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In this paper we discuss the links between Mumford and Shah’s variational problem for (signal and) image segmentation, based on an energy functional of a continuous grey-level function, and the numerical algorithms proposed to solve it. These numerical approaches are based on a discrete functional. We recall that, in one dimension, this discrete functional is asymptotically equivalent to the continuous functional. This can be summarized in a -convergence result. We show that the same result holds in dimension two, provided that the continuous energy is adapted to the anisotropy of the discrete approaches. We display a few experimental results in dimensions one and two.