Abstract
In the theoretical part of the present work the input-output relation for a multi-input system is developed into a functional power series. This is formally equivalent to a decomposition of the system into a sum of all possible combinations of 1-, 2-, 3-... input subsystems. The average response of the system to a uniformly moving patern is known to be a Fourier series with respect to spatial frequency. The coefficients of the series are linear combinations of the “weights” by which different subsystems contribute to the total reaction. If a system can be shown to have essential nonlinearities of no higher than second order it is possible to calculate, from a Fourier analysis of the average movement response, the “weight” by which the nonlinear interaction between any two input elements contributes to the total reaction. This interaction is termed “elementary movement detector”. By the analysis presented here the arrangement of the elementary movement detectors may be determined for a two-dimensional array of input elements and the strength of their contributions to the total movement reaction may be calculated. Special experimental methods have been developed which allow one to apply this analysis to the visual system of the fruitfly Drosophila. The preliminary data presented show that the direction sensitive optomotor response of Drosophila can be attributed predominantly to the contributions from two “elementary movement detectors” which interconnect neighbouring visual elements. The detectors are oriented in the hexagonal array of the compound eye at +30° and at-30° with respect to the horizontal line of symmetry. A weak contribution from a detector between neighbouring elements along the horizontal line of symmetry is suggested by the present data. In the course of the analysis the contrast transfer properties of the compound eye are characterized.
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Barlow, H.B., Levick, W.R.: The mechanism of diretionally sensitive units in rabbits retina. J. Physiol. (Lond.) 178, 477–504 (1965)
Buchner, E.: Bewegungsperzeption in einem visuellen System mit gerastertem Eingang. Dissertaion, Eberhard-Karls-Universität Tübingen (1974)
Eckert, H.: Optomotorische Untersuchungen am visuellen System der Stubenfliege Musca domestica L. Kybernetik 14, 1–23 (1973)
Franceschini, N.: Sur le traitement optique de l'information visuelle dans l'œil composé de la drosophile. Thèse 1972 C.N.R.S. (Paris) No. A.O. 3802 (1972a)
Franceschini, N.: Pupil and pseudopupil in the compound eye of Drosophila. In: Information processing in the visual system of arthropods. Ed.: Wehner, R, Berlin-Heidelberg-New York: Springer 1972b
Franceschini, N.: Sampling of the visual environment by the compound eye of the fly: Fundamentals and applications. In: Photoreceptor optics. Eds.: Snyder, A. W., Menzel, R., Berlin-Heidelberg-New York: Springer 1975
Gavel, L. v.: Die “kritische Streifenbreite” als Maß der Sehschärfe bei Drosophila melanoaster. Z. vergl. Physiol. 27, 80–135 (1939)
Geiger, G., Poggio, T.: The orientation of flies towards visual patterns: On the search for the underlying functional interactions. Biol. Cybernetics 19, 39–54 (1975)
Götz, K.G.: Optomotorische Untersuchung des visuellen Systems einiger Augenmutanten der Fruchtfliege Drosophila. Kybernetik 2, 77–92 (1964)
Götz, K. G.: Die optischen Übertragungseigenschaften der Komplexaugen von Drosophila. Kybernetik 2, 215–221 (1965)
Götz, K.G.: Flight control in Drosophila by visual perception of motion. Kybernetik 4, 199–208 (1968)
Götz, K.G.: Movement discrimination in insects. In: S.I.F. Course XLIII. Ed.: Reichardt, W. London, New York: Academic Press 1969
Götz, K.G.: The optomotor equilibrium of the Drosophila navigation system. J. comp. Physiol. 99, 187–210 (1975)
Götz, K.G.: Hirnforschung am Navigationssystem der Fliegen. Naturwissenschaften 62, 468–475 (1975)
Götz, K.G., Wenking, H.: Visual control of locomotion in the walking fruitfly Drosophila. J. comp. Physiol. 85, 235–266 (1973)
Hassenstein, B.: Ommatidienraster und afferente Bewegungsintegration. Z. vergl. Physiol. 33, 301–326 (1951)
Hassenstein, B.: Optokinetische Wirksakeit bewegter periodischer Muster. Z. Naturforsch. 14 b, 659–674 (1959)
Hassenstein, B., Reichardt, W.: Systemtheoretische Analyse der Zeit-, Reihenfolgen- und Vorzeichenauswertung bei der Bewegungsperzeption des Rüsselkäfers Chlorophanus. Z. Naturforsch 11b, 513–524 (1956)
Heisenberg, M.: Comparative behavioural studies of two visual mutants of Drosophila. J. comp. Physio. 80, 119–136 (1972)
Heisenberg, M., Götz, K.G.: The use of mutations for the partial degradation of vision in Drosophila melanogaser. J. comp. Physiol. 98, 217–241 (1975)
Hengsteinberg, R., Götz, K.G.: Der Einfluß des Schirmpigmentgehalts auf die Helligkeits- und Kontrastwahrehmung bei Drosophila-Augenmutanten. Kybernetik 3, 276–285 (1967)
Hille, E., Phillips, R.: Functional analysis and semi-groups. New York: Amer. Math. Soc. 1957
Kien, J.: Neuronal mechanisms subserving directional selectivity in the locust optomotor system. J. comp. Physiol. 102, 337–355 (1975)
Kirschfeld, K.: The visual system of Musca: Studies on optics, structure and function. In: Information processing in the visual system of arthropods. Ed.: Wehner R. Berlin-Heidelberg-New York: Springer 1972
Kirschfeld, K.: Das neurale Superpositionsauge. In: Linduer, M. (Ed.): Fortschr. Zool. 21, 229–257 (1973)
Kirschfeld, K., Lutz, B.: Lateral inhibition in the compound eye of the fly, Musca. Z. Naturforsch. 29c, 95–97 (1974)
Kunze, P.: Untersuchung de Bewegungssehens fixiert fliegender Bienen. Z. vergl. Physiol. 44, 656–684 (1961)
Land, M.F., Collett, T.S.: Chasing behaviour of houseflies (Fannia canicularis). J. comp. Physiol. 89, 331–357 (1974)
Marmarelis, P., McCann, G.D.: Development and application of white-noise modeling techniques for studies of insect visual nervous system. Kybernetik 12, 74–90 (1973)
McCann, G.D., MacGinitie, G.F.: Optomotor response studies of insect vision. Proc. roy. Soc., Ser. B. 163, 369–401 (1965)
McCann, G.D.: Nonlinear identification theory models for successive stages of visual nervous systems of flies. J. Neurophysiol. 37, 869–895 (1974)
Palm, G., Poggio, T.: The “Voltera” representation and the Wiener expansion: validity and pitfalls. In preparation (1976)
Pick, B.: Visual flicker induces orientation behaviour in the fly Musca. Z. Naturforsch. 29c, 310–312 (1974)
Pick, B.: Visual pattern discrimination as an element of the fly's orientation behaviour. Biol. Cybernetics 23, 171–180 (1976)
Poggio, T.: Processing of visual information in flies: from a phenomenological model towards the nervous mechanisms. First Symp. It. Soc. of Biophysics. Vecli, A., Ed., Parma: Tipolito 1974a
Poggio, T.: Stochastic linearization, central limit theorem and linearity in (nervous) “black boxes”. III. Symp. Biophys. S. Marino (1974b)
Poggio, T., Reichardt, W.: Considerations on models of movement detection. Kybernetik 13, 223–227 (1973a)
Poggio, T., Reichardt, W.: A theory of the patern induced flight orientation of the fly Musca domestica. Kybernetik 12, 185–203 (1973b)
Poggio, T., Reichardt, W.: Visual control of orientation behaviour in the fly. Part II: Towards the underlying neural interactions. Quart. Rev. Biophys. (in press) (1976)
Reichardt, W.: Autokorrelations-Auswertung als Funktionsprinzip des Zentralneryensystems Z. Naturforsch. 12b, 448–457 (1957)
Reichardt, W.: Musterinduzierte Flugorientierung. Verhaltensversuche an der Fliege Musca domestica. Naturwissenschaften 60, 122–138 (1973)
Reichardt, W., Varjú, D.: Übertragungseigenschaften im Auswertensystem für das Bewegungssehen. Z. Naturforsch. 14b, 674–689 (1959)
Reichardt, W., Poggio, T.: A theory of the pattern induced flight orientation of the fly Musca domestica II. Biol. Cybernetics 18, 69–80 (1975)
Reichardt, W., Poggio, T.: Visual control of behaviour in the fly. Part I: A quantitative analysis. Quart. Rev. Biophys. (in press) (1976)
Scholes, J.: The electrical responses of the retinal receptors and the lamina in the visual system of the fly Musca. Kybernetik 6, 149–162 (1969)
Shannon, C.E.: Communication in the presence of noise. Proc. IRE 37, 10 (1949)
Thorson, J.: Small signl analysis of a visual reflex in the locust I, II. Kybernetik 3, 41–66 (1966a, b)
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)
Virsik, R., Reichardt, W.: Tracking of moving objects by the fly Musca domestica. Naturwissenschaften 61, 132–133 (1974)
Wehrhahn, C., Reichardt, W.: Visually induced height orientation of the fly Musca domestica. Biol. Cybernetics 20, 37–50 (1975)
Zettler, F., Järvilehto, M.: Lateral inhibition in an insect eye. Z. vergl. Physiol. 76, 233–244 (1972)
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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Buchner, E. Elementary movement detectors in an insect visual system. Biol. Cybernetics 24, 85–101 (1976). https://doi.org/10.1007/BF00360648
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DOI: https://doi.org/10.1007/BF00360648