Adaptive Motion Segmentation Algorithm Based on the Principal Angles Configuration

Many motion segmentation algorithms based on manifold clustering rely on a accurate rank estimation of the trajectory matrix and on a meaningful affinity measure between the estimated manifolds. While it is known that rank estimation is a difficult task, we also point out the problems that can be induced by an affinity measure that neglects the distribution of the principal angles. In this paper we suggest a new interpretation of the rank of the trajectory matrix and a new affinity measure. The rank estimation is performed by analysing which rank leads to a configuration where small and large angles are best separated. The affinity measure is a new function automatically parametrized so that it is able to adapt to the actual configuration of the principal angles. Our technique has one of lowest misclassification rates on the Hopkins155 database and has good performances also on synthetic sequences with up to 5 motions and variable noise level.