## Indexing Hierarchical Structures Using Graph Spectra (2005)

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Citations: | 42 - 10 self |

### BibTeX

@MISC{Shokoufandeh05indexinghierarchical,

author = {Ali Shokoufandeh and Diego Macrini and Sven Dickinson and Kaleem Siddiqi and Steven W. Zucker},

title = {Indexing Hierarchical Structures Using Graph Spectra},

year = {2005}

}

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### Abstract

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.