The DOI matches its Crossref record; 26 of the 26 references it cites were found in a registry or an index.
Behavioral analysis of anisotropic diffusion in image processing
Open accessAbstract
In this paper, we analyze the behavior of the anisotropic diffusion model of Perona and Malik (1990). The main idea is to express the anisotropic diffusion equation as coming from a certain optimization problem, so its behavior can be analyzed based on the shape of the corresponding energy surface. We show that anisotropic diffusion is the steepest descent method for solving an energy minimization problem. It is demonstrated that an anisotropic diffusion is well posed when there exists a unique global minimum for the energy functional and that the ill posedness of a certain anisotropic diffusion is caused by the fact that its energy functional has an infinite number of global minima that are dense in the image space. We give a sufficient condition for an anisotropic diffusion to be well posed and a sufficient and necessary condition for it to be ill posed due to the dense global minima. The mechanism of smoothing and edge enhancement of anisotropic diffusion is illustrated through a particular orthogonal decomposition of the diffusion operator into two parts: one that diffuses tangentially to the edges and therefore acts as an anisotropic smoothing operator, and the other that flows normally to the edges and thus acts as an enhancement operator.
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Cites
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Gilboa, G., Sochen, N., & Zeevi, Y. Y. (2004) · Journal of Mathematical Imaging and Vision · doi:10.1023/b:jmiv.0000011320.81911.38 · Cited by 616
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Metadata
- Authors
- You, Y.-L., Xu, W., Tannenbaum, A., & Kaveh, M.
- Venue
- IEEE Transactions on Image Processing
- Published
- 1996-11
- Volume
- 5
- Issue
- 11
- Pages
- 1539-1553
- ISSN
- 1057-7149 (ISSN-L)
- 1941-0042
- OpenAlex
- W2151958211
- Cited by
- 490
- References
- 26
- FWCI
- 9.13
- Type
- journal article
- Language
- en
- Open access
- green
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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