The transition to Euclidean space and the discretization of quantum field theories on spatial or space-time lattices opens up opportunity investigate probabilistic machine learning within theory. Here, we will discuss how discretized theories, such as $\phi^{4}$ lattice theory a square lattice, are mathematically equivalent Markov fields, notable class graphical models with applications in vari...

In this paper, we present the region based hidden Markov random field model (RBHMRF), which encodes the characteristics of different brain regions into a probabilistic framework for brain MR image segmentation. The recently proposed TV+L model is used for region extraction. By utilizing different spatial characteristics in different brain regions, the RMHMRF model performs beyond the current st...