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Summary form only given: In this paper briefly review three formulations of the many-to-many matching problem as applied to model acquisition, model indexing, and object recognition. In the first scenario, I will describe the problem of learning a prototypical shape model from a set of exemplars in which the exemplars may not share a single local feature in common. We formulate the problem as a search through the intractable space of feature combinations, or abstractions, to find the "lowest common abstraction" that is derivable from each input exemplar. This abstraction, in turn, defines a many-to-many feature correspondence among the extracted input features.