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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 59, Iss. 3 — Mar. 1, 1969
  • pp: 345–348

Effect of Scaling Optic-Nerve Impulses on Increment Thresholds

EUGENE A. TRABKA  »View Author Affiliations

JOSA, Vol. 59, Issue 3, pp. 345-348 (1969)

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Renewal theory is applied to a particle-counter model of visual discrimination in order to determine the effects of neural-impulse scaling and dead time on the detection of increment thresholds. Let the ratio of absorbed photons to neural spikes (scaling factor) be denoted by r and the dead time by τ. We show that the particle counter is equivalent to one with dead time τ* = τ/r and scaling factor r* = 1. Further, if τ = 0, the particle counter does not exhibit the Weber-Fechner behavior for high background luminances as predicted by Barlow. These are asymptotic results, valid for large observation times. For more general observation times, the performance of a particle-counter mechanism with r=2 and τ=0 is evaluated for different types of starting procedures.

EUGENE A. TRABKA, "Effect of Scaling Optic-Nerve Impulses on Increment Thresholds," J. Opt. Soc. Am. 59, 345-348 (1969)

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  1. M. A. Bouman, J. J. Vos, and P. L. Walraven, J. Opt. Soc. Am. 53, 121 (1963).
  2. H. B. Barlow, Cold Spring Harbor Symp. Quant. Biol. 30, 539 (1965).
  3. Deterministic explanations, which do not attribute any significance to fluctuations, also exist. Rushton [W. A. H. Rushton, Proc. Roy. Soc. (London) 162B, 20 (1965)] exploits an analogy between a neural mechanism and a leaky electrical cable with feedback while van de Grind and Bouman [W. A. van de Grind and M. A. Bouman, Kybernetick 4, 136 (1968)] use a special type of adaptive-scaling mechanism but consider only mean values.
  4. E. A. Trabka, Vision Res. 8, 113 (1968).
  5. E. A. Trabka, Vision Res. 8, 613 (1968).
  6. D. R. Cox, Renewal Theory (John Wiley & Sons, Inc., New York, 1962).
  7. G. Sperling and M. Sondhi, J. Opt. Soc. Am. 58, 1133 (1968).
  8. D. M. MacKay, Science 159, 338 (1968).
  9. Sec. 5.5 of Ref. 6.
  10. Sec. 4.2 of Ref. 6.
  11. E. Parzen, Stochastic Processes (Holden-Day, Inc., San Francisco, 1962), p. 47.
  12. G. Wyszecki and W. S. Stiles, Color Science (John Wiley & Sons. Inc., New York, 1967), p. 569.
  13. These were obtained from the conditional moments about the origin, given t0, by taking expected values with respect to the assumed a priori density on t0. If we had instead started with the conditional moments about the mean, these would yield different expressions upon averaging although the numerical values plotted in Fig. 2 would not be significantly different.

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