Graph cuts methods are at the core of many state-of-theart algorithms in computer vision due to their efficiency in computing globally optimal solutions. In this paper, we solve the maximum flow/minimum cut problem in parallel by splitting the graph into multiple parts and hence, further increase the computational efficacy of graph cuts. Optimality of the solution is guaranteed by dual decomposition, or more specifically, the solutions to the subproblems are constrained to be equal on the overlap with dual variables.We demonstrate that our approach both allows (i) faster processing on multi-core computers and (ii) the capability to handle larger problems by splitting the graph across multiple computers on a distributed network. Even though our approach does not give a theoretical guarantee of speedup, an extensive empirical evaluation on several applications with many different data sets consistently shows good performance. An open source implementation of the dual decomposition method is also made publicly available.

No abstract

Abstract. Length and area regularization are commonplace for inverse problems today. It has however turned out to be much more difficult to incorporate a curvature prior. In this paper we propose several improvements to a recently proposed framework based on global optimization. We identify and solve an issue with extraneous arcs in the original formulation by introducing region consistency constraints. The mesh geometry is analyzed both from a theoretical and experimental viewpoint and hexagonal meshes are shown to be superior. We demonstrate that adaptively generated meshes significantly improve the performance. Our final contribution is that we generalize the framework to handle mean curvature regularization for 3D surface completion and segmentation.