Parallel and distributed graph cuts by dual decomposition

Abstract

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.

Optimization for Multi-Region Segmentation of Cardiac MRI

“…Instead we develop a Lagrangian dual approach that uses half of the memory compared to RD and it always produces a segmentation. The method can easily be parallelized as described in [16]. Our algorithm is tested on two different data sets, one of which was used in the MICCAI 2009 Cardiac MR Left Ventricle Segmentation Challenge [1], on which we achieve results on par with the competing methods.…”

“…Specifically, the method is easy to implement, but in general has worse convergence properties than first-order gradient-based methods. We refer the reader to [13,16] for details.…”

“…In the experiments the step size from [16] is used. Since supergradient methods do not guarantee improved value in each step the best solution thus far is always saved and once the relative duality gap (p − d)/|p| is small enough the algorithm terminates.…”

Simultaneous Segmentation and Filtering via Reduced Graph Cuts

“…In the image segmentation context, almost all graph cuts-based methods are impractical to solve such problems due to the memory requirements for storing the underlying graphs. To overcome this situation, some amount of work has been done in this direction and a number of heuristics [9,10,12,5] and exact methods [7,4,13] have been proposed in recent years.…”

Minimizing Energies with Hierarchical Costs

“…In practice, this sub-problem is solved by casting it as a graph cut (Greig et al, 1989) and using combinatorial algorithms to compute the optimal binary configuration (e.g. Goldberg and Tarjan, 1988;Boykov and Kolmogorov, 2004;Strandmark and Kahl, 2010). Figure 1 illustrates the steps behind a single expansion move.…”