Biological Cybernetics

, Volume 97, Issue 5–6, pp 461–477 | Cite as

A unified probabilistic model of the perception of three-dimensional structure from optic flow

  • Francis ColasEmail author
  • Jacques Droulez
  • Mark Wexler
  • Pierre Bessière
Original Paper


Human observers can perceive the three- dimensional (3-D) structure of their environment using various cues, an important one of which is optic flow. The motion of any point’s projection on the retina depends both on the point’s movement in space and on its distance from the eye. Therefore, retinal motion can be used to extract the 3-D structure of the environment and the shape of objects, in a process known as structure-from-motion (SFM). However, because many combinations of 3-D structure and motion can lead to the same optic flow, SFM is an ill-posed inverse problem. The rigidity hypothesis is a constraint supposed to formally solve the SFM problem and to account for human performance. Recently, however, a number of psychophysical results, with both moving and stationary human observers, have shown that the rigidity hypothesis alone cannot account for human performance in SFM tasks, but no model is known to account for the new results. Here, we construct a Bayesian model of SFM based mainly on one new hypothesis, that of stationarity, coupled with the rigidity hypothesis. The predictions of the model, calculated using a new and powerful methodology called Bayesian programming, account for a wide variety of experimental findings.


Angular Speed Reversal Rate Slant Angle Immobile Condition Simulated Plane 
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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Francis Colas
    • 1
    • 2
    • 3
    Email author
  • Jacques Droulez
    • 4
    • 5
  • Mark Wexler
    • 4
    • 5
  • Pierre Bessière
    • 3
    • 6
  1. 1.LPPACollège de FranceParis Cedex 05France
  2. 2.Gravir LaboratoryGrenoble UniversityMontbonnotFrance
  3. 3.Gravir LaboratoryINRIA Rhône-AlpesMontbonnotFrance
  4. 4.Collège de France, Laboratoire de la Physiologie de la Perception et de l’ActionParisFrance
  5. 5.CNRS, UMR 7152ParisFrance
  6. 6.CNRS, Grenoble UniversityMontbonnotFrance

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