Abstract: The surface reconstruction from multiple calibrated images has been mainly approached using local methods, either as a continuous optimization driven by level sets, or as a discrete volumetric method of space carving. We here propose a direct surface reconstruction approach. It starts from a continuous geometric functional that is then minimized up to a discretization by a global graph-cut algorithm operating on a 3D embedded graph. The method is related to the stereo disparity computation based on graph-cut formulation, but fundamentally different in two aspects. First, the existing stereo disparity methods are only interested in obtaining layers of constant disparity, while we focus on a surface geometry of high resolution. Second, only approximate solutions are reached by most of the existing graph-cut algorithms, while we reach a global minimum. The whole procedure is consistently incorporated into a voxel representation that handles both occlusions and discontinuities. It is demonstrated on real sequences, yielding remarkably detailed surface geometry up to $1/10$th pixel.