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): | Perzeptive Systeme |
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}, doi = {}, month_numeric = {3} } |