Summary
In the context of the quantum theory of vision scalers, coincidence scalers, adapting coincidence scalers and dead time mechanisms have been used as basic constituents of network models: van de Grind et al. (1970a), Koenderink et al. (1970a, b). The possibilities that these devices offer to construct network models of vision are presently further analysed. First of all a mechanistic analysis is given of the event rate reduction characteristics of “dead time boxes”. Next the interaction of these devices with scalers is discussed in relation with a number of “fluctuation models” of vision proposed in the literature. A critical evaluation of these fluctuation models shows an important defect of most of them, viz. that unrealizable detection criteria are postulated. Our reconsideration of this detection problem then leads to the proposal of some specific realizable detectors. An application of the developed theory of mechanisms (‘machines’) to the explanation of the flash detection characteristics of Limulus concludes the paper. Applications of the presented ideas to neural theory and modelling are treated hi a separate paper (van de Grind et al., 1970b) and for applications of the theory to psychophysically oriented visual modelling studies the reader is referred to Koenderink et al. (1970a, b) and van de Grind et al. (1970a).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature
Abramowitz, M., Stegun, I. A. (eds.): Handbook of mathematical functions. New York: Dover publications, Inc. 1965.
Alaoglu, L., Smith, N. M., Jr.: Statistical theory of a scaling circuit. Phys. Rev. 53, 832–836 (1938).
Barlow, H. B.: Optic nerve impulses and Weber's law. Cold Spr. Harb. Symp. quant. Biol. 30, Sensory receptors (1965).
— Scaling and refractoriness in pulse trains. J. opt. Soc. Amer. 59, 11, 1500 (1969).
— Levick, W. R.: Three factors limiting the reliable detection of light by retinal ganglion cells of the cat. J. Physiol. (Lond.) 200, 1–24 (1969a).
— Coding of light intensity by the cat retina. Proc. Int. School of Physics “Enrico Fermi”, ed. W. Reichardt, p. 384–396. New York: Academic Press 1969b.
Baumgardt, E.: Absolute Schwelle und Differentialschwellen. In: The visual system: Neurophysiology and psychophysics, eds. R. Jung, H. Kornhuber, p. 400–409. Berlin-Göttingen-Heidelberg: Springer 1961.
Bouman, M. A.: History and present status of quantum theory in vision. In: Sensory communications, ed. W. A. Rosenblith. Cambridge, Mass: M.I.T.-Press 1961.
— Efficiency and economy in impulse transmission in the visual system. Acta psychol. 28, 239 (1964). Proceedings of the XXVII-th internat, congr. of psychology.
— My image of the retina. Quart. Rev. Biophys. 2, 1, 25–64 (1969).
Bouman, M. A. Ampt, C. G. F.: Fluctuation theory in vision and its mechanistic model. In: Performance of the eye at low luminances, eds. M. A. Bouman, J. J. Vos. Excerpta Medica Int. Congr. Series No. 125, 67–69 (1966).
— Velden, H. A. van der: The two-quanta explanation of the dependence of the threshold values and visual acuity on the visual angle and the time of observation. J. opt. Soc. Amer. 37, 11, 908–919 (1947).
— Vos, J. J., Walraven, P. L.: Fluctuation theory of luminance and chromaticity discrimination. J. opt. Soc. Amer. 53, No. 1, 121–128 (1963).
Cox, D. R.: Renewal theory. New York: Methuen & Co./John Wiley & Sons 1962.
— Lewis, P. A. W.: The statistical analysis of series of events. New York: Methuen & Co./John Wiley & Sons 1966.
Dodge, F. A.: Inhibition and excitation in the Limulus eye. Proc. Int. School of Physics “Enrico Fermi”, ed. W. Reichardt, p. 341–365. New York: Academic Press 1969.
— Shapley, R. M., Knight, B. W.: Linear systems analysis of the Limulus retina. Behav. Sci. 15, 24–36 (1970).
Färber, G.: Berechnung und Messung des Informationsflusses der Nervenfaser. Kybernetik 5, 17–29 (1968).
Feller, W.: An introduction to probability theory and its applications, vol. I, 2nd ed. Chichester: John Wiley & Sons 1965.
Grind, W. A. van de, Bouman, M. A.: A model of a retinal sampling unit based on fluctuation theory. Kybernetik 4, 136–141 (1968).
— Koenderink, J. J., Bouman, M. A.: Models of the processing of quantum signals by the human peripheral retina. Kybernetik 6, 213–227 (1970a).
— Heyde, G. L. van der, Landman, H. A. A., Bouman, M. A.: Adapting coincidence scalers and neural modelling. Kybernetik 8, 85–105 (1971).
Harte, R. A.: Receptor elements of the human retina as semiconductors. J. opt. Soc. Amer. 51, 1275 (1961).
Hartline, H. K., Milne, L. J., Wagman, I. H.: Fluctuation of response of visual sense cells. Fed. Proc. 6, 124 (abstract only) (1947).
Hughes, G. W., Maffei, L.: On the origin of the dark discharge of retinal ganglion cells. Arch. ital. Biol. 103, 45–59 (1965).
— Retinal ganglion cell response to sinusoidal light stimulation. J. Neurophysiol. 29, 333–352 (1966).
Kabe, D. G.: A note on some distributions for non-linear switching elements with finite dead time. Kybernetik 3, 285–287 (1967).
Koenderink, J. J., Grind, W. A. van de, Bouman, M. A.: Models of the retinal signal processing at high luminances. Kybernetik 6, 227–237 (1970a).
Koenderink, J. J., Grind, W. A. van de, Bouman, M. A. Foveal information processing at high luminances. Kybernetik, in press (1971).
Murakami, M., Shigematsu, Y.: Duality of conduction mechanism in bipolar cells of the frog retina. Vision Res. 10, 1–10 (1970).
Naylor, T. H., Balintfy, J. L. Burdick, D. S., Kong Chu: Computer Simulation Techniques (1966).
Parzen, E.: Stochastic processes. San Francisco: Holden-Day 1962.
Ratliff, F.: Some interrelations among physics, physiology and psychology in the study of vision. In: Psychology: A study of a science, vol. 4, p. 417–482, ed. S. Koch. Maidenhead: McGraw-Hill 1962.
Ricciardi, L. M., Esposito, F.: On some distribution functions for non-linear switching elements with a finite dead time. Kybernetik 3, 148–152 (1966).
Rose, A.: The sensitivity performance of the human eye on an absolute scale. J. opt. Soc. Amer. 38, 196–208 (1948).
— Quantum effects in vision. Advanc. biol. med. Phys. 5, 211–242 (1957).
Stein, R. B.: A theoretical analysis of neuronal variability. Biophys. J. 5, 173–194 (1965).
— Some models of neuronal variability. Biophys. J. 7, 37–68 (1967a).
— The information capacity of nerve cells using a frequency code. Biophys. J. 7, 797–826 (1967b).
Trabka, E. A.: On Stiles's line element in brightness-color space and the color power of the blue. Vision Res. 8, 113–131 (1968a).
— Parameter values for nonideal detectors in a color vision model. Vision Res. 8, 613–616 (1968b).
Trabke, E. A.: Effect of scaling optic-nerve impulses on increment thresholds. J. opt. Soc. Amer. 59, 345–349 (1969).
Velden, H. A. van der: Over hot aantal lichtquanten dat nodig is voor een lichtprikkel bij het menselijk oog. Physica 11, 179–189 (1944).
Vries, Hl. de: The quantum character of light and its bearing upon threshold of vision, the differential sensitivity and visual acuity of the eye. Physica 10, 553–564 (1943).
— Die Reizschwelle der Sinnesorgane als physikalisches Problem. Experienta (Basel) 4, 205 (1948).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
van de Grind, W.A., Koenderink, J.J., Landman, H.A.A. et al. The concepts of scaling and refractoriness in psychophysical theories of vision. Kybernetik 8, 105–122 (1971). https://doi.org/10.1007/BF00272291
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00272291