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International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition

EMMCVPR 2005: Energy Minimization Methods in Computer Vision and Pattern Recognition pp 171–186Cite as

Probabilistic Subgraph Matching Based on Convex Relaxation

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3757))

Abstract

We present a novel approach to the matching of subgraphs for object recognition in computer vision. Feature similarities between object model and scene graph are complemented with a regularization term that measures differences of the relational structure. For the resulting quadratic integer program, a mathematically tight relaxation is derived by exploiting the degrees of freedom of the embedding space of positive semidefinite matrices. We show that the global minimum of the relaxed convex problem can be interpreted as probability distribution over the original space of matching matrices, providing a basis for efficiently sampling all close-to-optimal combinatorial matchings within the original solution space. As a result, the approach can even handle completely ambiguous situations, despite uniqueness of the relaxed convex problem. Exhaustive numerical experiments demonstrate the promising performance of the approach which – up to a single inevitable regularization parameter that weights feature similarity against structural similarity – is free of any further tuning parameters.

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Author information

Authors and Affiliations

  1. Computer Vision, Graphics, and Pattern Recognition Group, Department of Mathematics and Computer Science, University of Mannheim, D-68131, Mannheim, Germany

    Christian Schellewald & Christoph Schnörr

Authors
  1. Christian Schellewald
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  2. Christoph Schnörr
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Editor information

Editors and Affiliations

  1. Department of CISE, University of Florida, Gainesville, FL, USA

    Anand Rangarajan

  2. University of Florida, 32611, Gainesville, FL, USA

    Baba Vemuri

  3. Department of Statistics, University of California, Los Angeles

    Alan L. Yuille

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© 2005 Springer-Verlag Berlin Heidelberg

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Schellewald, C., Schnörr, C. (2005). Probabilistic Subgraph Matching Based on Convex Relaxation. In: Rangarajan, A., Vemuri, B., Yuille, A.L. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2005. Lecture Notes in Computer Science, vol 3757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11585978_12

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  • DOI: https://doi.org/10.1007/11585978_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30287-2

  • Online ISBN: 978-3-540-32098-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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