Projective Factorization of Multiple Rigid-Body Motions

Given point correspondences in multiple perspective views of a scene containing multiple rigid-body motions, we present an algorithm for segmenting the correspondences according to the multiple motions. We exploit the fact that when the depths of the points are known, the point trajectories associated with a single motion live in a subspace of dimension at most four. Thus motion segmentation with known depths can be achieved by methods of subspace separation, such as GPCA or LSA. When the depths are unknown, we proceed iteratively. Given the segmentation, we compute the depths using standard techniques. Given the depths, we use GPCA or LSA to segment the scene into multiple motions. Experiments on the Hopkins 155 motion segmentation database show that our method compares favorably against existing affine motion segmentation methods in terms of segmentation error and execution time.