Abstract
In two experiments, we evaluated the ability of human observers to make use of second-order temporal relations across three or more views of an apparent motion sequence for the perceptual analysis of three-dimensional form. Ratings of perceived rigidity were obtained in Experiment 1 for objects rotating in depth that were simultaneously subjected to sinusoidal affine stretching transformations along the line of sight or in a direction parallel to the image plane. Such transformations are theoretically interesting because they cannot be detected by analyses that are restricted to first-order temporal relations (i.e., two views), but they can be detected by more conventional analyses of structure from motion in which second-order temporal relations over three or more views are used. The current results show that human observers can perceive stretching transformations of a rotating 3-D object in a direction parallel to the image plane but that they fail to perceive stretching transformations along the line of sight. This result suggests that human observers can make use of some limited second-order temporal information. This finding was confirmed in Experiment 2, in which we investigated the effects of several specific optical consequences of sinusoidal stretching transformations applied in different directions. The results indicate that observers may be sensitive to the sign of acceleration, but that. they cannot make use of the precise magnitude of second-order relations necessary to recover euclidean metric structure.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bennett, B. M., &Hoffman, D. D. (1985). The computation of structure from fixed-axis motion: Nonrigid structures.Biological Cybernetics,51, 293–300.
Bennett, B. M., Hoffman, D. D., Nicola, J. E., &Prakash, C. (1989). Structure from two orthographic views of rigid motion.Journal of the Optical Society of America A,6, 1052–1069.
Braunstein, M. L. (1962). Depth perception in rotating dot patterns: Effects of numerosity and perspective.Journal of Experimental Psychology,64, 415–420.
Braunstein, M. L., Hoffman, D. D., &Pollick, F. E. (1990). Discriminating rigid from nonrigid motion: Minimum points and views.Perception & Psychophysics,47, 205–214.
Braunstein, M. L., Hoffman, O. D., Shapiro, L. R., Andersen, G. J., &Bennett, B. M. (1987). Minimum points and views for the recovery of three-dimensional structure.Journal of Experimental Psychology: Human Perception & Performance,13, 335–343.
Dosher, B. A., Landy, M. S., &Sperling, G. (1989). Kinetic depth effect and optic flow: I. 3D shape from fourier motion.Vision Research,29, 1789–1813.
Gibson, J. J., &Gibson, E. J. (1957). Continuous perspective transformations and the perception of rigid motion.Journal of Experimental Psychology,54, 129–138.
Gibson, E. J., Gibson, J. J., Smith, O, W., &Flock, H. (1959). Motion parallax as a determinant of perceived depth.Journal of Experimental Psychology,58, 40–51.
Green, B. F. (1961). Figure coherence in the kinetic depth effect.Journal of Experimental Psychology,62, 272–282.
Hildreth, E. C., Grzywacz, N. M., Adelson, E. H., &Inada, V. K. (1990). The perceptual buildup of three-dimensional structure from motion.Perception & Psychophysics,48, 19–36.
Hoffman, D. D., &Bennett, B. M. (1986). The computation of structure from fixed-axis motion: Rigid structures.Biological Cybernetics,54, 71–83.
Hoffman, D. D., &Flinchbaugh, B. E. (1982). The interpretation of biological motion.Biological Cybernetics,42, 195–204.
Huang, T. S., &Lee, C. H. (1989). Motion and structure from orthographic projections.IEEE Transactions on Pattern Analysis & Machine Intelligence,11, 536–540.
Johansson, G. (1964). Perception of motion and changing form: A study of visual perception from continuous transformations of a solid angle of light at the eye.Scandinavian Journal of Psychology,5, 181–208.
Johansson, G., &Jansson, G. (1968). Perceived rotary motion from changes in a straight line.Perception & Psychophysics,4, 165–170.
Julesz, B. (1971).Foundations of cyclopean perception. Chicago, IL: University of Chicago Press.
Koenderink, J. J., &van Doorn, A. J. (1991). Affine structure from motion.Journal of the Optical Society of America A,8, 377–385.
Lappin, J. S., &Fuqua, M. A. (1983). Accurate visual measurement of three-dimensional moving patterns.Science,221, 480–482.
Lappin, J. S., &Love, S. R. (1992). Planar motion permits perception of metric structure in stereopsis.Perception & Psychophysics,51, 86–102.
Metzger, W. (1934). Beobachtungen über phänomenale Identität.Psychologische Forschung,19, 1–60.
Miles, W. R. (1931). Movement interpretations of the silhouette of a revolving fan.American Journal of Psychology,43, 392–405.
Norman, J. F., &Todd, J. T. (1991). The perception of rigid motion for affine distortions in depth.Investigative Ophthalmology & Visual Science (Suppl.),33 958.
Norman, J. F., &Todd, J. T. (1992). The visual perception of 3-dimensional form. In G. A. Carpenter & S. Grossbery (Eds.),Neural networks for vision and image processing (pp. 92–101) Cambridge, MA: MIT Press.
Todd, J. T. (1982). Visual information about rigid and nonrigid motion: A geometric analysis.Journal of Experimental Psychology: Human Perception & Performance,8, 238–252.
Todd, J. T. (1985). Perception of structure from motion: Is projective correspondence of moving elements a necessary condition?Journal of Experimental Psychology: Human Perception & Performance,11, 689–710.
Todd, J. T., Akerstrom, R. A., Reichel, F. D., &Hayes, W. (1988). Apparent rotation in three-dimensional space: Effects of temporal, spatial, and structural factors.Perception & Psychophysics,43, 179–188.
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.
Ullman, S. (1977).The interpretation of visual motion. Unpublished doctoral dissertation, Massachusetts Institute of Technology.
Ullman, S. (1979).The interpretation of visual motion. Cambridge, MA: MIT Press.
Wallach, H., &O’Connell, D. N. (1953). The kinetic depth effect.Journal of Experimental Psychology,45, 205–217.
Author information
Authors and Affiliations
Additional information
This research was supported by Grant 89-0016 from the Air Force Office of Scientific Research and BNS-8908426 from the National Science Foundation, the Office of Naval Research, and the Air Force Office of Scientific Research to J. T.
Rights and permissions
About this article
Cite this article
Norman, J.F., Todd, J.T. The perceptual analysis of structure from motion for rotating objects undergoing affine stretching transformations. Perception & Psychophysics 53, 279–291 (1993). https://doi.org/10.3758/BF03205183
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.3758/BF03205183