Graph-Theoretical Methods in Computer Vision

The management of large databases of hierarchical (e.g., multi-scale or multilevel) image features is a common problem in object recognition. Such structures are often represented as trees or directed acyclic graphs (DAGs), where nodes represent image feature abstractions and arcs represent spatial relations, mappings across resolution levels, component parts, etc. Object recognition consists of two processes: indexing and verification. In the indexing process, a collection of one or more extracted image features belonging to an object is used to select, from a large database of object models, a small set of candidates likely to contain the object. Given this relatively small set of candidates, a verification, or matching procedure is used to select the most promising candidate. Such matching problems can be formulated as largest isomorphic subgraph or largest isomorphic subtree problems, for which a wealth of literature exists in the graph algorithms community. However, the nature of the vision instantiation of this problem often precludes the direct application of these methods. Due to occlusion and noise, no significant isomorphisms may exists between two graphs or trees. In this paper, we review our application of spectral encoding of a graph for indexing to large database of image features represented as DAGs. We will also review a more general class of matching methods, called bipartite matching, to two problems in object recognition.