Bayesian Consistent Estimation in Deformable Models using Stochastic Algorithms: Applications to Medical Images

This paper aims at summarising and validating a methodology proposed in [2, 3, 4] for estimating a Bayesian Mixed Effect (BME) atlas, i.e. coupled templates and geometrical metrics for estimated clusters, in a statistically consistent way given a sample of images. We recall the generative statistical model applied to the observations which enables the simultaneous estimation of the clusters, the templates and geometrical variabilities (related to the metric) in the population. Following [2, 3, 4], we work in a Bayesian framework, use a Maximum A Posteriori estimator and approach its value using a stochastic variant of the Expectation Maximisation (EM) algorithm. The method is validated with two data set consisting of medical images of part of the human cortex and dendrite spines from a mouse model of Parkinson's disease. We present the performances of the method on the estimation of the template, the geometrical variability and the clustering.