Linear Design of a Nonlinear Observer for Perspective Systems

Estimation of three-dimensional information from two-dimensional images is an important requirement in many computer vision applications. The estimation task can often be formulated as a problem of estimating states and/or parameters in nonlinear dynamic systems. This paper presents an algorithm for recursive state estimation in nonlinear dynamic systems, where the estimated states correspond to three-dimensional positions of feature points on an observed object. The algorithm is designed as a nonlinear observer, with a gain matrix that can be determined using methods from linear control theory. A stability criterion for the resulting nonlinear system is derived, and simulations are presented in order to illustrate the estimation performance.