Abstract

Over the last decade, a number of methods for geometric matching based on a branch-and-bound approach have been proposed. Such algorithms work by recursively subdividing transformation space and bounding the quality of match over each subdivision. No direct comparison of the major implemen- tation strategies has been made so far, so it has been unclear what the relative performance of the different approaches is. This paper examines experimentally the relative performance of different implementation choices in the implementa- tion of branch-and-bound algorithms for geometric matching: alternatives for the computation of upper bounds across a collection of features, and alternatives the order in which search nodes are expanded. Two major approaches to computing the bounds have been proposed: the matchlist based approach, and approaches based on point location data structures. A second issue that is addressed in the paper is the question of search strategy; branch-and-bound algorithms tradition- ally use a “best-first” search strategy, but a “depth-first” strategy is a plausible alternative. These alternative implementations are compared on an easily repro- ducible and commonly used class of test problems, a statistical model of feature distributions and matching within the COIL-20 image database. The experimen- tal results show that matchlist based approaches outperform point location based approaches on common tasks. The paper also shows that a depth-first approach to matching results in a 50-200 fold reduction in memory usage with only a small increase in running time. Since matchlist-based approaches are signi ficantly easier to implement and can easily cope with a much wider variety of feature types and error bounds that point location based approaches, they should probably the pri- mary implementation strategy for branch-and-bound based methods for geometric matching.