Inference of multiple subspaces from high-dimensional data and application to multibody grouping

Multibody grouping is a representative of applying subspace constraints in computer vision tasks. Under linear projection models, feature points of multibody reside in multiple subspaces. We formulate the problem of multibody grouping as multiple subspace inference from high-dimensional data space. The theoretical value and practical advantage of this formulation come from the relaxation of the motion independency assumption which has to be enforced in most factorization based methods. In the proposed method, an Oriented-Frame (OF), which is a multidimensional coordinate frame, is associated with each data point indicating the point's preferred subspace structure. Then, a similarity measurement of these OFs is introduced and a novel mechanism is devised for conveying the information of the inherent subspace structure among the data points. In contrast to the existing factorization-based algorithms that can not find correct segmentation of correlated motions such as articulated motion, the proposed method can robustly handle motion segmentation of both independent and correlated cases. Results on controlled and real experiments show the effectiveness of the proposed subspace inference method.