Lyapunov-based range and motion identification for a nonaffine perspective dynamic system

Many applications require the interpretation of the Euclidean motion of features of a 3-dimensional (3D) object through 2D images. In this paper, the range and the Euclidean coordinates of an object undergoing general affine motion are determined for a paraboloid imaging system. Unlike image systems that are based on a planar image surface (or spherical or ellipsoidal surfaces), the perspective dynamic system resulting from the paraboloid projected image does not maintain an affine form. Because of the nonaffine form, existing range identification observers can not be directly utilized. The contribution of the current result is the development of a nonlinear state estimator that can be applied to the nonaffine perspective dynamic system to determine the range and Euclidean coordinates of an object feature without the use of linear approximations. The nonlinear estimator asymptotically determines the range information from a single camera provided some observability conditions are satisfied and that the Euclidean motion parameters are known. The proposed technique is developed through a Lyapunov-based design and stability analysis, and simulation results are provided that illustrate the performance of the state estimator

[1]  Thomas S. Huang,et al.  Estimating three-dimensional motion parameters of a rigid planar patch , 1981 .

[2]  H. C. Longuet-Higgins,et al.  A computer algorithm for reconstructing a scene from two projections , 1981, Nature.

[3]  Thomas S. Huang,et al.  Uniqueness and Estimation of Three-Dimensional Motion Parameters of Rigid Objects with Curved Surfaces , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  R. Chellappa,et al.  Recursive 3-D motion estimation from a monocular image sequence , 1990 .

[5]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

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

[7]  Kenneth Turkowski,et al.  Creating image-based VR using a self-calibrating fisheye lens , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[8]  Jun Hu,et al.  Nonlinear Control of Electric Machinery , 1998 .

[9]  S. Nayar,et al.  Nonmetric Calibration of Wide-Angle Lenses and Polycameras , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Narendra Ahuja,et al.  High dynamic range panoramic imaging , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[11]  Yael Pritch,et al.  Omnistereo: Panoramic Stereo Imaging , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

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

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

[14]  Kevin L. Moore,et al.  Range identification for perspective dynamic systems using linear approximation , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[15]  Kevin L. Moore,et al.  Range identification for perspective dynamic system with single homogeneous observation , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[16]  K. Moore,et al.  Range identification for perspective dynamic systems with 3D imaging surfaces , 2005, Proceedings of the 2005, American Control Conference, 2005..