Biological Cybernetics

, Volume 60, Issue 2, pp 79–87 | Cite as

A computational approach to motion perception

  • S. Uras
  • F. Girosi
  • A. Verri
  • V. Torre


In this paper it is shown that the computation of the optical flow from a sequence of timevarying images is not, in general, an underconstrained problem. A local algorithm for the computation of the optical flow which uses second order derivatives of the image brightness pattern, and that avoids the aperture problem, is presented. The obtained optical flow is very similar to the true motion field — which is the vector field associated with moving features on the image plane — and can be used to recover 3D motion information. Experimental results on sequences of real images, together with estimates of relevant motion parameters, like time-to-crash for translation and angular velocity for rotation, are presented and discussed. Due to the remarkable accuracy which can be achieved in estimating motion parameters, the proposed method is likely to be very useful in a number of computer vision applications.


Optical Flow Order Derivative Motion Parameter Local Algorithm Real Image 
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. Bertero M, Poggio T, Torre V (1988) Ill-posed problems in early vision. In: Proceedings of IEEE on Computer Vision, (in press)Google Scholar
  2. Enkelmann W (1986) Investigation of multigrid algorithms for the estimation of optical flow fields in image sequences. In: Proceedings Workshop on Motion: Representation and Analysis, Charlestone, SC, pp 81–87Google Scholar
  3. Fenmena CL, Thompson WB (1979) Velocity determination in scenes containing several moving objects. Comput Graph Image Proc 9:301–315Google Scholar
  4. Gibson JJ (1950) The perception of the visual world. Houghton Mifflin, BostonGoogle Scholar
  5. Haralick RM, Lee JS, (1983) The facet approach to optic flow. In: Baumann LS (eds) Proceedings image understanding workshop. Science Applications, Arlington Va, pp 84–93Google Scholar
  6. Heeger DJ (1987) Optical flow from spatiotemporal filters. In: Proceedings First International Conference on Computer Vision, London, pp 181–190Google Scholar
  7. Hildreth EC (1984a) The measurement of visual motion. MIT Press, Cambridge LondonGoogle Scholar
  8. Hildreth EC (1984b) The computation of the velocity field. Proc R Soc London B 221:189–220Google Scholar
  9. Hirsh MW, Smale S (1974) Differential equations, dynamical systems, and linear algebra. Academic Press, New YorkGoogle Scholar
  10. Horn BKP, Schunck BG (1981) Determining optical flow. Artif Intell 17:185–203Google Scholar
  11. Kanatani K (1985) Structure from motion without correspondence: general principle. In: Proceedings of the Image Understanding Workshop, Miami, pp 110–116Google Scholar
  12. Koenderink JJ, Doom AJ van (1977) How an ambulant observer can construct a model of the environment from the geometrical structure of the visual inflow. In: Hauske G, Butendant E (eds) Kibernetic 1977. Oldenbourg, MünchenGoogle Scholar
  13. Longuet-Higgins HC, Prazdny K (1980) The interpretation of a moving retinal image. Proc R Soc London B 208:385–397Google Scholar
  14. Marr D (1982) Vision. Freeman, New YorkGoogle Scholar
  15. Nagel H-H (1983) Displacement vectors derived from second order intensity variations in image sequences. Comput Vision Graph Image Process 21:85–117Google Scholar
  16. Nagel H-H (1986) Image sequences-ten(octal)years-from phenomenolgy towards a theoretical foundations. In: Proceedings of the Eighth International Conference on Pattern Recognition, Paris, pp 1174–1185Google Scholar
  17. Nagel H-H (1987) On the estimation of optical flow: relations between different approaches and some new results. Artif Intell 33:299–324Google Scholar
  18. Poggio T, Torre V, Koch C (1985) Computational vision and regularization theory. Nature 317:314–319Google Scholar
  19. Reichardt W, Schlögl RW, Egelhaaf M (1988) Movement detector of the correlation-type provide sufficient information for local computation of 2D velocity field. Naturwissenschaften 75:313–315Google Scholar
  20. Tretiak O, Pastor L (1984) Velocity estimation from image sequences with second order differential operators. In: Proceedings of the International Conference on Pattern Recognition, Montreal, Que, pp 16–19Google Scholar
  21. Tsai RY, Huang TS (1982) Uniqueness and estimation of three-dimensional motion parameters of rigid objects with curved surfaces. University of Illinois at Urbana-Champaign Coordinated Science Laboratory Report R-921Google Scholar
  22. Ullmann S (1979) The interpretation of visual motion. MIT Press, Cambridge LondonGoogle Scholar
  23. Ullmann S (1983) Recent computational studies in the interpretation of structure from motion. In: Rosenfeld A, Beck J (eds) Human and machine vision. Academic Press, New YorkGoogle Scholar
  24. Verri A, Poggio T (1987) Against quantitative optical flow. In: Proceedings of the First International Conference on Computer Vision, London, pp 171–180Google Scholar
  25. Waxman AM (1984) An image flow paradigm. In: Proceedings of the Workshop on Computer Vision: Representation and Control, Annapolis: IEEE, pp 49–57Google Scholar
  26. Waxman AM, Ullmann S (1983) Surface structure and 3D motion from image flow: a kinematic analysis. University of Maryland Computer Science Technical Report CS-TR-1332Google Scholar
  27. Westphal H, Nagel H-H (1986) Toward the derivations of three-dimensional descriptions from image sequences for nonconvex moving objects. Comput Vision Graph Image Process 24:302–320Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • S. Uras
    • 1
  • F. Girosi
    • 1
  • A. Verri
    • 1
  • V. Torre
    • 1
  1. 1.Department of PhysicsUniversity of GenoaGenoaItaly

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