THE COMBINATORICS OF HEURISTIC-SEARCH TERMINATION FOR OBJECT RECOGNITION IN CLUTTERED ENVIRONMENTS

Many current recognition systems use constrained search to locate objects in cluttered environments. Earlier analysis of one class of methods has shown that the expected amount of search is quadratic in the number of model and data features, if all the data is known to come from a single object, but is exponential when spurious data is included. To overcome this, many methods terminate a search once an interpretation that is "good enough" is found. In this paper, we formally examine the combinatorics of this approach, showing that choosing correct termination procedures can dramatically reduce the search. In particular, we provide conditions on the object model and the scene clutter such that the expected search is at most quartic. The analytic results are shown to be in agreement with empirical data for cluttered object recognition. These results imply that it is critical to use techniques that select subsets of the data likely to have come from a single object before establishing a correspondence between data and model features.