Abstract

Vertical sinusoidal gratings of slightly differing spatial frequencies presented to each eye lead to the perception of a slanted plane. If a complex pattern is created by presenting two different frequencies to one eye, while the other eye views an increment of one of those frequencies and a decrement of the other, then the stimulus is equivalent to two superimposed vertical planes slanted in opposite directions. Yet the observer generally sees only a single surface at a slant intermediate to the possible extremes. As the relative spatial-frequency content of the two opposing planes is varied, the observed slant is a measure of the strengths of the connecting interactions of the underlying stereomechanisms. From these data the bandwidth of the monocular input channels for the binocular slant mechanism can be estimated and is found to be about two octaves.

© 1981 Optical Society of America

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References

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  1. K. N. Ogle, Researches in Binocular Vision (Hafner, New York, 1950);“The optical space sense,” in The Eye, H. Davidson, ed. (Academic, London, 1964), Vol. 4, pp. 209–417.
  2. B. Gillam, “Changes in the direction of induced aniseikonic slant as a function of distance,” Vision Res. 7, 777–783 (1967).
    [CrossRef] [PubMed]
  3. C. Blakemore, “A new kind of stereoscopic vision,” Vision Res. 10, 1181–1199 (1970).
    [CrossRef] [PubMed]
  4. A. Fiorentini and L. Maffei, “Binocular depth perception with geometrical cues,” Vision Res. 11, 1299–1305 (1971).
    [CrossRef] [PubMed]
  5. H. R. Wilson, “The significance of frequency gradients in binocular grating perception,” Vision Res. 16, 983–989 (1979).
    [CrossRef]
  6. H. C. van der Meer, “Linear combinations of stereoscopic depth effects in dichoptic perception of gratings,” Vision Res. 18, 707–714 (1978).
    [CrossRef] [PubMed]
  7. C. W. Tyler and E. E. Sutter, “Depth from spatial frequency difference: an old kind of stereopsis?” Vision Res. 16, 859–965 (1979).
    [CrossRef]
  8. D. Marr and E. Hildreth, “Theory of edge detection,” Proc. R. Soc. Lon. B 207, 187–217 (1980).
    [CrossRef]
  9. E. Levinson and R. Blake, “Stereopsis by harmonic analysis,” Vision Res. 19, 73–78 (1979).
    [CrossRef] [PubMed]
  10. B. Julesz and J. E. Miller, “Independent spatial-frequency tuned channels in binocular fusion and rivalry,” Percept. 4, 125–143 (1975).
    [CrossRef]
  11. C. Blakemore and F. W. Campbell, “On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. 203, 237–260 (1969).
  12. L. Kaufman, J. Bacon, and F. Barroso, “Stereopsis without image segregation,” Vision Res. 13, 137–147 (1973).
    [CrossRef] [PubMed]
  13. J. M. Foley, “Binocular depth mixture,” Vision Res. 16, 1263–1267 (1976).
    [CrossRef] [PubMed]
  14. J. M. Foley and W. Richards, “Binocular depth mixtures with non-symmetric disparities,” Vision Res. 18, 251–256 (1978).
    [CrossRef]
  15. D. J. Tolhurst, “Adaptation to square-wave gratings: inhibition between spatial frequency channels in the human visual system,” J. Physiol. Lon. 226, 231–248 (1972).
  16. K. K. DeVelois, “Spatial frequency adaptation can enhance contrast sensitivity,” Vision Res. 17, 1057–1065 (1977).
    [CrossRef]
  17. The fact that the descending portion of WR’s curves in Fig. 3 does not fall below the 1.0 line suggests that the negative side lobes may occur only on the low frequency side of the channel.

1980 (1)

D. Marr and E. Hildreth, “Theory of edge detection,” Proc. R. Soc. Lon. B 207, 187–217 (1980).
[CrossRef]

1979 (3)

E. Levinson and R. Blake, “Stereopsis by harmonic analysis,” Vision Res. 19, 73–78 (1979).
[CrossRef] [PubMed]

H. R. Wilson, “The significance of frequency gradients in binocular grating perception,” Vision Res. 16, 983–989 (1979).
[CrossRef]

C. W. Tyler and E. E. Sutter, “Depth from spatial frequency difference: an old kind of stereopsis?” Vision Res. 16, 859–965 (1979).
[CrossRef]

1978 (2)

J. M. Foley and W. Richards, “Binocular depth mixtures with non-symmetric disparities,” Vision Res. 18, 251–256 (1978).
[CrossRef]

H. C. van der Meer, “Linear combinations of stereoscopic depth effects in dichoptic perception of gratings,” Vision Res. 18, 707–714 (1978).
[CrossRef] [PubMed]

1977 (1)

K. K. DeVelois, “Spatial frequency adaptation can enhance contrast sensitivity,” Vision Res. 17, 1057–1065 (1977).
[CrossRef]

1976 (1)

J. M. Foley, “Binocular depth mixture,” Vision Res. 16, 1263–1267 (1976).
[CrossRef] [PubMed]

1975 (1)

B. Julesz and J. E. Miller, “Independent spatial-frequency tuned channels in binocular fusion and rivalry,” Percept. 4, 125–143 (1975).
[CrossRef]

1973 (1)

L. Kaufman, J. Bacon, and F. Barroso, “Stereopsis without image segregation,” Vision Res. 13, 137–147 (1973).
[CrossRef] [PubMed]

1972 (1)

D. J. Tolhurst, “Adaptation to square-wave gratings: inhibition between spatial frequency channels in the human visual system,” J. Physiol. Lon. 226, 231–248 (1972).

1971 (1)

A. Fiorentini and L. Maffei, “Binocular depth perception with geometrical cues,” Vision Res. 11, 1299–1305 (1971).
[CrossRef] [PubMed]

1970 (1)

C. Blakemore, “A new kind of stereoscopic vision,” Vision Res. 10, 1181–1199 (1970).
[CrossRef] [PubMed]

1969 (1)

C. Blakemore and F. W. Campbell, “On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. 203, 237–260 (1969).

1967 (1)

B. Gillam, “Changes in the direction of induced aniseikonic slant as a function of distance,” Vision Res. 7, 777–783 (1967).
[CrossRef] [PubMed]

Bacon, J.

L. Kaufman, J. Bacon, and F. Barroso, “Stereopsis without image segregation,” Vision Res. 13, 137–147 (1973).
[CrossRef] [PubMed]

Barroso, F.

L. Kaufman, J. Bacon, and F. Barroso, “Stereopsis without image segregation,” Vision Res. 13, 137–147 (1973).
[CrossRef] [PubMed]

Blake, R.

E. Levinson and R. Blake, “Stereopsis by harmonic analysis,” Vision Res. 19, 73–78 (1979).
[CrossRef] [PubMed]

Blakemore, C.

C. Blakemore, “A new kind of stereoscopic vision,” Vision Res. 10, 1181–1199 (1970).
[CrossRef] [PubMed]

C. Blakemore and F. W. Campbell, “On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. 203, 237–260 (1969).

Campbell, F. W.

C. Blakemore and F. W. Campbell, “On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. 203, 237–260 (1969).

DeVelois, K. K.

K. K. DeVelois, “Spatial frequency adaptation can enhance contrast sensitivity,” Vision Res. 17, 1057–1065 (1977).
[CrossRef]

Fiorentini, A.

A. Fiorentini and L. Maffei, “Binocular depth perception with geometrical cues,” Vision Res. 11, 1299–1305 (1971).
[CrossRef] [PubMed]

Foley, J. M.

J. M. Foley and W. Richards, “Binocular depth mixtures with non-symmetric disparities,” Vision Res. 18, 251–256 (1978).
[CrossRef]

J. M. Foley, “Binocular depth mixture,” Vision Res. 16, 1263–1267 (1976).
[CrossRef] [PubMed]

Gillam, B.

B. Gillam, “Changes in the direction of induced aniseikonic slant as a function of distance,” Vision Res. 7, 777–783 (1967).
[CrossRef] [PubMed]

Hildreth, E.

D. Marr and E. Hildreth, “Theory of edge detection,” Proc. R. Soc. Lon. B 207, 187–217 (1980).
[CrossRef]

Julesz, B.

B. Julesz and J. E. Miller, “Independent spatial-frequency tuned channels in binocular fusion and rivalry,” Percept. 4, 125–143 (1975).
[CrossRef]

Kaufman, L.

L. Kaufman, J. Bacon, and F. Barroso, “Stereopsis without image segregation,” Vision Res. 13, 137–147 (1973).
[CrossRef] [PubMed]

Levinson, E.

E. Levinson and R. Blake, “Stereopsis by harmonic analysis,” Vision Res. 19, 73–78 (1979).
[CrossRef] [PubMed]

Maffei, L.

A. Fiorentini and L. Maffei, “Binocular depth perception with geometrical cues,” Vision Res. 11, 1299–1305 (1971).
[CrossRef] [PubMed]

Marr, D.

D. Marr and E. Hildreth, “Theory of edge detection,” Proc. R. Soc. Lon. B 207, 187–217 (1980).
[CrossRef]

Miller, J. E.

B. Julesz and J. E. Miller, “Independent spatial-frequency tuned channels in binocular fusion and rivalry,” Percept. 4, 125–143 (1975).
[CrossRef]

Ogle, K. N.

K. N. Ogle, Researches in Binocular Vision (Hafner, New York, 1950);“The optical space sense,” in The Eye, H. Davidson, ed. (Academic, London, 1964), Vol. 4, pp. 209–417.

Richards, W.

J. M. Foley and W. Richards, “Binocular depth mixtures with non-symmetric disparities,” Vision Res. 18, 251–256 (1978).
[CrossRef]

Sutter, E. E.

C. W. Tyler and E. E. Sutter, “Depth from spatial frequency difference: an old kind of stereopsis?” Vision Res. 16, 859–965 (1979).
[CrossRef]

Tolhurst, D. J.

D. J. Tolhurst, “Adaptation to square-wave gratings: inhibition between spatial frequency channels in the human visual system,” J. Physiol. Lon. 226, 231–248 (1972).

Tyler, C. W.

C. W. Tyler and E. E. Sutter, “Depth from spatial frequency difference: an old kind of stereopsis?” Vision Res. 16, 859–965 (1979).
[CrossRef]

van der Meer, H. C.

H. C. van der Meer, “Linear combinations of stereoscopic depth effects in dichoptic perception of gratings,” Vision Res. 18, 707–714 (1978).
[CrossRef] [PubMed]

Wilson, H. R.

H. R. Wilson, “The significance of frequency gradients in binocular grating perception,” Vision Res. 16, 983–989 (1979).
[CrossRef]

J. Physiol. (1)

C. Blakemore and F. W. Campbell, “On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. 203, 237–260 (1969).

J. Physiol. Lon. (1)

D. J. Tolhurst, “Adaptation to square-wave gratings: inhibition between spatial frequency channels in the human visual system,” J. Physiol. Lon. 226, 231–248 (1972).

Percept. (1)

B. Julesz and J. E. Miller, “Independent spatial-frequency tuned channels in binocular fusion and rivalry,” Percept. 4, 125–143 (1975).
[CrossRef]

Proc. R. Soc. Lon. B (1)

D. Marr and E. Hildreth, “Theory of edge detection,” Proc. R. Soc. Lon. B 207, 187–217 (1980).
[CrossRef]

Vision Res. (11)

E. Levinson and R. Blake, “Stereopsis by harmonic analysis,” Vision Res. 19, 73–78 (1979).
[CrossRef] [PubMed]

B. Gillam, “Changes in the direction of induced aniseikonic slant as a function of distance,” Vision Res. 7, 777–783 (1967).
[CrossRef] [PubMed]

C. Blakemore, “A new kind of stereoscopic vision,” Vision Res. 10, 1181–1199 (1970).
[CrossRef] [PubMed]

A. Fiorentini and L. Maffei, “Binocular depth perception with geometrical cues,” Vision Res. 11, 1299–1305 (1971).
[CrossRef] [PubMed]

H. R. Wilson, “The significance of frequency gradients in binocular grating perception,” Vision Res. 16, 983–989 (1979).
[CrossRef]

H. C. van der Meer, “Linear combinations of stereoscopic depth effects in dichoptic perception of gratings,” Vision Res. 18, 707–714 (1978).
[CrossRef] [PubMed]

C. W. Tyler and E. E. Sutter, “Depth from spatial frequency difference: an old kind of stereopsis?” Vision Res. 16, 859–965 (1979).
[CrossRef]

K. K. DeVelois, “Spatial frequency adaptation can enhance contrast sensitivity,” Vision Res. 17, 1057–1065 (1977).
[CrossRef]

L. Kaufman, J. Bacon, and F. Barroso, “Stereopsis without image segregation,” Vision Res. 13, 137–147 (1973).
[CrossRef] [PubMed]

J. M. Foley, “Binocular depth mixture,” Vision Res. 16, 1263–1267 (1976).
[CrossRef] [PubMed]

J. M. Foley and W. Richards, “Binocular depth mixtures with non-symmetric disparities,” Vision Res. 18, 251–256 (1978).
[CrossRef]

Other (2)

The fact that the descending portion of WR’s curves in Fig. 3 does not fall below the 1.0 line suggests that the negative side lobes may occur only on the low frequency side of the channel.

K. N. Ogle, Researches in Binocular Vision (Hafner, New York, 1950);“The optical space sense,” in The Eye, H. Davidson, ed. (Academic, London, 1964), Vol. 4, pp. 209–417.

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Figures (5)

Fig. 1
Fig. 1

Slant settings produced by two subjects for 2.3 cycles/deg (circles) and 6.0 cycles/deg (crosses) seen alone with their increments (or decrements) presented to the opposite eye. The T’s indicate half the range of the settings at the point of maximum variability.

Fig. 2
Fig. 2

The resultant slant for JF (dots) and WR (squares) when two planes of opposing tilt are combined. The maximum contrast of each frequency (and its increment or decrement presented to the opposite eye) is given on the abscissa. The T’s indicate half the range of settings in the region of maximum variability. These two sets of data represent the extremes of the form of the slant mixture judgments found in our limited sample of observers.

Fig. 3
Fig. 3

Slant seen with complex gratings compared with a single grating pair only. A ratio of 1.0 indicates that the slant of the complex stimulus equaled that obtained from the single grating pair. A ratio of zero indicates that no slant was seen with the complex grating. The arrow indicates the frequency ratio of the complex grating used in Fig. 2. The dots indicate measurements obtained from JF; the squares are the data of WR. Both results suggest a full stereo-channel bandwidth of about two octaves, but the nature of the channels is quite different for both observers (see Fig. 4).

Fig. 4
Fig. 4

Explanation of the observer differences, seen in Fig. 3, in terms of the concept of bandpass channels of the Blakemore type. The upper set of illustrations shows channel activities elicited from two pairs of gratings, one set centered near a spatial frequency of f1 and the other centered near f2. The cross-hatched region is where f1 and f2 both stimulate the same channels, although to different extents. The area of the cross-hatching is a measure of the strength of the channel interactions from the different stimulus pairs f1 and f2. As the stimulus frequencies become more separated (moving from the left-hand to the right-hand side in the upper illustration), the region of overlap decreases, and hence the strength of the interactions between channels decreases. The dashed line in Fig. 3 is the result if it is assumed that the amount of overlap (cross hatching) is proportional to the attenuation of slant by the opposing stereo pairs generated from f1 and f2, based on Blakemore-type channels. This line is a good fit to the data for JF. The lower set of illustrations indicates the situation in which the channels have inhibitory sidebands. Activity below the axes is taken as facilatory if it lies beneath positive activity elicited from the other stimulus, as indicated by the pluses. For appropriate separations between f1 and f2, the resultant combined activities of these channels will increase because of the facilitory effects of the sidebands.17 In this case, the slant may increase beyond that for any single-frequency pair, as it does for WR in Fig. 3, over the region in which the data points fall above the 1.0 line.

Fig. 5
Fig. 5

Another interpretation of the different slant results seen for WR and JF is the way the higher-frequency components (narrow bands) add to the lower frequency components (wider bands). For observers like JF, these narrower bands can reduce the slant, as in the lower fence, whereas for WR the narrow bands can increase the slant, as in the upper fence. In other words, for JF each narrow band acts to push the next wide panel forward, whereas for WR the narrow band is interpreted as part of an occluding edge, causing the next wide panel to be pushed backward.