Structure from Visual Motion as a Nonlinear Observation Problem

Abstract

Over the last decade, estimating scene structure from visual motion has become a central task of computational vision. As it is well known, the estimation task is nonlinear due to the perspective nature of the measurements. One may ask whether there exists a smart choice of coordinates that simplifies the estimation task. In particular, since "linearity" is a coordinate-dependent notion, one may seek for a particular choice of coordinates such that the problem of estimating structure from motion becomes linear and spectrally assignable. Unfortunately, such a choice of coordinates does not exist, even if we allow for a nonlinear change of output coordinates or an embedding into a higher-dimensional state-space. As a consequence of this result, we study some alternative estimators with nonlinear error dynamics which are proved to converge, and legitimate the use of local linearization-based techniques for estimating structure from known motion and visual information. In most of the cases, however, the true motion undergone by the viewer is unknown. We propose a novel dynamic estimator for scene structure which is independent of the motion of the viewer. The method consists in the identification of an Exterior Differential System with parameters on a sphere.