Abstract
We investigated whether distortions of perceived distance and shape could be captured by a single continuous one-to-one transformation of the underlying space. In Experiment 1, the participants reached to touch points around the perimeter of spherical targets viewed at five different distances, to yield simultaneous measures of perceived distance and shape. Different participants reached while using dynamic monocular, static binocular, or dynamic binocular vision. Thin plate spline (TPS) analysis was applied so as to transform a Cartesian grid in such a way as to carry the original target points to the mean reach locations. In all cases, discontinuities appeared in the transformed grid from folding of the space. In Experiment 2, the participants reached to points that lay at the same locus in reach space, but on different portions of the visible target spheres (e.g., front vs. side). The participants reached to different locations when the points were different with respect to shape (e.g., front vs. side) but reached to the same locations when the points were the same with respect to shape (left vs. right side). TPS analysis revealed discontinuities from holes torn in the underlying space. The results show that perceived distance and perceived shape entail different distortions and cannot be captured by a single continuous transformation of reach space.
Article PDF
Similar content being viewed by others
References
Baird, J. C., &Biersdorf, W. R. (1967). Quantitative functions for size and distance judgments.Perception & Psychophysics,2, 161–166.
Bingham, G. P . (2003).Calibration of distance and size does not calibrate shape information: Comparison of dynamic monocular and static and dynamic binocular vision. Manuscript submitted for publication.
Bingham, G. P., Bradley, A., Bailey, M., &Vinner, R. (2001). Accommodation, occlusion and disparity matching are used to guide reaching: A comparison of actual versus virtual environments.Journal of Experimental Psychology: Human Perception & Performance,27, 1314–1344.
Bingham, G. P ., Crowell, J. A., & Todd, J. T. (2001, May).Distortions of distance and shape do not reflect a single continuous transformation on reach space. Paper presented at the annual meeting of the Vision Sciences Society, Sarasota, FL.
Bingham, G. P., Zaal, F., Robin, D., &Shull, J. A. (2000). Distortions in definite distance and shape perception as measured by reaching without and with haptic feedback.Journal of Experimental Psychology: Human Perception & Performance,26, 1436–1460.
Brenner, E., &van Damme, W. J. M. (1997). The distance used for scaling disparities is the same as the one used for scaling retinal size.Vision Research,37, 757–764.
Brenner, E., &Van Damme, W. J. M. (1999). Perceived distance, shape and size.Vision Research,39, 975–986.
Crowell, J. A., Todd, J. T., & Bingham, G. P . (2000, November).Distinct visuomotor transformations for visually guided reaching. Paper presented at the 41st Annual Meeting of the Psychonomic Society, New Orleans.
Crowell, J. A., Todd, J. T., & Bingham, G. P . (2001, May).Distinct perceptual representations for visually guided reaches. Paper presented at the annual meeting of the Vision Sciences Society, Sarasota, FL.
Domini, F., &Caudek, C. (1999). Perceiving surface slant from deformation of optic flow.Journal of Experimental Psychology: Human Perception & Performance,25, 426–444.
Dryden, I. L., &Mardia, K. V. (1998).Statistical shape analysis. Chichester, UK: Wiley.
Ferris, S. H. (1972). Motion parallax and absolute distance.Journal of Experimental Psychology: Human Perception & Performance,95, 258–263.
Gilinsky, A. (1951). Perceived size and distance in visual space.Psychological Review,58, 460–482.
Gillam, B. (1995). The perception of spatial layout from static optical information. In W. Epstein & S. J. Rogers (Eds.),Perception of space and motion (pp. 23–67). San Diego: Academic Press.
Gillam, B., &Chambers, D. (1985). Size and position are incongruous: Measurements on the Müller-Lyer figure.Perception & Psychophysics,37, 549–556.
Gogel, W. C. (1977). The metric of visual space. In W. Epstein (Ed.),Stability and constancy in visual perception: Mechanisms and processes (pp. 129–181). New York: Wiley.
Gruber, H. (1954). The relation of perceived size to perceived distance.American Journal of Psychology,67, 411–426.
Helmholtz, H. von (1925).Physiological optics (Vol. 3). New York: Optical Society of America.
Hochberg, J. E. (1978).Perception (2nd ed.). Englewood Cliffs, NJ: Prentice-Hall.
Howard, I. P., &Rogers, B. J. (1995).Binocular vision and stereopsis. New York: Oxford University Press.
Indow, T. (1991). A critical review of Luneburg’s model with regard to global structure of visual space.Psychological Review,98, 430–453.
Johnston, E. B. (1991). Systematic distortions of shape from stereopsis.Vision Research,31, 1351–1360.
Kilpatrick, F. P., &Ittleson, W. (1953). The size-distance invariance hypothesis.Psychological Review,60, 223–231.
Koenderink, J. J., &van Doorn, A. J. (1987). Facts on optic flow.Biological Cybernetics,56, 247–254.
Koenderink, J. J., &van Doorn, A. J. (1991). Affine structure from motion.Journal of the Optical Society of America A,8, 377–385.
Lind, M. (1996). Perceiving motion and rigid structure from optic flow: A combined weak-perspective and polar-perspective approach.Perception & Psychophysics,58, 1085–1102.
Lind, M., &Börjesson, E. (2001). Perceived structure from optic flow: Consistent versus variable mapping of 3-D Euclidean structure.Scandinavian Journal of Psychology,42, 105–112.
Loomis, J.M., Philbeck, J.W., &Zahorik, P. (2002). Dissociation between location and shape in visual space.Journal of Experimental Psychology: Human Perception & Performance,28, 1202–1212.
Luneburg, R. K. (1950). The metric of binocular space.Journal of the Optical Society of America,40, 627–642.
Norman, J. F. (2002). Two visual systems and two theories of perception: An attempt to reconcile the constructivist and ecological approaches.Behavioral & Brain Sciences,25, 73–96.
Norman, J. F., &Todd, J. T. (1993). The perceptual analysis of structure from motion for rotating objects undergoing affine stretching transformations.Perception & Psychophysics,3, 279–291.
Pagano, C. C., &Bingham, G. P. (1998). Comparing measures of monocular distance perception: Verbal and reaching errors are not correlated.Journal of Experimental Psychology: Human Perception & Performance,24, 1037–1051.
Sedgwick, H. A. (1986). Space perception. In K. R. Boff, L. Kaufman, & J. P. Thomas (Eds.),Handbook of perception and human performance (Vol. 1, pp. 21.1–21.57). New York: Wiley.
Sedgwick, H. A. (2001). Visual space perception. In E. B. Goldstein (Ed.),Blackwell handbook of perception (pp. 128–167). Oxford: Blackwell.
Thompson, D. W. (1961).On growth and form. Cambridge: Cambridge University Press.
Tittle, J. S., Todd, J. T., Perotti, V. J., &Norman, J. F. (1995). Systematic distortion of perceived three-dimensional structure from motion and binocular stereopsis.Journal of Experimental Psychology: Human Perception & Performance,21, 663–678.
Todd, J. T., &Bressan, P. (1990). The perception of 3-dimensional affine structure from minimal apparent motion sequences.Perception & Psychophysics,48, 419–430.
Todd, J. T., &Norman, J. F. (1991). The visual perception of smoothly curved surfaces from minimal apparent motion sequences.Perception & Psychophysics,50, 509–523.
Todd, J. T., &Perotti, V. J. (1999). The visual perception of surface orientation from optical motion.Perception & Psychophysics,61, 1577–1589.
Todd, J. T., Tittle, J. S., &Norman, J. F. (1995). Distortions of threedimensional space in the perceptual analysis of motion and stereo.Perception,24, 75–86.
Wagner, M. (1985). The metric of visual space.Perception & Psychophysics,38, 483–495.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by Grant R01 EY11741-01A1 from the National Eye Institute to the first author.
Rights and permissions
About this article
Cite this article
Bingham, G.P., Crowell, J.A. & Todd, J.T. Distortions of distance and shape are not produced by a single continuous transformation of reach space. Perception & Psychophysics 66, 152–169 (2004). https://doi.org/10.3758/BF03194869
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.3758/BF03194869