Skip to main content

Model of Visual Perceptual Space

  • Chapter
Models of the Visual System

Abstract

Space is a fundamental concept in physics and psychology. We consider space around us to be 3-dimensional and Euclidean. Can the same be said about the representation of this world in our perceptual system? This 3- dimensional manifold1 of objects we are surrounded by have form and localization, in addition to characteristic qualities of color and brightness. (A brief definition of superscripted terms are given in the Notes (Section 16.4) at the end of the chapter). In a visual sensation, we are aware not only of a distribution of colors and brightness but also that certain of these qualities are combined into objects which have a definite geometric form and localization in a 3-dimensional space. This (the sensed space) is the visual space. The visual space is the final product of a long series of transformations/processes from the retina to the brain and it is coherent, self-organized, dynamic and complex (Indow 1991). Phenomenologically, it is articulated into individual objects, backgrounds and the “self”. The self is a percept that is due to visual and proprioceptive experiences. Other visual percepts arise from stimuli in physical space. Luneberg (1947, 1950), in his classic work on binocular vision, defined visual space as a space obtained by transforming, using a specific mapping, a physical space into a cyclopean egocentered space with orthogonal coordinates.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Adler, R., Bazan, M., Schiffer, M., 1965, Introduction to general relativity, McGraw Hill, New York.

    MATH  Google Scholar 

  • Blank, A. A., 1958, Analysis of experiments in binocular space perception, J. Opt. Soc. Am. 48: 911–925.

    Article  MathSciNet  Google Scholar 

  • Blank, A. A., 1978, Metric geometry in human binocular perception — theory and fact, In: Leewenberg, E. and Buffart, H., (Eds) Formal theories of visual perception, Wiley, New York.

    Google Scholar 

  • Blumenfeld, W., 1913, Unterschugen über die schienbare grosse in sehraume, Zeitschri for psyhcologie and physiologie der sinnesargane, 65: 241–404.

    Google Scholar 

  • Caelli, T., 1977, Psychophysical interpretations and experimental evidence for the Hoffinan LTG/NP theory of perception. Cahiers de Psychologie, 20: 107–134.

    Google Scholar 

  • Caelli, T. 1981, Visual perception theory and practice, Pergamon Press, Oxford, U.K.

    Google Scholar 

  • Carlton, E. H., 1988, Connection between internal representation of rigid transformation and cortical activity patterns, Biol. Cybernetics, 59: 419–429.

    Article  MathSciNet  MATH  Google Scholar 

  • DeValois, K. K., Lakshminarayanan, V., Nygaard, R., Schlussel, S., Sladkey, J., 1988, Relative position comparisons between dissimilar patterns, paper TUR5, Technical Digest Series, Vol II, Optical Society of America, Washington, D.C.

    Google Scholar 

  • DeValois, K. K., Lakshminarayanan, V., Nygaard, R., Schlussel, S., Sladkey, J., 1989, Perceptual space as an elastic manifold, Inves. Opthal. Vis. Sci. ARVO supplement 30: 486.

    Google Scholar 

  • DeValois, K. K., Lakshminarayanan, V., Nygaard, R., Schlussel, S., Sladkey, J., 1990, Discrimination of relative spatial position, Vision Res. 30: 1649–1660.

    Article  Google Scholar 

  • Dirac, P. A. M., 1954, Letter, Sci. Monthly, 79 (#4).

    Google Scholar 

  • Dodwell, P., 1970, Visual pattern recognition, Holt, Reinhart and Winston, New York. Eisenhart, L. P., 1927, Non-Riemannian geometry, American Mathematical Society Colloquia Publications, Vol 8, American Mathematical Society, Providence, R. I.

    Google Scholar 

  • Foley, J. M., 1964, Desarguesian property in visual space, J. Opt. Soc. Am 54: 684–692. Hoffman, W. C., 1966, The Lie algebra of visual perception, J. Math. Psych., 3: 65–98, errata: ibid 4: 348–349.

    Google Scholar 

  • Hoffman, W. C., 1968, The neuron as a Lie group germ and a Lie group product, Quat. J. Applied. Math., 25: 423–441.

    MATH  Google Scholar 

  • Hoffinan, W. C., 1970, Higher visual perception as a prolongation of the basic Lie transformation group, Math. Biosci., 6: 437–471.

    Article  MathSciNet  Google Scholar 

  • Hoffman, W. C., 1977, An informal, historical description (with biography) of the LTG/NP, Cahiers de Psychologie, 20: 139–150.

    Google Scholar 

  • Hoffman, W. C., 1980, Subjective geometry and geometric psychology, Mathematical Modeling, 1: 349–367.

    Article  MATH  Google Scholar 

  • Hoffman, W. C., 1984, Figural synthesis by vector fields: Geometric neuropsychology, In: Dodwell, P., Caelli, T., (Eds) Figural Synthesis, Erlbaum, Hillsdale, NJ.

    Google Scholar 

  • Indow, T., 1974, On geometry of frameless binocular perceptual space, Psychologia, 17: 5063.

    Google Scholar 

  • Indow, T., 1979, Alleys in visual space, J. Math. Psycho!. 19: 221–258.

    Article  MathSciNet  MATH  Google Scholar 

  • Indow, T., Watanabe, T., 1988, Alleys on an extensive apparent fronto-parallel plane: A second experiment, Perception 17: 647–666.

    Article  Google Scholar 

  • Indow, T., 1991, A critical review of Luneberg’s model with regard to global structure of visual space, Psychol. Rev. 98: 430–453

    Google Scholar 

  • Lakshminarayanan, V., Santhanam, T. S., 1995, Representation of Rigid Stimulus transformations by cortical activity patterns, In: Luce, D. R., D’Zmura, M., Hoffman, D., Ivesron, G. J., Romney, A. K., (Eds), Geometric representations of perceptual phenomena, Lawrence Erlbaum, Mahwah, N.J., pp. 61–68.

    Google Scholar 

  • Lakshminarayanan, V., Parthasarathy, R., DeValois, K. K., 2000, A generalized perceptual space, Neurol. Res. 22: 699–702.

    Google Scholar 

  • Luneberg, R. K., 1947, Mathematical analysis of binocular vision, Princeton University Press, Princeton, N.J.

    Google Scholar 

  • Luneberg, R. K., 1950, The metric of binocular visual space, J. Opt. Soc. Am. 40: 627–642.

    Article  Google Scholar 

  • MacLeod, D. A., Willer, J. D., 1995, Is there a visual space?, In: Luce, D. R., D’Zmura, M.,Hoffrnan, D., Ivesron, G. J., Romney, A. K., (Eds), Geometric representations of perceptual phenomena, Lawrence Erlbaum, Mahwah, N.J., pp. 47–60.

    Google Scholar 

  • Pedoe, D., 1976, Geometry and the liberal arts, Peregrine, New York.

    Google Scholar 

  • Schwartz, E. L., 1980, Computational anatomy and functional architecture of striate cortex: A spatial mapping approach to perceptual coding, Vision Res. 20: 645–669.

    Article  Google Scholar 

  • Spivak, M., 1979, A comprehensive introduction to differential geometry, Publish or Perish, Inc., Berkeley, CA.

    Google Scholar 

  • Suppes, P., Krantz, D. H., Luce, D. R., Tversky, A., 1989, Foundations of measurements, Vol II: Geometrical, threshold and probabilistic representations, Academic Press, New York.

    Google Scholar 

  • Suppes, P., 1995, Some fundamental problems in the theory of visual space, In: Luce, D. R., D’Zmura, M., Hoffman, D., Ivesron, G. J., Romney, A. K., (Eds), Geometric representations of perceptual phenomena, Lawrence Erlbaum, Mahwah, N.J., pp. 37–45.

    Google Scholar 

  • Wagner, M., 1985, The metric of visual space, Perception and Psychophysics 38: 483–495.

    Article  Google Scholar 

  • Wheeler, J., 1990, Information, physics, quantum: The search for the links: In: Zurek, W. (Ed), Complexity, entropy and physics of information, Addison- Wesley, Reading, MA, pp. 3–28.

    Google Scholar 

  • Yamazaki, T., 1987, Non-Riemannian approach to geometry of visual space: An approach to affinely connected geometry to visual alleys and horopter, J. Math. Psycho!. 31: 270–298.

    Article  MATH  Google Scholar 

  • Zhang, J., Wu, S., 1990, Structures of visual perception, Proc. Natl. Acad. Sci. USA 87: 7819–7823.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Science+Business Media New York

About this chapter

Cite this chapter

Lakshminarayanan, V. (2002). Model of Visual Perceptual Space. In: Hung, G.K., Ciuffreda, K.J. (eds) Models of the Visual System. Topics in Biomedical Engineering International Book Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5865-8_16

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-5865-8_16

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-3377-5

  • Online ISBN: 978-1-4757-5865-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics