The Inversion Camera Model

  • Christian Perwass
  • Gerald Sommer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4174)


In this paper a novel camera model, the inversion camera model, is introduced, which encompasses the standard pinhole camera model, an extension of the division model for lens distortion, and the model for catadioptric cameras with parabolic mirror. All these different camera types can be modeled by essentially varying two parameters. The feasibility of this camera model is presented in experiments where object pose, camera focal length and lens distortion are estimated simultaneously.


Root Mean Square Focal Length Image Point Geometric Algebra Camera Model 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Claus, D., Fitzgibbon, A.W.: A rational function lens distortion model for general cameras. In: CVPR (1), pp. 213–219 (2005)Google Scholar
  2. 2.
    Dorst, L.: Honing geometric algebra for its use in the computer sciences. In: Sommer, G. (ed.) Geometric Computing with Clifford Algebra, pp. 127–151. Springer, Heidelberg (2001)Google Scholar
  3. 3.
    Fitzgibbon, A.W.: Simultaneous linear estimation of multiple view geometry and lens distortion. In: CVPR (1), pp. 125–132 (2001)Google Scholar
  4. 4.
    Geyer, C., Daniilidis, K.: Catadioptric projective geometry. International Journal of Computer Vision (45), 223–243 (2001)MATHCrossRefGoogle Scholar
  5. 5.
    Hartley, R.I., Zissermann, A.: Multiple View Geometry in Computer Vision, 2nd edn. CUP, Cambridge (2003)Google Scholar
  6. 6.
    Hestenes, D., Sobczyk, G.: Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics. Reidel, Dordrecht (1984)MATHGoogle Scholar
  7. 7.
    Kilpelä, E.: Compensation of systematic errors of image and model coordinates. International Archives of Photogrammetry XXIII(B9), 407–427 (1980)Google Scholar
  8. 8.
    Perwass, C.: CLUCalc (2005),
  9. 9.
    Perwass, C., Förstner, W.: Uncertain Geometry with Circles, Spheres and Conics. In: Computational Imaging and Vision, vol. 31, pp. 23–41. Springer, Heidelberg (2006)Google Scholar
  10. 10.
    Perwass, C., Gebken, C., Sommer, G.: Estimation of Geometric Entities and Operators from Uncertain Data. In: Kropatsch, W.G., Sablatnig, R., Hanbury, A. (eds.) DAGM 2005. LNCS, vol. 3663, pp. 459–467. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Perwass, C., Hildenbrand, D.: Aspects of geometric algebra in Euclidean, projective and conformal space. Technical Report Number 0310, CAU Kiel, Institut für Informatik (September 2003)Google Scholar
  12. 12.
    Perwass, C., Sommer, G.: Numerical evaluation of versors with Clifford algebra. In: Dorst, L., Doran, C., Lasenby, J. (eds.) Applications of Geometric Algebra in Computer Science and Engineering, pp. 341–349. Birkhäuser, Basel (2002)Google Scholar
  13. 13.
    Rosenhahn, B., Sommer, G.: Pose estimation in conformal geometric algebra, part II: Real-time pose estimation using extended feature concepts. Journal of Mathematical Imaging and Vision 22, 49–70 (2005)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Christian Perwass
    • 1
  • Gerald Sommer
    • 1
  1. 1.Institut für InformatikCAU KielKielGermany

Personalised recommendations