Structure from Visual Motion as a Nonlinear Observation Problem

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 simpli es 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 identi cation of an Exterior Di erential System with parameters on a sphere