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This paper presents a new volumetric stereo algorithm to reconstruct the 3D shape of an arbitrary object. Our method is based on finding the minimum cut in an octahedral graph structure embedded into the volumetric grid, which establishes a well defined relationship between the integrated photo-consistency function of a region in space and the corresponding edge weights of the embedded graph. This new graph structure allows for a highly efficient hierarchical implementation supporting high volumetric resolutions and large numbers of input images. Furthermore we will show how the resulting cut surface can be directly converted into a consistent, closed and manifold mesh. Hence this work provides a complete multi-view stereo reconstruction pipeline. We demonstrate the robustness and efficiency of our technique by a number of high quality reconstructions of real objects.