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Many-to-Many Matching of Scale-Space Feature Hierarchies Using Metric Embedding

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Scale Space Methods in Computer Vision (Scale-Space 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2695))

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Abstract

Scale-space feature hierarchies can be conveniently represented as graphs, in which edges are directed from coarser features to finer features. Consequently, feature matching (or view-based object matching) can be formulated as graph matching. Most approaches to graph matching assume a one-to-one correspondence between nodes (features) which, due to noise, scale discretization, and feature extraction errors, is overly restrictive. In general, a subset of features in one hierarchy, representing an abstraction of those features, may best match a subset of features in another. We present a framework for the many-to-many matching of multi-scale feature hierarchies, in which features and their relations are captured in a vertex-labeled, edge-weighted graph. The matching algorithm is based on a metric-tree representation of labeled graphs and their low-distortion metric embedding into normed vector spaces. This two-step transformation reduces the many-to-many graph matching problem to that of computing a distribution-based distance measure between two such embeddings. To compute the distance between two sets of embedded, weighted vectors, we use the Earth Mover’s Distance under transformation. To demonstrate the approach, we target the domain of multi-scale, qualitative shape description, in which an image is decomposed into a set of blobs and ridges with automatic scale selection. We conduct an extensive set of view-based matching trials, and compare the results favorably to matching under a one-to-one assumption.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Drexel University, Philadelphia, PA, 19104, USA

    M. Fatih Demirci & Ali Shokoufandeh

  2. School of Computer Science, Telecommunications and Information Systems, DePaul University, Chicago, IL, 60604, USA

    Yakov Keselman

  3. Department of Computer Science, University of Toronto, Toronto, Ontario, Canada, M5S 3G4

    Sven Dickinson

  4. Computational Vision and Active Perception Laboatory, Department Of Numerical Analysis and Computer Science, KTH, Stockholm, Sweden

    Lars Bretzner

Authors
  1. M. Fatih Demirci
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  2. Ali Shokoufandeh
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  3. Yakov Keselman
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  4. Sven Dickinson
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  5. Lars Bretzner
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Editor information

Editors and Affiliations

  1. Imaging Sciences, 5th Floor Thomas Guy House, Guy’s Campus, London, SE1 9RT, UK

    Lewis D. Griffin

  2. IT University of Copenhagen, Glentevej 67-69, Copenhagen NV, Denmark

    Martin Lillholm

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© 2003 Springer-Verlag Berlin Heidelberg

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Fatih Demirci, M., Shokoufandeh, A., Keselman, Y., Dickinson, S., Bretzner, L. (2003). Many-to-Many Matching of Scale-Space Feature Hierarchies Using Metric Embedding. In: Griffin, L.D., Lillholm, M. (eds) Scale Space Methods in Computer Vision. Scale-Space 2003. Lecture Notes in Computer Science, vol 2695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44935-3_2

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  • DOI: https://doi.org/10.1007/3-540-44935-3_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40368-5

  • Online ISBN: 978-3-540-44935-5

  • eBook Packages: Springer Book Archive

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