Published in:

Image Processing, IEEE Transactions on  (Volume:7 ,  Issue: 3 )

Date of Publication:

Mar 1998

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