Inserted: 1 mar 2009
Last Updated: 3 apr 2010
Journal: ESAIM Math. Model. Numer. Anal.
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 comunity. We study the limit in the continuum of these functionals, show that they always converge to some "crystalline" perimetertotal variation, and provide an almost explicit formula for the limiting functional.
Keywords: Total variation, generalized coarea formula, anisotropic perimeter