Nonlinear and Adaptive Observers for Perspective Dynamic Systems

Estimation of 3D structure and motion from 2D images in computer vision systems can be performed using a dynamic system, often referred to as a perspective dynamic system. This paper presents a novel parametrization of the nonlinear perspective dynamic system, from which different estimators for rigid body structure as well as motion can be derived in a straightforward manner. The parametrization allows a structure estimator to be formulated as a nonlinear observer which estimates 3D position, assuming knowledge of angular and linear velocities. The observer performance is demonstrated using simulation examples, where it is also shown how a time scaling parameter can be used to tune the transient response. The parametrization also allows a motion estimator to be formulated as an adaptive observer, estimating angular velocity and 3D position assuming knowledge of the linear velocity. This is demonstrated by deriving an estimator and illustrating its performance in a simulation example. The presented investigations and simulations indicate that the parametrization has a potential for future development of estimators for structure as well as motion in perspective dynamic systems, and for the investigation of similarities and differences in comparison to discrete, projective geometry based, methods.