Latent-Smoothness Nonrigid Structure From Motion by Revisiting Multilinear Factorization.

How to implement an effective factorization for nonrigid structure from motion (NRSFM) has attracted much attention in recent years. A straightforward factorization scheme is to multilinearly solve NRSFM in an alternating manner, where each of the unknown variables in NRSFM is updated by fixing the others at each iteration. However, recent works show that most existing multilinear factorization (MLF) methods achieve poorer performances than some state-of-the-art sequential factorization methods. In this paper, we reinvestigate the MLF scheme for improving factorization accuracy, and first propose an MLF method with the only low-rank prior for NRSFM in the presence of missing data. Then, for further improving the performances of such MLF methods, a latent ``smoothness'' characteristic on unknown 3-D deformable shapes is investigated, which is independent of temporal relations among deformable shapes. Accordingly, a latent-smoothness prior for solving NRSFM is derived from the latent smoothness characteristic, and it is able to effectively recover 3-D deformable shapes from unordered data, which is hard for the traditional temporal-smoothness prior to handle. Finally, a regularized factorization method is proposed by integrating MLF with the explored latent-smoothness prior for further pursuing better performances. Extensive experimental results show the effectiveness of our methods in comparison to eight existing multilinear/sequential methods.