A Procrustean Markov Process for Non-rigid Structure Recovery

Recovering a non-rigid 3D structure from a series of 2D observations is still a difficult problem to solve accurately. Many constraints have been proposed to facilitate the recovery, and one of the most successful constraints is smoothness due to the fact that most real-world objects change continuously. However, many existing methods require to determine the degree of smoothness beforehand, which is not viable in practical situations. In this paper, we propose a new probabilistic model that incorporates the smoothness constraint without requiring any prior knowledge. Our approach regards the sequence of 3D shapes as a simple stationary Markov process with Procrustes alignment, whose parameters are learned during the fitting process. The Markov process is assumed to be stationary because deformation is finite and recurrent in general, and the 3D shapes are assumed to be Procrustes aligned in order to discriminate deformation from motion. The proposed method outperforms the state-of-the-art methods, even though the computation time is rather moderate compared to the other existing methods.