Stereo geometry from 3-D ego-motion streams

This paper addresses the problem of geometry determination of a stereo rig that undergoes general rigid motions. Neither known reference objects nor stereo correspondence is required. With almost no exception, all existing' online solutions attempt to recover the stereo geometry by first establishing stereo correspondences. This paper has the following main contributions. First, we describe a mathematical framework that allows us to solve for the stereo geometry, i.e., the rotation and the translation between the two cameras, using only motion c orrespofidences that are far easier to acquire than stereo orresp ondences. Second, we show how to recover the rotation and present two linear methods, as well as, a nonlinear one to solve'forthe translation. Third, we perform a stability study for the developed methods in the presence of image noise, camera parameters noise, and ego-motion noise. We also address some accuracy issues. Experiments with real image 'data are presented. The work allows the concept of online calibration to be broadened, as it *is no longer true that only single cameras can exploit structure-from-motion strategies; even the extrinsic parameters of a'stereo rig of cameras can do so- without solving the stereo correspondence. The developed framework is.applicable for estimating the relative three-dimensional (3-D) geometry associated with a wide variety of mounted devices used in vision and robotics, by exploiting their scaled ego-motion streams.