Evaluation of a convex relaxation to a quadratic assignment matching approach for relational object views

We introduce a convex relaxation approach for the quadratic assignment problem to the field of computer vision. Due to convexity, a favourable property of this approach is the absence of any tuning parameters and the computation of high-quality combinatorial solutions by solving a mathematically simple optimization problem. Furthermore, the relaxation step always computes a tight lower bound of the objective function and thus can additionally be used as an efficient subroutine of an exact search algorithm. We report the results of both established benchmark experiments from combinatorial mathematics and random ground-truth experiments using computer-generated graphs. For comparison, a deterministic annealing approach is investigated as well. Both approaches show similarly good performance. In contrast to the convex approach, however, the annealing approach yields no problem relaxation, and four parameters have to be tuned by hand for the annealing algorithm to become competitive.