Metropolis-Hasting techniques for finite-element-based registration

In this paper, we focus on the design of Markov Chain Monte Carlo techniques in a statistical registration framework based on finite element basis (FE). Due to the use of FE basis, this framework has specific features. The main feature is that displacement random fields are Markovian. We construct two hybrid Gibbs/Metropolis-Hasting algorithms which take fully advantage of this Markovian property. The second technique is defined in a coarse-to-fine way by introducing a penalization on the sampled posterior distribution. We present some promising results suggesting that both techniques can accurately register images. Experiments also show that the penalized technique is more robust to local maxima of the posterior distribution than the first technique. This study is a preliminary step towards the estimation of model parameters in complex image registration problems.