Physics of MRF regularization for segmentation of materials microstructure images

The Markov Random Field (MRF) has been used extensively in Image Processing as a means of smoothing interfaces between differing regions in an image. The MRF applies a total boundary length `energy´ penalty that is subsequently minimized by an inversion algorithm. The minimization of energy implies a force associated with boundaries, the sum of which must equal zero at every point at equilibrium. This requirement leads to long range interactions, resulting from the short-range interactions of the MRF, which biases segmentation results. This work uses a simple Bayesian MRF regularized segmentation method to show that classical results from Surface Science are reproduced when segmenting regions of low contrast. This has implications, both in the Materials Science and Image Processing fields.