In this work, we introduce a robust energy model for multiview 3D reconstruction that fuses silhouette- and stereo-based image information. It allows to cope with significant amounts of noise without manual pre-segmentation of the input images. Moreover, we suggest a method that can globally optimize this energy up to the visibility constraint. While similar global optimization has been presented in the discrete context in form of the maxflow-mincut framework, we suggest the use of a continuous counterpart. In contrast to graph cut methods, discretizations of the continuous optimization technique are consistent and independent of the choice of the grid connectivity. Our experiments demonstrate that this leads to visible improvements. Moreover, memory requirements are reduced, allowing for global reconstructions at higher resolutions.