Continuous limits of discrete perimeters
CMAP, École polytechnique, CNRS 91128, Palaiseau, France. email@example.com
2 Dipartimento di Matematica, Facoltà di Ingegneria, Università degli Studi di Brescia, Via Valotti 9, 25133 Brescia, Italy. firstname.lastname@example.org
3 Dipartimento di Matematica, I Facoltà di Ingegneria, Politecnico di Torino, c.so Duca degli Abruzzi 24, 10129 Torino, Italy. email@example.com
We consider a class of discrete convex functionals which satisfy a (generalized) coarea formula. These functionals, based on submodular interactions, arise in discrete optimization and are known as a large class of problems which can be solved in polynomial time. In particular, some of them can be solved very efficiently by maximal flow algorithms and are quite popular in the image processing community. We study the limit in the continuum of these functionals, show that they always converge to some “crystalline” perimeter/total variation, and provide an almost explicit formula for the limiting functional.
Mathematics Subject Classification: 49Q20 / 65K10
Key words: Generalized coarea formula / total variation / anisotropic perimeter
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