Indexing Hierarchical Structures Using Graph Spectra
IEEE Transactions on Pattern Analysis and Machine Intelligence
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In this paper we explore how to represent object view-structure by embedding the neighbourhood graphs of feature points in a pattern-space. We adopt a graph-spectral approach. We use the leading eigenvectors of the graph adjacency matrix to define clusters of nodes. For each cluster, we compute vectors of cluster properties. We embed these vectors in a pattern-space using two contrasting approaches. The first of these involves performing principal components analysis on the covariance matrix for the spectral pattern vectors. The second approach involves performing multidimensional scaling on the L2 norm for pairs of pattern vectors. We demonstrate the both methods result in well-structured view spaces for graph-data extracted from 2D views of 3D objects.