Abstract

Translation of an observer through a static environment generates a pattern of optical flow that specifies the direction of self-motion, but the retinal flow pattern is confounded by pursuit eye movements. How does the visual system decompose the translational and rotational components of flow to determine heading? It is shown that observers can perceive their direction of self-motion during stationary fixations and pursuit eye movements and with displays that simulate the optical effects of eye movements. Results indicate that the visual system can perform the decomposition with both continuous and discontinuous fields on the basis of flow-field information alone but requires a three-dimensional environmental structure to do so. The findings are inconsistent with general computational models and theories based on the maximum of divergence, oculomotor signals, or multiple fixations but are consistent with the theory of reliance on differential motion produced by environmental variation in depth.

© 1990 Optical Society of America

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References

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  2. W. H. Warren, M. W. Morris, M. Kalish, “Perception of translational heading from optical flow,” J. Exp. Psychol. Hum. Percep. Perf. 14, 646–660 (1988).
    [Crossref]
  3. J. J. Gibson, The Senses Considered as Perceptual Systems (Houghton Mifflin, Boston, Mass., 1966).
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    [Crossref] [PubMed]
  6. H. C. Longuet-Higgins, “A computer algorithm for reconstructing a scene from two projections,” Nature 293, 133–135 (1981).
    [Crossref]
  7. H. C. Longuet-Higgins, “The visual ambiguity of a moving plane,” Proc. R. Soc. London Ser. B 223, 165–175 (1984).
    [Crossref]
  8. R. Y. Tsai, T. S. Huang, “Estimating three-dimensional motion parameters of a rigid planar patch,” IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 1147–1152 (1981).
    [Crossref]
  9. R. Y. Tsai, T. S. Huang, “Estimating three-dimensional motion parameters of a rigid planar patch: III. Finite point correspondences and the three-view problem,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 213–220 (1984).
    [Crossref]
  10. R. Y. Tsai, T. S. Huang, “Uniqueness and estimation of three-dimensional motion parameters of rigid objects with curved surfaces,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 13–27 (1984).
    [Crossref]
  11. K. Prazdny, “Egomotion and relative depth map from optical flow,” Biol. Cybern. 36, 87–102 (1980).
    [Crossref] [PubMed]
  12. H.-H. Nagel, “On the derivation of 3D rigid point configurations from image sequences,” in Proceedings of the IEEE Conference on Pattern Recognition and Image Processing (IEEE Computer Society Press, New York, 1981).
  13. A. Mitiche, “Computation of optical flow and rigid motion,” in Proceedings of the IEEE Workshop on Computer Vision: Representation and Control (IEEE Computer Society, New York, 1984).
  14. W. H. Warren, W. Griesar, A. W. Blackwell, M. Kalish, N. G. Hatsopoulos, “On the sufficiency of the velocity field for perception of heading,” to be submitted to Biol. Cybern.
  15. J. J. Koenderink, A. J. van Doorn, “Invariant properties of the motion parallax field due to the movement of rigid bodies relative to an observer,” Opt. Acta 22, 773–791 (1975).
    [Crossref]
  16. J. J. Koenderink, A. J. van Doorn, “Local structure of movement parallax of the plane,” J. Opt. Soc. Am. 66, 717–723 (1976).
    [Crossref]
  17. J. J. Koenderink, A. J. van Doorn, “Exterospecific component of the motion parallax field,” J. Opt. Soc. Am. 71, 953–957 (1981).
    [Crossref] [PubMed]
  18. K. Nakayama, “Extraction of higher-order derivatives of the optical velocity vector field: limitations imposed by biological hardware,” in Brain Mechanisms and Spatial Vision, D. Ingle, M. Jeannerod, D. Lee, eds. (Martinus-Nijhoff, The Hague, The Netherlands, 1985).
    [Crossref]
  19. H. C. Longuet-Higgins, K. Prazdny, “The interpretation of a moving retinal image,” Proc.R. Soc. London Ser. B 208, 385–397 (1980).
    [Crossref]
  20. A. M. Waxman, S. Ullman, “Surface structure and 3D motion from image flow: a kinematic analysis,” Int. J. Robotics Res. 4, 72–94 (1985).
    [Crossref]
  21. K. Prazdny, “Determining the instantaneous direction of motion from optical flow generated by a curvilinearly moving observer,” Comput. Graphics Image Process. 17, 238–258 (1981).
    [Crossref]
  22. A. R. Bruss, B. K. P. Horn, “Passive navigation,” Comput. Graphics Image Process. 21, 3–20 (1983).
    [Crossref]
  23. D. H. Ballard, O. A. Kimball, “Rigid body motion from depth and optical flow,” Comput. Vision Graphics Image Process. 22, 95–115 (1983).
    [Crossref]
  24. A. Verri, F. Girosi, V. Torre, “Mathematical properties of the two-dimensional motion field: from singular points to motion parameters,” J. Opt. Soc. Am. A 6, 698–712 (1989).
    [Crossref]
  25. J. H. Rieger, D. T. Lawton, “Processing differential image motion,” J. Opt. Soc. Am. A 2, 354–360 (1985).
    [Crossref] [PubMed]
  26. J. Cutting, Perception with an Eye for Motion (MIT Press, Cambridge, Mass., 1986).
  27. W. Richards, “Visual space perception,” in, Handbook of Perception, E. C. Carterette, M. P. Friedman, eds. (Academic, New York, 1975), Vol. 5, pp. 351–386.
  28. D. Regan, “Visual flow and the direction of locomotion,” Science 277, 1064–1065 (1985).
    [Crossref]
  29. E. von Holst, “Relations between the central nervous system and the peripheral organs,” Animal Behav. 2, 89–94 (1954).
    [Crossref]
  30. I. R. Johnston, G. R. White, R. W. Cumming, “The role of optical expansion patterns in locomotor control,” Am. J. Psychol. 86, 311–324 (1973).
    [Crossref] [PubMed]
  31. J. J. Gibson, “What gives rise to the perception of motion?” Psychol. Rev. 75, 335–346 (1968).
    [Crossref] [PubMed]
  32. D. Regan, K. I. Beverley, “How do we avoid confounding the direction we are looking and the direction we are moving?” Science 215, 194–196 (1982).
    [Crossref] [PubMed]
  33. J. H. Rieger, L. Toet, “Human visual navigation in the presence of 3D rotations,” Biol. Cybern. 52, 377–381 (1985).
    [Crossref]
  34. J. J. Koenderink, A. J. van Doorn, “Facts on optic flow,” Biol. Cybern. 56, 247–254 (1987).
    [Crossref] [PubMed]
  35. J. Lappin, F. Norman, “Detectabilities of the components of optical flow,” presented at the Psychonomic Society Annual Meeting, Chicago, Ill., November 10–12 1988.
  36. B. Gillam, “Is orientation disparity a stereoscopic primitive?” presented at the Psychonomic Society Annual Meeting, Chicago, Ill., November 10–12 1988.
  37. P. Hammond, A. T. Smith, “On the sensitivity of complex cells in feline striate cortex to relative motion,” Exp. Brain Res. 47, 457–460 (1982).
    [Crossref] [PubMed]
  38. B. Frost, K. Nakayama, “Single visual neurons code opposing motion independent of direction,” Science 220, 744–745 (1983).
    [Crossref] [PubMed]
  39. G. A. Orban, B. Gulyas, R. Vogels, “Influence of a moving textured background on direction selectivity of cat striate neurons,” J. Neurophys. 57, 1792–1812 (1987).
  40. J. H. Rieger, “Information in optical flows induced by curved paths of observation,” J. Opt. Soc. Am. 73, 339–344 (1983).
    [Crossref] [PubMed]
  41. W. H. Warren, D. R. Mestre, A. W. Blackwell, M. W. Morris, “Perception of curvilinear heading from optical flow,” submitted to J. Exp. Psychol. Hum. Percep. Perf.
  42. W. H. Hannon, D. J. Hannon, “Direction of self-motion is perceived from optical flow,” Nature 336, 162–163 (1988).
    [Crossref]

1989 (1)

1988 (2)

W. H. Hannon, D. J. Hannon, “Direction of self-motion is perceived from optical flow,” Nature 336, 162–163 (1988).
[Crossref]

W. H. Warren, M. W. Morris, M. Kalish, “Perception of translational heading from optical flow,” J. Exp. Psychol. Hum. Percep. Perf. 14, 646–660 (1988).
[Crossref]

1987 (2)

G. A. Orban, B. Gulyas, R. Vogels, “Influence of a moving textured background on direction selectivity of cat striate neurons,” J. Neurophys. 57, 1792–1812 (1987).

J. J. Koenderink, A. J. van Doorn, “Facts on optic flow,” Biol. Cybern. 56, 247–254 (1987).
[Crossref] [PubMed]

1985 (4)

J. H. Rieger, L. Toet, “Human visual navigation in the presence of 3D rotations,” Biol. Cybern. 52, 377–381 (1985).
[Crossref]

J. H. Rieger, D. T. Lawton, “Processing differential image motion,” J. Opt. Soc. Am. A 2, 354–360 (1985).
[Crossref] [PubMed]

D. Regan, “Visual flow and the direction of locomotion,” Science 277, 1064–1065 (1985).
[Crossref]

A. M. Waxman, S. Ullman, “Surface structure and 3D motion from image flow: a kinematic analysis,” Int. J. Robotics Res. 4, 72–94 (1985).
[Crossref]

1984 (3)

H. C. Longuet-Higgins, “The visual ambiguity of a moving plane,” Proc. R. Soc. London Ser. B 223, 165–175 (1984).
[Crossref]

R. Y. Tsai, T. S. Huang, “Estimating three-dimensional motion parameters of a rigid planar patch: III. Finite point correspondences and the three-view problem,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 213–220 (1984).
[Crossref]

R. Y. Tsai, T. S. Huang, “Uniqueness and estimation of three-dimensional motion parameters of rigid objects with curved surfaces,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 13–27 (1984).
[Crossref]

1983 (4)

A. R. Bruss, B. K. P. Horn, “Passive navigation,” Comput. Graphics Image Process. 21, 3–20 (1983).
[Crossref]

D. H. Ballard, O. A. Kimball, “Rigid body motion from depth and optical flow,” Comput. Vision Graphics Image Process. 22, 95–115 (1983).
[Crossref]

B. Frost, K. Nakayama, “Single visual neurons code opposing motion independent of direction,” Science 220, 744–745 (1983).
[Crossref] [PubMed]

J. H. Rieger, “Information in optical flows induced by curved paths of observation,” J. Opt. Soc. Am. 73, 339–344 (1983).
[Crossref] [PubMed]

1982 (2)

P. Hammond, A. T. Smith, “On the sensitivity of complex cells in feline striate cortex to relative motion,” Exp. Brain Res. 47, 457–460 (1982).
[Crossref] [PubMed]

D. Regan, K. I. Beverley, “How do we avoid confounding the direction we are looking and the direction we are moving?” Science 215, 194–196 (1982).
[Crossref] [PubMed]

1981 (4)

K. Prazdny, “Determining the instantaneous direction of motion from optical flow generated by a curvilinearly moving observer,” Comput. Graphics Image Process. 17, 238–258 (1981).
[Crossref]

R. Y. Tsai, T. S. Huang, “Estimating three-dimensional motion parameters of a rigid planar patch,” IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 1147–1152 (1981).
[Crossref]

J. J. Koenderink, A. J. van Doorn, “Exterospecific component of the motion parallax field,” J. Opt. Soc. Am. 71, 953–957 (1981).
[Crossref] [PubMed]

H. C. Longuet-Higgins, “A computer algorithm for reconstructing a scene from two projections,” Nature 293, 133–135 (1981).
[Crossref]

1980 (2)

K. Prazdny, “Egomotion and relative depth map from optical flow,” Biol. Cybern. 36, 87–102 (1980).
[Crossref] [PubMed]

H. C. Longuet-Higgins, K. Prazdny, “The interpretation of a moving retinal image,” Proc.R. Soc. London Ser. B 208, 385–397 (1980).
[Crossref]

1976 (1)

1975 (1)

J. J. Koenderink, A. J. van Doorn, “Invariant properties of the motion parallax field due to the movement of rigid bodies relative to an observer,” Opt. Acta 22, 773–791 (1975).
[Crossref]

1973 (1)

I. R. Johnston, G. R. White, R. W. Cumming, “The role of optical expansion patterns in locomotor control,” Am. J. Psychol. 86, 311–324 (1973).
[Crossref] [PubMed]

1968 (1)

J. J. Gibson, “What gives rise to the perception of motion?” Psychol. Rev. 75, 335–346 (1968).
[Crossref] [PubMed]

1954 (2)

E. von Holst, “Relations between the central nervous system and the peripheral organs,” Animal Behav. 2, 89–94 (1954).
[Crossref]

J. J. Gibson, “The visual perception of objective motion and subjective movement,” Psychol. Rev. 61, 304–314 (1954).
[Crossref] [PubMed]

1065 (1)

C. Torrey, “Visual flow and the direction of locomotion,” Science 277, 1064 (1065).

Ballard, D. H.

D. H. Ballard, O. A. Kimball, “Rigid body motion from depth and optical flow,” Comput. Vision Graphics Image Process. 22, 95–115 (1983).
[Crossref]

Beverley, K. I.

D. Regan, K. I. Beverley, “How do we avoid confounding the direction we are looking and the direction we are moving?” Science 215, 194–196 (1982).
[Crossref] [PubMed]

Blackwell, A. W.

W. H. Warren, D. R. Mestre, A. W. Blackwell, M. W. Morris, “Perception of curvilinear heading from optical flow,” submitted to J. Exp. Psychol. Hum. Percep. Perf.

W. H. Warren, W. Griesar, A. W. Blackwell, M. Kalish, N. G. Hatsopoulos, “On the sufficiency of the velocity field for perception of heading,” to be submitted to Biol. Cybern.

Bruss, A. R.

A. R. Bruss, B. K. P. Horn, “Passive navigation,” Comput. Graphics Image Process. 21, 3–20 (1983).
[Crossref]

Cumming, R. W.

I. R. Johnston, G. R. White, R. W. Cumming, “The role of optical expansion patterns in locomotor control,” Am. J. Psychol. 86, 311–324 (1973).
[Crossref] [PubMed]

Cutting, J.

J. Cutting, Perception with an Eye for Motion (MIT Press, Cambridge, Mass., 1986).

Frost, B.

B. Frost, K. Nakayama, “Single visual neurons code opposing motion independent of direction,” Science 220, 744–745 (1983).
[Crossref] [PubMed]

Gibson, J. J.

J. J. Gibson, “What gives rise to the perception of motion?” Psychol. Rev. 75, 335–346 (1968).
[Crossref] [PubMed]

J. J. Gibson, “The visual perception of objective motion and subjective movement,” Psychol. Rev. 61, 304–314 (1954).
[Crossref] [PubMed]

J. J. Gibson, The Senses Considered as Perceptual Systems (Houghton Mifflin, Boston, Mass., 1966).

J. J. Gibson, Perception of the Visual World (Houghton Mifflin, Boston, Mass., 1950).

Gillam, B.

B. Gillam, “Is orientation disparity a stereoscopic primitive?” presented at the Psychonomic Society Annual Meeting, Chicago, Ill., November 10–12 1988.

Girosi, F.

Griesar, W.

W. H. Warren, W. Griesar, A. W. Blackwell, M. Kalish, N. G. Hatsopoulos, “On the sufficiency of the velocity field for perception of heading,” to be submitted to Biol. Cybern.

Gulyas, B.

G. A. Orban, B. Gulyas, R. Vogels, “Influence of a moving textured background on direction selectivity of cat striate neurons,” J. Neurophys. 57, 1792–1812 (1987).

Hammond, P.

P. Hammond, A. T. Smith, “On the sensitivity of complex cells in feline striate cortex to relative motion,” Exp. Brain Res. 47, 457–460 (1982).
[Crossref] [PubMed]

Hannon, D. J.

W. H. Hannon, D. J. Hannon, “Direction of self-motion is perceived from optical flow,” Nature 336, 162–163 (1988).
[Crossref]

Hannon, W. H.

W. H. Hannon, D. J. Hannon, “Direction of self-motion is perceived from optical flow,” Nature 336, 162–163 (1988).
[Crossref]

Hatsopoulos, N. G.

W. H. Warren, W. Griesar, A. W. Blackwell, M. Kalish, N. G. Hatsopoulos, “On the sufficiency of the velocity field for perception of heading,” to be submitted to Biol. Cybern.

Horn, B. K. P.

A. R. Bruss, B. K. P. Horn, “Passive navigation,” Comput. Graphics Image Process. 21, 3–20 (1983).
[Crossref]

Huang, T. S.

R. Y. Tsai, T. S. Huang, “Estimating three-dimensional motion parameters of a rigid planar patch: III. Finite point correspondences and the three-view problem,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 213–220 (1984).
[Crossref]

R. Y. Tsai, T. S. Huang, “Uniqueness and estimation of three-dimensional motion parameters of rigid objects with curved surfaces,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 13–27 (1984).
[Crossref]

R. Y. Tsai, T. S. Huang, “Estimating three-dimensional motion parameters of a rigid planar patch,” IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 1147–1152 (1981).
[Crossref]

Johnston, I. R.

I. R. Johnston, G. R. White, R. W. Cumming, “The role of optical expansion patterns in locomotor control,” Am. J. Psychol. 86, 311–324 (1973).
[Crossref] [PubMed]

Kalish, M.

W. H. Warren, M. W. Morris, M. Kalish, “Perception of translational heading from optical flow,” J. Exp. Psychol. Hum. Percep. Perf. 14, 646–660 (1988).
[Crossref]

W. H. Warren, W. Griesar, A. W. Blackwell, M. Kalish, N. G. Hatsopoulos, “On the sufficiency of the velocity field for perception of heading,” to be submitted to Biol. Cybern.

Kimball, O. A.

D. H. Ballard, O. A. Kimball, “Rigid body motion from depth and optical flow,” Comput. Vision Graphics Image Process. 22, 95–115 (1983).
[Crossref]

Koenderink, J. J.

J. J. Koenderink, A. J. van Doorn, “Facts on optic flow,” Biol. Cybern. 56, 247–254 (1987).
[Crossref] [PubMed]

J. J. Koenderink, A. J. van Doorn, “Exterospecific component of the motion parallax field,” J. Opt. Soc. Am. 71, 953–957 (1981).
[Crossref] [PubMed]

J. J. Koenderink, A. J. van Doorn, “Local structure of movement parallax of the plane,” J. Opt. Soc. Am. 66, 717–723 (1976).
[Crossref]

J. J. Koenderink, A. J. van Doorn, “Invariant properties of the motion parallax field due to the movement of rigid bodies relative to an observer,” Opt. Acta 22, 773–791 (1975).
[Crossref]

Lappin, J.

J. Lappin, F. Norman, “Detectabilities of the components of optical flow,” presented at the Psychonomic Society Annual Meeting, Chicago, Ill., November 10–12 1988.

Lawton, D. T.

Longuet-Higgins, H. C.

H. C. Longuet-Higgins, “The visual ambiguity of a moving plane,” Proc. R. Soc. London Ser. B 223, 165–175 (1984).
[Crossref]

H. C. Longuet-Higgins, “A computer algorithm for reconstructing a scene from two projections,” Nature 293, 133–135 (1981).
[Crossref]

H. C. Longuet-Higgins, K. Prazdny, “The interpretation of a moving retinal image,” Proc.R. Soc. London Ser. B 208, 385–397 (1980).
[Crossref]

Mestre, D. R.

W. H. Warren, D. R. Mestre, A. W. Blackwell, M. W. Morris, “Perception of curvilinear heading from optical flow,” submitted to J. Exp. Psychol. Hum. Percep. Perf.

Mitiche, A.

A. Mitiche, “Computation of optical flow and rigid motion,” in Proceedings of the IEEE Workshop on Computer Vision: Representation and Control (IEEE Computer Society, New York, 1984).

Morris, M. W.

W. H. Warren, M. W. Morris, M. Kalish, “Perception of translational heading from optical flow,” J. Exp. Psychol. Hum. Percep. Perf. 14, 646–660 (1988).
[Crossref]

W. H. Warren, D. R. Mestre, A. W. Blackwell, M. W. Morris, “Perception of curvilinear heading from optical flow,” submitted to J. Exp. Psychol. Hum. Percep. Perf.

Nagel, H.-H.

H.-H. Nagel, “On the derivation of 3D rigid point configurations from image sequences,” in Proceedings of the IEEE Conference on Pattern Recognition and Image Processing (IEEE Computer Society Press, New York, 1981).

Nakayama, K.

B. Frost, K. Nakayama, “Single visual neurons code opposing motion independent of direction,” Science 220, 744–745 (1983).
[Crossref] [PubMed]

K. Nakayama, “Extraction of higher-order derivatives of the optical velocity vector field: limitations imposed by biological hardware,” in Brain Mechanisms and Spatial Vision, D. Ingle, M. Jeannerod, D. Lee, eds. (Martinus-Nijhoff, The Hague, The Netherlands, 1985).
[Crossref]

Norman, F.

J. Lappin, F. Norman, “Detectabilities of the components of optical flow,” presented at the Psychonomic Society Annual Meeting, Chicago, Ill., November 10–12 1988.

Orban, G. A.

G. A. Orban, B. Gulyas, R. Vogels, “Influence of a moving textured background on direction selectivity of cat striate neurons,” J. Neurophys. 57, 1792–1812 (1987).

Prazdny, K.

K. Prazdny, “Determining the instantaneous direction of motion from optical flow generated by a curvilinearly moving observer,” Comput. Graphics Image Process. 17, 238–258 (1981).
[Crossref]

H. C. Longuet-Higgins, K. Prazdny, “The interpretation of a moving retinal image,” Proc.R. Soc. London Ser. B 208, 385–397 (1980).
[Crossref]

K. Prazdny, “Egomotion and relative depth map from optical flow,” Biol. Cybern. 36, 87–102 (1980).
[Crossref] [PubMed]

Regan, D.

D. Regan, “Visual flow and the direction of locomotion,” Science 277, 1064–1065 (1985).
[Crossref]

D. Regan, K. I. Beverley, “How do we avoid confounding the direction we are looking and the direction we are moving?” Science 215, 194–196 (1982).
[Crossref] [PubMed]

Richards, W.

W. Richards, “Visual space perception,” in, Handbook of Perception, E. C. Carterette, M. P. Friedman, eds. (Academic, New York, 1975), Vol. 5, pp. 351–386.

Rieger, J. H.

Smith, A. T.

P. Hammond, A. T. Smith, “On the sensitivity of complex cells in feline striate cortex to relative motion,” Exp. Brain Res. 47, 457–460 (1982).
[Crossref] [PubMed]

Toet, L.

J. H. Rieger, L. Toet, “Human visual navigation in the presence of 3D rotations,” Biol. Cybern. 52, 377–381 (1985).
[Crossref]

Torre, V.

Torrey, C.

C. Torrey, “Visual flow and the direction of locomotion,” Science 277, 1064 (1065).

Tsai, R. Y.

R. Y. Tsai, T. S. Huang, “Uniqueness and estimation of three-dimensional motion parameters of rigid objects with curved surfaces,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 13–27 (1984).
[Crossref]

R. Y. Tsai, T. S. Huang, “Estimating three-dimensional motion parameters of a rigid planar patch: III. Finite point correspondences and the three-view problem,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 213–220 (1984).
[Crossref]

R. Y. Tsai, T. S. Huang, “Estimating three-dimensional motion parameters of a rigid planar patch,” IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 1147–1152 (1981).
[Crossref]

Ullman, S.

A. M. Waxman, S. Ullman, “Surface structure and 3D motion from image flow: a kinematic analysis,” Int. J. Robotics Res. 4, 72–94 (1985).
[Crossref]

van Doorn, A. J.

J. J. Koenderink, A. J. van Doorn, “Facts on optic flow,” Biol. Cybern. 56, 247–254 (1987).
[Crossref] [PubMed]

J. J. Koenderink, A. J. van Doorn, “Exterospecific component of the motion parallax field,” J. Opt. Soc. Am. 71, 953–957 (1981).
[Crossref] [PubMed]

J. J. Koenderink, A. J. van Doorn, “Local structure of movement parallax of the plane,” J. Opt. Soc. Am. 66, 717–723 (1976).
[Crossref]

J. J. Koenderink, A. J. van Doorn, “Invariant properties of the motion parallax field due to the movement of rigid bodies relative to an observer,” Opt. Acta 22, 773–791 (1975).
[Crossref]

Verri, A.

Vogels, R.

G. A. Orban, B. Gulyas, R. Vogels, “Influence of a moving textured background on direction selectivity of cat striate neurons,” J. Neurophys. 57, 1792–1812 (1987).

von Holst, E.

E. von Holst, “Relations between the central nervous system and the peripheral organs,” Animal Behav. 2, 89–94 (1954).
[Crossref]

Warren, W. H.

W. H. Warren, M. W. Morris, M. Kalish, “Perception of translational heading from optical flow,” J. Exp. Psychol. Hum. Percep. Perf. 14, 646–660 (1988).
[Crossref]

W. H. Warren, W. Griesar, A. W. Blackwell, M. Kalish, N. G. Hatsopoulos, “On the sufficiency of the velocity field for perception of heading,” to be submitted to Biol. Cybern.

W. H. Warren, D. R. Mestre, A. W. Blackwell, M. W. Morris, “Perception of curvilinear heading from optical flow,” submitted to J. Exp. Psychol. Hum. Percep. Perf.

Waxman, A. M.

A. M. Waxman, S. Ullman, “Surface structure and 3D motion from image flow: a kinematic analysis,” Int. J. Robotics Res. 4, 72–94 (1985).
[Crossref]

White, G. R.

I. R. Johnston, G. R. White, R. W. Cumming, “The role of optical expansion patterns in locomotor control,” Am. J. Psychol. 86, 311–324 (1973).
[Crossref] [PubMed]

Am. J. Psychol. (1)

I. R. Johnston, G. R. White, R. W. Cumming, “The role of optical expansion patterns in locomotor control,” Am. J. Psychol. 86, 311–324 (1973).
[Crossref] [PubMed]

Animal Behav. (1)

E. von Holst, “Relations between the central nervous system and the peripheral organs,” Animal Behav. 2, 89–94 (1954).
[Crossref]

Biol. Cybern. (3)

J. H. Rieger, L. Toet, “Human visual navigation in the presence of 3D rotations,” Biol. Cybern. 52, 377–381 (1985).
[Crossref]

J. J. Koenderink, A. J. van Doorn, “Facts on optic flow,” Biol. Cybern. 56, 247–254 (1987).
[Crossref] [PubMed]

K. Prazdny, “Egomotion and relative depth map from optical flow,” Biol. Cybern. 36, 87–102 (1980).
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[Crossref]

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Figures (11)

Fig. 1
Fig. 1

Instantaneous velocity field produced by pure observer translation parallel to the ground plane. Vertical line indicates heading; vectors (line segments) indicate optical motions of environmental elements (corresponding dots).

Fig. 2
Fig. 2

Velocity field produced by pure eye rotation down and to the right. Note that this system yields approximately parallel flow in the central visual field.

Fig. 3
Fig. 3

Velocity field produced by combined translation and rotation, resulting from translating toward the vertical line while fixating the circle on the passing ground surface.

Fig. 4
Fig. 4

Percentage of correct responses as a function of heading angle with stationary and moving fixation points (experiment 1, ground surface). Chance-level performance is 50% correct.

Fig. 5
Fig. 5

Percentage of correct responses as a function of heading angle with moving fixation point and simulated eye rotation (experiment 2, ground).

Fig. 6
Fig. 6

Velocity field produced by observer translation through a 3D cloud of elements. The X indicates heading.

Fig. 7
Fig. 7

Velocity field produced by combined observer translation and rotation through a 3D cloud of dots, resulting from translating toward the X while fixating the circle in the middle of the cloud.

Fig. 8
Fig. 8

Percent correct as a function of heading angle with moving fixation point and simulated eye rotation (experiment 3, cloud).

Fig. 9
Fig. 9

Velocity field produced by combined observer translation and rotation relative to a wall surface, resulting from translating toward the X while fixating circle on the wall.

Fig. 10
Fig. 10

Percentage of correct responses as a function of heading angle with moving fixation point and simulated eye rotation (experiment 4, wall).

Fig. 11
Fig. 11

Percentage of correct responses as a function of neighborhood size and dot density with moving fixation point and simulated eye rotation (experiment 5, cloud).

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