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The authors show how large efficiencies can be achieved in model-based 3-D vision by combining the notions of discrete relaxation and bipartite matching. The computational approach presented is capable of pruning large segments of search space-an indispensable step when the number of objects in the model library is large and when recognition of complex objects with a large number of surfaces is called for. Bipartite matching is used for quick wholesale rejection of inapplicable models and for the determination of compatibility of a scene surface with a potential model surface taking into account relational considerations. The time complexity function associated with those aspects of the procedure that are implemented via bipartite matching is provided. The algorithms do not take more than a couple of iterations, even for objects with more than 30 surfaces.