Probabilistic Subgraph Matching Based on Convex Relaxation

  • Christian Schellewald
  • Christoph Schnörr
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3757)


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.


Graph Match Quadratic Assignment Problem Convex Relaxation Ambiguous Situation Model Node 
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 2005

Authors and Affiliations

  • Christian Schellewald
    • 1
  • Christoph Schnörr
    • 1
  1. 1.Computer Vision, Graphics, and Pattern Recognition Group, Department of Mathematics and Computer ScienceUniversity of MannheimMannheimGermany

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