Abstract

Although a great deal of experimental evidence supports the notion of a Reichardt correlator as a mechanism for biological motion detection, the correlator does not signal true image velocity. This study examines the accuracy with which realistic Reichardt correlators can provide velocity estimates in an organism’s natural visual environment. The predictable statistics of natural images imply a consistent correspondence between mean correlator response and velocity, allowing the otherwise ambiguous Reichardt correlator to act as a practical velocity estimator. Analysis and simulations suggest that processes commonly found in visual systems, such as prefiltering, response compression, integration, and adaptation, improve the reliability of velocity estimation and expand the range of velocities coded. Experimental recordings confirm our predictions of correlator response to broadband images.

© 2001 Optical Society of America

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    [PubMed]
  36. G. Nalbach, R. Hengstenberg, “The halteres of the blowfly Calliphora,” J. Comp. Physiol. A 175, 695–708 (1994).
    [CrossRef]
  37. S. Single, A. Borst, “Dendritic integration and its role in computing image velocity,” Science 281, 1848–1850 (1998).
    [CrossRef] [PubMed]
  38. K. Hausen, M. Egelhaaf, “Neural mechanisms of visualcourse control in insects,” in Facets of Vision, D. G. Stavenga, R. C. Hardie, eds. (Springer-Verlag, Heidelberg, 1989), pp. 391–424.
  39. 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).
    [CrossRef]
  40. D. W. Dong, J. J. Atick, “Statistics of natural time-varying images,” Network Comput. Neural Syst. 6, 345–358 (1995).
    [CrossRef]
  41. N. Franceschini, J. M. Pichon, C. Blanes, “From insect vision to robot vision,” Philos. Trans. R. Soc. London Ser. B 337, 283–294 (1992).
    [CrossRef]
  42. R. Sarpeshkar, W. Bair, C. Koch, “An analog VLSI chip for local velocity estimation based on Reichardt’s motion algorithm,” in Advances in Neural Information Processing Systems, S. Hanson, J. Cowan, L. Giles, eds. (Morgan Kauffman, San Mateo, Calif., 1993), Vol. 5, pp. 781–788.
  43. R. O. Dror, D. C. O’Carroll, S. B. Laughlin, “The role of natural image statistics in biological motion estimation,” Springer Lect. Notes Comput. Sci. 1811, 492–501 (2000).
    [CrossRef]
  44. M. F. Land, H. M. Eckert, “Maps of the acute zones of fly eyes,” J. Comp. Physiol. A 156, 525–538 (1985).
    [CrossRef]

2000 (2)

R. O. Dror, D. C. O’Carroll, S. B. Laughlin, “The role of natural image statistics in biological motion estimation,” Springer Lect. Notes Comput. Sci. 1811, 492–501 (2000).
[CrossRef]

B. Tatler, D. C. O’Carroll, S. B. Laughlin, “Temperature and temporal resolving power of fly photoreceptors,” J. Comp. Physiol. A 186, 399–407 (2000).
[CrossRef] [PubMed]

1999 (1)

R. A. Harris, D. C. O’Carroll, S. B. Laughlin, “Adaptation and the temporal delay filter of fly motion detectors,” Vision Res. 39, 2603–2613 (1999).
[CrossRef] [PubMed]

1998 (1)

S. Single, A. Borst, “Dendritic integration and its role in computing image velocity,” Science 281, 1848–1850 (1998).
[CrossRef] [PubMed]

1997 (3)

D. C. O’Carroll, S. B. Laughlin, N. J. Bidwell, R. A. Harris, “Spatio-temporal properties of motion detectors matched to low image velocities in hovering insects,” Vision Res. 37, 3427–3439 (1997).
[CrossRef]

S. Single, J. Haag, A. Borst, “Dendritic computation of direction selectivity and gain control in visual interneurons,” J. Neurosci. 17, 6023–6030 (1997).
[PubMed]

J. H. van Hateren, “Processing of natural time series of intensities by the visual system of the blowfly,” Vision Res. 37, 3407–3416 (1997).
[CrossRef]

1996 (2)

A. van der Schaaf, J. H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
[CrossRef] [PubMed]

M. V. Srinivasan, S. W. Zhang, M. Lehrer, T. S. Collett, “Honeybee navigation en route to the goal: visual flight control and odometry,” J. Exp. Biol. 199, 237–244 (1996).
[PubMed]

1995 (2)

J. K. Douglass, N. J. Strausfeld, “Visual motion detection circuits in flies: peripheral motion computation by identified small-field retinotopic neurons,” J. Neurosci. 15, 5596–5611 (1995).
[PubMed]

D. W. Dong, J. J. Atick, “Statistics of natural time-varying images,” Network Comput. Neural Syst. 6, 345–358 (1995).
[CrossRef]

1994 (4)

G. Nalbach, R. Hengstenberg, “The halteres of the blowfly Calliphora,” J. Comp. Physiol. A 175, 695–708 (1994).
[CrossRef]

S. B. Laughlin, “Matching coding, circuits, cells and molecules to signals: general principles of retinal design in the fly’s eye,” Prog. Retinal Res. 13, 165–195 (1994).
[CrossRef]

F. Wolf-Oberhollenzer, K. Kirschfeld, “Motion sensitivity in the nucleus of the basal optic root of the pigeon,” J. Neurophysiol. 71, 1559–1573 (1994).
[PubMed]

D. L. Ruderman, “The statistics of natural images,” Network Comput. Neural Syst. 5, 517–48 (1994).
[CrossRef]

1992 (4)

G. A. Horridge, L. Marcelja, “On the existence of fast and slow directionally sensitive motion detector neurons in insects,” Proc. R. Soc. London, Ser. B 248, 47–54 (1992).
[CrossRef]

D. J. Tolhurst, Y. Tadmor, T. Chao, “Amplitude spectra of natural images,” Ophthalmol. Physiol. Opt. 12, 229–232 (1992).
[CrossRef]

D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181–197 (1992).
[CrossRef]

N. Franceschini, J. M. Pichon, C. Blanes, “From insect vision to robot vision,” Philos. Trans. R. Soc. London Ser. B 337, 283–294 (1992).
[CrossRef]

1991 (1)

D. Osorio, “Mechanisms of early visual processing in the medulla of the locust optic lobe: how self-inhibition, spatial-pooling and signal rectification contribute to the properties of transient cells,” Visual Neurosci. 7, 345–355 (1991).
[CrossRef]

1989 (2)

1987 (4)

G. J. Burton, I. R. Moorhead, “Color and spatial structure in natural scenes,” Appl. Opt. 26, 157–170 (1987).
[CrossRef] [PubMed]

D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” J. Opt. Soc. Am. A 4, 2379–2394 (1987).
[CrossRef] [PubMed]

R. C. Emerson, M. C. Citron, W. J. Vaughn, S. A. Klein, “Nonlinear directionally selective subunits in complex cells of cat striate cortex,” J. Neurophysiol. 58, 33–65 (1987).
[PubMed]

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).
[CrossRef]

1986 (1)

S. P. McKee, G. H. Silverman, K. Nakayama, “Precise velocity discrimination despite random variations in temporal frequency and contrast,” Vision Res. 26, 609–619 (1986).
[CrossRef] [PubMed]

1985 (4)

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

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

M. F. Land, H. M. Eckert, “Maps of the acute zones of fly eyes,” J. Comp. Physiol. A 156, 525–538 (1985).
[CrossRef]

T. Maddess, S. B. Laughlin, “Adaptation of the motion-sensitive neuron H1 is generated locally and governed by contrast frequency,” Proc. R. Soc. London Ser. B 225, 251–275 (1985).
[CrossRef]

1981 (1)

R. Payne, J. Howard, “Response of an insect photoreceptor: a simple log-normal model,” Nature 290, 415–416 (1981).
[CrossRef]

1976 (1)

T. Poggio, W. Reichardt, “Visual control of orientation behaviour in the fly. II. Towards the underlying neural interactions,” Q. Rev. Biophys. 9, 377–438 (1976).
[CrossRef] [PubMed]

1974 (1)

M. F. Land, T. S. Collett, “Chasing behaviour of houseflies (Fannia canicularis): a description and analysis,” J. Comp. Physiol. A 89, 331–357 (1974).
[CrossRef]

Adelson, E. H.

Atick, J. J.

D. W. Dong, J. J. Atick, “Statistics of natural time-varying images,” Network Comput. Neural Syst. 6, 345–358 (1995).
[CrossRef]

Bair, W.

R. Sarpeshkar, W. Bair, C. Koch, “An analog VLSI chip for local velocity estimation based on Reichardt’s motion algorithm,” in Advances in Neural Information Processing Systems, S. Hanson, J. Cowan, L. Giles, eds. (Morgan Kauffman, San Mateo, Calif., 1993), Vol. 5, pp. 781–788.

Bergen, J.

Bidwell, N. J.

D. C. O’Carroll, S. B. Laughlin, N. J. Bidwell, R. A. Harris, “Spatio-temporal properties of motion detectors matched to low image velocities in hovering insects,” Vision Res. 37, 3427–3439 (1997).
[CrossRef]

Blanes, C.

N. Franceschini, J. M. Pichon, C. Blanes, “From insect vision to robot vision,” Philos. Trans. R. Soc. London Ser. B 337, 283–294 (1992).
[CrossRef]

Borst, A.

S. Single, A. Borst, “Dendritic integration and its role in computing image velocity,” Science 281, 1848–1850 (1998).
[CrossRef] [PubMed]

S. Single, J. Haag, A. Borst, “Dendritic computation of direction selectivity and gain control in visual interneurons,” J. Neurosci. 17, 6023–6030 (1997).
[PubMed]

M. Egelhaaf, A. Borst, W. Reichardt, “Computational structure of a biological motion-detection system as revealed by local detector analysis in the fly’s nervous system,” J. Opt. Soc. Am. A 6, 1070–1087 (1989).
[CrossRef] [PubMed]

M. Egelhaaf, A. Borst, “Transient and steady-state response properties of movement detectors,” J. Opt. Soc. Am. A 6, 116–127 (1989).
[CrossRef] [PubMed]

M. Egelhaaf, A. Borst, “Movement detection in arthropods,” in Visual Motion and Its Role in the Stabilization of Gaze, J. Wallman, F. A. Miles, eds. (Elsevier, Amsterdam, 1993), pp. 53–77.

Burton, G. J.

Chao, T.

D. J. Tolhurst, Y. Tadmor, T. Chao, “Amplitude spectra of natural images,” Ophthalmol. Physiol. Opt. 12, 229–232 (1992).
[CrossRef]

Citron, M. C.

R. C. Emerson, M. C. Citron, W. J. Vaughn, S. A. Klein, “Nonlinear directionally selective subunits in complex cells of cat striate cortex,” J. Neurophysiol. 58, 33–65 (1987).
[PubMed]

Collett, T. S.

M. V. Srinivasan, S. W. Zhang, M. Lehrer, T. S. Collett, “Honeybee navigation en route to the goal: visual flight control and odometry,” J. Exp. Biol. 199, 237–244 (1996).
[PubMed]

M. F. Land, T. S. Collett, “Chasing behaviour of houseflies (Fannia canicularis): a description and analysis,” J. Comp. Physiol. A 89, 331–357 (1974).
[CrossRef]

Dong, D. W.

D. W. Dong, J. J. Atick, “Statistics of natural time-varying images,” Network Comput. Neural Syst. 6, 345–358 (1995).
[CrossRef]

Douglass, J. K.

J. K. Douglass, N. J. Strausfeld, “Visual motion detection circuits in flies: peripheral motion computation by identified small-field retinotopic neurons,” J. Neurosci. 15, 5596–5611 (1995).
[PubMed]

Dror, R. O.

R. O. Dror, D. C. O’Carroll, S. B. Laughlin, “The role of natural image statistics in biological motion estimation,” Springer Lect. Notes Comput. Sci. 1811, 492–501 (2000).
[CrossRef]

R. O. Dror, “Accuracy of visual velocity estimation by Reichardt correlators,” Master’s thesis (University of Cambridge, Cambridge, UK, 1998).

Eckert, H. M.

M. F. Land, H. M. Eckert, “Maps of the acute zones of fly eyes,” J. Comp. Physiol. A 156, 525–538 (1985).
[CrossRef]

Egelhaaf, M.

M. Egelhaaf, A. Borst, W. Reichardt, “Computational structure of a biological motion-detection system as revealed by local detector analysis in the fly’s nervous system,” J. Opt. Soc. Am. A 6, 1070–1087 (1989).
[CrossRef] [PubMed]

M. Egelhaaf, A. Borst, “Transient and steady-state response properties of movement detectors,” J. Opt. Soc. Am. A 6, 116–127 (1989).
[CrossRef] [PubMed]

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).
[CrossRef]

M. Egelhaaf, A. Borst, “Movement detection in arthropods,” in Visual Motion and Its Role in the Stabilization of Gaze, J. Wallman, F. A. Miles, eds. (Elsevier, Amsterdam, 1993), pp. 53–77.

K. Hausen, M. Egelhaaf, “Neural mechanisms of visualcourse control in insects,” in Facets of Vision, D. G. Stavenga, R. C. Hardie, eds. (Springer-Verlag, Heidelberg, 1989), pp. 391–424.

Emerson, R. C.

R. C. Emerson, M. C. Citron, W. J. Vaughn, S. A. Klein, “Nonlinear directionally selective subunits in complex cells of cat striate cortex,” J. Neurophysiol. 58, 33–65 (1987).
[PubMed]

Field, D. J.

Franceschini, N.

N. Franceschini, J. M. Pichon, C. Blanes, “From insect vision to robot vision,” Philos. Trans. R. Soc. London Ser. B 337, 283–294 (1992).
[CrossRef]

N. Franceschini, A. Riehle, A. le Nestour, “Directionally selective motion detection by insect neurons,” in Facets of Vision, D. G. Stavenga, R. C. Hardie, eds. (Springer-Verlag, Berlin, 1989), pp. 360–390.

Haag, J.

S. Single, J. Haag, A. Borst, “Dendritic computation of direction selectivity and gain control in visual interneurons,” J. Neurosci. 17, 6023–6030 (1997).
[PubMed]

Hardie, R. C.

R. C. Hardie, “Functional organization of the fly retina,” in Progress in Sensory Physiology, D. Ottoson, ed. (Springer-Verlag, Berlin, 1985), Vol. 5, pp. 1–80.

Harris, R. A.

R. A. Harris, D. C. O’Carroll, S. B. Laughlin, “Adaptation and the temporal delay filter of fly motion detectors,” Vision Res. 39, 2603–2613 (1999).
[CrossRef] [PubMed]

D. C. O’Carroll, S. B. Laughlin, N. J. Bidwell, R. A. Harris, “Spatio-temporal properties of motion detectors matched to low image velocities in hovering insects,” Vision Res. 37, 3427–3439 (1997).
[CrossRef]

Hausen, K.

K. Hausen, M. Egelhaaf, “Neural mechanisms of visualcourse control in insects,” in Facets of Vision, D. G. Stavenga, R. C. Hardie, eds. (Springer-Verlag, Heidelberg, 1989), pp. 391–424.

Heeger, D. J.

D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181–197 (1992).
[CrossRef]

Hengstenberg, R.

G. Nalbach, R. Hengstenberg, “The halteres of the blowfly Calliphora,” J. Comp. Physiol. A 175, 695–708 (1994).
[CrossRef]

Horridge, G. A.

G. A. Horridge, L. Marcelja, “On the existence of fast and slow directionally sensitive motion detector neurons in insects,” Proc. R. Soc. London, Ser. B 248, 47–54 (1992).
[CrossRef]

Howard, J.

R. Payne, J. Howard, “Response of an insect photoreceptor: a simple log-normal model,” Nature 290, 415–416 (1981).
[CrossRef]

James, A. C.

A. C. James, “White-noise studies in the fly Lamina,” Ph.D. thesis (Australian National University, Canberra, Australia, 1990).

Kirschfeld, K.

F. Wolf-Oberhollenzer, K. Kirschfeld, “Motion sensitivity in the nucleus of the basal optic root of the pigeon,” J. Neurophysiol. 71, 1559–1573 (1994).
[PubMed]

Klein, S. A.

R. C. Emerson, M. C. Citron, W. J. Vaughn, S. A. Klein, “Nonlinear directionally selective subunits in complex cells of cat striate cortex,” J. Neurophysiol. 58, 33–65 (1987).
[PubMed]

Koch, C.

R. Sarpeshkar, W. Bair, C. Koch, “An analog VLSI chip for local velocity estimation based on Reichardt’s motion algorithm,” in Advances in Neural Information Processing Systems, S. Hanson, J. Cowan, L. Giles, eds. (Morgan Kauffman, San Mateo, Calif., 1993), Vol. 5, pp. 781–788.

Land, M. F.

M. F. Land, H. M. Eckert, “Maps of the acute zones of fly eyes,” J. Comp. Physiol. A 156, 525–538 (1985).
[CrossRef]

M. F. Land, T. S. Collett, “Chasing behaviour of houseflies (Fannia canicularis): a description and analysis,” J. Comp. Physiol. A 89, 331–357 (1974).
[CrossRef]

Laughlin, S. B.

B. Tatler, D. C. O’Carroll, S. B. Laughlin, “Temperature and temporal resolving power of fly photoreceptors,” J. Comp. Physiol. A 186, 399–407 (2000).
[CrossRef] [PubMed]

R. O. Dror, D. C. O’Carroll, S. B. Laughlin, “The role of natural image statistics in biological motion estimation,” Springer Lect. Notes Comput. Sci. 1811, 492–501 (2000).
[CrossRef]

R. A. Harris, D. C. O’Carroll, S. B. Laughlin, “Adaptation and the temporal delay filter of fly motion detectors,” Vision Res. 39, 2603–2613 (1999).
[CrossRef] [PubMed]

D. C. O’Carroll, S. B. Laughlin, N. J. Bidwell, R. A. Harris, “Spatio-temporal properties of motion detectors matched to low image velocities in hovering insects,” Vision Res. 37, 3427–3439 (1997).
[CrossRef]

S. B. Laughlin, “Matching coding, circuits, cells and molecules to signals: general principles of retinal design in the fly’s eye,” Prog. Retinal Res. 13, 165–195 (1994).
[CrossRef]

T. Maddess, S. B. Laughlin, “Adaptation of the motion-sensitive neuron H1 is generated locally and governed by contrast frequency,” Proc. R. Soc. London Ser. B 225, 251–275 (1985).
[CrossRef]

le Nestour, A.

N. Franceschini, A. Riehle, A. le Nestour, “Directionally selective motion detection by insect neurons,” in Facets of Vision, D. G. Stavenga, R. C. Hardie, eds. (Springer-Verlag, Berlin, 1989), pp. 360–390.

Lehrer, M.

M. V. Srinivasan, S. W. Zhang, M. Lehrer, T. S. Collett, “Honeybee navigation en route to the goal: visual flight control and odometry,” J. Exp. Biol. 199, 237–244 (1996).
[PubMed]

Maddess, T.

T. Maddess, S. B. Laughlin, “Adaptation of the motion-sensitive neuron H1 is generated locally and governed by contrast frequency,” Proc. R. Soc. London Ser. B 225, 251–275 (1985).
[CrossRef]

Marcelja, L.

G. A. Horridge, L. Marcelja, “On the existence of fast and slow directionally sensitive motion detector neurons in insects,” Proc. R. Soc. London, Ser. B 248, 47–54 (1992).
[CrossRef]

McKee, S. P.

S. P. McKee, G. H. Silverman, K. Nakayama, “Precise velocity discrimination despite random variations in temporal frequency and contrast,” Vision Res. 26, 609–619 (1986).
[CrossRef] [PubMed]

Moorhead, I. R.

Nakayama, K.

S. P. McKee, G. H. Silverman, K. Nakayama, “Precise velocity discrimination despite random variations in temporal frequency and contrast,” Vision Res. 26, 609–619 (1986).
[CrossRef] [PubMed]

Nalbach, G.

G. Nalbach, R. Hengstenberg, “The halteres of the blowfly Calliphora,” J. Comp. Physiol. A 175, 695–708 (1994).
[CrossRef]

O’Carroll, D. C.

R. O. Dror, D. C. O’Carroll, S. B. Laughlin, “The role of natural image statistics in biological motion estimation,” Springer Lect. Notes Comput. Sci. 1811, 492–501 (2000).
[CrossRef]

B. Tatler, D. C. O’Carroll, S. B. Laughlin, “Temperature and temporal resolving power of fly photoreceptors,” J. Comp. Physiol. A 186, 399–407 (2000).
[CrossRef] [PubMed]

R. A. Harris, D. C. O’Carroll, S. B. Laughlin, “Adaptation and the temporal delay filter of fly motion detectors,” Vision Res. 39, 2603–2613 (1999).
[CrossRef] [PubMed]

D. C. O’Carroll, S. B. Laughlin, N. J. Bidwell, R. A. Harris, “Spatio-temporal properties of motion detectors matched to low image velocities in hovering insects,” Vision Res. 37, 3427–3439 (1997).
[CrossRef]

Osorio, D.

D. Osorio, “Mechanisms of early visual processing in the medulla of the locust optic lobe: how self-inhibition, spatial-pooling and signal rectification contribute to the properties of transient cells,” Visual Neurosci. 7, 345–355 (1991).
[CrossRef]

Payne, R.

R. Payne, J. Howard, “Response of an insect photoreceptor: a simple log-normal model,” Nature 290, 415–416 (1981).
[CrossRef]

Pichon, J. M.

N. Franceschini, J. M. Pichon, C. Blanes, “From insect vision to robot vision,” Philos. Trans. R. Soc. London Ser. B 337, 283–294 (1992).
[CrossRef]

Poggio, T.

T. Poggio, W. Reichardt, “Visual control of orientation behaviour in the fly. II. Towards the underlying neural interactions,” Q. Rev. Biophys. 9, 377–438 (1976).
[CrossRef] [PubMed]

Reichardt, W.

M. Egelhaaf, A. Borst, W. Reichardt, “Computational structure of a biological motion-detection system as revealed by local detector analysis in the fly’s nervous system,” J. Opt. Soc. Am. A 6, 1070–1087 (1989).
[CrossRef] [PubMed]

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).
[CrossRef]

T. Poggio, W. Reichardt, “Visual control of orientation behaviour in the fly. II. Towards the underlying neural interactions,” Q. Rev. Biophys. 9, 377–438 (1976).
[CrossRef] [PubMed]

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

Riehle, A.

N. Franceschini, A. Riehle, A. le Nestour, “Directionally selective motion detection by insect neurons,” in Facets of Vision, D. G. Stavenga, R. C. Hardie, eds. (Springer-Verlag, Berlin, 1989), pp. 360–390.

Ruderman, D. L.

D. L. Ruderman, “The statistics of natural images,” Network Comput. Neural Syst. 5, 517–48 (1994).
[CrossRef]

Sarpeshkar, R.

R. Sarpeshkar, W. Bair, C. Koch, “An analog VLSI chip for local velocity estimation based on Reichardt’s motion algorithm,” in Advances in Neural Information Processing Systems, S. Hanson, J. Cowan, L. Giles, eds. (Morgan Kauffman, San Mateo, Calif., 1993), Vol. 5, pp. 781–788.

Silverman, G. H.

S. P. McKee, G. H. Silverman, K. Nakayama, “Precise velocity discrimination despite random variations in temporal frequency and contrast,” Vision Res. 26, 609–619 (1986).
[CrossRef] [PubMed]

Single, S.

S. Single, A. Borst, “Dendritic integration and its role in computing image velocity,” Science 281, 1848–1850 (1998).
[CrossRef] [PubMed]

S. Single, J. Haag, A. Borst, “Dendritic computation of direction selectivity and gain control in visual interneurons,” J. Neurosci. 17, 6023–6030 (1997).
[PubMed]

Snyder, A. W.

A. W. Snyder, “The physics of vision in compound eyes,” in Comparative Physiology and Evolution of Vision in Invertebrates: Invertebrate Photoreceptors, Vol. 6A of Handbook of Sensory Physiology, H. Autrum, ed. (Springer-Verlag, Berlin, 1979), pp. 225–313.

Sperling, G.

Srinivasan, M. V.

M. V. Srinivasan, S. W. Zhang, M. Lehrer, T. S. Collett, “Honeybee navigation en route to the goal: visual flight control and odometry,” J. Exp. Biol. 199, 237–244 (1996).
[PubMed]

Strausfeld, N. J.

J. K. Douglass, N. J. Strausfeld, “Visual motion detection circuits in flies: peripheral motion computation by identified small-field retinotopic neurons,” J. Neurosci. 15, 5596–5611 (1995).
[PubMed]

Tadmor, Y.

D. J. Tolhurst, Y. Tadmor, T. Chao, “Amplitude spectra of natural images,” Ophthalmol. Physiol. Opt. 12, 229–232 (1992).
[CrossRef]

Tatler, B.

B. Tatler, D. C. O’Carroll, S. B. Laughlin, “Temperature and temporal resolving power of fly photoreceptors,” J. Comp. Physiol. A 186, 399–407 (2000).
[CrossRef] [PubMed]

Tolhurst, D. J.

D. J. Tolhurst, Y. Tadmor, T. Chao, “Amplitude spectra of natural images,” Ophthalmol. Physiol. Opt. 12, 229–232 (1992).
[CrossRef]

van der Schaaf, A.

A. van der Schaaf, J. H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
[CrossRef] [PubMed]

van Hateren, J. H.

J. H. van Hateren, “Processing of natural time series of intensities by the visual system of the blowfly,” Vision Res. 37, 3407–3416 (1997).
[CrossRef]

A. van der Schaaf, J. H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
[CrossRef] [PubMed]

van Santen, J. P. H.

Vaughn, W. J.

R. C. Emerson, M. C. Citron, W. J. Vaughn, S. A. Klein, “Nonlinear directionally selective subunits in complex cells of cat striate cortex,” J. Neurophysiol. 58, 33–65 (1987).
[PubMed]

Wolf-Oberhollenzer, F.

F. Wolf-Oberhollenzer, K. Kirschfeld, “Motion sensitivity in the nucleus of the basal optic root of the pigeon,” J. Neurophysiol. 71, 1559–1573 (1994).
[PubMed]

Zhang, S. W.

M. V. Srinivasan, S. W. Zhang, M. Lehrer, T. S. Collett, “Honeybee navigation en route to the goal: visual flight control and odometry,” J. Exp. Biol. 199, 237–244 (1996).
[PubMed]

Appl. Opt. (1)

Biol. Cybern. (1)

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).
[CrossRef]

J. Comp. Physiol. A (4)

M. F. Land, H. M. Eckert, “Maps of the acute zones of fly eyes,” J. Comp. Physiol. A 156, 525–538 (1985).
[CrossRef]

M. F. Land, T. S. Collett, “Chasing behaviour of houseflies (Fannia canicularis): a description and analysis,” J. Comp. Physiol. A 89, 331–357 (1974).
[CrossRef]

G. Nalbach, R. Hengstenberg, “The halteres of the blowfly Calliphora,” J. Comp. Physiol. A 175, 695–708 (1994).
[CrossRef]

B. Tatler, D. C. O’Carroll, S. B. Laughlin, “Temperature and temporal resolving power of fly photoreceptors,” J. Comp. Physiol. A 186, 399–407 (2000).
[CrossRef] [PubMed]

J. Exp. Biol. (1)

M. V. Srinivasan, S. W. Zhang, M. Lehrer, T. S. Collett, “Honeybee navigation en route to the goal: visual flight control and odometry,” J. Exp. Biol. 199, 237–244 (1996).
[PubMed]

J. Neurophysiol. (2)

F. Wolf-Oberhollenzer, K. Kirschfeld, “Motion sensitivity in the nucleus of the basal optic root of the pigeon,” J. Neurophysiol. 71, 1559–1573 (1994).
[PubMed]

R. C. Emerson, M. C. Citron, W. J. Vaughn, S. A. Klein, “Nonlinear directionally selective subunits in complex cells of cat striate cortex,” J. Neurophysiol. 58, 33–65 (1987).
[PubMed]

J. Neurosci. (2)

S. Single, J. Haag, A. Borst, “Dendritic computation of direction selectivity and gain control in visual interneurons,” J. Neurosci. 17, 6023–6030 (1997).
[PubMed]

J. K. Douglass, N. J. Strausfeld, “Visual motion detection circuits in flies: peripheral motion computation by identified small-field retinotopic neurons,” J. Neurosci. 15, 5596–5611 (1995).
[PubMed]

J. Opt. Soc. Am. A (5)

Nature (1)

R. Payne, J. Howard, “Response of an insect photoreceptor: a simple log-normal model,” Nature 290, 415–416 (1981).
[CrossRef]

Network Comput. Neural Syst. (2)

D. L. Ruderman, “The statistics of natural images,” Network Comput. Neural Syst. 5, 517–48 (1994).
[CrossRef]

D. W. Dong, J. J. Atick, “Statistics of natural time-varying images,” Network Comput. Neural Syst. 6, 345–358 (1995).
[CrossRef]

Ophthalmol. Physiol. Opt. (1)

D. J. Tolhurst, Y. Tadmor, T. Chao, “Amplitude spectra of natural images,” Ophthalmol. Physiol. Opt. 12, 229–232 (1992).
[CrossRef]

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

N. Franceschini, J. M. Pichon, C. Blanes, “From insect vision to robot vision,” Philos. Trans. R. Soc. London Ser. B 337, 283–294 (1992).
[CrossRef]

Proc. R. Soc. London Ser. B (1)

T. Maddess, S. B. Laughlin, “Adaptation of the motion-sensitive neuron H1 is generated locally and governed by contrast frequency,” Proc. R. Soc. London Ser. B 225, 251–275 (1985).
[CrossRef]

Proc. R. Soc. London, Ser. B (1)

G. A. Horridge, L. Marcelja, “On the existence of fast and slow directionally sensitive motion detector neurons in insects,” Proc. R. Soc. London, Ser. B 248, 47–54 (1992).
[CrossRef]

Prog. Retinal Res. (1)

S. B. Laughlin, “Matching coding, circuits, cells and molecules to signals: general principles of retinal design in the fly’s eye,” Prog. Retinal Res. 13, 165–195 (1994).
[CrossRef]

Q. Rev. Biophys. (1)

T. Poggio, W. Reichardt, “Visual control of orientation behaviour in the fly. II. Towards the underlying neural interactions,” Q. Rev. Biophys. 9, 377–438 (1976).
[CrossRef] [PubMed]

Science (1)

S. Single, A. Borst, “Dendritic integration and its role in computing image velocity,” Science 281, 1848–1850 (1998).
[CrossRef] [PubMed]

Springer Lect. Notes Comput. Sci. (1)

R. O. Dror, D. C. O’Carroll, S. B. Laughlin, “The role of natural image statistics in biological motion estimation,” Springer Lect. Notes Comput. Sci. 1811, 492–501 (2000).
[CrossRef]

Vision Res. (5)

J. H. van Hateren, “Processing of natural time series of intensities by the visual system of the blowfly,” Vision Res. 37, 3407–3416 (1997).
[CrossRef]

A. van der Schaaf, J. H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
[CrossRef] [PubMed]

S. P. McKee, G. H. Silverman, K. Nakayama, “Precise velocity discrimination despite random variations in temporal frequency and contrast,” Vision Res. 26, 609–619 (1986).
[CrossRef] [PubMed]

R. A. Harris, D. C. O’Carroll, S. B. Laughlin, “Adaptation and the temporal delay filter of fly motion detectors,” Vision Res. 39, 2603–2613 (1999).
[CrossRef] [PubMed]

D. C. O’Carroll, S. B. Laughlin, N. J. Bidwell, R. A. Harris, “Spatio-temporal properties of motion detectors matched to low image velocities in hovering insects,” Vision Res. 37, 3427–3439 (1997).
[CrossRef]

Visual Neurosci. (2)

D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181–197 (1992).
[CrossRef]

D. Osorio, “Mechanisms of early visual processing in the medulla of the locust optic lobe: how self-inhibition, spatial-pooling and signal rectification contribute to the properties of transient cells,” Visual Neurosci. 7, 345–355 (1991).
[CrossRef]

Other (10)

K. Hausen, M. Egelhaaf, “Neural mechanisms of visualcourse control in insects,” in Facets of Vision, D. G. Stavenga, R. C. Hardie, eds. (Springer-Verlag, Heidelberg, 1989), pp. 391–424.

R. O. Dror, “Accuracy of visual velocity estimation by Reichardt correlators,” Master’s thesis (University of Cambridge, Cambridge, UK, 1998).

A. W. Snyder, “The physics of vision in compound eyes,” in Comparative Physiology and Evolution of Vision in Invertebrates: Invertebrate Photoreceptors, Vol. 6A of Handbook of Sensory Physiology, H. Autrum, ed. (Springer-Verlag, Berlin, 1979), pp. 225–313.

R. Sarpeshkar, W. Bair, C. Koch, “An analog VLSI chip for local velocity estimation based on Reichardt’s motion algorithm,” in Advances in Neural Information Processing Systems, S. Hanson, J. Cowan, L. Giles, eds. (Morgan Kauffman, San Mateo, Calif., 1993), Vol. 5, pp. 781–788.

A. C. James, “White-noise studies in the fly Lamina,” Ph.D. thesis (Australian National University, Canberra, Australia, 1990).

Information is available from David C. O’Carroll, Department of Zoology, University of Washington, Box 351800, Seattle, Wash. 98195-1800; davidoc@u.washington.edu.

N. Franceschini, A. Riehle, A. le Nestour, “Directionally selective motion detection by insect neurons,” in Facets of Vision, D. G. Stavenga, R. C. Hardie, eds. (Springer-Verlag, Berlin, 1989), pp. 360–390.

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

M. Egelhaaf, A. Borst, “Movement detection in arthropods,” in Visual Motion and Its Role in the Stabilization of Gaze, J. Wallman, F. A. Miles, eds. (Elsevier, Amsterdam, 1993), pp. 53–77.

R. C. Hardie, “Functional organization of the fly retina,” in Progress in Sensory Physiology, D. Ottoson, ed. (Springer-Verlag, Berlin, 1985), Vol. 5, pp. 1–80.

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