- Research Article
- Open Access
Topological Optimization with the -Laplacian Operator and an Application in Image Processing
© A. Sy and D. Seck. 2009
- Received: 14 April 2009
- Accepted: 28 July 2009
- Published: 15 September 2009
We focus in this paper on the theoretical and numerical aspect os image processing. We consider a non linear boundary value problem (the -Laplacian) from which we will derive the asymptotic expansion of the Mumford-Shah functional. We give a theoretical expression of the topological gradient as well as a numerical confirmation of the result in the restoration and segmentation of images.
- Differential Equation
- Partial Differential Equation
- Ordinary Differential Equation
- Functional Equation
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