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Quantitative determination of the three-dimensional appearances of a rotating ellipse without a rigidity assumption

Biological Cybernetics volume 65, pages 433–440 (1991)Cite this article

Abstract

When a flat figure of uniform color and with an elliptic contour is slowly rotated around an axis orthogonal to the plane of the image, an observer set in the frontal position will perceive it first as a rotating ellipse. After a few seconds of inspection, the ellipse appears to deform with an amoeba-like movement until it appears as a rigid, circular disk tilting back and forth in 3-D space; finally it is seen as a rotating ellipsoid tilted in depth at a constant inclination angle with respect to the rotating platform. In an attempt to provide an explanation for the apparent ellipsoid, the authors present a mathematical model based on an hypothesis of velocity differences minimization, successfully used to describe other stereokinetic phenomena, such as “the rotating cone” and the ”tilted bar”. This technique does not make use of Ullman's “ridigity hypothesis” for extracting depth from 2-D moving stimuli. A comparison with experimental results supports the validity of the model.

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Author information

Affiliations

  1. Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Belzoni, 7, I-35131, Padova, Italy

    L. Beghi & E. Xausa

  2. Dipartimento di Psicologia Generale, Università di Padova, Piazza Capitaniato, 3, I-35100, Padova, Italy

    C. De Biasio &  M. Zanforlin

Authors
  1. L. Beghi
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  2. E. Xausa
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  3. C. De Biasio
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  4. M. Zanforlin
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Beghi, L., Xausa, E., De Biasio, C. et al. Quantitative determination of the three-dimensional appearances of a rotating ellipse without a rigidity assumption. Biol. Cybern. 65, 433–440 (1991). https://doi.org/10.1007/BF00204656

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  • DOI: https://doi.org/10.1007/BF00204656

Keywords

  • Color
  • Mathematical Model
  • Quantitative Determination
  • Inclination Angle
  • Difference Minimization