Gaussian Unit-simplex Markov random fields as a fast proxy for MRF sampling

Markov random fields are classical models for Bayesian image modeling, but their sampling relies on traditionally Gibbs techniques, implying a non-negligible computational cost. On the other hand, Gaussian Markov random fields (GMRF), which are used to model continuous and spatially-homogeneous variables, can benefit from highly efficient sampling techniques. In this paper, we propose a new discrete Markov field, based on a unit-simplex geometry, and coined Gaussian unit- simplex Markov field (GUM). This model is specifically designed to benefit from the GMRF approach for sampling. We show that its sampling complexity is related to the GMRF sampling complexity. Numerical results show this leverages drastic improvement in the sampling time, while sharing similar empirical properties with a classical Markov random field.