title: Closed-form relaxation for MRF-MAP tissue classification using discrete Laplace equations.
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.
authors.affiliation: Siemens Research, CIBM, Lausanne, Switzerland. alexis.roche@epfl.ch
authors.forename: Alexis
authors.initials: A
authors.lastname: Roche
mesh_terms: D000368:Aged; D000465:Algorithms; D000544:Alzheimer Disease / Q000473:pathology*; D001921:Brain / Q000473:pathology*; D005260:Female; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008297:Male; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity