Perfect MCMC Sampling in Bayesian MRFs for Uncertainty Estimation in Segmentation

Abstract

Typical segmentation methods produce a single optimal solution and fail to inform about (i) the confidence/uncertainty in the object boundaries or (ii) alternate close-to-optimal solutions. To estimate uncertainty, some methods intend to sample segmentations from an associated posterior model using Markov chain Monte Carlo (MCMC) sampling or perturbation models. However, they cannot guarantee sampling from the true posterior, deviating significantly in practice. We propose a novel method that guarantees exact MCMC sampling, in finite time, of multi-label segmentations from generic Bayesian Markov random field (MRF) models. For exact sampling, we propose Fill’s strategy and extend it to generic MRF models via a novel bounding chain algorithm. Results on simulated data and clinical brain images from 4 classic problems show that our uncertainty estimates gain accuracy over the state of the art.