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