Hamiltonian Monte Carlo for fitting point distribution models

The aim of this paper is to try to improve the performance of 3DMMs when reconstructing the 3D shape of a face from a single image. Since random walk MCMC models are characterized by highly correlated chains and poor explorations of the parameters space, we present a first approach to this computer graphics application using the Hamiltonian Monte Carlo algorithm introduced by Neal (2010). The novel approach uses the Hamiltonian dynamics to provide a different proposal distribution that can be used in a valid MCMC sampling method. In our simplistic setting we will not consider real face images but synthesized images from which we know the groundtruth's parameters. The goal is to estimate the 3DMM camera and shape parameters by the correspondence between the 2D target's landmarks and the corresponding 3D model's landmarks. We will then conduct an analysis and an evaluation of the approach in terms of fitting quality and speed time-convergence and show the progresses obtained. In particular, we will compare in terms of convergence and mixing exploration the current MCMC algorithm with the one presented in Schoenborn et al. (2017) and study the influence of the gradient's posterior distribution in the construction of Markov chains.