Abstract

A novel phenomenon in stereopsis can be observed when viewing binocularly stabilized retinal images. This phenomenon is particularly impressive for random-dot stereoscopic images in foveal vision. If initially the left and right images are brought within Panum’s fusional area (6-min arc alignment), fusion and stereopsis are perceived; the images can then be pulled apart symmetrically by about 2 deg in the horizontal direction without loss of stereopsis or fusion. The images are actually pulled apart on the retinae, since the binocular retinal stabilization compensates for the convergence-divergence motions of the eyes; hence a supra-retinal function must be responsible for this type of fusion. If the pulling proceeds too fast, or exceeds the 2-deg limit, or if the stimulus is occluded briefly, the fusional mechanism fails and the fused image abruptly breaks apart into two separate images which have to be brought within Panum’s area again to re-establish fusion. For line stimuli, the maximum disparity without loss of fusion is much less than for random-dot patterns; it is always largest for disparity in the horizontal direction and is less in the vertical direction. These findings indicate that stereopsis and the classically conceived corresponding points greatly depend both on the class of stimulus used and on the recent history of the stimulation.

© 1967 Optical Society of America

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Corrections

Derek Fender and Bela Julesz, "Erratum," J. Opt. Soc. Am. 57, 1402-1402 (1967)
https://www.osapublishing.org/josa/abstract.cfm?uri=josa-57-11-1402

References

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  1. H. W. Dove, Ber. Preuss. Akad. Wiss. 1841, 251 (1841)and Ann. Physik, Ser. 2,  110, 494 (1860).
  2. K. N. Ogle, Researches in Binocular Vision (Saunders, Philadelphia, 1950).
  3. K. N. Ogle, J. Exptl. Psychol. 44, 253 (1952).
    [Crossref]
  4. B. Julesz, Bell System Tech. J. 39, 1125 (1960).For an up-to-date review see: Science 145, 356 (1964).
    [Crossref]
  5. D. H. Fender and P. W. Nye, Kybernetik. 1, 81 (1961).
    [Crossref] [PubMed]
  6. S. L. Polyak, The Retina (The University of Chicago Press, Chicago, 1941), Ch. 15, p. 204.
  7. G. H. Byford, Nature 184, 1493 (1959).
    [Crossref]
  8. G. D. McCann and D. H. Fender, Neural Theory and Modeling (Stanford University Press, Stanford, California, 1964), p. 232.
  9. Subject G was unable to obtain more than fleeting glimpses of the stereoscopic effect in stabilized vision despite considerable training. Most subjects can examine a considerable area of a stabilized image with high acuity even though they cannot shift their line of regard over the target. This area is usually elliptical, subtending about 2 deg horizontally by 1 deg vertically; outside of this area, acuity in stabilized vision falls off rapidly. Subject G does not have this faculty; his area of high acuity in stabilized vision is at most 20-min arc wide; thus very rarely is he able to resolve a sufficient number of picture elements belonging to the central square and some belonging to the surround at the same time a condition which appears to be necessary for perception of the stereoscopic effect. Subject G showed normal stereopsis with line targets in normal and in stabilized vision, and also with random-dot targets in normal vision.
  10. B. Julesz, J. Opt. Soc. Am. 53, 994 (1963).
    [Crossref] [PubMed]
  11. The actual binocular parallax in these targets was 8-min arc, so some of these saccadic changes of disparity may have been purposeful. The probability of a saccade changing the disparity by less than 5-min arc or more than 11-min arc is 0.65.
  12. G. W. Beeler, Ph.D. thesis (California Institute of Technology, 1965).

1963 (1)

1961 (1)

D. H. Fender and P. W. Nye, Kybernetik. 1, 81 (1961).
[Crossref] [PubMed]

1960 (1)

B. Julesz, Bell System Tech. J. 39, 1125 (1960).For an up-to-date review see: Science 145, 356 (1964).
[Crossref]

1959 (1)

G. H. Byford, Nature 184, 1493 (1959).
[Crossref]

1952 (1)

K. N. Ogle, J. Exptl. Psychol. 44, 253 (1952).
[Crossref]

1841 (1)

H. W. Dove, Ber. Preuss. Akad. Wiss. 1841, 251 (1841)and Ann. Physik, Ser. 2,  110, 494 (1860).

Beeler, G. W.

G. W. Beeler, Ph.D. thesis (California Institute of Technology, 1965).

Byford, G. H.

G. H. Byford, Nature 184, 1493 (1959).
[Crossref]

Dove, H. W.

H. W. Dove, Ber. Preuss. Akad. Wiss. 1841, 251 (1841)and Ann. Physik, Ser. 2,  110, 494 (1860).

Fender, D. H.

D. H. Fender and P. W. Nye, Kybernetik. 1, 81 (1961).
[Crossref] [PubMed]

G. D. McCann and D. H. Fender, Neural Theory and Modeling (Stanford University Press, Stanford, California, 1964), p. 232.

Julesz, B.

B. Julesz, J. Opt. Soc. Am. 53, 994 (1963).
[Crossref] [PubMed]

B. Julesz, Bell System Tech. J. 39, 1125 (1960).For an up-to-date review see: Science 145, 356 (1964).
[Crossref]

McCann, G. D.

G. D. McCann and D. H. Fender, Neural Theory and Modeling (Stanford University Press, Stanford, California, 1964), p. 232.

Nye, P. W.

D. H. Fender and P. W. Nye, Kybernetik. 1, 81 (1961).
[Crossref] [PubMed]

Ogle, K. N.

K. N. Ogle, J. Exptl. Psychol. 44, 253 (1952).
[Crossref]

K. N. Ogle, Researches in Binocular Vision (Saunders, Philadelphia, 1950).

Polyak, S. L.

S. L. Polyak, The Retina (The University of Chicago Press, Chicago, 1941), Ch. 15, p. 204.

Bell System Tech. J. (1)

B. Julesz, Bell System Tech. J. 39, 1125 (1960).For an up-to-date review see: Science 145, 356 (1964).
[Crossref]

Ber. Preuss. Akad. Wiss. (1)

H. W. Dove, Ber. Preuss. Akad. Wiss. 1841, 251 (1841)and Ann. Physik, Ser. 2,  110, 494 (1860).

J. Exptl. Psychol. (1)

K. N. Ogle, J. Exptl. Psychol. 44, 253 (1952).
[Crossref]

J. Opt. Soc. Am. (1)

Kybernetik. (1)

D. H. Fender and P. W. Nye, Kybernetik. 1, 81 (1961).
[Crossref] [PubMed]

Nature (1)

G. H. Byford, Nature 184, 1493 (1959).
[Crossref]

Other (6)

G. D. McCann and D. H. Fender, Neural Theory and Modeling (Stanford University Press, Stanford, California, 1964), p. 232.

Subject G was unable to obtain more than fleeting glimpses of the stereoscopic effect in stabilized vision despite considerable training. Most subjects can examine a considerable area of a stabilized image with high acuity even though they cannot shift their line of regard over the target. This area is usually elliptical, subtending about 2 deg horizontally by 1 deg vertically; outside of this area, acuity in stabilized vision falls off rapidly. Subject G does not have this faculty; his area of high acuity in stabilized vision is at most 20-min arc wide; thus very rarely is he able to resolve a sufficient number of picture elements belonging to the central square and some belonging to the surround at the same time a condition which appears to be necessary for perception of the stereoscopic effect. Subject G showed normal stereopsis with line targets in normal and in stabilized vision, and also with random-dot targets in normal vision.

The actual binocular parallax in these targets was 8-min arc, so some of these saccadic changes of disparity may have been purposeful. The probability of a saccade changing the disparity by less than 5-min arc or more than 11-min arc is 0.65.

G. W. Beeler, Ph.D. thesis (California Institute of Technology, 1965).

S. L. Polyak, The Retina (The University of Chicago Press, Chicago, 1941), Ch. 15, p. 204.

K. N. Ogle, Researches in Binocular Vision (Saunders, Philadelphia, 1950).

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Figures (10)

F. 1
F. 1

Pair of random-dot stereo targets as used in this research. If the pictures are examined through a suitable stereoscopic viewer, a central square area of 40×40 picture elements can be seen in depth.

F. 2
F. 2

Left-eye component of equipment for producing binocular stabilized images. Parallel rays enter from a projector at the left.

F. 3
F. 3

Breakaway and fusional limits for vertical lines moved into horizontal disparity; stabilized vision. The dotted line indicates a region of transient fusion between the lines and fiducial marks. This is not reproducible from one experiment to the next.

F. 4
F. 4

Retinal areas over which fusion (dotted curve) of single line targets is possible. The solid curves show the limits at which breakaway occurs. Only points in the temporal direction have been tested; we assume that the diagrams are symmetrical about the vertical axis.

F. 5
F. 5

Two-dimensional histogram, illustrating the motion of the right visual axis with respect to the left during a 2-min viewing period. The number printed in each cell should be multiplied by 20 to get the total duration in msec of the disparity whose value is shown by the coordinates of the cell. The zeros in the center of the diagram represent times longer than 2 sec.

F. 6
F. 6

Breakaway and fusional limits for random-dot stereo patterns moved into horizontal disparity; stabilized vision. Dotted region as in Fig. 3, except that transient fusion now occurs between small groups of picture elements which happen to have high correlation between left and right images.

F. 7
F. 7

These histograms show along the ordinate the probability, p, that a spontaneous saccade causes a change in vergence (and hence of image disparity) of magnitude shown along the abscissa. Upper diagram, pinhole target viewed binocularly; lower diagram, random-dot stereo-pair targets. This diagram refers to subject G.

F. 8
F. 8

This diagram compares the performance of subjects G and N. Vertical-line targets were pulled rapidly apart after fusion and the time for re-fusion was measured. Solid lines, normal vision; dashed lines, stabilized vision. The encircled number at the end of each curve gives the maximum disparity at which re-fusion could be achieved.

F. 9
F. 9

Time taken by subject N to re-fuse random-dot targets after they had been pulled rapidly apart. Solid lines, normal vision; dashed lines, stabilized vision. The encircled number at the end of each curve gives the maximum disparity at which fusion could be achieved.

F. 10
F. 10

This diagram shows the maximum disparity that would still permit re-fusion of random-dot stereo images after they have been occluded for a brief period.

Tables (4)

Tables Icon

Table I Horizontal disparity at which vertical-line targets fuse or separate. The standard deviations quoted in this and all subsequent tables refer to the values obtained for one subject.

Tables Icon

Table II Vertical disparity at which horizontal-line targets fuse or separate.

Tables Icon

Table III Oblique disparity at which inclined-line targets fuse or separate.

Tables Icon

Table IV Disparity at which random-dot stereoscopic patterns fuse or separate.