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Variational approach for edge-preserving regularization using coupled PDEs

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4 Author(s)
Teboul, S. ; Lab. Inf. Signaux et Syst. de Sophia Antipolis, Valbonne, France ; Blanc-Feraud, L. ; Aubert, G. ; Barlaud, M.

This paper deals with edge-preserving regularization for inverse problems in image processing. We first present a synthesis of the main results we have obtained in edge-preserving regularization by using a variational approach. We recall the model involving regularizing functions φ and we analyze the geometry-driven diffusion process of this model in the three-dimensional (3-D) case. Then a half-quadratic theorem is used to give a very simple reconstruction algorithm. After a critical analysis of this model, we propose another functional to minimize for edge-preserving reconstruction purposes. It results in solving two coupled partial differential equations (PDEs): one processes the intensity, the other the edges. We study the relationship with similar PDE systems in particular with the functional proposed by Ambrosio-Tortorelli (1990, 1992) in order to approach the Mumford-Shah (1989) functional developed in the segmentation application. Experimental results on synthetic and real images are presented

Published in:

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

Date of Publication:

Mar 1998

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