Abstract
A general characterization of multi-input movement detection models is given in terms of the Volterra series formalism. When nonlinearities of order higher than the second are negligible, an n-input system can be decomposed into a set of 2-input systems, summing linearly. For a (symmetrical) 2-input system which has significant nonlinearities only up to the second order, the correlation model is its most general expression, if the infinite time average of the output is taken. Specific observations from optomotor experiments (e.g. phase invariance and contrast frequency dependence) can be interpreted in a general way in terms of properties of the Volterra representation.
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References
Barlow,H.B., Levick,W.R.: The mechanism of directionally sensitive units in rabbits retina. J. Physiol. (Lond.) 178, 477–504 (1965)
Bedrosian,E., Rice,S.O.: The output properties of Volterra systems. Proc. IEEE 59, 12 (1971)
Eckert,H.: Optomotorische Untersuchungen am visuellen System der Stubenfliege Musca domestica. Kybernetik (1973), in print
Foster,D.H.: A model of the human visual system in its response to certain classes of moving stimuli. Kybernetik 8, 69–84 (1971)
Götz,K.G.: Optomotorische Untersuchung des visuellen Systems einiger Augenmutanten der Fruchtfliege Drosophila. Kybernetik 2, 77–92 (1964)
Götz,K.G.: Principles of optomotor reactions in insects. Bibl. ophthal. (Basel) 82, 251–259 (1972)
Hassenstein,B.: Optokinetische Wirksamkeit bewegter periodischer Muster. Z. Naturforsch. 14b, 659–674 (1959)
Kirschfeld,K.: The visual system of Musca: Studies on optics, structure and function. In: Wehner,R. (Ed.): Information processing in the visual systems of arthropods. Berlin-Heidelberg-New York: Springer 1972
Lee,Y.W., Schetzen,M.: Measurement of the Wiener kernels of a non-linear system. Int. J. Control 2, 237 (1965)
Marmarelis,P.Z., McCann,G.D.: Development and application of white-noise modeling techniques for studies of insect visual nervous system. Kybernetik 12, 74–90 (1973)
Poggio,T.: Internal note, 1972
Reichardt,W.: Autokorrelations-Auswertung als Funktionsprinzip des Zentralnervensystems. Z. Naturforsch. 12b, 448–457 (1957)
Reichardt,W.: Autocorrelation, a principle for the evaluation of sensory information by the central nervous system. In: Rosenblith,W.A. (Ed.): Sensory communication, pp. 303–317, Cambridge, Mass. M.I.T. Press 1961
Reichardt,W.: Musterinduzierte Flugorientierung. Verhaltensversuche an der Fliege Musca domestica. Naturwissenschaften 60, 122–138 (1973)
Reichardt,W., Varjú,D.: Übertragungseigenschaften im Auswertesystem für das Bewegungssehen. Z. Naturforsch. 14b, 676–689 (1959)
Thorson,J.: Small signal analysis of a visual reflex in the Locust I and II. Kybernetik 3, 41–66 (1966)
Varjú,D.: Optomotorische Reaktionen auf die Bewegung periodischer Helligkeitsmuster. Z. Naturforsch. 14b, 724–735 (1959)
Varjú,D., Reichardt,W.: Übertragungseigenschaften im Auswertesystem für das Bewegungssehen II. Z. Naturforsch. 22b, 1343–1351 (1967)
Wiener,N.: Nonlinear problems in random theory. New York: M.I.T. Press and John Wiley 1958
Zimmermann,G.: Der Einfluß stehender und bewegter Musteranteile auf die Optomotorische Reaktion der Fliege Drosophila. Dissertation Eberhard-Karls-Universität Tübingen (1973)
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We would like to thank Mr. E. Buchner, Dr. K. Kirschfeld, Mr. B. Pick, Mr. Ch. Wehrhahn and especially Dr. K. G. Götz for critical remarks. Thanks are also due to Dr. B. Rosser for reading and to Mrs. I. Geiss for typing the English manuscript.
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Poggio, T., Reichardt, W. Considerations on models of movement detection. Kybernetik 13, 223–227 (1973). https://doi.org/10.1007/BF00274887
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DOI: https://doi.org/10.1007/BF00274887