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.