Mumford-Shah functional as $\Gamma$-limit
of Discrete Perona-Malik Energies



Massimiliano Morini
Department of Mathematics
Carnegie Mellon University
5000 Forbes Avenue
Pittsburgh, PA 15213, USA
morini@asdf4.math.cmu.edu



and

Matteo Negri
Max Planck Institute for Mathematics in the Sciences
Inselstrasse 22
04103 Leipzig, Germany
negri@mis.mpg.de



Abstract: We prove that a suitable rescaling of biased Perona-Malik energies, defined in the discrete setting, $\Gamma$-converges to an anisotropic version of the Mumford-Shah functional. Numerical results are discussed.

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