Abstract.
We cast the problem of motion segmentation of feature tra- jectories as linear manifold finding problems and propose a general frame- work for motion segmentation under affine pro jections which utilizes two properties of tra jectory data: geometric constraint and locality. The geo- metric constraint states that the tra jectories of the same motion lie in a low dimensional linear manifold and different motions result in different linear manifolds; locality, by which we mean in a transformed space a data and its neighbors tend to lie in the same linear manifold, provides a cue for efficient estimation of these manifolds. Our algorithm estimates a number of linear manifolds, whose dimensions are unknown before- hand, and segment the tra jectories accordingly. It first transforms and normalizes the tra jectories; secondly, for each tra jectory it estimates a local linear manifold through local sampling; then it derives the a?nity matrix based on principal subspace angles between these estimated linear manifolds; at last, spectral clustering is applied to the matrix and gives the segmentation result. Our algorithm is general without restriction on the number of linear manifolds and without prior knowledge of the dimensions of the linear manifolds. We demonstrate in our experiments that it can segment a wide range of motions including independent, artic- ulated, rigid, non-rigid, degenerate, non-degenerate or any combination of them. In some highly challenging cases where other state-of-the-art motion segmentation algorithms may fail, our algorithm gives expected results.