Exact Observer Error Linearization for Perspective Dynamic Systems

Estimation of 3D position information from 2D images in computer vision systems can be formulated as a state estimation problem for a nonlinear perspective dynamic system. The state estimation can be performed using different kinds of nonlinear observers. In this paper we investigate observer error linearization, where the goal is to find a coordinate transformation that results in a system for which a linear observer can be constructed. It is shown that using a state transformation combined with an output transformation, the system admits an observer form which leads to an observer with linear error dynamics.

[1]  Larry H. Matthies,et al.  Kalman filter-based algorithms for estimating depth from image sequences , 1989, International Journal of Computer Vision.

[2]  Alex Pentland,et al.  Recursive Estimation of Motion, Structure, and Focal Length , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  X. Xia,et al.  Nonlinear observer design by observer error linearization , 1989 .

[4]  D. Dawson,et al.  Range identification for perspective vision systems , 2003, Proceedings of the 2003 American Control Conference, 2003..

[5]  B. Ghosh,et al.  Visually guided ranging from observations of points, lines and curves via an identifier based nonlinear observer , 1995 .

[6]  Pietro Perona,et al.  On the Exact Linearization of Structure From Motion , 1994 .

[7]  Xinkai Chen,et al.  A new state observer for perspective systems , 2002, IEEE Trans. Autom. Control..

[8]  Anders Heyden,et al.  Linear Design of a Nonlinear Observer for Perspective Systems , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[9]  H. Inaba,et al.  Nonlinear observers for perspective time-invariant linear systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[10]  W. Dixon,et al.  Lyapunov-based range and motion identification for a nonaffine perspective dynamic system , 2006, 2006 American Control Conference.

[11]  P. Perona,et al.  Motion estimation via dynamic vision , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[12]  A. Krener,et al.  Nonlinear observers with linearizable error dynamics , 1985 .

[13]  O. Dahl,et al.  On Observer Error Linearization for Perspective Dynamic Systems , 2007, 2007 American Control Conference.

[14]  Riccardo Marino,et al.  Nonlinear control design: geometric, adaptive and robust , 1995 .

[15]  Xinkai Chen,et al.  State observer for a class of nonlinear systems and its application to machine vision , 2004, IEEE Transactions on Automatic Control.

[16]  A. Heyden,et al.  Structure and motion estimation in perspective systems using a dynamic vision parametrization , 2007, 2007 European Control Conference (ECC).

[17]  Alfredo Germani,et al.  Design of observers for systems with rational output function , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[18]  S. Shankar Sastry,et al.  An Invitation to 3-D Vision , 2004 .