Factorization-based segmentation of motions

This paper addresses the problem of motion segmentation using the Singular Value Decomposition of a feature track matrix. It is shown that, under general assumptions, the number of numerically nonzero singular values can be used to determine the number of motions. Furthermore, motions can be separated using the right singular vectors associated with the nonzero singular values. A relationship is derived between a good segmentation, the number of nonzero singular values in the input and the sum of the number of nonzero singular values in the segments. The approach is demonstrated on real and synthetic examples. The paper ends with a critical analysis of the approach.