Skip to main content

The height of a stereokinetic cone: A quantitative determination of a 3-D effect from 2-D moving patterns without a “rigidity assumption”

Psychological Research volume 50, pages 162–172 (1988)Cite this article

Summary

When a circular disc with an eccentric dot painted on it is set in slow circular motion, a three-dimensional solid object appears to the observer: the stereokinetic cone. The cone shows a well-defined height and tilt. All current theories of how the visual system can extract 3-D percepts from 2-D moving patterns, are based on a “rigidity assumption” hypothesis. But this assumption cannot explain why the stereokinetic cone appears to have a well-defined height. An alternative hypothesis is proposed here, which avoids the rigidity assumption and is based on a minimization process of the relative velocity differences between all the points of the rotating pattern. The hypothesis allows a quantitative prediction of the stereokinetic cone height both when the rotating disc is circular and when it is elliptical. The predictions are in good agreement with previously reported experimental results and with our own observations.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

43,34 €

Price includes VAT (Finland)
Tax calculation will be finalised during checkout.

References

  • Braunstein, M. L., & Andersen, G. J. (1984). A counter example to the rigidity assumption in the visual perception of structure from motion. Perception, 13, 213–217.

    Article  Google Scholar 

  • Beghi, L., Vicario, G., & Zanforlin, M. (1984). The perceptual centre of visual configurations. Accademia Patavina di Scienze, Lettere ed Arti, XCV (1982–83), III, 133–148.

    Google Scholar 

  • Carlson, V. R. (1977). Instruction and perceptual Constancy judgements. In: W. Epstein (Ed.), Stability and constancy in visual perception (pp. 217–254). New York: Wiley.

    Google Scholar 

  • Cutting, J. E. (1986). Perception with an eye for motion. Cambridge, Mass.: MIT Press.

    Google Scholar 

  • Cutting, J. E. (1987). Perception and information. Annual Review of Psychology, 38, 61–90.

    Article  Google Scholar 

  • Cutting, D. R., & Proffitt, D. R. (1982). The minimum principle and the perception of absolute, common, and relative motions. Cognitive Psychology, 14, 211–246.

    Article  Google Scholar 

  • Duncker, K. (1929). Über induzierte Bewegung. Ein Beitrag zur Theorie optischer wahrgenommener Bewegung. Psychologische Forschung, 12, 159–180.

    Article  Google Scholar 

  • Epstein, W. (1961). The known-size-apparent-distance hypothesis. American Journal of Psychology, 74, 333–346.

    Article  Google Scholar 

  • Eriksson, E. S. (1974). A theory of veridical space perception. Scandinavian Journal of Psychology, 15, 225–235.

    Article  Google Scholar 

  • Fischer, G. T. (1956). Factors affecting estimation of depth with variation of the stereokinetic effect. American Journal of Psychology, 69, 252–257.

    Article  Google Scholar 

  • Gibson, J. J. (1958). What gives rise to the perception of motion? Psychological Review, 75, 335–345.

    Article  Google Scholar 

  • Gogel, W. C. (1977). The metric of visual space. In: W. Epstein (Ed.), Stability and constancy in visual perception (pp. 129–181). New York: Wiley.

    Google Scholar 

  • Hildred, E. C. (1984). Computations underlying the measurement of visual motion. Artificial Intelligence, 23, 309–354.

    Article  Google Scholar 

  • Hopfield, J. J., & Tank, D. W. (1986). Computing with neural circuits. Science, 233, (4764), 625–633.

    Article  Google Scholar 

  • Johansson, G. (1964). Perception of motion and changing form. Scandinavian Journal of Psychology, 5, 181–208.

    Article  Google Scholar 

  • Johansson, G. (1974a). Visual perception of rotary motion as transformations of conic sections — A contribution to the theory of visual space perception. Psychology, 17, 226–237.

    Google Scholar 

  • Johansson, G. (1974b). Vector analysis in visual perception of rolling motion: a quantitative approach, Psychologische Forschung, 36, 311–319.

    Article  Google Scholar 

  • Johansson, G. (1978). About the geometry underlying spontaneous visual decoding of the optical message. In E. L. J. Leeuwenberg and H. F. J. M. Buffart (Eds.), Formal theories of visual perception (pp. 265–276). Chichester, England: Wiley.

    Google Scholar 

  • Lappin, J. S., Doner, J. F., & Kottas, B. L. (1980). Minimal conditions for the visual detection of structure and motion in three dimensions. Science, 209, 717–719.

    Article  Google Scholar 

  • Longuet-Higgins, H. C. (1986). Visual motion ambiguity. Vision Research, 26, 181–183.

    Article  Google Scholar 

  • Mefferd, R. B. Jr. (1968). Perception of depth in rotating objects: 7. Influence of attributes of depth on stereokinetic percepts. Perceptual and Motor Skills, 27, 1179–1193.

    Article  Google Scholar 

  • Metelli, F. (1940). Ricerche sperimentali sulla percezione del movimento. Rivista di psicologia, 36, 319–370.

    Google Scholar 

  • Metelli, F. (1960). Un particolare effetto della struttura percettiva sul movimento relativo di due cerchi. Rivista di psicologia, 54 (2), 178–179.

    Google Scholar 

  • Metelli, F. (1964). Repos apparent et phénomènes de “totalisation cyclique” dans la perception visuelle. Journal de psychologie normale et pathologique, 51 (1), 1–38.

    Google Scholar 

  • Metelli, F. (1975). A contribution to the theory of motion perception. In G. B. Flores D'Arcais (Ed.), Studies in perception. Festschrift for Fabio Metelli (pp. 488–496). Milan: Martello-Giunti.

    Google Scholar 

  • Movson, J. A., Adelson, E. H., Gizzi, M. S., & Newsome, W. T. (1983). The analysis of moving visual patterns. In C. Chagas, R. Gattas, C. Gross (Ed.), Pattern recognition mechanisms. (pp. 117–151). Rome: Pontificia Accademia Scientiarum.

    Google Scholar 

  • Musatti, C. L. (1924). Sui fenomeni stereocinetici. Archivio italiano di psicologia, 3, 105–120.

    Google Scholar 

  • Musatti, C. L. (1928). Sui movimenti apparenti dovuti ad illusione di identità di figura. Archivio italiano di psicologia, 6, 205–219.

    Google Scholar 

  • Musatti, C. L. (1928–9). Sulla percezione di forme di figurea oblique rispetto al piano frontale. Rivista di psicologia, 25, 1–14.

    Google Scholar 

  • Musatti, C. L. (1931). Forma e assimilazione. Archivio italiano di psicologia, 9, 61–156.

    Google Scholar 

  • Musatti, C. L. (1955). La stereocinesi e il problema della struttura dello spazio visibile. Rivista di psicologia, 49, 3–57.

    Google Scholar 

  • Musatti, C. L. (1975). Stereokinetic phenomena and their interpretation. In G. B. Flores d'Arcais (Ed.), Studies in perception. Festschrift for Fabio Metelli (pp. 166–189). Milan: Martello-Giunti.

    Google Scholar 

  • Nakayama, K. (1985). Biological image motion processing: a review. Vision Research, 25 (5), 625–660.

    Article  Google Scholar 

  • Renwall, P. (1929). Zur Theorie des stereokinetischen Phänomenes. Annales Universitatis Aboensis. Ser. B, 10, 13–75.

    Google Scholar 

  • Robinson, J. O., Piggins J. D., & Wilson J. A. (1985). Shape, height and angular movement in stereokinesis. Perception, 14, 677–683.

    Article  Google Scholar 

  • Rubin, E. (1927). Visuell wahrgenommene wirkliche Bewegungen, Zeitschrift für Psychologie, 103, 384–392.

    Google Scholar 

  • Sato, I. (1964). An investigation on the stereokinetic effect. Tohoku Psychologica Folia, 221, 94–99 (quoted in Wieland and Mefferd, 1968).

    Google Scholar 

  • Todd, J. T. (1981). Visual information about moving objects. Journal of Experimental Psychology: Human Perception and Performance, 7 (4), 795–810.

    Google Scholar 

  • Todd, J. T. (1982). Visual information about rigid and non-rigid motion: a geometric analysis. Journal of Experimental Psychology: Human Perception and Performance, 8, 238–252.

    PubMed  Google Scholar 

  • Todd, J. T. (1985). Perception of structure from motion. Is projective correspondence of moving elements a necessary condition? Journal of Experimental Psychology: Human Perception and Performance, 11 (6), 689–710.

    PubMed  Google Scholar 

  • Ullman, S. (1979). The interpretation of visual motion. Cambridge, Mass.: MIT Press.

    Book  Google Scholar 

  • Ullman, S. (1984). Maximizing rigidity: The incremental recovery of 3-D structure from rigid and non-rigid motion. Perception, 13, 255–274.

    Article  Google Scholar 

  • Wallach, H., & O'Connell, D. N. (1953). The kinetic depth effect. Journal of Experimental Psychology, 45, 205–217.

    Article  Google Scholar 

  • Wallach, H., Weisz, A., & Adams, P. A. (1956). Circles and derived figures in rotation. American Journal of Psychology, 69, 48–59 (1956).

    Article  Google Scholar 

  • Wieland, B. A., & Mefferd, R. B. (1968). Perception of depth in rotating objects: 3. Asymmetry and velocity as determinants of the stereokinetic effect. Perceptual and Motor Skills, 26, 671–681.

    Article  Google Scholar 

  • Wilson, J. A., Robinson, J. O., & Piggins, D. J. (1983). Wobble cones and wobble holes: the stereokinetic effect revisited. Perception, 12, 187–193.

    Article  Google Scholar 

  • Wilson, J. A., Robinson, J. O., & Piggins, D. J. (1986). Apparent height of a stereokinetic cone is decreased by departure from circularity. Perception, 11, 399–403.

    Article  Google Scholar 

  • Zanforlin, M. (1987a). La determinazione teorica del cono stereocinetico di Musatti. Atti e Memorie della Accademia Patavina di Science, LL. AA, 99, 33–46.

    Google Scholar 

  • Zanforlin, M. (1987b). The height of Musatti's stereokinetic cone. Fourth International Conference on Event Perception and Action, August 24–28, 1987, Trieste.

  • Zanforlin, M., & Vallortigara, G. (1988). Depth effect from a rotating line of constant length. Perception & Psychophysics, in press.

Download references

Author information

Affiliations

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

    Mario Zanforlin

Authors
  1. Mario Zanforlin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Zanforlin, M. The height of a stereokinetic cone: A quantitative determination of a 3-D effect from 2-D moving patterns without a “rigidity assumption”. Psychol. Res 50, 162–172 (1988). https://doi.org/10.1007/BF00310177

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00310177

Keywords

  • Visual System
  • Alternative Hypothesis
  • Quantitative Determination
  • Relative Velocity
  • Current Theory