Illumination subspace for multibody motion segmentation

This paper presents a new method for automatically separating the motion of multiple independently moving objects in a sequence of images based on the notion of illumination subspace. We show that intensities of observed trajectories of image features on a single body lie on a linearly independent frame space with three, or fewer, dimensions. We then argue that it is possible in theory to determine the grouping of the feature points by way of separating the illumination subspaces. As a clue for practical separation, we also introduce the surface interaction matrix which is valid for Lambertian reflectance surface. Recently, several authors have presented different algorithms on this task of grouping by factorization-based procedures using the coordinates of image features. While the challenges in their approaches are to realize the robust performance in the presence of noise, we propose to incorporate the above photometric analysis available at given feature points in the conventional schemes of motion segmentation, and show that the performance is indeed stabilized through experiments on real and synthetic image sequences.