Multibody structure from motion could be solved by the factorization approach. However, the noise measurements would make the segmentation difficult when analyzing the shape interaction matrix. This paper presents an orthogonal subspace decomposition and grouping technique to approach such a problem. We decompose the object shape spaces into signal subspaces and noise subspaces. We show that the signal subspaces of the object shape spaces are orthogonal to each other. Instead of using the shape interaction matrix contaminated by noise, we introduce the shape signal subspace distance matrix for shape space grouping. Outliers could be easily identified by this approach. The robustness of the proposed approach lies in the fact that the shape space decomposition alleviates the influence of noise, and has been verified with extensive experiments.

Vision-based motion capturing of hand articulation is a challenging task, since the hand presents a motion of high degrees of freedom. Model-based approaches could be taken to approach this problem by searching in a high dimensional hand state space, and matching projections of a hand model and image observations. However, it is highly inefficient due to the curse of dimensionality. Fortunately, natural hand articulation is highly constrained, which largely reduces the dimensionality of hand state space. This paper presents a model-based method to capture hand articulation by learning hand natural constraints. Our study shows that natural hand articulation lies in a lower dimensional configurations space characterized by a union of liner manifolds spanned by a set of basis configurations. By integrating hand motion constraints, an efficient articulated motion-capturing algorithm is proposed based on sequential Monte Carlo techniques. Our experiments show that this algorithm is robust and accurate for tracking natural hand movements. This algorithm is easy to extend to other articulated motion capturing tasks.