Perception & Psychophysics

, Volume 32, Issue 3, pp 230–240 | Cite as

Symmetropy, an entropy-like measure of visual symmetry

  • Eiji Yodogawa
Article

Abstract

A new objective measure of symmetry for single patterns, called symmetropy, is developed on two bases, the two-dimensional discrete Walsh transform of a pattern and the entropy concept in information theory. It is extended to a more general measure, called the symmetropy vector. In order to test the predictive power of the symmetropy vector, multiple regression analyses of judged pattern goodness and of judged pattern complexity were carried out. The analyses show that the symmetropy vector predicts pattern goodness and pattern complexity, as well as the amount of symmetry in a pattern. They also suggest that pattern goodness is a concept based on the holistic properties of a pattern, while pattern complexity (or simplicity) is a concept based on both holistic and partial properties of a pattern.

References

  1. Abramson, N.Information theory and coding. New York: McGraw-Hill, 1963.Google Scholar
  2. Attneave, F. Some informational aspects of visual perception.Psychological Review, 1954,61, 183–193,CrossRefPubMedGoogle Scholar
  3. Attneave, F. Symmetry, information and memory for patterns.American Journal of Psychology, 1955,68, 209–222.CrossRefPubMedGoogle Scholar
  4. Beauchamp, K. G.Walsh functions and their applications. London: Academic Press, 1975.Google Scholar
  5. Blachman, N. M. Sinusoids versus Walsh functions.Proceedings of the IEEE, 1974,62, No. 3, 346–354.CrossRefGoogle Scholar
  6. Carl, J. W. A biologically derived model for image classification utilizing Walsh functions.Proceedings of the 22nd National Aerospace Electronics Convention (NAECON), 1970, 253–259.Google Scholar
  7. Chipman, S. F. Complexity and structure in visual patterns.Journal of Experimental Psychology: General, 1977,106, 269–301.CrossRefGoogle Scholar
  8. Corballis, M. C. &Roldan, C. E. Detection of symmetry as a function of angular orientation.Journal of Experimental Psychology: Human Perception and Performance, 1975,1, 221–230.CrossRefPubMedGoogle Scholar
  9. Garner, W. R.Uncertainty and structure as psychological concepts. New York: Wiley, 1962.Google Scholar
  10. Garner, W. R., &Clement, D. E. Goodness of patterns and pattern uncertainty.Journal of Verbal Learning & Behavior, 1963,2, 446–452.CrossRefGoogle Scholar
  11. Harmuth, H. F.Transmission of information by orthogonal functions. New York: Springer, 1972.Google Scholar
  12. Hochberg, J., &Mcalister, E. A quantitative approach to figurai “goodness.”Journal of Experimental Psychology, 1953,46, 361–364.CrossRefPubMedGoogle Scholar
  13. Howe, E. S. Effects of partial symmetry, exposure time, and backward masking on judged goodness and reproduction of visual patterns.Quarterly Journal of Experimental Psychology, 1980,32, 27–55.CrossRefPubMedGoogle Scholar
  14. Imai, S., Ito, S., &Ito, T. [Effects of intra-pattern transformation structures and the number of runs upon goodness and complexity judgments of patterns.]Japanese Psychological Review, 1976,19, 77–94 (in Japanese).Google Scholar
  15. Koffka, K.Principles of Gestalt psychology. New York: Harcourt Brace Jovanovich, 1935.Google Scholar
  16. Palmer, S. E., &Hemenway, K. Orientation and symmetry: Effects of multiple, rotational, and near symmetries.Journal of Experimental Psychology: Human Perception and Performance, 1978,4, 691–702.CrossRefPubMedGoogle Scholar
  17. Szilagyi, P. G., &Baird, J. C. A quantitative approach to the study of visual symmetry.Perception & Psychophysics, 1977,22, 287–292.CrossRefGoogle Scholar
  18. Walsh, J. L. A closed set of orthogonal functions.American Journal of Mathematics, 1923,45, 5–24.CrossRefGoogle Scholar
  19. Zusne, L. Moments of area and of the perimeter of visual form as predictors of discrimination performance.Journal of Experimental Psychology, 1965,69, 213–220.CrossRefPubMedGoogle Scholar
  20. Zusne, L. Measures of symmetry.Perception & Psychophysics, 1971,9, 363–366.Google Scholar

Copyright information

© Psychonomic Society, Inc. 1982

Authors and Affiliations

  • Eiji Yodogawa
    • 1
  1. 1.Musashino Electrical Communication LaboratoryNITTokyoJapan

Personalised recommendations