Sequential mean field variational analysis of structured deformable shapes

A novel approach is proposed to analyzing and tracking the motion of structured deformable shapes, which consist of multiple correlated deformable subparts. Since this problem is high dimensional in nature, existing methods are plagued either by the inability to capture the detailed local deformation or by the enormous complexity induced by the curse of dimensionality. Taking advantage of the structured constraints of the different deformable subparts, we propose a new statistical representation, i.e., the Markov network, to structured deformable shapes. Then, the deformation of the structured deformable shapes is modelled by a dynamic Markov network which is proven to be very efficient in overcoming the challenges induced by the high dimensionality. Probabilistic variational analysis of this dynamic Markov model reveals a set of fixed point equations, i.e., the sequential mean field equations, which manifest the interactions among the motion posteriors of different deformable subparts. Therefore, we achieve an efficient solution to such a high-dimensional motion analysis problem. Combined with a Monte Carlo strategy, the new algorithm, namely sequential mean field Monte Carlo, achieves very efficient Bayesian inference of the structured deformation with close-to-linear complexity. Extensive experiments on tracking human lips and human faces demonstrate the effectiveness and efficiency of the proposed method.