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Indexing Hierarchical Structures Using Graph Spectra
July 2005 (vol. 27 no. 7)
pp. 1125-1140
Hierarchical image structures are abundant in computer vision and have been used to encode part structure, scale spaces, and a variety of multiresolution features. In this paper, we describe a framework for indexing such representations that embeds the topological structure of a directed acyclic graph (DAG) into a low-dimensional vector space. Based on a novel spectral characterization of a DAG, this topological signature allows us to efficiently retrieve a promising set of candidates from a database of models using a simple nearest-neighbor search. We establish the insensitivity of the signature to minor perturbation of graph structure due to noise, occlusion, or node split/merge. To accommodate large-scale occlusion, the DAG rooted at each nonleaf node of the query "votes” for model objects that share that "part,” effectively accumulating local evidence in a model DAG's topological subspaces. We demonstrate the approach with a series of indexing experiments in the domain of view-based 3D object recognition using shock graphs.

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Index Terms:
Index Terms- Structural indexing, graph spectra, object recognition, shock graphs.
Citation:
Ali Shokoufandeh, Diego Macrini, Sven Dickinson, Kaleem Siddiqi, Steven W. Zucker, "Indexing Hierarchical Structures Using Graph Spectra," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 7, pp. 1125-1140, July 2005, doi:10.1109/TPAMI.2005.142
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