Abstract
Evidence is presented to show that in stereoscopic vision a constant ratio of perceived size to perceived distance corresponds to a constant visual angle (the size-distance invariance hypothesis). The functions relating the size/ distance ratio to visual angle and the depth/distance ratio to disparity are determined for three as using the methods of magnitude estimation and magnitude production. The results for each a may be represented by power functions, the depth/ distance function having the higher exponent. These scales are used to predict the outcome of an experiment in which depth is matched to size. The agreement of predictions with results is good for the combined data of the group, but significant deviations occur from curves predicted for individual as. An experiment in which an oblique line is matched to a frontal extent yields data consistent with Luneburg’s hypothesis that the intrinsic geometry of visual space is non-Euclidean. The indicated curvature is negative for two as and varying from positive to negative for the third.
Article PDF
Similar content being viewed by others
References
Bellman, R. Functional equations. In D. Luce, R. Bush. & E. Galanter (Eds.),Handbook of mathematical psychology, Vol. 3. New York: Wiley, 1965. Pp. 487–513.
Blank, A. A. Analysis of experiments in binocular space perception.J. opt. Soc. Amer., 1958, 48, 911–925.
Blank, A. A. The Luneburg theory of binocular space perception. In S. Koch (Ed.),Psychology: A study of a science. New York: McGraw-Hill, 1959. Pp. 395–426.
Foley, J. M. Desarguesian property in visual space.J. opt. Soc. Amer., 1964, 54, 684–692.
Foley, J. M. Visual space: A scale of perceived relative direction.Proc. Amer. Psychol. Assn., 1965, 1, 49–50.
Foley, J. M. Locus of perceived equidistance as a function of viewing distance.J. Opt Soc Amer., 1966, 56, 822–827.
Foley, J. M. Binocular disparity and perceived relative distance: An examination of two bypotheses.Vis. Res., 1967a, 7, 655–670.
Foley, J. M. Disparity increase with convergence for constant perceptual criteria.Percept. & Psychophys., 1967b, 2, 605–608.
Gamer, W. R., & Creelman, C. D. Problems and metbods of psvchological scaling. In H. Helson & W. Bevan (Eds.),Contemporary approaches to psychology. Van Nostrand, 1967. Pp. 1–34.
Graham, C. H. Who makes the measurements-the subject or the experimenter?J. opt. Soc. Amer., 1966, 56, 1408–1409.
Gogel, W. C. The effect of convergence and angular size upon the computed value of a hypothetical observer constant in binocular vision. U. S. Army Medical Research Laboratory, Fort Knox, Kentucky, Report No. 372, 1958.
Gogel, W. C. Perceived frontal size as a determiner of perceived binocular depth.J. Psychol., 1960a, 50, 119–131.
Gogel, W. C. The perception of shape from binocular disparity cues.J. Psychol., 1960b, 50, 179–192.
Gogel, W. C. The perception of a depth interval with binocular disparity cues.J. Psychol., 1960c, 50, 257–269.
Gogel, W. C. Convergence as a cue to absolute distance.J. Psychol., 1961, 52, 287–301.
Gogel, W. C. Perception of depth from binocular disparity.J. exp. Psychol., 1964a, 67, 379–386.
Gogel, W. C. Visual perception of spatial extent.J. opt. Soc. Amer., 1964b, 54, 411–416.
Gogel, W. C., Wist, E. R., &Harker, G. S. A test of the invariance of the ratio of perceived size to perceived distance.Amer. J. Psychol., 1963, 76, 537–553.
Heinemann, K. G., Tulving, K., &Nachmias, J. The effect of oculomotor adjustments on apparent size.Amer. J. Psychol., 1959, 72, 32–45.
Indow, T., Inoue, K., &Matsushima, K. An experimental study of the Luneburg the ory of binocular space perception (2). The alley experiments.Jap. Psychol, Res., 1962, 4, 17–24.
Luneburg, R. K. The metric of binocular visual space.J. opt. Soc. Amer., 1950, 40, 627–642.
Luneburg, R. K. Mathematical analysis of binocular vision. Princeton University Press. 1947.
Ogle, K. N. Researches in binocular rision, Saunders. 1950.
Over, R. Size and distance judgments under reduction conditions.Austral. J. Psychol., 1960, 12, 162–168.
Rump, E. K. The relationship between perceived size and perceived distance.Brit. J. Psychol., 1961, 52, 111–124.
Shipley, T. An experimental study of the frontal reference curves of binocular visual space.Doc. Opthal., 1959, 15, 321–350.
Stevens, S. S. Matching functions between loudness and ten other continua.Percept. & Psychophys., 1966, 1, 5–8.
Stevens, S. S. Concerning the measurement of brightness.J. opt. Soc. Amer., 1966, 56, 1135–1136.
Stevens, S. S., &Guirao, M. Loudness, reciprocality, and partition scales.J. Acoust. Soc. Amer., 1962, 34, 1466–1471.
Zajaczkowska, A. Experimental test of Luneburg’s theory. Horopter and alley experiments.J. opt. Soc. Amer., 1956, 46, 514–527.
Author information
Authors and Affiliations
Additional information
This research was supported by U. S. Public Health Service Grant MH 08878 from the National Institute of Mental Health. The author is grateful to Walter Thode for his assistance in conducting and analyzing these experiments, and to Dr. A. A. Blank and Dr. W. C. Gogel for their reading of the manuscript.
Rights and permissions
About this article
Cite this article
Foley, J.M. Depth, size and distance in stereoscopic vision. Perception & Psychophysics 3, 265–274 (1968). https://doi.org/10.3758/BF03212742
Accepted:
Issue Date:
DOI: https://doi.org/10.3758/BF03212742