On the statistics of vision: The Julesz conjecture

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Abstract

This paper describes a class of random patterns which have the same first-, second-, and third-order statistics as coin tossing, but are visually different. The patterns are counterexamples to a conjecture of Julesz that all the eye can discriminate is first- and second-order statistics.

References (21)

  • D. Aldous

    Representations for partially exchangeable arrays of random variables

    Journal of Multivariate Analysis

    (1981)
  • T. Caelli et al.

    On perceptual analyzers underlying visual texture discrimination: Part I

    Biological Cybernetics

    (1978)
  • T. Caelli et al.

    On perceptual analyzers underlying visual texture discrimination: Part II

    Biological Cybernetics

    (1978)
  • D. Conway

    Distributions with prescribed margins

  • W. Feller
  • D. Freedman

    Markov chains

    (1971)
  • E. Gilbert

    Random colorings of a lattice of squares in the plane

    SIAM Journal of Algebra and Disc. Methods

    (1980)
  • P.J. Green et al.

    Computing Dirichlet tesselations in the plane

    Computer Journal

    (1978)
  • D. Hoover

    Relations on probability spaces and arrays of random variables

    (1981)
  • B. Julesz

    Experiments in the visual perception of textures

    Scientific American

    (1975)
There are more references available in the full text version of this article.

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    Julesz (1962) famously conjectured that all preattentive texture discrimination used linear filtering followed by a squaring nonlinearity. And indeed, spectral energy accounts well for many cases of preattentive texture discrimination (Bergen & Adelson, 1988); however, many counterexamples exist (Diaconis & Freedman, 1981; Julesz, Gilbert, Sheppand, & Frisch, 1973; Julesz, Gilbert, & Victor, 1978; Pollack, 1971a,b, 1972, 1973). Although such examples and the models proposed to explain them are suggestive, little progress has been made in actually discovering and measuring the dimensions of preattentive visual sensitivity.

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Research was partially supported by NSF Grants MCS-77-16974 (P. Diaconis) and MCS-80-02535 (D. Freedman).

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