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Many-to-Many Feature Matching Using Spherical Coding of Directed Graphs

  • M. Fatih Demirci
  • Ali Shokoufandeh
  • Sven Dickinson
  • Yakov Keselman
  • Lars Bretzner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3021)

Abstract

In recent work, we presented a framework for many-to-many matching of multi-scale feature hierarchies, in which features and their relations were captured in a vertex-labeled, edge-weighted directed graph. The algorithm was based on a metric-tree representation of labeled graphs and their metric embedding into normed vector spaces, using the embedding algorithm of Matousek [13]. However, the method was limited by the fact that two graphs to be matched were typically embedded into vector spaces with different dimensionality. Before the embeddings could be matched, a dimensionality reduction technique (PCA) was required, which was both costly and prone to error. In this paper, we introduce a more efficient embedding procedure based on a spherical coding of directed graphs. The advantage of this novel embedding technique is that it prescribes a single vector space into which both graphs are embedded. This reduces the problem of directed graph matching to the problem of geometric point matching, for which efficient many-to-many matching algorithms exist, such as the Earth Mover’s Distance. We apply the approach to the problem of multi-scale, view-based object recognition, in which an image is decomposed into a set of blobs and ridges with automatic scale selection.

Keywords

Feature Match Graph Match Normed Vector Space Graph Edit Distance Spherical Code 
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 2004

Authors and Affiliations

  • M. Fatih Demirci
    • 1
  • Ali Shokoufandeh
    • 1
  • Sven Dickinson
    • 2
  • Yakov Keselman
    • 3
  • Lars Bretzner
    • 4
  1. 1.Department of Computer ScienceDrexel UniversityPhiladelphiaUSA
  2. 2.Department of Computer ScienceUniversity of TorontoTorontoCanada
  3. 3.School of Computer Science, Telecommunications and Information SystemsDePaul UniversityChicagoUSA
  4. 4.Computational Vision and Active Perception Laboratory, Department Of Numerical Analysis and Computer ScienceKTHStockholmSweden

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