MAP Image Labeling Using Wasserstein Messages and Geometric Assignment

  • Freddie ÅströmEmail author
  • Ruben Hühnerbein
  • Fabrizio Savarino
  • Judit Recknagel
  • Christoph Schnörr
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10302)


Recently, a smooth geometric approach to the image labeling problem was proposed [1] by following the Riemannian gradient flow of a given objective function on the so-called assignment manifold. The approach evaluates user-defined data term and additionally performs Riemannian averaging of the assignment vectors for spatial regularization. In this paper, we consider more elaborate graphical models, given by both data and pairwise regularization terms, and we show how they can be evaluated using the geometric approach. This leads to a novel inference algorithm on the assignment manifold, driven by local Wasserstein flows that are generated by pairwise model parameters. The algorithm is massively edge-parallel and converges to an integral labeling solution.


Image labeling Graphical models Message passing Wasserstein distance Assignment manifold Riemannian gradient flow Replicator equation Multiplicative updates 



We gratefully acknowledge support by the German Science Foundation, grant GRK 1653.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Freddie Åström
    • 1
    Email author
  • Ruben Hühnerbein
    • 1
  • Fabrizio Savarino
    • 1
  • Judit Recknagel
    • 1
  • Christoph Schnörr
    • 1
  1. 1.Image and Pattern Analysis Group, RTG 1653Heidelberg UniversityHeidelbergGermany

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