The main purpose of this paper is to develop the mathematical analysis of anisotropic total variation problems with a degenerate metric and the computation of the associated Cheeger sets. We illustrate our analysis with the computation of Cheeger sets with respect to different anisotropic norms of relevance in applications to image processing. In particular, we describe the computation of global minima of geodesic active contour models, and we illustrate the use of Cheeger sets for the problem of edge linking.
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Caselles et al. (2009) studied this question.
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