Cellular matrix model for parallel combinatorial optimization algorithms in Euclidean plane

Abstract

Listen

Translate article

We propose a parallel computation model, called cellular matrix model (CMM), to address large-size Euclidean graph matching problems in the plane. The parallel computation takes place by partitioning the plane into a regular grid of cells, each cell being affected to a single processor. Each processor operates on local data, starting from its cell location and extending its search to the neighborhood cells in a spiral search way. In order to deal with large-size problems, memory size and processor number are fixed as O(N), where N is the problem size. Then one key point is that closest point searching in the plane is performed in O(1) expected time for uniform or bounded distribution, for each processor independently. We define a generic loop that models the parallel projection between graphs and their matching, as executed by the many cells at a given level of computation granularity. To illustrate its efficacy and versatility, we apply the CMM, on GPU platforms, to two problems in image processing: superpixel segmentation and stereo matching energy minimization. Firstly, we propose an extended version of the well-known SLIC superpixel segmentation algorithm, which we call SPASM algorithm, by using a parallel 2D self-organizing map instead of k-means algorithm. Secondly, we investigate the idea of distributed variable neighborhood search, and propose a parallel search heuristic, called distributed local search (DLS), for global energy minimization of stereo matching problem. We evaluate the approach with regards to the state-of-the-art graph cut and belief propagation algorithms. For each problem, we argue that the parallel GPU implementation provides new competitive quality/time trade-offs, with substantial acceleration factors as the problem size increases.