We study the problem of estimating the motion of independently moving objects observed by a moving perspective camera. We show that infinitesimal image measurements corresponding to independent motions lie on orthogonal six-dimensional subspaces of a higher-dimensional linear space. We propose a factorization algorithm that estimates the number of independent motions, the segmentation of the image points, and the motion of each object relative to the camera from a set of image points and their optical flows in multiple frames. We evaluate the proposed algorithm on synthetic and real image sequences.
Figure 1: Segmentation of two independent motions: the camera and the car.