Optical Flow Computation for Compound Eyes: Variational Analysis of Omni-Directional Views

  • Akihiko Torii
  • Atsushi Imiya
  • Hironobu Sugaya
  • Yoshihiko Mochizuki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3704)


This paper focuses on variational optical flow computation for spherical images. It is said that some insects recognise the world through optical flow observed by their compound eyes, which observe spherical views. Furthermore, images observed through a catadioptric system with a conic mirror and a fish-eye-lens camera are transformed to images on the sphere. Spherical motion field on the spherical retina has some advantages for the ego-motion estimation of autonomous mobile observer. We provide a framework for motion field analysis on the spherical retina using variational method for image analysis.


Robot Vision Spherical Image Real World Image Omnidirectional Image Optical Flow Computation 
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.
    Neuman, T.R.: Modeling insect compound eyes: Space-vriant spherica vision. In: Bülthoff, H.H., Lee, S.-W., Poggio, T.A., Wallraven, C. (eds.) BMCV 2002. LNCS, vol. 2525, pp. 360–367. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Dahmen, H.-J., Franz, M.O., Krapp, H.G.: Extracting egmotion from optical flow: Limits of accuracy and nural matched filters. In: Zanker, J.M., Zeil, J. (eds.) Motion Vision-Computational Neural, and Ecological Constraints, pp. 143–168. Springer, Heidelberg (2001)Google Scholar
  3. 3.
    Nelson, R.C., Aloimonos, J.: Finding motion parameters from spherical flow fields (or the advantage of having eyes in the back of your head). Biological Cybernetics 58, 261–273 (1988)CrossRefGoogle Scholar
  4. 4.
    Fermüller, C., Aloimonos, J.: Ambiguity in structure from motion: sphere versus plane. IJCV 28, 137–154 (1998)CrossRefGoogle Scholar
  5. 5.
    Horn, B.K.P., Schunck, B.G.: Determining optical flow. Artificial Intelligence 17, 185–204 (1981)CrossRefGoogle Scholar
  6. 6.
    Nagel, H.-H.: On the estimation of optical flow:Relations between different approaches and some new results. Artificial Intelligence 33, 299–324 (1987)CrossRefGoogle Scholar
  7. 7.
    Barron, J.L., Fleet, D.J., Beauchemin, S.S.: Performance of optical flow techniques. International Journal of Computer Vision 12, 43–77 (1994)CrossRefGoogle Scholar
  8. 8.
    Morel, J.-M., Solimini, S.: Variational Methods in Image Segmentation. Rirkhaäuser (1995)Google Scholar
  9. 9.
    Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing: Partial Differencial Equations and the Calculus of Variations. Springer, Heidelberg (2002)Google Scholar
  10. 10.
    Sapiro, G.: Geometric Partial Differencial Equations and Image Analysis. Cambridge University Press, Cambridge (2001)CrossRefGoogle Scholar
  11. 11.
    Osher, S., Paragios, N. (eds.): Geometric Level Set Methods in Imaging, Vision, and Graphics. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  12. 12.
    Benosman, R., Kang, S.-B. (eds.): Panoramic Vision, Sensor, Theory, and Applications. Springer, New York (2001)Google Scholar
  13. 13.
    Baker, S., Nayer, S.: A theory of single-viewpoint catadioptric image formation. International Journal of Computer Vision 35, 175–196 (1999)CrossRefGoogle Scholar
  14. 14.
    Geyer, C., Daniilidis, K.: Catadioptric projective geometry. International Journal of Computer Vision 45, 223–243 (2001)zbMATHCrossRefGoogle Scholar
  15. 15.
    Svoboda, T., Pajdla, T.: Epipolar geometry for central catadioptric cameras. International Journal of Computer Vision 49, 23–37 (2002)zbMATHCrossRefGoogle Scholar
  16. 16.
    Imiya, A., Torii, A., Sugaya, H.: Optical flow computation of omni-directional images (submitted)Google Scholar
  17. 17.
    Imiya, A., Iwawaki, K.: Voting method for subpixel flow detection. Pattern Recognition Letters 24, 197–214 (2003)zbMATHCrossRefGoogle Scholar
  18. 18.
    Zdunkowski, W., Bott, A.: Dynamics of the Atmosphere. Cambridge University Press, Cambridge (2003)Google Scholar
  19. 19.
    Freeden, W., Schreiner, M., Franke, R.: A survey on spherical spline approximation. Surveys on Mathematics for Industry 7 (1997)Google Scholar
  20. 20.
    Randol, D., et al.: Climate modeling with spherical geodesic grids. IEEE Computing in Science and Engineering 4, 32–41 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Akihiko Torii
    • 1
  • Atsushi Imiya
    • 2
  • Hironobu Sugaya
    • 1
  • Yoshihiko Mochizuki
    • 1
  1. 1.School of Science and TechnologyChiba University 
  2. 2.Institute of Media and Information TechnologyChiba UniversityChibaJapan

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