Issue No. 07 - July (2005 vol. 27)
Steven W. Zucker , IEEE
Diego Macrini , IEEE Computer Society
Ali Shokoufandeh , IEEE
Sven Dickinson , IEEE
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.
Index Terms- Structural indexing, graph spectra, object recognition, shock graphs.
Steven W. Zucker, Diego Macrini, Ali Shokoufandeh, Kaleem Siddiqi, Sven Dickinson, "Indexing Hierarchical Structures Using Graph Spectra", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 27, no. , pp. 1125-1140, July 2005, doi:10.1109/TPAMI.2005.142