Higher order motion models and spectral clustering

Motion segmentation based on point trajectories can integrate information of a whole video shot to detect and separate moving objects. Commonly, similarities are defined between pairs of trajectories. However, pairwise similarities restrict the motion model to translations. Non-translational motion, such as rotation or scaling, is penalized in such an approach. We propose to define similarities on higher order tuples rather than pairs, which leads to hypergraphs. To apply spectral clustering, the hypergraph is transferred to an ordinary graph, an operation that can be interpreted as a projection. We propose a specific nonlinear projection via a regularized maximum operator, and show that it yields significant improvements both compared to pairwise similarities and alternative hypergraph projections.