  We propose an approach for dense semantic 3D reconstruction which uses a data
term that is defined as potentials over viewing rays, combined with continuous
surface area penalization. Our formulation is a convex relaxation which we
augment with a crucial non-convex constraint that ensures exact handling of
visibility. To tackle the non-convex minimization problem, we propose a
majorize-minimize type strategy which converges to a critical point. We
demonstrate the benefits of using the non-convex constraint experimentally. For
the geometry-only case, we set a new state of the art on two datasets of the
commonly used Middlebury multi-view stereo benchmark. Moreover, our
general-purpose formulation directly reconstructs thin objects, which are
usually treated with specialized algorithms. A qualitative evaluation on the
dense semantic 3D reconstruction task shows that we improve significantly over
previous methods.
