Abstract: In this paper, a new formulation and solution to volumetric reconstruction from multiple calibrated images is presented. This problem has been previously formulated either as a continuous geometric optimization process driven by local numerical methods, or as a discrete labelling problem solved by global techniques for computing only stereo disparities. Our new formulation builds a bridge between these two approaches and takes advantage of both: a continuous geometric functional is minimized up to a discretization by a global graph cut algorithm. The relation between the continuous and discrete formulations is straightforwardly established. The minimization operates on a 3D embedded graph whose minimal cut is a solution of the discrete problem, leading to a global minimum. This new approach handling both occlusions and discontinuities has been demonstrated on real sequences, giving remarkably detailed surface geometry up to 1/10th pixel.