Abstract

The transient and steady-state responses of movement detectors are studied at various pattern contrasts (i) by intracellularly recording from an identified movement-sensitive interneuron in the fly’s brain and (ii) by comparing these results with computer simulations of an array of movement detectors of the correlation type. At the onset of stimulus motion, the membrane potential oscillates with a frequency corresponding to the temporal frequency of the stimulus pattern before it settles at its steady-state level. Both the transient and the steady-state response amplitudes show a characteristic contrast dependence. As is shown by computer modeling, the transient behavior that we found in the experiments reflects an intrinsic property of the general scheme of movement detectors of the correlation type. To account for the contrast dependence, however, this general scheme has to be elaborated by (i) a subtraction stage, which eliminates the background light intensity from the detector input signal, and (ii) saturation characteristics in both branches of each movement-detector subunit.

© 1989 Optical Society of America

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  2. W. Reichardt, “Evaluation of optical motion information by movement detectors,”J. Comp. Physiol. A 161, 533–547 (1987).
  3. E. Buchner, “Behavioral analysis of spatial vision in insects,” in Photoreception and Vision in Invertebrates, M. A. Ali, ed. (Plenum, New York, 1984), pp. 561–621.
  4. K. Nakayama, “Biological image motion processing: a review,” Vision Res. 25, 625–660 (1985).
  5. E. C. Hildreth, C. Koch, “The analysis of visual motion: from computation theory to neuronal mechanisms,” Annu. Rev. Neurosci. 10, 477–533 (1987).
  6. B. Hassenstein, W. Reichardt, “Systemtheoretische Analyse der Zeit-, Reihenfolgen- und Vorzeichenauswertung bei der Bewegungsperzeption des Rüsselkäfers Chlorophanus,”Z. Naturforsch. 11b, 513–524 (1956).
  7. W. Reichardt, “Autokorrelations–Auswertung als Funktions-prinzip des Zentralnervensystems (bei der optischen Wahrnehmung eines Insektes),”Z. Naturforsch. 12b, 448–457 (1957).
  8. W. Reichardt, D. Varjú, “Ubertragungseigenschaften im Auswertesystem für das Bewegungssehen (Folgerungen aus Experimenten an dem Rüsselkäfer Chlorophanus viridis),” Z. Naturforsch. 14b, 674–689 (1959).
  9. D. Varjú, “Optomotorische Reaktionen auf die Bewegung periodischer Helligkeitsmuster (Anwendung der Systemtheorie auf Experimente am Rüsselkäfer Chlorophanus viridis),”Z. Naturforsch. 14b, 724–735 (1959).
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  12. J. P. H. van Santen, G. Sperling, “Temporal covariance model of human motion perception,” J. Opt. Soc. Am. A 1, 451–473 (1984).
  13. H. R. Wilson, “A model for direction selectivity in threshold motion perception,” Biol. Cybern. 51, 213–222 (1985).
  14. L. B. Baker, O. J. Braddick, “Temporal properties of the short-range process in apparent motion,” Perception 14, 181–192 (1985).
  15. J. P. H. van Santen, G. Sperling, “Elaborated Reichardt detectors,” J. Opt. Soc. Am. A 2, 300–321 (1985).
  16. E. H. Adelson, J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).
  17. A. B. Watson, A. J. Ahumada, “Model of human visual-motion sensing,” J. Opt. Soc. Am. A 2, 322–342 (1985).
  18. J. Thorson, “Dynamics of motion perception in the desert locust,” Science 145, 69–71 (1964).
  19. W. Reichardt, A. Guo, “Elementary pattern discrimination (behavioural experiments with the fly Musca domestica),” Biol. Cybern. 53, 285–306 (1986).
  20. M. Egelhaaf, W. Reichardt, “Dynamic response properties of movement detectors: theoretical analysis and electrophysiological investigation in the visual system of the fly,” Biol. Cybern. 56, 69–87 (1987).
  21. A. Borst, S. Bahde, “What kind of movement detector is triggering the landing response of the housefly?” Biol. Cybern. 55, 59–69 (1986).
  22. W. Reichardt, “Processing of optical information by the visual system of the fly,” Vision Res. 26, 113–126 (1986).
  23. K. Hausen, “The lobula-complex of the fly: structure, function and significance in visual behaviour,” in Photoreception and Vision in Invertebrats, M. A. Ali, ed. (Plenum, New York, 1984), pp. 523–559.
  24. K. Hausen, “Motion sensitive interneurons in the optomotor system of the fly. I. The horizontal cells: structure and signals,” Biol. Cybern. 45, 143–156 (1982).
  25. N. Franceschini, K. Kirschfeld, “Les phénombnès de pseudopupille dans l’oeil composé de Drosophila,” Kybernetik 9, 159–182 (1971).
  26. A. Borst, S. Bahde, Max-Planck-Institut für Biologische Kybernetik, Spemanstrasse 38, D-7400 Tübingen, Federal Republic of Germany (personal communication).
  27. K. Hausen, “Motion sensitive interneurons in the optomotor system of the fly. II. The horizontal cells: receptive field organization and response characteristics,” Biol. Cybern. 46, 67–79 (1982).
  28. R. R. de Ruyter van Steveninck, W. H. Zaagman, H. A. K. Mastebroek, “Adaptation of transient responses of a movement-sensitive neuron in the visual system of the blowfly Calliphora erythrocephala,” Biol. Cybern. 54, 223–236 (1986).
  29. A. Borst, M. Egelhaaf, “Temporal modulation of luminance adapts time constant of fly movement detectors,” Biol. Cybern. 56, 209–215 (1987).
  30. K. Kirschfeld, “The visual system of Musca: studies on optics, structure and function,” in Information Processing in the Visual System of Arthropods, R. Wehner, ed. (Springer-Verlag, Berlin, 1972), pp. 61–74.
  31. K. G. Götz, “Optomotorische Untersuchung des visuellen Systems einiger Augenmutanten der Fruchtfliege Drosophila,” Kybernetik 2, 77–92 (1964).
  32. D. J. Tolhurst, “Separate channels for the analysis of the shape and the movement of a moving visual stimulus,”J. Physiol. 231, 385–402 (1973).
  33. A. Pantle, “Motion aftereffect magnitude as a measure of the spatio-temporal response properties of direction-sensitive analyzer,” Vision Res. 14, 1229–1236 (1974).
  34. H. C. Diener, E. R. Wist, J. Dichgans, T. Brandt, “The spatial frequency effect on perceived velocity,” Vision Res. 16, 169–176 (1976).
  35. D. H. Kelly, “Motion and vision. II. Stabilized spatio-temporal threshold surface,”J. Opt. Soc. Am. 69, 1340–1349 (1979).
  36. D. C. Burr, J. Ross, “Contrast sensitivity at high velocities,” Vision Res. 22, 479–484 (1982).
  37. S. J. Anderson, D. C. Burr, “Spatial and temporal selectivity of the human motion detection system,” Vision Res. 25, 1147–1154 (1985).
  38. M. J. Wright, A. Johnston, “Invariant tuning of motion aftereffect,” Vision Res. 25, 1947–1955 (1985).
  39. T. Maddess, S. B. Laughlin, “Adaptation of the motion-sensitive neuron Hi is generated locally and governed by contrast frequency,” Proc. R. Soc. London Ser. B 225, 251–275 (1985).
  40. H. Eckert, K. Hamdorf, “The contrast frequency-dependence: a criterion for judging the non-participation of neurones in the control of behavioural responses,”J. Comp. Physiol. 145, 241–247 (1981).
  41. T. Maddess, “Adaptive processes affecting the response of the motion sensitive neuron H1,” in Proceedings of the International 1985 Conference on Cybernetics and Society (Institute of Electrical and Electronics Engineers, New York, 1985), pp. 862–866.
  42. T. Maddess, “Afterimage-like effects in the motion-sensitive neuron H1,” Proc. R. Soc. London Ser. B 228, 433–459 (1986).
  43. A. M. Derrington, G. B. Henning, “Errors in direction-of-motion discrimination with complex stimuli,” Vision Res. 27, 61–75 (1987).
  44. C. Enroth-Cugell, J. G. Robson, “The contrast sensitivity of retinal ganglion cells of the cat,”J. Physiol. 187, 517–552 (1966).
  45. S. B. Laughlin, R. C. Hardie, “Common strategies for light adaptation in the peripheral visual systems of fly and dragonfly,”J. Comp. Physiol. 128, 319–340 (1978).
  46. S. B. Laughlin, “Form and function in retinal processing,” Trends Neurosci. 10, 478–483 (1987).
  47. E. Buchner, “Elementary movement detectors in an insect visual system,” Biol. Cybern. 24, 85–101 (1976).
  48. B. P. M. Lenting, H. A. K. Mastebroek, W. H. Zaagman, “Saturation in a wide-field, directionally selective movement detection system in fly vision,” Vision Res. 24, 1342–1347 (1984).
  49. H. Bülthoff, K. G. Götz, “Analogous motion illusion in man and fly,” Nature 278, 636–638 (1979).
  50. K. G. Götz, “Behavioral analysis of the visual system of the fruitfly Drosophila,” in Proceedings of the Symposium on Information Processing in Sight Sensory Systems (California Institute of Technology, Pasadena, Calif., 1965), pp. 85–100.
  51. A. Borst, S. Bahde, “Comparison between the movement detection systems underlying the optomotor and the landing response in the housefly,” Biol. Cybern. 56, 217–224 (1987).
  52. H. Wagner, “Aspects of the free flight behaviour of houseflies (Musca domestica),” in Insect Locomotion, M. Gewecke, G. Wendler, eds. (Paul Parey Verlag, Berlin, 1985), pp. 223–232.
  53. M. Egelhaaf, “Dynamic properties of two control systems underlying visually guided turning in house-flies,”J. Comp. Physiol. A 161, 777–783 (1987).
  54. H. Wagner, “Flight performance and visual control of flight of the free-flying housefly (Musca domestica L.) III. Interactions between angular movement induced by wide- and small-field stimuli,” Philos. Trans. R. Soc. London Ser. B 312, 581–595 (1986).
  55. C. Wehrhahn, T. Poggio, H. Bülthoff, “Tracking and chasing in houseflies (Musca). An analysis of 3-D flight trajectories,” Biol. Cybern. 45, 123–130 (1982).
  56. J. O. Limb, J. A. Murphy, “Estimating the velocity of moving objects in television signals,” Comput. Graphics Image Process. 4, 311–327 (1975).
  57. S. Ullman, “Analysis of visual motion by biological and computer systems,” Computer 14, 57–69 (1981).
  58. V. Torre, T. Poggio, “A synaptic mechanism possibly underlying directional selectivity to motion,” Proc. R. Soc. London Ser. B 202, 409–416 (1978).
  59. N. Grzywacz, C. Koch, “Functional properties of models for direction selectivity in the retina,” Synapse 1, 417–434 (1987).
  60. A. Schmid, H. Bülthoff, “Using neuropharmacology to distinguish between excitatory and inhibitory movement detection mechanisms in the fly Calliphora erythrocephala,” Biol. Cybern. 59, 71–80 (1988).

1988 (1)

A. Schmid, H. Bülthoff, “Using neuropharmacology to distinguish between excitatory and inhibitory movement detection mechanisms in the fly Calliphora erythrocephala,” Biol. Cybern. 59, 71–80 (1988).

1987 (9)

N. Grzywacz, C. Koch, “Functional properties of models for direction selectivity in the retina,” Synapse 1, 417–434 (1987).

A. Borst, S. Bahde, “Comparison between the movement detection systems underlying the optomotor and the landing response in the housefly,” Biol. Cybern. 56, 217–224 (1987).

M. Egelhaaf, “Dynamic properties of two control systems underlying visually guided turning in house-flies,”J. Comp. Physiol. A 161, 777–783 (1987).

A. M. Derrington, G. B. Henning, “Errors in direction-of-motion discrimination with complex stimuli,” Vision Res. 27, 61–75 (1987).

S. B. Laughlin, “Form and function in retinal processing,” Trends Neurosci. 10, 478–483 (1987).

W. Reichardt, “Evaluation of optical motion information by movement detectors,”J. Comp. Physiol. A 161, 533–547 (1987).

E. C. Hildreth, C. Koch, “The analysis of visual motion: from computation theory to neuronal mechanisms,” Annu. Rev. Neurosci. 10, 477–533 (1987).

M. Egelhaaf, W. Reichardt, “Dynamic response properties of movement detectors: theoretical analysis and electrophysiological investigation in the visual system of the fly,” Biol. Cybern. 56, 69–87 (1987).

A. Borst, M. Egelhaaf, “Temporal modulation of luminance adapts time constant of fly movement detectors,” Biol. Cybern. 56, 209–215 (1987).

1986 (6)

R. R. de Ruyter van Steveninck, W. H. Zaagman, H. A. K. Mastebroek, “Adaptation of transient responses of a movement-sensitive neuron in the visual system of the blowfly Calliphora erythrocephala,” Biol. Cybern. 54, 223–236 (1986).

W. Reichardt, A. Guo, “Elementary pattern discrimination (behavioural experiments with the fly Musca domestica),” Biol. Cybern. 53, 285–306 (1986).

A. Borst, S. Bahde, “What kind of movement detector is triggering the landing response of the housefly?” Biol. Cybern. 55, 59–69 (1986).

W. Reichardt, “Processing of optical information by the visual system of the fly,” Vision Res. 26, 113–126 (1986).

T. Maddess, “Afterimage-like effects in the motion-sensitive neuron H1,” Proc. R. Soc. London Ser. B 228, 433–459 (1986).

H. Wagner, “Flight performance and visual control of flight of the free-flying housefly (Musca domestica L.) III. Interactions between angular movement induced by wide- and small-field stimuli,” Philos. Trans. R. Soc. London Ser. B 312, 581–595 (1986).

1985 (9)

H. R. Wilson, “A model for direction selectivity in threshold motion perception,” Biol. Cybern. 51, 213–222 (1985).

L. B. Baker, O. J. Braddick, “Temporal properties of the short-range process in apparent motion,” Perception 14, 181–192 (1985).

J. P. H. van Santen, G. Sperling, “Elaborated Reichardt detectors,” J. Opt. Soc. Am. A 2, 300–321 (1985).

E. H. Adelson, J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).

A. B. Watson, A. J. Ahumada, “Model of human visual-motion sensing,” J. Opt. Soc. Am. A 2, 322–342 (1985).

K. Nakayama, “Biological image motion processing: a review,” Vision Res. 25, 625–660 (1985).

S. J. Anderson, D. C. Burr, “Spatial and temporal selectivity of the human motion detection system,” Vision Res. 25, 1147–1154 (1985).

M. J. Wright, A. Johnston, “Invariant tuning of motion aftereffect,” Vision Res. 25, 1947–1955 (1985).

T. Maddess, S. B. Laughlin, “Adaptation of the motion-sensitive neuron Hi is generated locally and governed by contrast frequency,” Proc. R. Soc. London Ser. B 225, 251–275 (1985).

1984 (2)

J. P. H. van Santen, G. Sperling, “Temporal covariance model of human motion perception,” J. Opt. Soc. Am. A 1, 451–473 (1984).

B. P. M. Lenting, H. A. K. Mastebroek, W. H. Zaagman, “Saturation in a wide-field, directionally selective movement detection system in fly vision,” Vision Res. 24, 1342–1347 (1984).

1982 (6)

C. Wehrhahn, T. Poggio, H. Bülthoff, “Tracking and chasing in houseflies (Musca). An analysis of 3-D flight trajectories,” Biol. Cybern. 45, 123–130 (1982).

K. Hausen, “Motion sensitive interneurons in the optomotor system of the fly. II. The horizontal cells: receptive field organization and response characteristics,” Biol. Cybern. 46, 67–79 (1982).

D. C. Burr, J. Ross, “Contrast sensitivity at high velocities,” Vision Res. 22, 479–484 (1982).

A. J. van Doorn, J. J. Koenderink, “Temporal properties of the visual detectability of moving spatial white noise,” Exp. Brain Res. 45, 179–188 (1982).

A. J. van Doorn, J. J. Koenderink, “Spatial properties of the visual detectability of moving white noise,” Exp. Brain Res. 45, 189–195 (1982).

K. Hausen, “Motion sensitive interneurons in the optomotor system of the fly. I. The horizontal cells: structure and signals,” Biol. Cybern. 45, 143–156 (1982).

1981 (2)

H. Eckert, K. Hamdorf, “The contrast frequency-dependence: a criterion for judging the non-participation of neurones in the control of behavioural responses,”J. Comp. Physiol. 145, 241–247 (1981).

S. Ullman, “Analysis of visual motion by biological and computer systems,” Computer 14, 57–69 (1981).

1979 (2)

H. Bülthoff, K. G. Götz, “Analogous motion illusion in man and fly,” Nature 278, 636–638 (1979).

D. H. Kelly, “Motion and vision. II. Stabilized spatio-temporal threshold surface,”J. Opt. Soc. Am. 69, 1340–1349 (1979).

1978 (2)

S. B. Laughlin, R. C. Hardie, “Common strategies for light adaptation in the peripheral visual systems of fly and dragonfly,”J. Comp. Physiol. 128, 319–340 (1978).

V. Torre, T. Poggio, “A synaptic mechanism possibly underlying directional selectivity to motion,” Proc. R. Soc. London Ser. B 202, 409–416 (1978).

1976 (2)

E. Buchner, “Elementary movement detectors in an insect visual system,” Biol. Cybern. 24, 85–101 (1976).

H. C. Diener, E. R. Wist, J. Dichgans, T. Brandt, “The spatial frequency effect on perceived velocity,” Vision Res. 16, 169–176 (1976).

1975 (1)

J. O. Limb, J. A. Murphy, “Estimating the velocity of moving objects in television signals,” Comput. Graphics Image Process. 4, 311–327 (1975).

1974 (1)

A. Pantle, “Motion aftereffect magnitude as a measure of the spatio-temporal response properties of direction-sensitive analyzer,” Vision Res. 14, 1229–1236 (1974).

1973 (1)

D. J. Tolhurst, “Separate channels for the analysis of the shape and the movement of a moving visual stimulus,”J. Physiol. 231, 385–402 (1973).

1971 (1)

N. Franceschini, K. Kirschfeld, “Les phénombnès de pseudopupille dans l’oeil composé de Drosophila,” Kybernetik 9, 159–182 (1971).

1966 (1)

C. Enroth-Cugell, J. G. Robson, “The contrast sensitivity of retinal ganglion cells of the cat,”J. Physiol. 187, 517–552 (1966).

1964 (2)

J. Thorson, “Dynamics of motion perception in the desert locust,” Science 145, 69–71 (1964).

K. G. Götz, “Optomotorische Untersuchung des visuellen Systems einiger Augenmutanten der Fruchtfliege Drosophila,” Kybernetik 2, 77–92 (1964).

1959 (2)

W. Reichardt, D. Varjú, “Ubertragungseigenschaften im Auswertesystem für das Bewegungssehen (Folgerungen aus Experimenten an dem Rüsselkäfer Chlorophanus viridis),” Z. Naturforsch. 14b, 674–689 (1959).

D. Varjú, “Optomotorische Reaktionen auf die Bewegung periodischer Helligkeitsmuster (Anwendung der Systemtheorie auf Experimente am Rüsselkäfer Chlorophanus viridis),”Z. Naturforsch. 14b, 724–735 (1959).

1957 (1)

W. Reichardt, “Autokorrelations–Auswertung als Funktions-prinzip des Zentralnervensystems (bei der optischen Wahrnehmung eines Insektes),”Z. Naturforsch. 12b, 448–457 (1957).

1956 (1)

B. Hassenstein, W. Reichardt, “Systemtheoretische Analyse der Zeit-, Reihenfolgen- und Vorzeichenauswertung bei der Bewegungsperzeption des Rüsselkäfers Chlorophanus,”Z. Naturforsch. 11b, 513–524 (1956).

Adelson, E. H.

Ahumada, A. J.

Anderson, S. J.

S. J. Anderson, D. C. Burr, “Spatial and temporal selectivity of the human motion detection system,” Vision Res. 25, 1147–1154 (1985).

Bahde, S.

A. Borst, S. Bahde, “Comparison between the movement detection systems underlying the optomotor and the landing response in the housefly,” Biol. Cybern. 56, 217–224 (1987).

A. Borst, S. Bahde, “What kind of movement detector is triggering the landing response of the housefly?” Biol. Cybern. 55, 59–69 (1986).

A. Borst, S. Bahde, Max-Planck-Institut für Biologische Kybernetik, Spemanstrasse 38, D-7400 Tübingen, Federal Republic of Germany (personal communication).

Baker, L. B.

L. B. Baker, O. J. Braddick, “Temporal properties of the short-range process in apparent motion,” Perception 14, 181–192 (1985).

Bergen, J. R.

Borst, A.

A. Borst, S. Bahde, “Comparison between the movement detection systems underlying the optomotor and the landing response in the housefly,” Biol. Cybern. 56, 217–224 (1987).

A. Borst, M. Egelhaaf, “Temporal modulation of luminance adapts time constant of fly movement detectors,” Biol. Cybern. 56, 209–215 (1987).

A. Borst, S. Bahde, “What kind of movement detector is triggering the landing response of the housefly?” Biol. Cybern. 55, 59–69 (1986).

A. Borst, S. Bahde, Max-Planck-Institut für Biologische Kybernetik, Spemanstrasse 38, D-7400 Tübingen, Federal Republic of Germany (personal communication).

Braddick, O. J.

L. B. Baker, O. J. Braddick, “Temporal properties of the short-range process in apparent motion,” Perception 14, 181–192 (1985).

Brandt, T.

H. C. Diener, E. R. Wist, J. Dichgans, T. Brandt, “The spatial frequency effect on perceived velocity,” Vision Res. 16, 169–176 (1976).

Buchner, E.

E. Buchner, “Elementary movement detectors in an insect visual system,” Biol. Cybern. 24, 85–101 (1976).

E. Buchner, “Behavioral analysis of spatial vision in insects,” in Photoreception and Vision in Invertebrates, M. A. Ali, ed. (Plenum, New York, 1984), pp. 561–621.

Bülthoff, H.

A. Schmid, H. Bülthoff, “Using neuropharmacology to distinguish between excitatory and inhibitory movement detection mechanisms in the fly Calliphora erythrocephala,” Biol. Cybern. 59, 71–80 (1988).

C. Wehrhahn, T. Poggio, H. Bülthoff, “Tracking and chasing in houseflies (Musca). An analysis of 3-D flight trajectories,” Biol. Cybern. 45, 123–130 (1982).

H. Bülthoff, K. G. Götz, “Analogous motion illusion in man and fly,” Nature 278, 636–638 (1979).

Burr, D. C.

S. J. Anderson, D. C. Burr, “Spatial and temporal selectivity of the human motion detection system,” Vision Res. 25, 1147–1154 (1985).

D. C. Burr, J. Ross, “Contrast sensitivity at high velocities,” Vision Res. 22, 479–484 (1982).

de Ruyter van Steveninck, R. R.

R. R. de Ruyter van Steveninck, W. H. Zaagman, H. A. K. Mastebroek, “Adaptation of transient responses of a movement-sensitive neuron in the visual system of the blowfly Calliphora erythrocephala,” Biol. Cybern. 54, 223–236 (1986).

Derrington, A. M.

A. M. Derrington, G. B. Henning, “Errors in direction-of-motion discrimination with complex stimuli,” Vision Res. 27, 61–75 (1987).

Dichgans, J.

H. C. Diener, E. R. Wist, J. Dichgans, T. Brandt, “The spatial frequency effect on perceived velocity,” Vision Res. 16, 169–176 (1976).

Diener, H. C.

H. C. Diener, E. R. Wist, J. Dichgans, T. Brandt, “The spatial frequency effect on perceived velocity,” Vision Res. 16, 169–176 (1976).

Eckert, H.

H. Eckert, K. Hamdorf, “The contrast frequency-dependence: a criterion for judging the non-participation of neurones in the control of behavioural responses,”J. Comp. Physiol. 145, 241–247 (1981).

Egelhaaf, M.

A. Borst, M. Egelhaaf, “Temporal modulation of luminance adapts time constant of fly movement detectors,” Biol. Cybern. 56, 209–215 (1987).

M. Egelhaaf, W. Reichardt, “Dynamic response properties of movement detectors: theoretical analysis and electrophysiological investigation in the visual system of the fly,” Biol. Cybern. 56, 69–87 (1987).

M. Egelhaaf, “Dynamic properties of two control systems underlying visually guided turning in house-flies,”J. Comp. Physiol. A 161, 777–783 (1987).

Enroth-Cugell, C.

C. Enroth-Cugell, J. G. Robson, “The contrast sensitivity of retinal ganglion cells of the cat,”J. Physiol. 187, 517–552 (1966).

Franceschini, N.

N. Franceschini, K. Kirschfeld, “Les phénombnès de pseudopupille dans l’oeil composé de Drosophila,” Kybernetik 9, 159–182 (1971).

Götz, K. G.

H. Bülthoff, K. G. Götz, “Analogous motion illusion in man and fly,” Nature 278, 636–638 (1979).

K. G. Götz, “Optomotorische Untersuchung des visuellen Systems einiger Augenmutanten der Fruchtfliege Drosophila,” Kybernetik 2, 77–92 (1964).

K. G. Götz, “Behavioral analysis of the visual system of the fruitfly Drosophila,” in Proceedings of the Symposium on Information Processing in Sight Sensory Systems (California Institute of Technology, Pasadena, Calif., 1965), pp. 85–100.

Grzywacz, N.

N. Grzywacz, C. Koch, “Functional properties of models for direction selectivity in the retina,” Synapse 1, 417–434 (1987).

Guo, A.

W. Reichardt, A. Guo, “Elementary pattern discrimination (behavioural experiments with the fly Musca domestica),” Biol. Cybern. 53, 285–306 (1986).

Hamdorf, K.

H. Eckert, K. Hamdorf, “The contrast frequency-dependence: a criterion for judging the non-participation of neurones in the control of behavioural responses,”J. Comp. Physiol. 145, 241–247 (1981).

Hardie, R. C.

S. B. Laughlin, R. C. Hardie, “Common strategies for light adaptation in the peripheral visual systems of fly and dragonfly,”J. Comp. Physiol. 128, 319–340 (1978).

Hassenstein, B.

B. Hassenstein, W. Reichardt, “Systemtheoretische Analyse der Zeit-, Reihenfolgen- und Vorzeichenauswertung bei der Bewegungsperzeption des Rüsselkäfers Chlorophanus,”Z. Naturforsch. 11b, 513–524 (1956).

Hausen, K.

K. Hausen, “Motion sensitive interneurons in the optomotor system of the fly. I. The horizontal cells: structure and signals,” Biol. Cybern. 45, 143–156 (1982).

K. Hausen, “Motion sensitive interneurons in the optomotor system of the fly. II. The horizontal cells: receptive field organization and response characteristics,” Biol. Cybern. 46, 67–79 (1982).

K. Hausen, “The lobula-complex of the fly: structure, function and significance in visual behaviour,” in Photoreception and Vision in Invertebrats, M. A. Ali, ed. (Plenum, New York, 1984), pp. 523–559.

Henning, G. B.

A. M. Derrington, G. B. Henning, “Errors in direction-of-motion discrimination with complex stimuli,” Vision Res. 27, 61–75 (1987).

Hildreth, E. C.

E. C. Hildreth, C. Koch, “The analysis of visual motion: from computation theory to neuronal mechanisms,” Annu. Rev. Neurosci. 10, 477–533 (1987).

Johnston, A.

M. J. Wright, A. Johnston, “Invariant tuning of motion aftereffect,” Vision Res. 25, 1947–1955 (1985).

Kelly, D. H.

Kirschfeld, K.

N. Franceschini, K. Kirschfeld, “Les phénombnès de pseudopupille dans l’oeil composé de Drosophila,” Kybernetik 9, 159–182 (1971).

K. Kirschfeld, “The visual system of Musca: studies on optics, structure and function,” in Information Processing in the Visual System of Arthropods, R. Wehner, ed. (Springer-Verlag, Berlin, 1972), pp. 61–74.

Koch, C.

E. C. Hildreth, C. Koch, “The analysis of visual motion: from computation theory to neuronal mechanisms,” Annu. Rev. Neurosci. 10, 477–533 (1987).

N. Grzywacz, C. Koch, “Functional properties of models for direction selectivity in the retina,” Synapse 1, 417–434 (1987).

Koenderink, J. J.

A. J. van Doorn, J. J. Koenderink, “Temporal properties of the visual detectability of moving spatial white noise,” Exp. Brain Res. 45, 179–188 (1982).

A. J. van Doorn, J. J. Koenderink, “Spatial properties of the visual detectability of moving white noise,” Exp. Brain Res. 45, 189–195 (1982).

Laughlin, S. B.

S. B. Laughlin, “Form and function in retinal processing,” Trends Neurosci. 10, 478–483 (1987).

T. Maddess, S. B. Laughlin, “Adaptation of the motion-sensitive neuron Hi is generated locally and governed by contrast frequency,” Proc. R. Soc. London Ser. B 225, 251–275 (1985).

S. B. Laughlin, R. C. Hardie, “Common strategies for light adaptation in the peripheral visual systems of fly and dragonfly,”J. Comp. Physiol. 128, 319–340 (1978).

Lenting, B. P. M.

B. P. M. Lenting, H. A. K. Mastebroek, W. H. Zaagman, “Saturation in a wide-field, directionally selective movement detection system in fly vision,” Vision Res. 24, 1342–1347 (1984).

Limb, J. O.

J. O. Limb, J. A. Murphy, “Estimating the velocity of moving objects in television signals,” Comput. Graphics Image Process. 4, 311–327 (1975).

Maddess, T.

T. Maddess, “Afterimage-like effects in the motion-sensitive neuron H1,” Proc. R. Soc. London Ser. B 228, 433–459 (1986).

T. Maddess, S. B. Laughlin, “Adaptation of the motion-sensitive neuron Hi is generated locally and governed by contrast frequency,” Proc. R. Soc. London Ser. B 225, 251–275 (1985).

T. Maddess, “Adaptive processes affecting the response of the motion sensitive neuron H1,” in Proceedings of the International 1985 Conference on Cybernetics and Society (Institute of Electrical and Electronics Engineers, New York, 1985), pp. 862–866.

Mastebroek, H. A. K.

R. R. de Ruyter van Steveninck, W. H. Zaagman, H. A. K. Mastebroek, “Adaptation of transient responses of a movement-sensitive neuron in the visual system of the blowfly Calliphora erythrocephala,” Biol. Cybern. 54, 223–236 (1986).

B. P. M. Lenting, H. A. K. Mastebroek, W. H. Zaagman, “Saturation in a wide-field, directionally selective movement detection system in fly vision,” Vision Res. 24, 1342–1347 (1984).

Murphy, J. A.

J. O. Limb, J. A. Murphy, “Estimating the velocity of moving objects in television signals,” Comput. Graphics Image Process. 4, 311–327 (1975).

Nakayama, K.

K. Nakayama, “Biological image motion processing: a review,” Vision Res. 25, 625–660 (1985).

Pantle, A.

A. Pantle, “Motion aftereffect magnitude as a measure of the spatio-temporal response properties of direction-sensitive analyzer,” Vision Res. 14, 1229–1236 (1974).

Poggio, T.

C. Wehrhahn, T. Poggio, H. Bülthoff, “Tracking and chasing in houseflies (Musca). An analysis of 3-D flight trajectories,” Biol. Cybern. 45, 123–130 (1982).

V. Torre, T. Poggio, “A synaptic mechanism possibly underlying directional selectivity to motion,” Proc. R. Soc. London Ser. B 202, 409–416 (1978).

Reichardt, W.

W. Reichardt, “Evaluation of optical motion information by movement detectors,”J. Comp. Physiol. A 161, 533–547 (1987).

M. Egelhaaf, W. Reichardt, “Dynamic response properties of movement detectors: theoretical analysis and electrophysiological investigation in the visual system of the fly,” Biol. Cybern. 56, 69–87 (1987).

W. Reichardt, A. Guo, “Elementary pattern discrimination (behavioural experiments with the fly Musca domestica),” Biol. Cybern. 53, 285–306 (1986).

W. Reichardt, “Processing of optical information by the visual system of the fly,” Vision Res. 26, 113–126 (1986).

W. Reichardt, D. Varjú, “Ubertragungseigenschaften im Auswertesystem für das Bewegungssehen (Folgerungen aus Experimenten an dem Rüsselkäfer Chlorophanus viridis),” Z. Naturforsch. 14b, 674–689 (1959).

W. Reichardt, “Autokorrelations–Auswertung als Funktions-prinzip des Zentralnervensystems (bei der optischen Wahrnehmung eines Insektes),”Z. Naturforsch. 12b, 448–457 (1957).

B. Hassenstein, W. Reichardt, “Systemtheoretische Analyse der Zeit-, Reihenfolgen- und Vorzeichenauswertung bei der Bewegungsperzeption des Rüsselkäfers Chlorophanus,”Z. Naturforsch. 11b, 513–524 (1956).

W. Reichardt, “Autocorrelation, a principle for evaluation of sensory information by the central nervous system,” in Principles of Sensory Communication, W. A. Rosenblith, ed. (Wiley, New York, 1961), pp. 303–317.

Robson, J. G.

C. Enroth-Cugell, J. G. Robson, “The contrast sensitivity of retinal ganglion cells of the cat,”J. Physiol. 187, 517–552 (1966).

Ross, J.

D. C. Burr, J. Ross, “Contrast sensitivity at high velocities,” Vision Res. 22, 479–484 (1982).

Schmid, A.

A. Schmid, H. Bülthoff, “Using neuropharmacology to distinguish between excitatory and inhibitory movement detection mechanisms in the fly Calliphora erythrocephala,” Biol. Cybern. 59, 71–80 (1988).

Sperling, G.

Thorson, J.

J. Thorson, “Dynamics of motion perception in the desert locust,” Science 145, 69–71 (1964).

Tolhurst, D. J.

D. J. Tolhurst, “Separate channels for the analysis of the shape and the movement of a moving visual stimulus,”J. Physiol. 231, 385–402 (1973).

Torre, V.

V. Torre, T. Poggio, “A synaptic mechanism possibly underlying directional selectivity to motion,” Proc. R. Soc. London Ser. B 202, 409–416 (1978).

Ullman, S.

S. Ullman, “Analysis of visual motion by biological and computer systems,” Computer 14, 57–69 (1981).

van Doorn, A. J.

A. J. van Doorn, J. J. Koenderink, “Spatial properties of the visual detectability of moving white noise,” Exp. Brain Res. 45, 189–195 (1982).

A. J. van Doorn, J. J. Koenderink, “Temporal properties of the visual detectability of moving spatial white noise,” Exp. Brain Res. 45, 179–188 (1982).

van Santen, J. P. H.

Varjú, D.

W. Reichardt, D. Varjú, “Ubertragungseigenschaften im Auswertesystem für das Bewegungssehen (Folgerungen aus Experimenten an dem Rüsselkäfer Chlorophanus viridis),” Z. Naturforsch. 14b, 674–689 (1959).

D. Varjú, “Optomotorische Reaktionen auf die Bewegung periodischer Helligkeitsmuster (Anwendung der Systemtheorie auf Experimente am Rüsselkäfer Chlorophanus viridis),”Z. Naturforsch. 14b, 724–735 (1959).

Wagner, H.

H. Wagner, “Flight performance and visual control of flight of the free-flying housefly (Musca domestica L.) III. Interactions between angular movement induced by wide- and small-field stimuli,” Philos. Trans. R. Soc. London Ser. B 312, 581–595 (1986).

H. Wagner, “Aspects of the free flight behaviour of houseflies (Musca domestica),” in Insect Locomotion, M. Gewecke, G. Wendler, eds. (Paul Parey Verlag, Berlin, 1985), pp. 223–232.

Watson, A. B.

Wehrhahn, C.

C. Wehrhahn, T. Poggio, H. Bülthoff, “Tracking and chasing in houseflies (Musca). An analysis of 3-D flight trajectories,” Biol. Cybern. 45, 123–130 (1982).

Wilson, H. R.

H. R. Wilson, “A model for direction selectivity in threshold motion perception,” Biol. Cybern. 51, 213–222 (1985).

Wist, E. R.

H. C. Diener, E. R. Wist, J. Dichgans, T. Brandt, “The spatial frequency effect on perceived velocity,” Vision Res. 16, 169–176 (1976).

Wright, M. J.

M. J. Wright, A. Johnston, “Invariant tuning of motion aftereffect,” Vision Res. 25, 1947–1955 (1985).

Zaagman, W. H.

R. R. de Ruyter van Steveninck, W. H. Zaagman, H. A. K. Mastebroek, “Adaptation of transient responses of a movement-sensitive neuron in the visual system of the blowfly Calliphora erythrocephala,” Biol. Cybern. 54, 223–236 (1986).

B. P. M. Lenting, H. A. K. Mastebroek, W. H. Zaagman, “Saturation in a wide-field, directionally selective movement detection system in fly vision,” Vision Res. 24, 1342–1347 (1984).

Annu. Rev. Neurosci. (1)

E. C. Hildreth, C. Koch, “The analysis of visual motion: from computation theory to neuronal mechanisms,” Annu. Rev. Neurosci. 10, 477–533 (1987).

Biol. Cybern. (12)

H. R. Wilson, “A model for direction selectivity in threshold motion perception,” Biol. Cybern. 51, 213–222 (1985).

W. Reichardt, A. Guo, “Elementary pattern discrimination (behavioural experiments with the fly Musca domestica),” Biol. Cybern. 53, 285–306 (1986).

M. Egelhaaf, W. Reichardt, “Dynamic response properties of movement detectors: theoretical analysis and electrophysiological investigation in the visual system of the fly,” Biol. Cybern. 56, 69–87 (1987).

A. Borst, S. Bahde, “What kind of movement detector is triggering the landing response of the housefly?” Biol. Cybern. 55, 59–69 (1986).

K. Hausen, “Motion sensitive interneurons in the optomotor system of the fly. II. The horizontal cells: receptive field organization and response characteristics,” Biol. Cybern. 46, 67–79 (1982).

R. R. de Ruyter van Steveninck, W. H. Zaagman, H. A. K. Mastebroek, “Adaptation of transient responses of a movement-sensitive neuron in the visual system of the blowfly Calliphora erythrocephala,” Biol. Cybern. 54, 223–236 (1986).

A. Borst, M. Egelhaaf, “Temporal modulation of luminance adapts time constant of fly movement detectors,” Biol. Cybern. 56, 209–215 (1987).

K. Hausen, “Motion sensitive interneurons in the optomotor system of the fly. I. The horizontal cells: structure and signals,” Biol. Cybern. 45, 143–156 (1982).

E. Buchner, “Elementary movement detectors in an insect visual system,” Biol. Cybern. 24, 85–101 (1976).

A. Borst, S. Bahde, “Comparison between the movement detection systems underlying the optomotor and the landing response in the housefly,” Biol. Cybern. 56, 217–224 (1987).

C. Wehrhahn, T. Poggio, H. Bülthoff, “Tracking and chasing in houseflies (Musca). An analysis of 3-D flight trajectories,” Biol. Cybern. 45, 123–130 (1982).

A. Schmid, H. Bülthoff, “Using neuropharmacology to distinguish between excitatory and inhibitory movement detection mechanisms in the fly Calliphora erythrocephala,” Biol. Cybern. 59, 71–80 (1988).

Comput. Graphics Image Process. (1)

J. O. Limb, J. A. Murphy, “Estimating the velocity of moving objects in television signals,” Comput. Graphics Image Process. 4, 311–327 (1975).

Computer (1)

S. Ullman, “Analysis of visual motion by biological and computer systems,” Computer 14, 57–69 (1981).

Exp. Brain Res. (2)

A. J. van Doorn, J. J. Koenderink, “Temporal properties of the visual detectability of moving spatial white noise,” Exp. Brain Res. 45, 179–188 (1982).

A. J. van Doorn, J. J. Koenderink, “Spatial properties of the visual detectability of moving white noise,” Exp. Brain Res. 45, 189–195 (1982).

J. Comp. Physiol. (2)

H. Eckert, K. Hamdorf, “The contrast frequency-dependence: a criterion for judging the non-participation of neurones in the control of behavioural responses,”J. Comp. Physiol. 145, 241–247 (1981).

S. B. Laughlin, R. C. Hardie, “Common strategies for light adaptation in the peripheral visual systems of fly and dragonfly,”J. Comp. Physiol. 128, 319–340 (1978).

J. Comp. Physiol. A (2)

M. Egelhaaf, “Dynamic properties of two control systems underlying visually guided turning in house-flies,”J. Comp. Physiol. A 161, 777–783 (1987).

W. Reichardt, “Evaluation of optical motion information by movement detectors,”J. Comp. Physiol. A 161, 533–547 (1987).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

J. Physiol. (2)

D. J. Tolhurst, “Separate channels for the analysis of the shape and the movement of a moving visual stimulus,”J. Physiol. 231, 385–402 (1973).

C. Enroth-Cugell, J. G. Robson, “The contrast sensitivity of retinal ganglion cells of the cat,”J. Physiol. 187, 517–552 (1966).

Kybernetik (2)

K. G. Götz, “Optomotorische Untersuchung des visuellen Systems einiger Augenmutanten der Fruchtfliege Drosophila,” Kybernetik 2, 77–92 (1964).

N. Franceschini, K. Kirschfeld, “Les phénombnès de pseudopupille dans l’oeil composé de Drosophila,” Kybernetik 9, 159–182 (1971).

Nature (1)

H. Bülthoff, K. G. Götz, “Analogous motion illusion in man and fly,” Nature 278, 636–638 (1979).

Perception (1)

L. B. Baker, O. J. Braddick, “Temporal properties of the short-range process in apparent motion,” Perception 14, 181–192 (1985).

Philos. Trans. R. Soc. London Ser. B (1)

H. Wagner, “Flight performance and visual control of flight of the free-flying housefly (Musca domestica L.) III. Interactions between angular movement induced by wide- and small-field stimuli,” Philos. Trans. R. Soc. London Ser. B 312, 581–595 (1986).

Proc. R. Soc. London Ser. B (3)

T. Maddess, S. B. Laughlin, “Adaptation of the motion-sensitive neuron Hi is generated locally and governed by contrast frequency,” Proc. R. Soc. London Ser. B 225, 251–275 (1985).

T. Maddess, “Afterimage-like effects in the motion-sensitive neuron H1,” Proc. R. Soc. London Ser. B 228, 433–459 (1986).

V. Torre, T. Poggio, “A synaptic mechanism possibly underlying directional selectivity to motion,” Proc. R. Soc. London Ser. B 202, 409–416 (1978).

Science (1)

J. Thorson, “Dynamics of motion perception in the desert locust,” Science 145, 69–71 (1964).

Synapse (1)

N. Grzywacz, C. Koch, “Functional properties of models for direction selectivity in the retina,” Synapse 1, 417–434 (1987).

Trends Neurosci. (1)

S. B. Laughlin, “Form and function in retinal processing,” Trends Neurosci. 10, 478–483 (1987).

Vision Res. (9)

A. M. Derrington, G. B. Henning, “Errors in direction-of-motion discrimination with complex stimuli,” Vision Res. 27, 61–75 (1987).

B. P. M. Lenting, H. A. K. Mastebroek, W. H. Zaagman, “Saturation in a wide-field, directionally selective movement detection system in fly vision,” Vision Res. 24, 1342–1347 (1984).

K. Nakayama, “Biological image motion processing: a review,” Vision Res. 25, 625–660 (1985).

A. Pantle, “Motion aftereffect magnitude as a measure of the spatio-temporal response properties of direction-sensitive analyzer,” Vision Res. 14, 1229–1236 (1974).

H. C. Diener, E. R. Wist, J. Dichgans, T. Brandt, “The spatial frequency effect on perceived velocity,” Vision Res. 16, 169–176 (1976).

D. C. Burr, J. Ross, “Contrast sensitivity at high velocities,” Vision Res. 22, 479–484 (1982).

S. J. Anderson, D. C. Burr, “Spatial and temporal selectivity of the human motion detection system,” Vision Res. 25, 1147–1154 (1985).

M. J. Wright, A. Johnston, “Invariant tuning of motion aftereffect,” Vision Res. 25, 1947–1955 (1985).

W. Reichardt, “Processing of optical information by the visual system of the fly,” Vision Res. 26, 113–126 (1986).

Z. Naturforsch. (4)

B. Hassenstein, W. Reichardt, “Systemtheoretische Analyse der Zeit-, Reihenfolgen- und Vorzeichenauswertung bei der Bewegungsperzeption des Rüsselkäfers Chlorophanus,”Z. Naturforsch. 11b, 513–524 (1956).

W. Reichardt, “Autokorrelations–Auswertung als Funktions-prinzip des Zentralnervensystems (bei der optischen Wahrnehmung eines Insektes),”Z. Naturforsch. 12b, 448–457 (1957).

W. Reichardt, D. Varjú, “Ubertragungseigenschaften im Auswertesystem für das Bewegungssehen (Folgerungen aus Experimenten an dem Rüsselkäfer Chlorophanus viridis),” Z. Naturforsch. 14b, 674–689 (1959).

D. Varjú, “Optomotorische Reaktionen auf die Bewegung periodischer Helligkeitsmuster (Anwendung der Systemtheorie auf Experimente am Rüsselkäfer Chlorophanus viridis),”Z. Naturforsch. 14b, 724–735 (1959).

Other (8)

W. Reichardt, “Autocorrelation, a principle for evaluation of sensory information by the central nervous system,” in Principles of Sensory Communication, W. A. Rosenblith, ed. (Wiley, New York, 1961), pp. 303–317.

E. Buchner, “Behavioral analysis of spatial vision in insects,” in Photoreception and Vision in Invertebrates, M. A. Ali, ed. (Plenum, New York, 1984), pp. 561–621.

K. Hausen, “The lobula-complex of the fly: structure, function and significance in visual behaviour,” in Photoreception and Vision in Invertebrats, M. A. Ali, ed. (Plenum, New York, 1984), pp. 523–559.

K. Kirschfeld, “The visual system of Musca: studies on optics, structure and function,” in Information Processing in the Visual System of Arthropods, R. Wehner, ed. (Springer-Verlag, Berlin, 1972), pp. 61–74.

A. Borst, S. Bahde, Max-Planck-Institut für Biologische Kybernetik, Spemanstrasse 38, D-7400 Tübingen, Federal Republic of Germany (personal communication).

K. G. Götz, “Behavioral analysis of the visual system of the fruitfly Drosophila,” in Proceedings of the Symposium on Information Processing in Sight Sensory Systems (California Institute of Technology, Pasadena, Calif., 1965), pp. 85–100.

H. Wagner, “Aspects of the free flight behaviour of houseflies (Musca domestica),” in Insect Locomotion, M. Gewecke, G. Wendler, eds. (Paul Parey Verlag, Berlin, 1985), pp. 223–232.

T. Maddess, “Adaptive processes affecting the response of the motion sensitive neuron H1,” in Proceedings of the International 1985 Conference on Cybernetics and Society (Institute of Electrical and Electronics Engineers, New York, 1985), pp. 862–866.

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the fly’s visual system. Photoreceptors are located in the retina in separate ommatidia. They project retinotopically through several ganglia (lamina, medulla) into the lobula complex, which is subdivided into the anterior lobula and the posterior lobula plate. In the lobula plate, local movement information is spatially integrated in some way by giant tangential cells. One of these cells (the HS cell) was used in the present study to monitor the response of the movement-detection system. Note that the specific structure of different cell types shown here, including the connectivity at different stages, is arbitrary.

Fig. 2
Fig. 2

General scheme of a movement detector of the correlation type. The input signals A and B are transmitted linearly by the receptors. Then they pass through linear filters F1 and F2. In the next step the filtered signals A1 and B2 are multiplied together. This procedure is repeated in the mirror-symmetrical subunit of the detector with the signals A2 and B1. The products A1B2 and A2B1 are subtracted from each other. In this way one results in a directionally selective movement detector that responds to leftward and rightward motion with the same strength but with the opposite sign. A retinotopic array of such movement detectors (schematically drawn) is shown below. Spatial integration is achieved by simply summing (∑) the output signals of all movement detectors. Both the steady-state and the transient responses of an array of detectors are calculated in Appendixes A and B for periodic input functions.

Fig. 3
Fig. 3

Intracellular responses of the HS cell to sine-wave gratings (contrast, 0.1) moving back to front at different temporal frequencies, as indicated in the figure. Note that initially the cell’s membrane potential is modulated with the pattern’s temporal frequency before reaching a steady-state level. The data are averaged from two flies, each stimulated 20 times with the entire stimulation program of all five temporal frequencies.

Fig. 4
Fig. 4

Computer simulation of the responses of an array of movement detectors stimulated by equivalent inputs as in the experiment shown in Fig. 3. The detector signal can be seen to oscillate with the pattern’s temporal frequency (given here in units of the filter time constant). Note the close similarity between the computer simulations and the experimental data of Fig. 3.

Fig. 5
Fig. 5

Average response amplitudes of the HS cell to sine-wave gratings of different contrast moving back to front at two different temporal frequencies (1 and 10 Hz). Schematic time-dependent response traces are shown as insets to illustrate how peak and steady-state responses were determined. The average peak and steady-state response amplitudes are shown as functions of the pattern contrast. The bars indicate the standard error of the mean. The data are averages from 9 flies and 36 repetitive presentations of the entire stimulus program. There is a difference in the contrast dependence of both peak response curves, of peak and steady-state responses to the same frequency, and of both steady-state response curves. Note the different ordinate scales used in the two diagrams.

Fig. 6
Fig. 6

Consequences of a saturation characteristic for contrast coding of a movement detector. A sinusoidal input signal (shown below the input–output characteristic) passes an element that saturates for both increments and decrements of its response. The resulting output signals are shown at the left of the input–output characteristic. a, If the signal is proportional to the light intensity received by the eye, it can be modulated only between twice its mean amplitude and the zero level. This range is indicated by the double-headed arrow above the saturation characteristic. As can be seen by comparing the input and the output modulations, the signal does not saturate at all under these conditions. Consequently the resulting movement-detector response (see inset) will increase steeply with increasing modulation amplitude of the input signal. b, If the mean luminance is removed in some way, the input signal is zero symmetrical and, thus, modulated about the steep-slope part of the input–output characteristic. In this case small modulation amplitudes will be transmitted with a high gain, whereas larger ones will approach a saturation level. Accordingly, the movement-detector response shown in the inset also saturates for larger modulation

Fig. 7
Fig. 7

Elaborated version of the model proposed to underlie the evaluation of movement in flies. The general scheme of a movement detector of the correlation type (see Fig. 2) is modified in three ways: (i) the mean luminance is subtracted from the input signals; (ii) saturation characteristics are inserted into both branches of the two movement-detector subunits, (iii) the filter F2 of the general movement-detector scheme shown in Fig. 2 is omitted. The filter F1 is specified here as low-pass filter L.

Fig. 8
Fig. 8

Contrast dependence of a one-dimensional array of movement detectors as elaborated in Fig. 7. Filter L, a first-order low-pass filter, was chosen. The peak and steady-state responses to the outset of motion were evaluated for two different temporal frequencies as the corresponding experimental data of Fig. 5. The temporal frequency of the stimulus is given in units of the time constant of the movement-detector filter. The computer simulations of the model account for the qualitative features of the corresponding experimentally determined responses (compare with Fig. 5).

Tables (1)

Tables Icon

Table 1 Definitions of All Parameters

Equations (9)

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A = I + Δ I sin ( ω t + φ ) , B = I + Δ I sin [ ω ( t - Δ t ) + φ ] .
B = I + Δ I sin [ ω t + φ - 2 π Δ φ / λ ] .
A 1 ( t ) = F 1 ( 0 ) I + F 1 ( ω ) Δ I sin [ ω t + φ + ϕ 1 ( ω ) ] , A 2 ( t ) = F 2 ( 0 ) I + F 2 ( ω ) Δ I sin [ ω t + φ + ϕ 2 ( ω ) ] , B 1 ( t ) = F 1 ( 0 ) I + F 1 ( ω ) Δ I sin [ ω t + φ + ϕ 1 ( ω ) - 2 π Δ φ / λ ] , B 2 ( t ) = F 2 ( 0 ) I + F 2 ( ω ) Δ I sin [ ω t + φ + ϕ 2 ( ω ) - 2 π Δ φ / λ ] .
R = F 1 ( ω ) F 2 ( ω ) Δ I 2 sin [ ϕ 1 ( ω ) - ϕ 2 ( ω ) ] sin ( 2 π Δ φ / λ ) .
F 1 ( ω ) = 1 ( 1 + τ 2 ω 2 ) 1 / 2 ,             ϕ 1 ( ω ) = - arctan ( τ ω ) .
R = Δ I 2 sin ( 2 π Δ φ λ ) τ ω 1 + τ 2 ω 2 .
A = { I + Δ I sin ( φ ) for t < 0 I + Δ I sin ( ω t + φ ) for t 0 , B = { I + Δ I sin ( φ - 2 π Δ φ λ ) for t < 0 I + Δ I sin ( ω t + φ - 2 π Δ φ λ ) for t 0 .
A 1 = I + Δ I cos ( φ ) τ 1 + τ 2 ω 2 × [ 1 τ sin ( ω t ) - ω cos ( ω t ) + ω exp ( - t τ ) ] + Δ I sin ( φ ) τ 1 + τ 2 ω 2 × [ 1 τ cos ( ω t ) - ω sin ( ω t ) - 1 τ exp ( - t τ ) ] , B 1 = I + Δ I cos ( φ - 2 π Δ φ λ ) τ 1 + τ 2 ω 2 × [ 1 τ sin ( ω t ) - ω cos ( ω t ) + ω exp ( - t τ ) ] + Δ I sin ( φ - 2 π Δ φ λ ) τ 1 + τ 2 ω 2 × [ 1 τ cos ( ω t ) - ω sin ( ω t ) - 1 τ exp ( - t τ ) ] .
R ( t ) = Δ I 2 sin ( 2 π Δ φ λ ) τ ω 1 + τ 2 ω 2 - Δ I 2 sin ( 2 π Δ φ λ ) 1 ( 1 + τ 2 ω 2 ) 1 / 2 × sin [ ω t + arctan ( τ ω ) ] exp ( - t τ ) .

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