Abstract

We studied the integration of image disparities, edge information, and shading in the three-dimensional perception of complex yet well-controlled images generated with a computer-graphics system. The images showed end-on views of flat- and smooth-shaded ellipsoids, i.e., images with and without intensity discontinuities (edges). A map of perceived depth was measured by adjusting a small stereo depth probe interactively to the perceived surface. Our data show that disparate shading (even in the absence of disparate edges) yields a vivid stereoscopic depth perception. The perceived depth is significantly reduced if the disparities are completely removed (shape-from-shading). If edge information is available, it overrides both shape-from-shading and disparate shading. Degradations of depth perception corresponded to a reduced depth rather than to an increased scatter in the depth measurement. The results are compared with computer-vision algorithms for both single cues and their integration for three-dimensional vision.

© 1988 Optical Society of America

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  1. B. Julesz, Foundations of Cyclopean Perception (U. Chicago Press, Chicago, Ill., 1971).
  2. D. Marr, T. Poggio, “A computational theory of human stereo vision,” Proc. R. Soc. London Ser. B 204, 301–328 (1979).
    [CrossRef]
  3. J. E. W. Mayhew, J. P. Frisby, “Psychophysical and computational studies towards a theory of human stereopsis,” Artif. Intell. 17, 349–386 (1981).
    [CrossRef]
  4. E. Mingolla, J. T. Todd, “Perception of solid shape from shading,” Biol. Cybern. 53, 137–151 (1986).
    [CrossRef] [PubMed]
  5. A. Blake, Zisserman, G. Knowles, “Surface description from stereo and shading,” Image Vision Comput. 3, 183–191 (1985).
    [CrossRef]
  6. K. Ikeuchi, B. K. P. Horn, “Numerical shape from shading and occluding boundaries,” Artif. Intell. 17, 141–184 (1981).
    [CrossRef]
  7. A. P. Pentland, “Local shading analysis,”IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 170–187 (1984).
    [CrossRef]
  8. R. Bajcsy, L. Lieberman, “Texture gradient as a depth cue,” Comput. Vision Graphics Image Process. 5, 52–67 (1976).
    [CrossRef]
  9. J. R. Render, “Shape from texture: an aggregation transform that maps a class of textures into surface orientation,” in Proceedings, International Joint Conference on Artificial IntelligenceKaufmann, Los Angeles, Calif., 1979).
  10. A. P. Witkin, “Recovering surface shape and orientation from texture,” Artif. Intell. 17, 17–47 (1981).
    [CrossRef]
  11. A. P. Pentland, “Shading into texture,” Artif. Intell. 29, 147–170 (1986).
    [CrossRef]
  12. H. G. Barrow, J. M. Tenenbaum, “Interpreting line drawings as three-dimensional surfaces,” Artif. Intell. 17, 75–116 (1981).
    [CrossRef]
  13. K. A. Stevens, “The visual interpretation of surface contours,” Artif. Intell. 17, 17–45 (1981).
    [CrossRef]
  14. K. A. Stevens, A. Brooks, “Probing depth in monocular images,” Biol. Cybern. 56, 355–366 (1987).
    [CrossRef] [PubMed]
  15. S. Ullman, The Interpretation of Visual Motion (MIT Press, Cambridge, Mass., 1979).
  16. H. C. Longuet-Higgins, K. Prazdny, “The interpretation of moving retinal image,” Proc. R. Soc. London Ser. B 208, 385–397 (1981).
    [CrossRef]
  17. N. M. Grzywacz, E. C. Hildreth, “Incremental rigidity scheme for recovering structure from motion: position-based versus velocity-based formulations,” J. Opt. Soc. Am. A 4, 503–518 (1987).
    [CrossRef] [PubMed]
  18. B. A. Dosher, G. Sperling, S. Wurst, “Tradeoffs between stereopsis and proximity luminance covariance as determinants of perceived 3D structure,” Vision Res. 26, 973–990 (1986).
    [CrossRef] [PubMed]
  19. T. Poggio, V. Torre, C. Koch, “Computational vision and regularization theory,” Nature 317, 314–319 (1985).
    [CrossRef] [PubMed]
  20. D. Terzopoulos, “Integrating visual information from multiple sources,” in From Pixels to Predicates, A. P. Pentland, ed. (Ablex, Norwood, N.J., 1986), pp. 111–142.
  21. J. L. Marroquin, S. K. Mitter, T. Poggio, “Probablistic solution of ill-posed problems in computational vision,”J. Am. Stat. Assoc. 82, 76–89 (1987).
    [CrossRef]
  22. M. L. Braunstein, G. J. Andersen, M. W. Rouse, J. S. Tittle, “Recovering viewer-centered depth from disparity, occlusion, and velocity gradients,” Percept. Psychophys. 40, 216–224 (1986).
    [CrossRef] [PubMed]
  23. H. H. Bülthoff, H. A. Mallot, “Integration of depth modules: local and global depth measurements,” Invest Ophthalmol. Vis. Sci. Suppl. 29, 400 (1988).
  24. Reviewed by A. Ardity, “Binocular vision,” in Sensory Process and Perception, Vol. I of Handbook of Perception and Human Performance, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986), Chap. 23.
  25. We write the equation of the ellipsoid asxTAx=1,A=[a−2000b−2000c−2], where a, b, and c denote the semidiameters. With a= b= 1, we have an ellipsoid of revolution. For a ray from viewpoint e to a point p′on the surface,x=e+μ(p′−e),μ∈R+, the ray tracing amounts to the solution for μ of the quadratic equation:[e+μ(p′−e)]TA[e+μ(p′−e)]=1. The image intensity at point p′was computed from this solution for an ideal Lambertian surface illuminated by parallel light from the z direction. Note that for a point x on the surface of the ellipsoid xTAx= 1, the surface normal is simply Ax/∥Ax∥. The viewing direction and the axis of revolution of the ellipsoid were aligned.
  26. B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
    [CrossRef]
  27. R. L. Gregory, Eye and Brain (McGraw-Hill, New York, 1966).
  28. D. Marr, E. Hildreth, “Theory of edge detection,” Proc. R. Soc. London Ser. B 207, 187–217 (1980).
    [CrossRef]
  29. J. Daugman, “Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters,” J. Opt. Soc. Am. A 2, 1160–1169 (1985).
    [CrossRef] [PubMed]
  30. H. H. Bülthoff, K. G. Götz, “Analogous motion illusion in man and fly,” Nature 278, 636–638 (1979).
    [CrossRef] [PubMed]
  31. K. I. Naka, W. A. H. Rushton, “S-potentials from color units in the retina of fish (Cyprinidae),”J. Physiol. (London) 185, 536–555 (1966).
  32. S. Hemilä, “The stimulus-response functions of visual systems,” Vision Res. 27, 1253–1261 (1987).
    [CrossRef] [PubMed]
  33. L. Kramer, “Interpretation of invertebrate photoreceptor potentials in terms of a quantitative model,” Biophys. Struct. Mechan. 1, 239–257 (1975).
    [CrossRef]
  34. G. Poggio, T. Poggio, “The analysis of stereopsis,” Annu. Rev. Neurosci. 7, 379–412 (1984).
    [CrossRef] [PubMed]
  35. W. E. L. Grimson, “Binocular shading and visual surface reconstruction,” Comput. Vision Graphics Image Process. 28, 19–43 (1984).
    [CrossRef]
  36. E. C. Hildreth, “The detection of intensity changes by computer and biological vision systems,” Comput. Vision Graphics Image Process. 22, 1–27 (1983).
    [CrossRef]
  37. M. A. Gennert, “A computational framework for understanding problems in stereo vision,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1987).
  38. B. K. P. Horn, M. J. Brooks, “The variational approach to shape from shading,”MIT Artif. Intell. Lab. Memo 813 (Massachusetts Institute of Technology, Cambridge, Mass., 1985), pp. 1–32.
  39. J. T. Todd, E. Mingolla, “Perception of surface curvature and direction of illumination from patterns of shading,”J. Exp. Psychol. Human Percept. Perform. 9, 583–595 (1983).
    [CrossRef]
  40. H. G. Barrow, J. M. Tenenbaum, “Recovering intrinsic scene characteristics from images,” in Computer Vision Systems, A. Hanson, E. Riseman, eds. (Academic, New York, 1978), pp. 3–26.
  41. W. E. L. Grimson, “A computational theory of visual surface interpolation,” Philos. Trans. R. Soc. London Ser. B 298, 395–427 (1982).
    [CrossRef]
  42. J. L. Marroquin, “Surface reconstruction preserving discontinuities,”MIT Artif. Intell. Lab. Memo 792 (Massachusetts Institute of Technology, Cambridge, Mass., 1984).
  43. T. Poggio, “Integrating vision modules with coupled MRFs,”MIT Artif. Intell. Lab. Working Paper 285 (Massachusetts Institute of Technology, Cambridge, Mass., 1985).

1988 (1)

H. H. Bülthoff, H. A. Mallot, “Integration of depth modules: local and global depth measurements,” Invest Ophthalmol. Vis. Sci. Suppl. 29, 400 (1988).

1987 (4)

J. L. Marroquin, S. K. Mitter, T. Poggio, “Probablistic solution of ill-posed problems in computational vision,”J. Am. Stat. Assoc. 82, 76–89 (1987).
[CrossRef]

K. A. Stevens, A. Brooks, “Probing depth in monocular images,” Biol. Cybern. 56, 355–366 (1987).
[CrossRef] [PubMed]

S. Hemilä, “The stimulus-response functions of visual systems,” Vision Res. 27, 1253–1261 (1987).
[CrossRef] [PubMed]

N. M. Grzywacz, E. C. Hildreth, “Incremental rigidity scheme for recovering structure from motion: position-based versus velocity-based formulations,” J. Opt. Soc. Am. A 4, 503–518 (1987).
[CrossRef] [PubMed]

1986 (4)

B. A. Dosher, G. Sperling, S. Wurst, “Tradeoffs between stereopsis and proximity luminance covariance as determinants of perceived 3D structure,” Vision Res. 26, 973–990 (1986).
[CrossRef] [PubMed]

M. L. Braunstein, G. J. Andersen, M. W. Rouse, J. S. Tittle, “Recovering viewer-centered depth from disparity, occlusion, and velocity gradients,” Percept. Psychophys. 40, 216–224 (1986).
[CrossRef] [PubMed]

E. Mingolla, J. T. Todd, “Perception of solid shape from shading,” Biol. Cybern. 53, 137–151 (1986).
[CrossRef] [PubMed]

A. P. Pentland, “Shading into texture,” Artif. Intell. 29, 147–170 (1986).
[CrossRef]

1985 (3)

A. Blake, Zisserman, G. Knowles, “Surface description from stereo and shading,” Image Vision Comput. 3, 183–191 (1985).
[CrossRef]

T. Poggio, V. Torre, C. Koch, “Computational vision and regularization theory,” Nature 317, 314–319 (1985).
[CrossRef] [PubMed]

J. Daugman, “Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters,” J. Opt. Soc. Am. A 2, 1160–1169 (1985).
[CrossRef] [PubMed]

1984 (3)

G. Poggio, T. Poggio, “The analysis of stereopsis,” Annu. Rev. Neurosci. 7, 379–412 (1984).
[CrossRef] [PubMed]

W. E. L. Grimson, “Binocular shading and visual surface reconstruction,” Comput. Vision Graphics Image Process. 28, 19–43 (1984).
[CrossRef]

A. P. Pentland, “Local shading analysis,”IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 170–187 (1984).
[CrossRef]

1983 (2)

E. C. Hildreth, “The detection of intensity changes by computer and biological vision systems,” Comput. Vision Graphics Image Process. 22, 1–27 (1983).
[CrossRef]

J. T. Todd, E. Mingolla, “Perception of surface curvature and direction of illumination from patterns of shading,”J. Exp. Psychol. Human Percept. Perform. 9, 583–595 (1983).
[CrossRef]

1982 (1)

W. E. L. Grimson, “A computational theory of visual surface interpolation,” Philos. Trans. R. Soc. London Ser. B 298, 395–427 (1982).
[CrossRef]

1981 (6)

A. P. Witkin, “Recovering surface shape and orientation from texture,” Artif. Intell. 17, 17–47 (1981).
[CrossRef]

H. G. Barrow, J. M. Tenenbaum, “Interpreting line drawings as three-dimensional surfaces,” Artif. Intell. 17, 75–116 (1981).
[CrossRef]

K. A. Stevens, “The visual interpretation of surface contours,” Artif. Intell. 17, 17–45 (1981).
[CrossRef]

K. Ikeuchi, B. K. P. Horn, “Numerical shape from shading and occluding boundaries,” Artif. Intell. 17, 141–184 (1981).
[CrossRef]

J. E. W. Mayhew, J. P. Frisby, “Psychophysical and computational studies towards a theory of human stereopsis,” Artif. Intell. 17, 349–386 (1981).
[CrossRef]

H. C. Longuet-Higgins, K. Prazdny, “The interpretation of moving retinal image,” Proc. R. Soc. London Ser. B 208, 385–397 (1981).
[CrossRef]

1980 (1)

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

1979 (2)

H. H. Bülthoff, K. G. Götz, “Analogous motion illusion in man and fly,” Nature 278, 636–638 (1979).
[CrossRef] [PubMed]

D. Marr, T. Poggio, “A computational theory of human stereo vision,” Proc. R. Soc. London Ser. B 204, 301–328 (1979).
[CrossRef]

1976 (1)

R. Bajcsy, L. Lieberman, “Texture gradient as a depth cue,” Comput. Vision Graphics Image Process. 5, 52–67 (1976).
[CrossRef]

1975 (2)

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
[CrossRef]

L. Kramer, “Interpretation of invertebrate photoreceptor potentials in terms of a quantitative model,” Biophys. Struct. Mechan. 1, 239–257 (1975).
[CrossRef]

1966 (1)

K. I. Naka, W. A. H. Rushton, “S-potentials from color units in the retina of fish (Cyprinidae),”J. Physiol. (London) 185, 536–555 (1966).

Andersen, G. J.

M. L. Braunstein, G. J. Andersen, M. W. Rouse, J. S. Tittle, “Recovering viewer-centered depth from disparity, occlusion, and velocity gradients,” Percept. Psychophys. 40, 216–224 (1986).
[CrossRef] [PubMed]

Ardity, A.

Reviewed by A. Ardity, “Binocular vision,” in Sensory Process and Perception, Vol. I of Handbook of Perception and Human Performance, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986), Chap. 23.

Bajcsy, R.

R. Bajcsy, L. Lieberman, “Texture gradient as a depth cue,” Comput. Vision Graphics Image Process. 5, 52–67 (1976).
[CrossRef]

Barrow, H. G.

H. G. Barrow, J. M. Tenenbaum, “Interpreting line drawings as three-dimensional surfaces,” Artif. Intell. 17, 75–116 (1981).
[CrossRef]

H. G. Barrow, J. M. Tenenbaum, “Recovering intrinsic scene characteristics from images,” in Computer Vision Systems, A. Hanson, E. Riseman, eds. (Academic, New York, 1978), pp. 3–26.

Blake, A.

A. Blake, Zisserman, G. Knowles, “Surface description from stereo and shading,” Image Vision Comput. 3, 183–191 (1985).
[CrossRef]

Braunstein, M. L.

M. L. Braunstein, G. J. Andersen, M. W. Rouse, J. S. Tittle, “Recovering viewer-centered depth from disparity, occlusion, and velocity gradients,” Percept. Psychophys. 40, 216–224 (1986).
[CrossRef] [PubMed]

Brooks, A.

K. A. Stevens, A. Brooks, “Probing depth in monocular images,” Biol. Cybern. 56, 355–366 (1987).
[CrossRef] [PubMed]

Brooks, M. J.

B. K. P. Horn, M. J. Brooks, “The variational approach to shape from shading,”MIT Artif. Intell. Lab. Memo 813 (Massachusetts Institute of Technology, Cambridge, Mass., 1985), pp. 1–32.

Bülthoff, H. H.

H. H. Bülthoff, H. A. Mallot, “Integration of depth modules: local and global depth measurements,” Invest Ophthalmol. Vis. Sci. Suppl. 29, 400 (1988).

H. H. Bülthoff, K. G. Götz, “Analogous motion illusion in man and fly,” Nature 278, 636–638 (1979).
[CrossRef] [PubMed]

Daugman, J.

Dosher, B. A.

B. A. Dosher, G. Sperling, S. Wurst, “Tradeoffs between stereopsis and proximity luminance covariance as determinants of perceived 3D structure,” Vision Res. 26, 973–990 (1986).
[CrossRef] [PubMed]

Frisby, J. P.

J. E. W. Mayhew, J. P. Frisby, “Psychophysical and computational studies towards a theory of human stereopsis,” Artif. Intell. 17, 349–386 (1981).
[CrossRef]

Gennert, M. A.

M. A. Gennert, “A computational framework for understanding problems in stereo vision,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1987).

Götz, K. G.

H. H. Bülthoff, K. G. Götz, “Analogous motion illusion in man and fly,” Nature 278, 636–638 (1979).
[CrossRef] [PubMed]

Gregory, R. L.

R. L. Gregory, Eye and Brain (McGraw-Hill, New York, 1966).

Grimson, W. E. L.

W. E. L. Grimson, “Binocular shading and visual surface reconstruction,” Comput. Vision Graphics Image Process. 28, 19–43 (1984).
[CrossRef]

W. E. L. Grimson, “A computational theory of visual surface interpolation,” Philos. Trans. R. Soc. London Ser. B 298, 395–427 (1982).
[CrossRef]

Grzywacz, N. M.

Hemilä, S.

S. Hemilä, “The stimulus-response functions of visual systems,” Vision Res. 27, 1253–1261 (1987).
[CrossRef] [PubMed]

Hildreth, E.

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

Hildreth, E. C.

N. M. Grzywacz, E. C. Hildreth, “Incremental rigidity scheme for recovering structure from motion: position-based versus velocity-based formulations,” J. Opt. Soc. Am. A 4, 503–518 (1987).
[CrossRef] [PubMed]

E. C. Hildreth, “The detection of intensity changes by computer and biological vision systems,” Comput. Vision Graphics Image Process. 22, 1–27 (1983).
[CrossRef]

Horn, B. K. P.

K. Ikeuchi, B. K. P. Horn, “Numerical shape from shading and occluding boundaries,” Artif. Intell. 17, 141–184 (1981).
[CrossRef]

B. K. P. Horn, M. J. Brooks, “The variational approach to shape from shading,”MIT Artif. Intell. Lab. Memo 813 (Massachusetts Institute of Technology, Cambridge, Mass., 1985), pp. 1–32.

Ikeuchi, K.

K. Ikeuchi, B. K. P. Horn, “Numerical shape from shading and occluding boundaries,” Artif. Intell. 17, 141–184 (1981).
[CrossRef]

Julesz, B.

B. Julesz, Foundations of Cyclopean Perception (U. Chicago Press, Chicago, Ill., 1971).

Knowles, G.

A. Blake, Zisserman, G. Knowles, “Surface description from stereo and shading,” Image Vision Comput. 3, 183–191 (1985).
[CrossRef]

Koch, C.

T. Poggio, V. Torre, C. Koch, “Computational vision and regularization theory,” Nature 317, 314–319 (1985).
[CrossRef] [PubMed]

Kramer, L.

L. Kramer, “Interpretation of invertebrate photoreceptor potentials in terms of a quantitative model,” Biophys. Struct. Mechan. 1, 239–257 (1975).
[CrossRef]

Lieberman, L.

R. Bajcsy, L. Lieberman, “Texture gradient as a depth cue,” Comput. Vision Graphics Image Process. 5, 52–67 (1976).
[CrossRef]

Longuet-Higgins, H. C.

H. C. Longuet-Higgins, K. Prazdny, “The interpretation of moving retinal image,” Proc. R. Soc. London Ser. B 208, 385–397 (1981).
[CrossRef]

Mallot, H. A.

H. H. Bülthoff, H. A. Mallot, “Integration of depth modules: local and global depth measurements,” Invest Ophthalmol. Vis. Sci. Suppl. 29, 400 (1988).

Marr, D.

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

D. Marr, T. Poggio, “A computational theory of human stereo vision,” Proc. R. Soc. London Ser. B 204, 301–328 (1979).
[CrossRef]

Marroquin, J. L.

J. L. Marroquin, S. K. Mitter, T. Poggio, “Probablistic solution of ill-posed problems in computational vision,”J. Am. Stat. Assoc. 82, 76–89 (1987).
[CrossRef]

J. L. Marroquin, “Surface reconstruction preserving discontinuities,”MIT Artif. Intell. Lab. Memo 792 (Massachusetts Institute of Technology, Cambridge, Mass., 1984).

Mayhew, J. E. W.

J. E. W. Mayhew, J. P. Frisby, “Psychophysical and computational studies towards a theory of human stereopsis,” Artif. Intell. 17, 349–386 (1981).
[CrossRef]

Mingolla, E.

E. Mingolla, J. T. Todd, “Perception of solid shape from shading,” Biol. Cybern. 53, 137–151 (1986).
[CrossRef] [PubMed]

J. T. Todd, E. Mingolla, “Perception of surface curvature and direction of illumination from patterns of shading,”J. Exp. Psychol. Human Percept. Perform. 9, 583–595 (1983).
[CrossRef]

Mitter, S. K.

J. L. Marroquin, S. K. Mitter, T. Poggio, “Probablistic solution of ill-posed problems in computational vision,”J. Am. Stat. Assoc. 82, 76–89 (1987).
[CrossRef]

Naka, K. I.

K. I. Naka, W. A. H. Rushton, “S-potentials from color units in the retina of fish (Cyprinidae),”J. Physiol. (London) 185, 536–555 (1966).

Pentland, A. P.

A. P. Pentland, “Shading into texture,” Artif. Intell. 29, 147–170 (1986).
[CrossRef]

A. P. Pentland, “Local shading analysis,”IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 170–187 (1984).
[CrossRef]

Phong, B. T.

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
[CrossRef]

Poggio, G.

G. Poggio, T. Poggio, “The analysis of stereopsis,” Annu. Rev. Neurosci. 7, 379–412 (1984).
[CrossRef] [PubMed]

Poggio, T.

J. L. Marroquin, S. K. Mitter, T. Poggio, “Probablistic solution of ill-posed problems in computational vision,”J. Am. Stat. Assoc. 82, 76–89 (1987).
[CrossRef]

T. Poggio, V. Torre, C. Koch, “Computational vision and regularization theory,” Nature 317, 314–319 (1985).
[CrossRef] [PubMed]

G. Poggio, T. Poggio, “The analysis of stereopsis,” Annu. Rev. Neurosci. 7, 379–412 (1984).
[CrossRef] [PubMed]

D. Marr, T. Poggio, “A computational theory of human stereo vision,” Proc. R. Soc. London Ser. B 204, 301–328 (1979).
[CrossRef]

T. Poggio, “Integrating vision modules with coupled MRFs,”MIT Artif. Intell. Lab. Working Paper 285 (Massachusetts Institute of Technology, Cambridge, Mass., 1985).

Prazdny, K.

H. C. Longuet-Higgins, K. Prazdny, “The interpretation of moving retinal image,” Proc. R. Soc. London Ser. B 208, 385–397 (1981).
[CrossRef]

Render, J. R.

J. R. Render, “Shape from texture: an aggregation transform that maps a class of textures into surface orientation,” in Proceedings, International Joint Conference on Artificial IntelligenceKaufmann, Los Angeles, Calif., 1979).

Rouse, M. W.

M. L. Braunstein, G. J. Andersen, M. W. Rouse, J. S. Tittle, “Recovering viewer-centered depth from disparity, occlusion, and velocity gradients,” Percept. Psychophys. 40, 216–224 (1986).
[CrossRef] [PubMed]

Rushton, W. A. H.

K. I. Naka, W. A. H. Rushton, “S-potentials from color units in the retina of fish (Cyprinidae),”J. Physiol. (London) 185, 536–555 (1966).

Sperling, G.

B. A. Dosher, G. Sperling, S. Wurst, “Tradeoffs between stereopsis and proximity luminance covariance as determinants of perceived 3D structure,” Vision Res. 26, 973–990 (1986).
[CrossRef] [PubMed]

Stevens, K. A.

K. A. Stevens, A. Brooks, “Probing depth in monocular images,” Biol. Cybern. 56, 355–366 (1987).
[CrossRef] [PubMed]

K. A. Stevens, “The visual interpretation of surface contours,” Artif. Intell. 17, 17–45 (1981).
[CrossRef]

Tenenbaum, J. M.

H. G. Barrow, J. M. Tenenbaum, “Interpreting line drawings as three-dimensional surfaces,” Artif. Intell. 17, 75–116 (1981).
[CrossRef]

H. G. Barrow, J. M. Tenenbaum, “Recovering intrinsic scene characteristics from images,” in Computer Vision Systems, A. Hanson, E. Riseman, eds. (Academic, New York, 1978), pp. 3–26.

Terzopoulos, D.

D. Terzopoulos, “Integrating visual information from multiple sources,” in From Pixels to Predicates, A. P. Pentland, ed. (Ablex, Norwood, N.J., 1986), pp. 111–142.

Tittle, J. S.

M. L. Braunstein, G. J. Andersen, M. W. Rouse, J. S. Tittle, “Recovering viewer-centered depth from disparity, occlusion, and velocity gradients,” Percept. Psychophys. 40, 216–224 (1986).
[CrossRef] [PubMed]

Todd, J. T.

E. Mingolla, J. T. Todd, “Perception of solid shape from shading,” Biol. Cybern. 53, 137–151 (1986).
[CrossRef] [PubMed]

J. T. Todd, E. Mingolla, “Perception of surface curvature and direction of illumination from patterns of shading,”J. Exp. Psychol. Human Percept. Perform. 9, 583–595 (1983).
[CrossRef]

Torre, V.

T. Poggio, V. Torre, C. Koch, “Computational vision and regularization theory,” Nature 317, 314–319 (1985).
[CrossRef] [PubMed]

Ullman, S.

S. Ullman, The Interpretation of Visual Motion (MIT Press, Cambridge, Mass., 1979).

Witkin, A. P.

A. P. Witkin, “Recovering surface shape and orientation from texture,” Artif. Intell. 17, 17–47 (1981).
[CrossRef]

Wurst, S.

B. A. Dosher, G. Sperling, S. Wurst, “Tradeoffs between stereopsis and proximity luminance covariance as determinants of perceived 3D structure,” Vision Res. 26, 973–990 (1986).
[CrossRef] [PubMed]

Zisserman,

A. Blake, Zisserman, G. Knowles, “Surface description from stereo and shading,” Image Vision Comput. 3, 183–191 (1985).
[CrossRef]

Annu. Rev. Neurosci. (1)

G. Poggio, T. Poggio, “The analysis of stereopsis,” Annu. Rev. Neurosci. 7, 379–412 (1984).
[CrossRef] [PubMed]

Artif. Intell. (6)

J. E. W. Mayhew, J. P. Frisby, “Psychophysical and computational studies towards a theory of human stereopsis,” Artif. Intell. 17, 349–386 (1981).
[CrossRef]

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We write the equation of the ellipsoid asxTAx=1,A=[a−2000b−2000c−2], where a, b, and c denote the semidiameters. With a= b= 1, we have an ellipsoid of revolution. For a ray from viewpoint e to a point p′on the surface,x=e+μ(p′−e),μ∈R+, the ray tracing amounts to the solution for μ of the quadratic equation:[e+μ(p′−e)]TA[e+μ(p′−e)]=1. The image intensity at point p′was computed from this solution for an ideal Lambertian surface illuminated by parallel light from the z direction. Note that for a point x on the surface of the ellipsoid xTAx= 1, the surface normal is simply Ax/∥Ax∥. The viewing direction and the axis of revolution of the ellipsoid were aligned.

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Figures (9)

Fig. 1
Fig. 1

Imaging geometry. Projection onto the xz plane. The viewing distance is 120 cm. El, Er: nodal points of the left and right eyes, respectively. The distance between El and Er is 6.5 cm. A point pR3 is imaged on the screen at Pl for the view from the left eye and at Pr for the view from the right eye.

Fig. 2
Fig. 2

Flat- and smooth-shaded surfaces. (a), (b) Discontinuous and smooth intensity variations in images of polyhedra and ellipsoids provide cues for edge-based stereo, shape-from-disparate-shading, and shape-from-shading (experiment 1). (c) A smooth ellipsoid with sparse edge information has been used in experiments on the interaction of edge-based stereo and shape-from-shading (experiment 3). All images could be displayed as stereograms or as pairs of identical images. In image (c) the disparities of shading and edge token (ring) could be varied independently.

Fig. 3
Fig. 3

Perceived surfaces (experiment 1; depth not drawn to scale). Each plot shows the average of 6–9 sessions from three subjects. Perceived depth decreases with the following sequence of cue combinations: disparity, edges, and shading (D+E+); disparity and shading but no edges (D+E); shading only (DE); contradictory disparity and shading (DE+).

Fig. 4
Fig. 4

Perceived elongation. Depth perception decreases as fewer cues are available. The significant separation between the middle and lower curves (smooth shading with and without any disparity) illustrates the influence of disparity information even in the absence of edges. Solid lines, Lambertian shading; dashed lines, Phong shading. Int, intensity.

Fig. 5
Fig. 5

Perceived surfaces for oblique illuminations (experiment 2). The data confirm the relevance of disparate shading and show the independence of the findings of experiment 1 from the lighting conditions. No depth was measured in the self-shadow regions.

Fig. 6
Fig. 6

Zero-disparity edge token overrides shading (experiment 3). Top, Shape-from-shading (n = 7). (Bottom) Shape-from-disparate-shading (n = 6). Only data for elongation 4.0 are shown.

Fig. 7
Fig. 7

Surface interpolation for sparse edge data (experiment 3). (a) Shape-from-disparate-shading plus disparate edge information leads to an almost correct percept (n = 6). (b) A single edge token in front of a uniformly gray disk yields a conelike subjective surface (n = 6). (c), (d) Shape-from-shading plus disparate edge information leads to an ambiguous perception (n = 3 + 3). Only data for elongation 4.0 are shown.

Fig. 8
Fig. 8

Luminance and simulated brightness profiles, (a) Luminance profiles of ellipsoids with different elongations. Note that for elongations larger than 2.0, inflections occur. (b) Brightness profiles for the ellipsoid with elongation 4.0 [the one with the pronounced inflections in (a)]. The nonlinear compression [Eq. (6)] tends to cancel the infections that might give rise to zero crossings rather than enhancing them.

Fig. 9
Fig. 9

Integration of depth cues. The sizes of the boxes and interaction channels reflect the contributions of the different depth cues for the overall perceived depth (accumulation). In contradictory cases, shape from both disparate and nondisparate shading is vetoed by edge-based stereo. An inhibitory influence of shape-from-disparate-shading on shape-from-shading is discussed in Subsection 4.H.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

z = 1 r 2 .
n = ( r cos φ , r sin φ , 1 r 2 ) .
I ( r ) = I 0 ( l · n ) = I 0 1 r 2 ,
2 I ( r ) = I ( r ) 1 r I ( r ) = I 0 r 2 ( 1 r 2 ) 3 / 2 .
I c ( r ) = I 0 1 r 2 [ 1 ( 1 c 2 ) r 2 ] 1 / 2 ,
f ( I ) = I I + I 0.5 ,
xTAx=1,A=[a2000b2000c2],
x=e+μ(pe),μR+,
[e+μ(pe)]TA[e+μ(pe)]=1.

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