Multi-Subspace Methods for Motion Segmentation from Affine, Perspective and Central Panoramic Cameras ∗

Abstract — Many robot navigation tasks require the computation of the motion of multiple objects moving in 3-D space from a collection of images taken by a moving robot. In this paper we present a unifying theoretical framework for both infinitesimal and discrete 3-D motion segmentation from optical flow or point correspondences in multiple affine, perspective or central panoramic views. We exploit the fact that for these motion and camera models, the image measurements associated with a single object live in a low dimensional subspace of a high dimensional space, hence motion segmentation is achieved by segmenting data living in multiple subspaces. We solve this problem in closed form using a polynomial fitting and differentiation technique called Generalized Principal Component Analysis. Unlike previous work, our method does not restrict the motion of the objects to be full dimensional or fully independent. Instead, our approach deals gracefully with all the spectrum of possible motions: from low dimensional and partially dependent to full dimensional and fully independent. We test our algorithm on various real and synthetic dynamic scenes with linear motions, planar and full motions, transparent motions, etc. Index Terms — Motion segmentation, subspace clustering, Generalized Principal Component Analysis