Fast Generalized Belief Propagation for MAP Estimation on 2D and 3D Grid-Like Markov Random Fields

Authors:
Kersten Petersen;Janis Fehr;Hans Burkhardt
Affiliations:
Institut für Informatik, Lehrstuhl für Mustererkennung und Bildverarbeitung, Albert-Ludwigs-Universität Freiburg, Freiburg, 79110;Institut für Informatik, Lehrstuhl für Mustererkennung und Bildverarbeitung, Albert-Ludwigs-Universität Freiburg, Freiburg, 79110;Institut für Informatik, Lehrstuhl für Mustererkennung und Bildverarbeitung, Albert-Ludwigs-Universität Freiburg, Freiburg, 79110
Venue:
Proceedings of the 30th DAGM symposium on Pattern Recognition
Year:
2008

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Abstract

In this paper, we present two novel speed-up techniques for deterministic inference on Markov random fields (MRF) via generalized belief propagation (GBP). Both methods require the MRF to have a grid-like graph structure, as it is generally encountered in 2D and 3D image processing applications, e.g. in image filtering, restoration or segmentation. First, we propose a caching method that significantly reduces the number of multiplications during GBP inference. And second, we introduce a speed-up for computing the MAP estimate of GBP cluster messages by presorting its factors and limiting the number of possible combinations. Experimental results suggest that the first technique improves the GBP complexity by roughly factor 10, whereas the acceleration for the second technique is linear in the number of possible labels. Both techniques can be used simultaneously.