On the parallelisation of MCMC-based image processing

The increasing availability of multi-core and multi-processor architectures provides new opportunities for improving the performance of many computer simulations. Markov Chain Monte Carlo (MCMC) simulations are widely used for approximate counting problems, Bayesian inference and as a means for estimating very high-dimensional integrals. As such MCMC has found a wide variety of applications in fields including computational biology and physics, financial econometrics, machine learning and image processing. Whilst divide and conquer is an obvious means to simplify image processing tasks, "naively" dividing an image into smaller images to be processed separately results in anomalies and breaks the statistical validity of the MCMC algorithm. We present a method of grouping the spatially local moves and temporarily partitioning the image to allow those moves to be processed in parallel, reducing the runtime whilst conserving the properties of the MCMC method. We calculate the theoretical reduction in runtime achievable by this method, and test its effectiveness on a number of different architectures. Experiments are presented that show reductions in runtime of 38% using a dual-core dual-processor machine. In circumstances where absolute statistical validity are not required, an algorithm based upon, but not strictly adhering to, MCMC may suffice. For such situation two additional algorithms are presented for partitioning of images to which MCMC will be applied. Assuming preconditions are met, these methods may be applied with minimal risk of anomalous results. Although the extent of the runtime reduction will be data dependent, the experiments performed showed the runtime reduced to 27% of its original value.