Pseudo-likelihood equations for Potts model on higher-order neighborhood systems: A quantitative approach for parameter estimation in image analysis

Abstract

This paper presents analytical pseudo-likelihood (PL) equations for Potts Markov random field (MRF) model parameter estimation on higher-order neighborhood systems by expanding the derivative of the log-PL function based on the enumeration of all possible contextual configuration patterns given a neighborhood system. The proposed equations allow the modeling of less restrictive neighborhood systems in a large number of MRF applications in a computationally feasible way. To evaluate the proposed estimation method we propose a hypothesis testing approach, derived by approximating the asymptotic variance of MPL parameter estimators using the observed Fisher information. The definition of the asymptotic variance, together with the test size α and p-values, provide a complete framework for quantitative analysis. Experiments with synthetic images generated by Markov chain Monte Carlo simulation methods assess the accuracy of the proposed estimation method, indicating that higher-order neighborhood systems reduce the MPL estimator asymptotic variance and improve estimation performance.