Interaction between 3D Shape and Motion: Theory and Applications

Research during the past few years has attempted to characterize the errors that arise in computing 3D motion (egomotion estimation) and in a scene's structure (structure from motion) from a sequence of images acquired by a moving sensor. This paper presents a new geometric framework that characterizes how the three-dimensional space recovered by a moving monocular observer, whose 3D motion is estimated with some error, is distorted. We characterize the space of distortions by its level sets, that is, by a family of iso-distortion surfaces, each of which describes the locus over which the depths of points in the scene are distorted by the same multiplicative factor. By analyzing the geometry of the regions where the distortion factor is negative, that is, where the visibility constraint is violated, we make explicit situations which are likely to give rise to ambiguities in motion estimation. We also apply our approach to a uniqueness analysis for 3D motion analysis from normal flow; we study the constraints on egomotion, object motion and depth for an independently moving object to be detectable by a moving observer; and we offer a quantitative account of the precision needed in an inertial sensor for accurate estimation of 3D motion.