Voxel based modeling is an attractive way to represent complex multi-material objects. Multi-labeled voxel models are also ubiquitous in material sciences, medical imaging or numerical simulations. We present here a variational method to regularize interfaces in multi-labeled digital images. It builds piecewise smooth quadran-gulated surfaces efficiently, with theoretical guarantees of stability. Complex topological events when several materials are considered are handled naturally. We show its usefulness for digital surface approximation, for voxel art regularization by transferring colori-metric information, and for upscaling voxel models to speed up coarse-to-fine modeling.