Interaction Between 3D Shape and Motion: Theory and Applications

摘要

A sequence of images acquired by a moving sensor contains information about thethree dimensional motion of the sensor and the shape of the imaged scene. Interesting research during the past few years has attempted to characterize the errors that arise in computing 3D motion (egomotion estimation) as well as the errors that result in the estimation of the scene's structure (structure from motion). Previous research is 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 errors. This paper presents a geometric framework that characterizes the relationship between 3D motion and shape when they are both corrupted by errors. We examine 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, we characterize the systematic distortion via a family of isodistortion surfaces, each of which describes the locus over which the depths of points in the scene in view are distorted by the same multiplicative factor. The framework introduced in this way has a number of applications: Since the visible surfaces have positive depth (visibility constraint), 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, independent of the algorithm used. We provide a uniqueness analysis for 3D motion analysis from normal flow.