In this paper, we make two contributions. Firstly, we replace the generic balloon constraints widely used in 3D reconstruction by a more sophisticated data-dependent regional term. The key idea is to propagate classical photoconsistency along visual rays into regional values describing voxel probabilities for being inside or outside the observed object. Secondly, we cast the optimization as one of minimizing a convex functional. Therefore (up to visibility) the reconstruction problem can be solved in a globally optimal manner in a spatially continuous setting. Compared to graph cut methods, this approach does not suffer from discretization artifacts and exhibits considerable reduction in memory requirements. Experimental comparisons clearly show the advantages of the proposed technique.