Rigid and articulated motion seen with an uncalibrated stereo rig

This paper establishes a link between uncalibrated stereo vision and the motion of rigid and articulated bodies. The variation in the projective reconstruction of a dynamic scene over time allows an uncalibrated stereo rig to be used as a faithful motion capturing device. We introduce an original theoretical framework-projective kinematics-which allows rigid and articulated motion to be represented within the transformation group of projective space. Corresponding projective velocities are defined in the tangent space. Most importantly, these projective motions inherit the Lie-group structure of the displacement group. These theoretical results lead immediately to non-metric formulations of visual servoing, tracking, motion capturing and motion synthesis systems, that no longer require the metric geometry of a stereo camera or of the articulated body to be known. We report on such a non-metric formulation of a visual servoing system and present simulated experimental results.