A path following algorithm for the graph matching problem
Abstract
We propose a convexconcave programming approach for the labeled weighted graph matching problem. The convexconcave programming formulation is obtained by rewriting the weighted graph matching problem as a leastsquare problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We therefore construct an approximation of the concave problem solution by following a solution path of a convexconcave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore to perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four datasets: simulated graphs, QAPLib, retina vessel images and handwritten chinese characters. In all cases, the results are competitive with the stateoftheart.
 Publication:

arXiv eprints
 Pub Date:
 January 2008
 DOI:
 10.48550/arXiv.0801.3654
 arXiv:
 arXiv:0801.3654
 Bibcode:
 2008arXiv0801.3654Z
 Keywords:

 Computer Science  Computer Vision and Pattern Recognition;
 Computer Science  Discrete Mathematics
 EPrint:
 23 pages, 13 figures,typo correction, new results in sections 4,5,6