Perimetric type functionals are known to be difficult to handle directly within topology optimization algorithms because of their high sensitivity to topology changes. I will present a Gamma-convergence approximation of some variants of the perimeter which are built upon the solution of elliptic boundary value problems. I will discuss the advantages and drawbacks of such a construction over local approximations, and I will in particular insist on an anisotropic version motivated by 3d printing applications. If time allows I will also address multiphase cases.