EFFECTS OF ERRORS IN THE VIEWING GEOMETRY ON SHAPE ESTIMATION

A sequence of images acquired by a moving sensor contains information about the three-dimensional motion of the sensor and the shape of the imaged scene. Interesting research during the past few years has attem pted to characterize the errors that arise in computing 3D motion (ego motion estimation) as well as the errors that result in the estimation of the scene's structure (structure from motion). Previous research i s characterized by the use of optic flow or correspondence of features in the analysis as well as by the employment of particular algorithms and models of the scene in recovering expressions for the resulting e rrors. This paper presents a geometric framework that characterizes th e relationship between 3D motion and shape in the presence of errors. We examine how the three-dimensional space recovered by a moving monoc ular observer, whose 3D motion is estimated with some error, is distor ted. We characterize the space of distortions by its level sets, that is, we characterize the systematic distortion via a family of iso-dist ortion surfaces, which describes the locus over which the depths of po ints in the scene in view are distorted by the same multiplicative fac tor. The framework introduced in this way has a number of applications : Since the visible surfaces have positive depth (visibility constrain t), by analyzing the geometry of the regions where the distortion fact or is negative, that is, where the visibility constraint is violated, we make explicit situations which are likely to give rise to ambiguiti es in motion estimation, independent of the algorithm used. We provide a uniqueness analysis for 3D motion analysis from normal flow. We stu dy the constraints on egomotion, object motion, and depth for an indep endently moving object to be detectable by a moving observer, and we o ffer a quantitative account of the precision needed in an inertial sen sor for accurate estimation of 3D motion. (C) 1998 Academic Press.