Indexing using a Spectral Encoding of Topological Structure

Ali Shokoufandeh, Sven J. Dickinson, Kaleem Siddiqi, Steven W. Zucker

Abstract: In an object recognition system, if the extracted image features are multilevel or multiscale, the indexing structure may take the form of a tree. Such structures are not only common in computer vision, but also appear in linguistics, graphics, computational biology, and a wide range of other domains. In this paper, we develop an indexing mechanism that maps the topological structure of a tree into a low-dimensional vector space. Based on a novel eigenvalue characterization of a tree, this topological signature allows us to efficiently retrieve a small set of candidates from a database of models. To accommodate occlusion and local deformation, local evidence is accumulated in each of the tree's topological subspaces. We demonstrate the approach with a series of indexing experiments in the domain of 2-D object recognition.