Analyzing Structured Deformable Shapes Via Mean Field Monte Carlo

This paper describes a novel approach to analyzing and tracking the motion of structured deformable shapes that consis t of multiple correlated deformable subparts. Due to the high dimensional nature of this problem, existing methods are plagued either by the inability of capturing detailed local deformation or the enormous complexity, induced by the curse of dimensionality. Taking advantage of the structure of the deformable shapes, the paper presents a new representation , i.e., dynamic Markov network model, to overcome the challenges induced by high dimensionality. Probabilistic vari ational analysis of this Markov network model reveals a set of fixed point equations, i.e., the mean field equations, which manifest the interactions among the posterior motions of these deformable subparts and suggest an efficient solution to such a high dimensional motion analysis problem. Combined with Monte Carlo strategies, the new algorithm, namely mean field Monte Carlo(MFMC), achieves very efficient Bayesian inference with close-to-linear com plexity. Experiments on tracking human faces and human lips demonstrate the effectiveness of the proposed method.