Abstract
The paper concerns 2D-3D pose estimation in the algebraic language of kinematics. The pose estimation problem is modeled on the base of several geometric constraint equations. In that way the projective geometric aspect of the topic is implicitly represented and thus, pose estimation is a pure kinematic problem. The authors propose the use of motor algebra to model screw displacements of lines or the use of rotor algebra to model the motion of points. Instead of using matrix based LMS optimization, the development of special extended Kalman filters is proposed. In this paper extended Kalman filters for estimating rotation and translation of several constraints in terms of rotors and motors will be presented. The experiments aim to compare the use of different constraints and different methods of optimal estimating the pose parameters.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
C. Perwass and J. Lasenby. A novel axiomatic derivation of geometric algebra. Technical Report CUED/F-INFENG/TR.347, Cambridge University Engineering Department, 1999.
Shevlin F. Analysis of orientation problems using Plucker lines. International Conference on Pattern Recognition, Brisbane, 1: 685–689, 1998.
Horaud R., Phong T.Q. and P.D. Tao. Object pose from 2-d to 3-d point and line correspondences. International Journal of Computer Vision, 15: 225–243, 1995.
Blaschke W. Mathematische Monographien 4, Kinematik und Quaternionen. Deutscher Verlag der Wissenschaften, Berlin, 1960.
Grimson W. E. L. Object Recognition by Computer. The MIT Press, Cambridge, MA, 1990.
Daniilidis K. Hand-eye calibration using dual quaternions. Int. Journ. Robotics Res, 18: 286–298, 1999.
Bayro-Corrochano E. The geometry and algebra of kinematics. In Sommer G., editor, Geometric Computing with Clifford Algebra. Springer Verlag, to be published, 2000.
Carceroni R. L. and C. M. Brown. Numerical methods for model-based pose recovery. Techn. Rept. 659, Comp. Sci. Dept., The Univ. of Rochester, Rochester, N. Y., August 1998.
Zhang Y., Sommer G., and E. Bayro-Corrochano. The motor extended Kalman filter for dynamic rigid motion estimation from line observations. In G. Sommer, editor, Geometric Computing with Clifford Algebra. Springer Verlag, to be published, 2000.
Sommer G., Rosenhahn B. and Zhang Y. Pose estimation using geometric constraints. Techn. Rept. 2003, Institut fur Informatik und Praktische Mathematik Christian-Albrechts-Universitat zu Kiel, 2000.
Hestenes D., Li H. and A. Rockwood. New algebraic tools for classical geometry. In Sommer G., editor, Geometric Computing with Clifford Algebra. Springer Verlag, to be published, 2000.
Zhang, Z. and O. Faugeras. 3D Dynamic Scene Analysis. Springer Verlag, 1992.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sommer, G., Rosenhahn, B., Zhang, Y. (2001). Pose Estimation Using Geometric Constraints. In: Klette, R., Gimel’farb, G., Huang, T. (eds) Multi-Image Analysis. Lecture Notes in Computer Science, vol 2032. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45134-X_12
Download citation
DOI: https://doi.org/10.1007/3-540-45134-X_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42122-1
Online ISBN: 978-3-540-45134-1
eBook Packages: Springer Book Archive