Abstract
Interpolation across orientation discontinuities in simulated three-dimensional (3-D). surfaces was studied in three experiments with the use of structure-from-motion (SFM). displays. The displays depicted dots on two slanted planes with a region devoid of dots (a gap). between them. If extended through the gap at constant slope, the planes would meet at a dihedral edge. Subjects were required to place an SFM probe dot, located within the gap, on the perceived surface. Probe dot placements indicated that subjects perceived a smooth surface connecting the planes rather than a surface with a discontinuity. Probe dot placements varied with slope of the planes, density of the dots, and gap size, but not with orientation (horizontal or vertical). of the dihedral edge or of the axis of rotation. Smoothing was consistent with models of 2-D interpolation proposed by Ullman (1976). and Kellman and Shipley (1991). and with a model of 3-D interpolation proposed by Grimson (1981).
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References
Blake, A. (1984).Reconstructing a visible surface. In Proceedings of AAAI Conference 1984 (pp. 23–26). Los Altos, CA: AAAI Press.
Blake, A., &Zisserman, A. (1986).Invariant surface reconstruction using weak continuity constraints. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (pp. 62–67). Washington, DC: IEEE Computer Society Press.
Blake, A., &Zisserman, A. (1987).Visual reconstruction. Cambridge, MA: MIT Press.
Brady, M., &Grimson, W. E. L. (1981).The perception of subjective surfaces (Memo No, 666). Cambridge, MA: Massachusetts Institute of Technology, Artificial Intelligence Laboratory.
Brady, M., &Horn, B. K. P. (1981).Rotationally symmetric operators for surface interpolation (Memo No. 654). Cambridge, MA: Massachusetts Institute of Technology, Artificial Intelligence Laboratory.
Braunstein, M. L. (1966). Sensitivity of the observer to transformations of the visual field.Journal of Experimental Psychology,72, 683–687.
Braunstein, M. L. (1978). Perception of motion. In E. Carterette & M. Friedman (Eds.)Handbook of perception (Vol. 8, pp. 147–172). New York: Academic Press.
Braunstein, M. L. (1983). Perception of rotation in depth: The psychophysical evidence. In N. I., Badler & J. K. Tsotsos (Eds.)Motion: Representation and perception (Proceedings of the ACM SIG-GRAPH/SIGART Interdisciplinary Workshop on Motion, Representation and Perception, pp. 242–247). New York: North Holland.
Braunstein, M. L. (1988). The empirical study of structure from motion. In W. N. Martin & J. K. Aggarwal (Eds.)Motion understanding: Robot and human vision (pp. 101–142). Hingham, MA: Kluwer Academic Publishers.
Braunstein, M. L., &Andersen, G. J. (1984). Shape and depth perception from parallel projections of three-dimensional motion.Journal of Experimental Psychology: Human Perception & Performance,10, 749–760.
Collett, T. S. (1985). Extrapolating and interpolating surfaces in depth.Proceedings of the Royal Society of London: Series B,224, 43–56.
Cornilleau-Pérès, V., &Droulez, J. (1989). Visual perception of surface curvature: Psychophysics of curvature detection induced by motion parallax.Perception & Psychophysics,46, 351–364.
Grimson, W. E.L. (1981).From images to surfaces: A computational study of the human early visual system. Cambridge, MA: MIT Press.
Halpern, D. F., &Salzman, B. (1983). The multiple determination of illusory contours: 1. A review.Perception,12, 281–291.
Horn, B. K. P. (1983). The curve of least energy.Association for Computing Machinery Transactions on Mathematical Software,9, 441–460.
Julesz, B. (1971).Foundations ofcyclopeanperception. Chicago: University of Chicago Press.
Julesz, B., &Frisby, P. (1975). Some new subjective contours in random-line stereograms.Perception,4, 145–150.
Kanizsa, G. (1979).Organization in vision. New York: Praeger.
Kellman, P. J., &Shipley, T. F. (1991). A theory of visual interpolation in object perception.Cognitive Psychology,23, 141–221.
Liter, J. C., Braunstein, M. L., & Hoffman, D. D. (in press). Inferring structure from motion in two-view and multi-view displays.Perception.
Norman, J. F., &Lappin, J. S. (1992). The detection of surface curvatures defined by optical motion.Perception & Psychophysics,51, 386–396.
Norman, J. F., Lapfin, I. S., &Zucker, S. W. (1991). The discriminability of smooth stereoscopic surfaces.Perception,20, 789–807.
Saitjpour, A., Braunstein, M. L., &Hoffman, D. D. (1992). Interpolation in structure from motion.Perception & Psychophysics,51, 105–117.
Stevens, K. A., &Brookes, A. (1987). Probing depth in monocular images.Biological Cybernetics,56, 355–366.
Terzofoulos, D. (1982).Multi-level computation of visual surface representation (Memo No, 671). Cambridge, MA: Massachusetts Institute of Technology, Artificial Intelligence Laboratory.
Terzopoulos, D. (1986). Integrating visual information from multiple sources. In A. P. Pentland (Ed.)From pixels to predicates: Recent advances in computational vision (pp. 111–142). Norwood, NJ: Ablex.
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,487, 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. (1976). Filling-in the gaps: The shape of subjective contours and a model for their generation.Biological Cybernetics,25, 1–6,
Ullman, S. (1979).The interpretation of visual motion. Cambridge, MA: MIT Press.
Uttal, W. R., Davis, N. S., Welke, C., &Kakarala, R. (1988), The reconstruction of static visual forms from sparse dotted samples.Perception & Psychophysics,43, 223–240
Wallach, H., &O’Connell, D. N. (1953). The kinetic depth effect.Journal of Experimental Psychology,45, 205–217.
Wetss, I. (1990). Shape reconstruction on a varying mesh.IEEE Transactions on Pattern Analysis & Machine Intelligence,12, 345–362.
Zucker, S. W., &Iverson, L. (1987). From orientation selection to optical flow.Computer Vision, Graphics, & Image Processing,37, 196–220
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This research was supported by National Science Foundation Grants DBS-9209973 and IRI-870O924 and Office of Naval Research Contract N00014-88-K-0354. A preliminary report of this research was presented at the annual meeting of the Association for Research in Vision and Ophthalmology, Sarasota, FL. May 1992.
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Saidpour, A., Braunstein, M.L. & Hoffman, D.D. Interpolation across surface discontinuities in structure from motion Asad Satdpour. Perception & Psychophysics 55, 611–622 (1994). https://doi.org/10.3758/BF03211676
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DOI: https://doi.org/10.3758/BF03211676