MAP Image Labeling Using Wasserstein Messages and Geometric Assignment
Recently, a smooth geometric approach to the image labeling problem was proposed  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.
KeywordsImage 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.
- 2.Bergmann, R., Fitschen, J.H., Persch, J., Steidl, G.: Iterative multiplicative filters for data labeling. Int. J. Comput. Vis. 1–19 (2017). http://dx.doi.org/10.1007/s11263-017-0995-9
- 4.Cuturi, M.: Sinkhorn Distances: Lightspeed Computation of Optimal Transport. In: Proceedings of the NIPS (2013)Google Scholar
- 7.Kappes, J., Andres, B., Hamprecht, F., Schnörr, C., Nowozin, S., Batra, D., Kim, S., Kausler, B., Kröger, T., Lellmann, J., Komodakis, N., Savchynskyy, B., Rother, C.: A comparative study of modern inference techniques for structured discrete energy minimization problems. Int. J. Comput. Vis. 115(2), 155–184 (2015)MathSciNetCrossRefGoogle Scholar
- 8.Kolouri, S., Park, S., Thorpe, M., Slepcev, D., Rohde, G.: Transport-based analysis, modeling, and learning from signal and data distributions (2016). preprint: https://arxiv.org/abs/1609.04767
- 12.Schmidt, M.: UGM: Matlab code for undirected graphical models, January 2017Google Scholar
- 15.Weiss, Y.: Comparing the mean field method and belief propagation for approximate inference in MRFs. In: Advanced Mean Field Methods: Theory and Practice, pp. 229–240. MIT Press (2001)Google Scholar