Closed-Form relaxation for MRF-MAP tissue classification using discrete laplace equations

Authors:
Alexis Roche
Affiliations:
Siemens Research, CIBM, Lausanne, Switzerland
Venue:
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
Year:
2012

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Abstract

While Markov random fields are very popular segmentation models in medical image processing, the associated maximum a posteriori (MAP) estimation problem is usually solved using iterative methods that are prone to local maxima. We show that a variant of the random walker algorithm can be seen as a relaxation method for the MAP problem under the Potts model. The key advantage of this technique is that it boils down to a sparse linear system with a uniquely defined explicit solution. Our experiments further demonstrate that the resulting MAP approximation can be used to improve the classical mean-field algorithm in terms of MAP estimation quality.