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Complex Fiedler Vectors for Shape Retrieval

  • Reinier H. van Leuken
  • Olga Symonova
  • Remco C. Veltkamp
  • Raffaele de Amicis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5342)

Abstract

Adjacency and Laplacian matrices are popular structures to use as representations of shape graphs, because their sorted sets of eigenvalues (spectra) can be used as signatures for shape retrieval. Unfortunately, the descriptiveness of these spectra is limited, and handling graphs of different size remains a challenge. In this work, we propose a new framework in which the shapes (3D models in our test corpus) are represented by multi-labeled graphs. A Hermitian matrix is associated to each graph, in which the entries are defined such that they contain all information stored in the graph edges. Additional constraints ensure that this Hermitian matrix mimics the well-studied spectral behaviour of the Laplcian matrix. We therefore use the Hermitian Fiedler vector as shape signature during retrieval. To deal with graphs of different size, we efficiently reuse the calculated Fiedler vector to decompose the graph into a limited number of non-overlapping, meaningful subgraphs. Retrieval results are based on both complete matching and subgraph matching.

Keywords

Shape Descriptor Shape Index Hermitian Matrix Laplacian Matrix Retrieval Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Reinier H. van Leuken
    • 1
  • Olga Symonova
    • 2
  • Remco C. Veltkamp
    • 1
  • Raffaele de Amicis
    • 2
  1. 1.Universiteit UtrechtThe Netherlands
  2. 2.Fondazione GraphitechTrentoItaly

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