Geometric Algebra for Pose Estimation and Surface Morphing in Human Motion Estimation

  • Bodo Rosenhahn
  • Reinhard Klette
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3322)


We exploit properties of geometric algebras (GAs) to model the 2D-3D pose estimation problem for free-form surfaces which are coupled with kinematic chains. We further describe local and global surface morphing approaches with GA and combine them with the 2D-3D pose estimation problem. As an application of the presented approach, human motion estimation is considered. The estimated joint angles are used to deform surface patches to gain more realistic human models and therefore more accurate pose estimation results.


Radial Basis Function Joint Angle Discrete Fourier Transform Kinematic Chain Geometric Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Allen, B., Curless, B., Popovic, Z.: Articulated body deformation from range scan data. In: Proceedings 29th Annual Conf. Computer Graphics and Interactive Techniques, San Antonio, Texas, pp. 612–619 (2002)Google Scholar
  2. 2.
    Arbter, K., Burkhardt, H.: Ein Fourier-Verfahren zur Bestimmung von Merkmalen und Schätzung der Lageparameter ebener Raumkurven. Informationstechnik 33(1), 19–26 (1991)Google Scholar
  3. 3.
    Besl, P.J.: The free-form surface matching problem. In: Freemann, H. (ed.) Machine Vision for Three-Dimensional Scenes, pp. 25–71. Academic Press, London (1990)Google Scholar
  4. 4.
    Bregler, C., Malik, J.: Tracking people with twists and exponential maps. In: Conf. on Computer Vision and Pattern Recognition, Santa Barbara, California, pp. 8–15 (1998)Google Scholar
  5. 5.
    Campbell, R.J., Flynn, P.J.: A survey of free-form object representation and recognition techniques. Computer Vision and Image Understanding 81, 166–210 (2001)zbMATHCrossRefGoogle Scholar
  6. 6.
    Chadwick, J.E., Haumann, D.R., Parent, R.E.: Layered construction for deformable animated characters Computer Graphics 23(3), 243–252 (1989)Google Scholar
  7. 7.
    Dorst, L.: The inner products of geometric algebra. In: Dorst, L., Doran, C., Lasenby, J. (eds.) Applied Geometric Algebras for Computer Science and Engineering, pp. 35–46. Birkhäuser, Basel (2001)Google Scholar
  8. 8.
    Dorst, L.: Honing geometric algebra for its use in the computer sciences. In: [21], pp. 127–152 (2001)Google Scholar
  9. 9.
    Fua, P., Plänkers, R., Thalmann, D.: Tracking and modeling people in video sequences. Computer Vision and Image Understanding 81(3), 285–302 (2001)zbMATHCrossRefGoogle Scholar
  10. 10.
    Gavrilla, D.M.: The visual analysis of human movement: A survey. Computer Vision and Image Understanding 73(1), 82–92 (1999)CrossRefGoogle Scholar
  11. 11.
    Grimson, W.E.L.: Object Recognition by Computer. MIT Press, Cambridge (1990)Google Scholar
  12. 12.
    Hestenes, D., Li, H., Rockwood, A.: New algebraic tools for classical geometry. In: [21], pp. 3–23 (2001)Google Scholar
  13. 13.
    Hestenes, D., Sobczyk, G.: Clifford Algebra to Geometric Calculus. D. Reidel Publ. Comp, Dordrecht (1984)zbMATHGoogle Scholar
  14. 14.
  15. 15.
    Li, H., Hestenes, D., Rockwood, A.: Generalized homogeneous coordinates for computational geometry. In: [21], pp. 27–52 (2001)Google Scholar
  16. 16.
    Mikic, I., Trivedi, M., Hunter, E., Cosman, P.: Human body model acquisition and tracking using voxel data. Computer Vision 53(3), 199–223 (2003)CrossRefGoogle Scholar
  17. 17.
    Murray, R.M., Li, Z., Sastry, S.S.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton (1994)zbMATHGoogle Scholar
  18. 18.
    Perwass, C., Hildenbrand, D.: Aspects of Geometric Algebra in Euclidean, Projective and Conformal Space. An Introductory Tutorial. Technical Report 0310, Christian-Albrechts-Universität zu Kiel, Institut für Informatik und Praktische Mathematik (2003)Google Scholar
  19. 19.
    Rosenhahn, B.: Pose Estimation Revisited (PhD-Thesis) Technical Report 0308, Christian-Albrechts-Universität zu Kiel, Institut für Informatik und Praktische Mathematik (2003), Available at
  20. 20.
    Rosenhahn, B., Perwass, C., Sommer, G.: Pose estimation of free-form surface models. In: Michaelis, B., Krell, G. (eds.) DAGM 2003. LNCS, vol. 2781, pp. 574–581. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  21. 21.
    Sommer, G. (ed.): Geometric Computing with Clifford Algebra. Springer, Berlin (2001)Google Scholar
  22. 22.
    Theobalt, C., Carranza, J., Magnor, A., Seidel, H.-P.: A parallel framework for silhouette based human motion capture. In: Proc. Vision, Modeling, Visualization 2003, Munich, November 19-21, pp. 207–214 (2003)Google Scholar
  23. 23.
    Zang, Z.: Iterative point matching for registration of free-form curves and surfaces. Computer Vision 13(2), 119–152 (1999)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Bodo Rosenhahn
    • 1
  • Reinhard Klette
    • 1
  1. 1.Computer Science DepartmentUniversity of Auckland (CITR)AucklandNew Zealand

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