  We provide the integral representation formula for the relaxation in
$BV(\Omega; \mathbb{R}^M)$ with respect to strong convergence in $L^1(\Omega;
\mathbb{R}^M)$ of a functional with a boundary contact energy term. This
characterization is valid for a large class of surface energy densities, and
for domains satisfying mild regularity assumptions. Motivated by some classical
examples where lower semicontinuity fails, we analyze the extent to which the
geometry of the set enters the relaxation procedure.
