Performance of region-based Markov random field with XY spins

Markov Random Field (MRF) models have become increasingly necessary especially in data-driven science. There are two kinds of MRF model applicable to image segmentation: edge-based and region-based. The region-based model is more easily implemented and is more robust to noise than the edge-based model. However, the region-based model often becomes trapped in a local minimum, which is sensitive to initial conditions. To overcome the issue of local minima, Okada proposed a region-based model with hidden variables formed by XY spins. This model has attracted attention regarding neuromorphic hardware implementations, but the efficacy of this model has not been thoroughly evaluated. In this paper, we verify the performance of the region-based model with XY spins, in comparison with that of the region-based model with Ising spins. To achieve this purpose, we construct variational Bayes algorithms and Markov chain Monte Carlo algorithms for both region-based models and evaluate their performances using synthetic data and real lithium-ion-battery imaging data.