  An Ahlfors-type regularity result for free-discontinuity energies defined on
the space $SBV^{\varphi}$ of special functions of bounded variation with
$\varphi$-growth, where $\varphi$ is a generalized Orlicz function, is proved.
Our analysis expands on the regularity theory for minimizers of a class of
free-discontinuity problems in the non-standard growth case.
