Recovery of the Motions of Rigid Bodies Using Multi-stage Extention of Hough Transform

Abstract

We propose a new method to recover the 3D structures and motions of rotating rigid bodies from a moving image. We assume that the image is taken under the perspective condition and each axis of rotation does not move. A rotation in 3D space becomes a circular trajectory. A circular trajectory projected into a 2D image plane becomes a conic section, for instance an ellipse. A recent work by Sawhney et al. showed that the elliptic trajectory in a 2D image plane could be used to recover the 3D space motions and structures. We emphasized the time factor to recover them. We employ the Hough transform method and also devide the transform into several stages. The division of the transform stage reduced the computation cost. Our method enables separation of two trajectories which cannot be separated by Sawhney's method.