Abstract

A deterministic model for monocular space perception is presented. According to the model, retinal luminance changes due to involuntary eye movements are detected and locally analyzed to yield the angular velocity of each image point. The stable three-dimensional spatial coordinates of viewed objects are then reconstructed using a method of infinitesimal transformations. The extraction of the movement (parallax) field from the optical flow is represented by a set of differential equations, the derivation of which is based on the conservation of energy principle. The relation of the model to retinal neurophysiology and to various aspects of visual space perception is discussed.

© 1980 Optical Society of America

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  1. H. von Helmholtz, Handbuch der Physiologischen Optik (Voss, Leipzig, 1866), Vol. 3.
  2. E. B. Holt, "Eye Movement and Central Anasthesia," Harvard Psychol. studies 1, 3–45 (1903).
  3. E. von Holst, "Relations between the central nervous system and the peripheral organs," Animal Behav. 2, 89–94 (1954).
  4. D. M. Mackay, "Visual Stability and Voluntary Eye Movements," in Handbook of Sensory Physiology, edited by R. Jung (Springer, Berlin, 1973), VII/3, pp. 307–331.
  5. J. J. Koenderink and A. J. van Doorn, "Local Structure of Movement Parallax of the Plane," J. Opt. Soc. Am. 66, 717–723 (1976).
  6. J. J. Gibson, The Perception of the Visual World (Houghton Mifflin, Boston, 1950).
  7. H. Wallach, "The Modification of Stereoscopic Depth-Perception and the Kinetic Depth Effect," Am. J. Psychol. 76, 429–435 (1963).
  8. G. Johansson, "Visual Motion Perception," Sci. Am., June, 76–88 (1975).
  9. M. Braunstein, Depth Perception Through Motion (Academic, New York, 1976).
  10. R. W. Ditchburn, Eye Movements and Visual Perception (Clarendon, Oxford, 1973).
  11. Our preliminary results show that under free view and stabilized image conditions, image displacements of the order of magnitude of that caused by involuntary eye movements are sufficient for some perception of depth. We display monocularly in alternation 2 of the Julesz's type stereograms in which the central square is shifted by 1′–2′. The subject clearly sees the square as being in front of or behind the background.
  12. The velocity and amplitude data relates to the eyeball motion. The magnitude of the image motion on the retina has to be multiplied by two since there is a magnification factor because the eyeball moves approximately around its center.
  13. A. L. Yarbus, Eye Movements and Vision (Plenum, New York, 1967).
  14. R. W. Ditchburn and J. A. Foley-Fisher, "Assembled Data in Eye Movements," Opt. Acta 14, 113–118 (1967).
  15. D. H. Fender and B. Julesz, "Extension of Panum's fusional area in binocular stabilized vision," J. Opt. Soc. Am. 57, 819–830 (1967).
  16. M. Alpern, "Eye Movement," in Handbook of Sensory Physiology, edited by D. Janson (Springer, Berlin, 1972), VII/4, pp. 303–330.
  17. C. Enroth, "Spike Frequency and Flicker Fusion Frequency in Retinal Gangelion Cells," J. Physiol. 117, 18–21 (1952).
  18. E. Dodt and C. Enroth, "Retinal Flicker Response in Cat," Acta Physiol. Scand. 30, 375–390 (1953).
  19. T. Ogawa, P. O. Bishop, and W. R. Levick, "Temporal Characteristics of Responses to Photic Stimulation by Single Ganglion Cells in the Unopened Eye of the Cat," J. Neurophysiol. 29, 1–30 (1966).
  20. W. A. van de Grind, O. J. Grusser, and H. V. Lunkenheimer, "Temporal Transfer Properties of the Afferant Visual System," in Handbook of Sensory Physiology, edited by R. Jung (Springer, Berlin, 1973), VII/3, pp. 431–573.
  21. R. W. Ditchburn, D. H. Fender, and S. Mayne, "Vision with Controlled Movements of the Retinal Image," J. Physiol. 145, 98–107 (1959).
  22. An alternative derivation using direction cosines and their derivatives gives an even more elegant system of equations but is more difficult to comprehend.
  23. G. Johansson, "Spatio—Temporal Differentiation and Integration in Visual Motion Perception," Psychol. Res. 38, 379–393 (1976).
  24. J. J. Gibson, The Senses Considered as Perceptual Systems (Houghton Mifflin, Boston, 1966).
  25. D. A. Gordon, "Static and dynamic visual fields in human space perception," J. Opt. Soc. Am. 55, 1296–1303 (1965).
  26. K. Nakayama and J. M. Loomis, "Optical Velocity Patterns, Velocity Sensitive Neurons and Space Perception: A Hypothesis," Perception 3, 63–80 (1974).
  27. E. Borjesson and C. von Hofsten, "A Vector Model for Perceived Object Rotation and Translation in Space," Psychol. Res. 38, 209–230 (1976).
  28. R. W. Rodieck, The Vertebrate Retina (Freeman, San Francisco, 1973).
  29. M. Gur and R. R. Purple, "Retinal Ganglion Cells Activity in the Ground Squirrel under Halothane Anasthesia," Vision Res. 18, 1–14 (1978).
  30. D. N. Lee, "Stimulus Pairing in Sequential Phi Motion," Perception 1, 85–91 (1972).
  31. B. Julesz, Foundations of Cyclopean Perception, University of Chicago, Chicago, 1971, p. 105.
  32. J. E. Dowling and B. B. Boycott, "Organization of the Primate Retina: Electron Microscopy," Proc. Roy. Soc. B, 166, 80–111 (1966).
  33. L. Matin, "Eye Movements and Perceived Visual Direction," in Handbook of Sensory Physiology, edited by D. Jamson (Springer, Berlin, 1972), VII/4, pp. 331–380.

1978

M. Gur and R. R. Purple, "Retinal Ganglion Cells Activity in the Ground Squirrel under Halothane Anasthesia," Vision Res. 18, 1–14 (1978).

1976

E. Borjesson and C. von Hofsten, "A Vector Model for Perceived Object Rotation and Translation in Space," Psychol. Res. 38, 209–230 (1976).

J. J. Koenderink and A. J. van Doorn, "Local Structure of Movement Parallax of the Plane," J. Opt. Soc. Am. 66, 717–723 (1976).

G. Johansson, "Spatio—Temporal Differentiation and Integration in Visual Motion Perception," Psychol. Res. 38, 379–393 (1976).

1975

G. Johansson, "Visual Motion Perception," Sci. Am., June, 76–88 (1975).

1974

K. Nakayama and J. M. Loomis, "Optical Velocity Patterns, Velocity Sensitive Neurons and Space Perception: A Hypothesis," Perception 3, 63–80 (1974).

1973

D. M. Mackay, "Visual Stability and Voluntary Eye Movements," in Handbook of Sensory Physiology, edited by R. Jung (Springer, Berlin, 1973), VII/3, pp. 307–331.

W. A. van de Grind, O. J. Grusser, and H. V. Lunkenheimer, "Temporal Transfer Properties of the Afferant Visual System," in Handbook of Sensory Physiology, edited by R. Jung (Springer, Berlin, 1973), VII/3, pp. 431–573.

1972

M. Alpern, "Eye Movement," in Handbook of Sensory Physiology, edited by D. Janson (Springer, Berlin, 1972), VII/4, pp. 303–330.

L. Matin, "Eye Movements and Perceived Visual Direction," in Handbook of Sensory Physiology, edited by D. Jamson (Springer, Berlin, 1972), VII/4, pp. 331–380.

D. N. Lee, "Stimulus Pairing in Sequential Phi Motion," Perception 1, 85–91 (1972).

1967

R. W. Ditchburn and J. A. Foley-Fisher, "Assembled Data in Eye Movements," Opt. Acta 14, 113–118 (1967).

D. H. Fender and B. Julesz, "Extension of Panum's fusional area in binocular stabilized vision," J. Opt. Soc. Am. 57, 819–830 (1967).

1966

T. Ogawa, P. O. Bishop, and W. R. Levick, "Temporal Characteristics of Responses to Photic Stimulation by Single Ganglion Cells in the Unopened Eye of the Cat," J. Neurophysiol. 29, 1–30 (1966).

J. E. Dowling and B. B. Boycott, "Organization of the Primate Retina: Electron Microscopy," Proc. Roy. Soc. B, 166, 80–111 (1966).

1965

1963

H. Wallach, "The Modification of Stereoscopic Depth-Perception and the Kinetic Depth Effect," Am. J. Psychol. 76, 429–435 (1963).

1959

R. W. Ditchburn, D. H. Fender, and S. Mayne, "Vision with Controlled Movements of the Retinal Image," J. Physiol. 145, 98–107 (1959).

1954

E. von Holst, "Relations between the central nervous system and the peripheral organs," Animal Behav. 2, 89–94 (1954).

1953

E. Dodt and C. Enroth, "Retinal Flicker Response in Cat," Acta Physiol. Scand. 30, 375–390 (1953).

1952

C. Enroth, "Spike Frequency and Flicker Fusion Frequency in Retinal Gangelion Cells," J. Physiol. 117, 18–21 (1952).

1903

E. B. Holt, "Eye Movement and Central Anasthesia," Harvard Psychol. studies 1, 3–45 (1903).

Alpern, M.

M. Alpern, "Eye Movement," in Handbook of Sensory Physiology, edited by D. Janson (Springer, Berlin, 1972), VII/4, pp. 303–330.

Bishop, P. O.

T. Ogawa, P. O. Bishop, and W. R. Levick, "Temporal Characteristics of Responses to Photic Stimulation by Single Ganglion Cells in the Unopened Eye of the Cat," J. Neurophysiol. 29, 1–30 (1966).

Borjesson, E.

E. Borjesson and C. von Hofsten, "A Vector Model for Perceived Object Rotation and Translation in Space," Psychol. Res. 38, 209–230 (1976).

Boycott, B. B.

J. E. Dowling and B. B. Boycott, "Organization of the Primate Retina: Electron Microscopy," Proc. Roy. Soc. B, 166, 80–111 (1966).

Braunstein, M.

M. Braunstein, Depth Perception Through Motion (Academic, New York, 1976).

Ditchburn, R. W.

R. W. Ditchburn and J. A. Foley-Fisher, "Assembled Data in Eye Movements," Opt. Acta 14, 113–118 (1967).

R. W. Ditchburn, D. H. Fender, and S. Mayne, "Vision with Controlled Movements of the Retinal Image," J. Physiol. 145, 98–107 (1959).

R. W. Ditchburn, Eye Movements and Visual Perception (Clarendon, Oxford, 1973).

Dodt, E.

E. Dodt and C. Enroth, "Retinal Flicker Response in Cat," Acta Physiol. Scand. 30, 375–390 (1953).

Dowling, J. E.

J. E. Dowling and B. B. Boycott, "Organization of the Primate Retina: Electron Microscopy," Proc. Roy. Soc. B, 166, 80–111 (1966).

Enroth, C.

E. Dodt and C. Enroth, "Retinal Flicker Response in Cat," Acta Physiol. Scand. 30, 375–390 (1953).

C. Enroth, "Spike Frequency and Flicker Fusion Frequency in Retinal Gangelion Cells," J. Physiol. 117, 18–21 (1952).

Fender, D. H.

D. H. Fender and B. Julesz, "Extension of Panum's fusional area in binocular stabilized vision," J. Opt. Soc. Am. 57, 819–830 (1967).

R. W. Ditchburn, D. H. Fender, and S. Mayne, "Vision with Controlled Movements of the Retinal Image," J. Physiol. 145, 98–107 (1959).

Foley-Fisher, J. A.

R. W. Ditchburn and J. A. Foley-Fisher, "Assembled Data in Eye Movements," Opt. Acta 14, 113–118 (1967).

Gibson, J. J.

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

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

Gordon, D. A.

Grusser, O. J.

W. A. van de Grind, O. J. Grusser, and H. V. Lunkenheimer, "Temporal Transfer Properties of the Afferant Visual System," in Handbook of Sensory Physiology, edited by R. Jung (Springer, Berlin, 1973), VII/3, pp. 431–573.

Gur, M.

M. Gur and R. R. Purple, "Retinal Ganglion Cells Activity in the Ground Squirrel under Halothane Anasthesia," Vision Res. 18, 1–14 (1978).

Holt, E. B.

E. B. Holt, "Eye Movement and Central Anasthesia," Harvard Psychol. studies 1, 3–45 (1903).

Johansson, G.

G. Johansson, "Spatio—Temporal Differentiation and Integration in Visual Motion Perception," Psychol. Res. 38, 379–393 (1976).

G. Johansson, "Visual Motion Perception," Sci. Am., June, 76–88 (1975).

Julesz, B.

D. H. Fender and B. Julesz, "Extension of Panum's fusional area in binocular stabilized vision," J. Opt. Soc. Am. 57, 819–830 (1967).

B. Julesz, Foundations of Cyclopean Perception, University of Chicago, Chicago, 1971, p. 105.

Koenderink, J. J.

Lee, D. N.

D. N. Lee, "Stimulus Pairing in Sequential Phi Motion," Perception 1, 85–91 (1972).

Levick, W. R.

T. Ogawa, P. O. Bishop, and W. R. Levick, "Temporal Characteristics of Responses to Photic Stimulation by Single Ganglion Cells in the Unopened Eye of the Cat," J. Neurophysiol. 29, 1–30 (1966).

Loomis, J. M.

K. Nakayama and J. M. Loomis, "Optical Velocity Patterns, Velocity Sensitive Neurons and Space Perception: A Hypothesis," Perception 3, 63–80 (1974).

Lunkenheimer, H. V.

W. A. van de Grind, O. J. Grusser, and H. V. Lunkenheimer, "Temporal Transfer Properties of the Afferant Visual System," in Handbook of Sensory Physiology, edited by R. Jung (Springer, Berlin, 1973), VII/3, pp. 431–573.

Mackay, D. M.

D. M. Mackay, "Visual Stability and Voluntary Eye Movements," in Handbook of Sensory Physiology, edited by R. Jung (Springer, Berlin, 1973), VII/3, pp. 307–331.

Matin, L.

L. Matin, "Eye Movements and Perceived Visual Direction," in Handbook of Sensory Physiology, edited by D. Jamson (Springer, Berlin, 1972), VII/4, pp. 331–380.

Mayne, S.

R. W. Ditchburn, D. H. Fender, and S. Mayne, "Vision with Controlled Movements of the Retinal Image," J. Physiol. 145, 98–107 (1959).

Nakayama, K.

K. Nakayama and J. M. Loomis, "Optical Velocity Patterns, Velocity Sensitive Neurons and Space Perception: A Hypothesis," Perception 3, 63–80 (1974).

Ogawa, T.

T. Ogawa, P. O. Bishop, and W. R. Levick, "Temporal Characteristics of Responses to Photic Stimulation by Single Ganglion Cells in the Unopened Eye of the Cat," J. Neurophysiol. 29, 1–30 (1966).

Purple, R. R.

M. Gur and R. R. Purple, "Retinal Ganglion Cells Activity in the Ground Squirrel under Halothane Anasthesia," Vision Res. 18, 1–14 (1978).

Rodieck, R. W.

R. W. Rodieck, The Vertebrate Retina (Freeman, San Francisco, 1973).

van de Grind, W. A.

W. A. van de Grind, O. J. Grusser, and H. V. Lunkenheimer, "Temporal Transfer Properties of the Afferant Visual System," in Handbook of Sensory Physiology, edited by R. Jung (Springer, Berlin, 1973), VII/3, pp. 431–573.

van Doorn, A. J.

von Helmholtz, H.

H. von Helmholtz, Handbuch der Physiologischen Optik (Voss, Leipzig, 1866), Vol. 3.

von Hofsten, C.

E. Borjesson and C. von Hofsten, "A Vector Model for Perceived Object Rotation and Translation in Space," Psychol. Res. 38, 209–230 (1976).

von Holst, E.

E. von Holst, "Relations between the central nervous system and the peripheral organs," Animal Behav. 2, 89–94 (1954).

Wallach, H.

H. Wallach, "The Modification of Stereoscopic Depth-Perception and the Kinetic Depth Effect," Am. J. Psychol. 76, 429–435 (1963).

Yarbus, A. L.

A. L. Yarbus, Eye Movements and Vision (Plenum, New York, 1967).

Acta Physiol. Scand.

E. Dodt and C. Enroth, "Retinal Flicker Response in Cat," Acta Physiol. Scand. 30, 375–390 (1953).

Am. J. Psychol.

H. Wallach, "The Modification of Stereoscopic Depth-Perception and the Kinetic Depth Effect," Am. J. Psychol. 76, 429–435 (1963).

Animal Behav.

E. von Holst, "Relations between the central nervous system and the peripheral organs," Animal Behav. 2, 89–94 (1954).

Harvard Psychol. studies

E. B. Holt, "Eye Movement and Central Anasthesia," Harvard Psychol. studies 1, 3–45 (1903).

J. Neurophysiol.

T. Ogawa, P. O. Bishop, and W. R. Levick, "Temporal Characteristics of Responses to Photic Stimulation by Single Ganglion Cells in the Unopened Eye of the Cat," J. Neurophysiol. 29, 1–30 (1966).

J. Opt. Soc. Am.

J. Physiol.

R. W. Ditchburn, D. H. Fender, and S. Mayne, "Vision with Controlled Movements of the Retinal Image," J. Physiol. 145, 98–107 (1959).

C. Enroth, "Spike Frequency and Flicker Fusion Frequency in Retinal Gangelion Cells," J. Physiol. 117, 18–21 (1952).

Opt. Acta

R. W. Ditchburn and J. A. Foley-Fisher, "Assembled Data in Eye Movements," Opt. Acta 14, 113–118 (1967).

Perception

K. Nakayama and J. M. Loomis, "Optical Velocity Patterns, Velocity Sensitive Neurons and Space Perception: A Hypothesis," Perception 3, 63–80 (1974).

D. N. Lee, "Stimulus Pairing in Sequential Phi Motion," Perception 1, 85–91 (1972).

Proc. Roy. Soc. B

J. E. Dowling and B. B. Boycott, "Organization of the Primate Retina: Electron Microscopy," Proc. Roy. Soc. B, 166, 80–111 (1966).

Psychol. Res.

E. Borjesson and C. von Hofsten, "A Vector Model for Perceived Object Rotation and Translation in Space," Psychol. Res. 38, 209–230 (1976).

G. Johansson, "Spatio—Temporal Differentiation and Integration in Visual Motion Perception," Psychol. Res. 38, 379–393 (1976).

Vision Res.

M. Gur and R. R. Purple, "Retinal Ganglion Cells Activity in the Ground Squirrel under Halothane Anasthesia," Vision Res. 18, 1–14 (1978).

Other

D. M. Mackay, "Visual Stability and Voluntary Eye Movements," in Handbook of Sensory Physiology, edited by R. Jung (Springer, Berlin, 1973), VII/3, pp. 307–331.

L. Matin, "Eye Movements and Perceived Visual Direction," in Handbook of Sensory Physiology, edited by D. Jamson (Springer, Berlin, 1972), VII/4, pp. 331–380.

H. von Helmholtz, Handbuch der Physiologischen Optik (Voss, Leipzig, 1866), Vol. 3.

B. Julesz, Foundations of Cyclopean Perception, University of Chicago, Chicago, 1971, p. 105.

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

R. W. Rodieck, The Vertebrate Retina (Freeman, San Francisco, 1973).

An alternative derivation using direction cosines and their derivatives gives an even more elegant system of equations but is more difficult to comprehend.

W. A. van de Grind, O. J. Grusser, and H. V. Lunkenheimer, "Temporal Transfer Properties of the Afferant Visual System," in Handbook of Sensory Physiology, edited by R. Jung (Springer, Berlin, 1973), VII/3, pp. 431–573.

M. Alpern, "Eye Movement," in Handbook of Sensory Physiology, edited by D. Janson (Springer, Berlin, 1972), VII/4, pp. 303–330.

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

G. Johansson, "Visual Motion Perception," Sci. Am., June, 76–88 (1975).

M. Braunstein, Depth Perception Through Motion (Academic, New York, 1976).

R. W. Ditchburn, Eye Movements and Visual Perception (Clarendon, Oxford, 1973).

Our preliminary results show that under free view and stabilized image conditions, image displacements of the order of magnitude of that caused by involuntary eye movements are sufficient for some perception of depth. We display monocularly in alternation 2 of the Julesz's type stereograms in which the central square is shifted by 1′–2′. The subject clearly sees the square as being in front of or behind the background.

The velocity and amplitude data relates to the eyeball motion. The magnitude of the image motion on the retina has to be multiplied by two since there is a magnification factor because the eyeball moves approximately around its center.

A. L. Yarbus, Eye Movements and Vision (Plenum, New York, 1967).

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