Markov Random Field (MRF) algorithms are powerful tools in image analysis to explore contextual information of data. However, the application of these methods to large data means that alternative approaches must be found to circumvent the NP-hard complexity of the MRF optimization. We introduce a MRF-based framework that overcomes this issue by using graph partitioning. The computational complexity is decreased as the optimization/parameter estimation is executed on small subgraphs. PMRF targets 3D microCT datasets, but we include evaluation on the Berkeley Segmentation Dataset (ranking 7th place) to fully compare our method with well-known segmentation algorithms. Segmentation results on the microCT datasets achieve precision higher than 95%.

We introduce a new embarrassingly parallel parameter learning algorithm for Markov random fields which is efficient for a large class of practical models. Our algorithm parallelizes naturally over cliques and, for graphs of bounded degree, its complexity is linear in the number of cliques. Unlike its competitors, our algorithm is fully parallel and for log-linear models it is also data efficient, requiring only the local sufficient statistics of the data to estimate parameters.