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Indexing hierarchical structures using graph spectra

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5 Author(s)
Shokoufandeh, A. ; Dept. of Comput. Sci., College of Eng., Philadelphia, PA, USA ; Macrini, D. ; Dickinson, S. ; Siddiqi, K.
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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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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:27 ,  Issue: 7 )