© 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.
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