Robust Motion Segmentation by Spectral Clustering

Multibody motion segmentation is important in many computer vision tasks. One way to solve this problem is factorization. But practically segmentation is difficult since the shape interaction matrix is contaminated by noise. This paper presents a novel approach to robustly segment multiple moving objects by spectral clustering. We introduce two new affinity matrixes. One is based on the shape interaction matrix and the other one is based on the motion trajectory. By computing the sensitivities of the larger eigenvalues of a related Markov transition matrix with respect to perturbations in the affinity matrix, we improve the piecewise constant eigenvectors condition dramatically. The feature points are mapped into a low dimensional subspace and clustered in this subspace using a graph spectral approach. This makes clustering much more reliable and robust, which we confirm with experiments.