A New Computational Framework for Efficient Parallelization and Optimization of Large Scale Graph Matching

Abstract

There are so many applications in data fusion, comparison, and recognition that require a robust and efficient algorithm to match features of multiple images. To improve accuracy and get a more stable result is important to take into consideration both local appearance and the pairwise relationship of features. Graphs are a powerful and flexible data structure, allowing for the description of complex relationships between data elements, whose nodes correspond to salient features and edges correspond to relational aspects between features. Therefore, the problem of graph matching is to find a mapping between the two sets of nodes that preserves the relationships between them as much as possible. This graph-matching problem is mathematically formulated as an IQP problem which solving it is NP-hard, and obtaining exact Optima only plausible for very small data. Therefore, handling large-scale scientific visual data is quite limited, necessitating both efficient serial algorithms, as well as scalable parallel formulations. In this thesis, we first focused on exploring techniques to reduce the computation cost as well as memory usage of Pairwise graph matching by adopting a heuristic pruning strategy together with a redundancy pattern suppression scheme. We also modified the structure of the affinity matrix for minimizing memory requirement and parallelizing our algorithm by employing CPU’s and GPU’s accelerated libraries. Any pair of features with similar distance from first image results in same sub-matrices, therefore instead of constructing the whole affinity matrix, we only built the sub-blocked affinity for those distinct feature distances. By employing this scheme not only saved large memory and reduced computation time tremendously but also, the matrix-vector multiplication of gradient computation performed in parallel, where each block-vector calculation computed independently without synchronization. The accelerated libraries such as MKL, cuSparse, cuBlas and thrust applied to solving the GM problem, following the scheme of the spectral matching algorithm. We also extended our work for Multi-graph imaging, since many tasks require finding correspondences across multiple images. Also, considering more graph improves the matching accuracy. Most algorithms obtain approximate solutions for solving the GM NP-hard problem, result in a weak optimal solution. Therefore, we proposed a new solver, which iteratively modified the affinity matrix and binarized the solution by optimizing the original problem with its integer constraints.