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This paper proves a $\Gamma$-convergence result for the discrete energy (tothe continuous one) of the matching problem for signals defined on surfaces. Inparticular, we highlight some geometric properties that must be guaranteed inthe discretization process to ensure the convergence of minimizers. The proofis given in the framework of functional shapes introduced in \cite{ABN}. Inparticular, we consider a varifold-type attachment term, and a $BV$ penaltyterm is used instead of the original $L^2$ norm.

The matching problem between functional shapes via a BV penalty term: a $\Gamma$-convergence result