Motion segmentation using the Hadamard product and spectral clustering

In this paper, we present a motion segmentation algorithm for image sequences based on the Hadamard (or Schur) product of shape interaction matrices computed over a range of dimensions of the ambient space and using a spectral clustering algorithm. Most motion segmentation algorithms proposed to date are based on the use of a shape interaction matrix, obtained via factorization, since it encodes the essential information to segment independently moving rigid objects. However, so far, most studies have been limited to using a single shape interaction matrix to cluster the motions of different objects. In this paper, we propose to combine the shape interaction matrices computed for different subspace dimensions using the Hadamard product. The benefit of this approach is that the affinity of trajectories belonging to the same object is stressed while the affinity between trajectories belonging to different objects is diminished. Once the final shape interaction matrix is computed, we use a spectral clustering algorithm to segment the different motions. Experiments on the Hopkins 155 data set for both independent and articulated motions show that our new algorithm provides a lower miss-classification error rate, outperforming other state of the art algorithms.