Chapter

Energy Minimization Methods in Computer Vision and Pattern Recognition

Volume 3757 of the series Lecture Notes in Computer Science pp 171-186

Probabilistic Subgraph Matching Based on Convex Relaxation

  • Christian SchellewaldAffiliated withComputer Vision, Graphics, and Pattern Recognition Group, Department of Mathematics and Computer Science, University of Mannheim
  • , Christoph SchnörrAffiliated withComputer Vision, Graphics, and Pattern Recognition Group, Department of Mathematics and Computer Science, University of Mannheim

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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.