Abstract

Unlike the Metelli monochrome transparencies, when overlays and their backgrounds have chromatic content, the inferred surface colors may not always be physically realizable, and are in some sense “imaginary.” In these cases, the inferred chromatic transmittance or reflectance of the overlay lies outside the RGB spectral boundaries. Using the classical Metelli configuration, we demonstrate this illusion and briefly explore some of its attributes. Some observer differences in perceiving transparencies are also highlighted. These results show that the perception of transparency is much more complex than conventionally envisioned.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Wysecki and W. S. Stiles, Color Science (Wiley, 1967).
  2. J. J. Koenderink, Color for the Sciences (MIT Press, 2009).
  3. W. Richards and A. Witkin, “Transparency. Part II in efficient computations and representations of visible surfaces,” W. Richards and K. Stevens, Final Report AFOSR Contract 79-0020, pp. 46-72, MIT Artificial Intelligence Laboratory (1979).
  4. F. Metelli, “An algebraic development of the theory of transparency,” Ergonomics 13, 59-66 (1970).
    [CrossRef] [PubMed]
  5. F. Metelli, “The perception of transparency,” Sci. Am. 230, 90-98 (1974).
    [CrossRef] [PubMed]
  6. F. Metelli, “Achromatic color conditions in the perception of transparency,” in Perceptions: Essays in Honor of J J. Gibson, R.B.MacLeod and H.L.Pick, eds. (Cornell University Press, 1974), pp. 96-116.
  7. M. Brill, “Physical and informational constraints on the perception of transparency and translucency,” Comput. Vis. Graph. Image Process. 28, 356-362 (1984).
    [CrossRef]
  8. F. Metelli, S. C. Masin, and M. Manganelli, “Partial transparency,” Atti dell' accademie Patavina di Scienze Lettere ed Arti 92, 115-169 (1981).
  9. J. Beck and R. Ivry, “On the role of figural organization in perceptual transparency,” Percept. Psychophys. 44, 585-594 (1988).
    [CrossRef] [PubMed]
  10. F. Metelli, O. da Pos, and A. Cavedon, “Balanced and unbalanced, complete and partial transparency,” Percept. Psychophys. 38, 354-366 (1985).
    [CrossRef] [PubMed]
  11. O. da Pos, Trasparenze (Icone, 1989).
  12. T. Kozaki, M. Fukuda, Y. Nakano, and N. Masuda, “Phenomenal transparency and other related phenomena,” Hiyoshi Rev. of Natural Science (Keio University) 6, 68-81 (1989).
  13. M. Fukuda and S. C. Masin, “Test of balanced transparency,” Perception 23, 37-43 (1994).
    [CrossRef] [PubMed]
  14. S. Masin, “The luminance conditions for transparency,” Perception 26, 39-50 (1997).
    [CrossRef] [PubMed]
  15. J. Beck, “Additive and subtractive mixture in color transparency,” Percept. Psychophys. 23, 256-267 (1978).
    [CrossRef]
  16. W. Gerbino, C. I. Stultiens, J. M. Troost, and C. M. de Weert, “Transparent layer constancy,” J. Exp. Psychol. Hum. Percept. Perform. 16, 3-20 (1990).
    [CrossRef] [PubMed]
  17. F. Faul and V. Ekroll, “Psychophysical model of chromatic perceptual transparency based on subtractive color mixture,” J. Opt. Soc. Am. A 19, 1084-1095 (2002).
    [CrossRef]
  18. S. Nakauchi, P. Silfsten, J. Parkkinen, and S. Ussui, “Computational theory of color transparency: recovery of spectral properties for overlapping surfaces,” J. Opt. Soc. Am. A 16, 2612-2624 (1999).
    [CrossRef]
  19. J. Hagedorn and M. D'Zmura, “Color appearance of surfaces viewed through fog,” Perception 29, 1169-1184 (2000).
    [CrossRef]
  20. B. G. Khang and Q. Zaidi, “Accuracy of color scission for spectral transparencies,” J. Vision 2, 451-466 (2002).
    [CrossRef]
  21. P. Kubelka and F. Munk, “Ein Beitrag zur Optik des Farbenstriche,” Z. Tech. Phys. (Leipzig) 12, 593 (1934).
  22. P. Kubelka, “New contributions to the optics of intensely light-scattering materials. Part II. Nonhomogeneous layers,” J. Opt. Soc. Am. 44, 330-334 (1954).
    [CrossRef]
  23. J. Koenderink, A. van Doorn, S. Pont, and W. Richards, “Gestalt and phenomenal transparency,” J. Opt. Soc. Am. A 25, 190-202 (2008).
    [CrossRef]
  24. M. D'Zmura, P. Colantoni, K. Knoblauch, and B. Laget, “Color transparency,” Perception 26, 471-492 (1997).
    [CrossRef] [PubMed]
  25. W. Metzger, “Ueber Durchsichtigkeits-Erscheinungen,” Rivista di Psicologia. Fascicolo Giubilare 49, 187-189 (1955).
  26. K. Nakayama, S. Shimojo, and V. S. Ramachandran, “Transparency: relations to depth, subjective contours, luminance and neon color spreading,” Perception 19, 497-513 (1990).
    [CrossRef] [PubMed]
  27. K. Nakayama and S. Shimojo, “Experiencing and perceiving visual surfaces,” Science 257, 1357-1363, (1992).
    [CrossRef] [PubMed]
  28. M. Singh and D. D. Hoffman, “Part boundaries alter the perception of transparency,” Psychol. Sci. 9, 370-378 (1988).
    [CrossRef]
  29. M. Singh and B. L. Anderson, “Toward a perceptual theory of transparency,” Psychol. Rev. 109, 492-519 (2002).
    [CrossRef] [PubMed]
  30. W. Richards, “Anomalous stereoscopic depth perception,” J. Opt. Soc. Am. 61, 410-414 (1971).
    [CrossRef] [PubMed]
  31. R. Van Ee and W. Richards, “A planar and volumetric test for stereoanomaly,” Perception 31, 51-64 (2002).
    [CrossRef] [PubMed]
  32. B. L. Anderson, “A theory of illusory lightness and transparency in monocular and binocular images,” Perception 26, 419-453 (1997).
    [CrossRef] [PubMed]
  33. V. J. Chen and M. D'Zmura, “Test of a convergence model for color transparency perception,” Perception 27, 595-608 (1988).
    [CrossRef]
  34. M. Singh and B. Anderson, “Photometric determinants of perceived transparency,” Vision Res. 46, 897-894 (2006).
    [CrossRef]
  35. B. L. Anderson, “The role of occlusion in the perception of depth, lightness and opacity,” Psychol. Rev. 110, 762-784 (2003).
    [CrossRef]
  36. M. Singh and B. L. Anderson, “Perceptual assignment of opacity to translucent surfaces: the role of image blur,” Perception 31, 531-552 (2002).
    [CrossRef] [PubMed]
  37. J. Wolfe, R. Birnkrant, M. Kunar, and T. Horowitz, “Visual search for transparencies and opacity: attentional guidance by cue combination?” J. Vision 5, 257-274 (2005).
    [CrossRef]
  38. J. M. Fulvio, M. Singh, and L. T. Maloney, “Combining achromatic and chromatic cues to transparency,” J. Vision 6, 760-776 (2006).
    [CrossRef]

2008 (1)

2006 (2)

M. Singh and B. Anderson, “Photometric determinants of perceived transparency,” Vision Res. 46, 897-894 (2006).
[CrossRef]

J. M. Fulvio, M. Singh, and L. T. Maloney, “Combining achromatic and chromatic cues to transparency,” J. Vision 6, 760-776 (2006).
[CrossRef]

2005 (1)

J. Wolfe, R. Birnkrant, M. Kunar, and T. Horowitz, “Visual search for transparencies and opacity: attentional guidance by cue combination?” J. Vision 5, 257-274 (2005).
[CrossRef]

2003 (1)

B. L. Anderson, “The role of occlusion in the perception of depth, lightness and opacity,” Psychol. Rev. 110, 762-784 (2003).
[CrossRef]

2002 (5)

M. Singh and B. L. Anderson, “Perceptual assignment of opacity to translucent surfaces: the role of image blur,” Perception 31, 531-552 (2002).
[CrossRef] [PubMed]

R. Van Ee and W. Richards, “A planar and volumetric test for stereoanomaly,” Perception 31, 51-64 (2002).
[CrossRef] [PubMed]

M. Singh and B. L. Anderson, “Toward a perceptual theory of transparency,” Psychol. Rev. 109, 492-519 (2002).
[CrossRef] [PubMed]

F. Faul and V. Ekroll, “Psychophysical model of chromatic perceptual transparency based on subtractive color mixture,” J. Opt. Soc. Am. A 19, 1084-1095 (2002).
[CrossRef]

B. G. Khang and Q. Zaidi, “Accuracy of color scission for spectral transparencies,” J. Vision 2, 451-466 (2002).
[CrossRef]

2000 (1)

J. Hagedorn and M. D'Zmura, “Color appearance of surfaces viewed through fog,” Perception 29, 1169-1184 (2000).
[CrossRef]

1999 (1)

1997 (3)

S. Masin, “The luminance conditions for transparency,” Perception 26, 39-50 (1997).
[CrossRef] [PubMed]

M. D'Zmura, P. Colantoni, K. Knoblauch, and B. Laget, “Color transparency,” Perception 26, 471-492 (1997).
[CrossRef] [PubMed]

B. L. Anderson, “A theory of illusory lightness and transparency in monocular and binocular images,” Perception 26, 419-453 (1997).
[CrossRef] [PubMed]

1994 (1)

M. Fukuda and S. C. Masin, “Test of balanced transparency,” Perception 23, 37-43 (1994).
[CrossRef] [PubMed]

1992 (1)

K. Nakayama and S. Shimojo, “Experiencing and perceiving visual surfaces,” Science 257, 1357-1363, (1992).
[CrossRef] [PubMed]

1990 (2)

K. Nakayama, S. Shimojo, and V. S. Ramachandran, “Transparency: relations to depth, subjective contours, luminance and neon color spreading,” Perception 19, 497-513 (1990).
[CrossRef] [PubMed]

W. Gerbino, C. I. Stultiens, J. M. Troost, and C. M. de Weert, “Transparent layer constancy,” J. Exp. Psychol. Hum. Percept. Perform. 16, 3-20 (1990).
[CrossRef] [PubMed]

1989 (1)

T. Kozaki, M. Fukuda, Y. Nakano, and N. Masuda, “Phenomenal transparency and other related phenomena,” Hiyoshi Rev. of Natural Science (Keio University) 6, 68-81 (1989).

1988 (3)

J. Beck and R. Ivry, “On the role of figural organization in perceptual transparency,” Percept. Psychophys. 44, 585-594 (1988).
[CrossRef] [PubMed]

M. Singh and D. D. Hoffman, “Part boundaries alter the perception of transparency,” Psychol. Sci. 9, 370-378 (1988).
[CrossRef]

V. J. Chen and M. D'Zmura, “Test of a convergence model for color transparency perception,” Perception 27, 595-608 (1988).
[CrossRef]

1985 (1)

F. Metelli, O. da Pos, and A. Cavedon, “Balanced and unbalanced, complete and partial transparency,” Percept. Psychophys. 38, 354-366 (1985).
[CrossRef] [PubMed]

1984 (1)

M. Brill, “Physical and informational constraints on the perception of transparency and translucency,” Comput. Vis. Graph. Image Process. 28, 356-362 (1984).
[CrossRef]

1981 (1)

F. Metelli, S. C. Masin, and M. Manganelli, “Partial transparency,” Atti dell' accademie Patavina di Scienze Lettere ed Arti 92, 115-169 (1981).

1978 (1)

J. Beck, “Additive and subtractive mixture in color transparency,” Percept. Psychophys. 23, 256-267 (1978).
[CrossRef]

1974 (1)

F. Metelli, “The perception of transparency,” Sci. Am. 230, 90-98 (1974).
[CrossRef] [PubMed]

1971 (1)

1970 (1)

F. Metelli, “An algebraic development of the theory of transparency,” Ergonomics 13, 59-66 (1970).
[CrossRef] [PubMed]

1955 (1)

W. Metzger, “Ueber Durchsichtigkeits-Erscheinungen,” Rivista di Psicologia. Fascicolo Giubilare 49, 187-189 (1955).

1954 (1)

1934 (1)

P. Kubelka and F. Munk, “Ein Beitrag zur Optik des Farbenstriche,” Z. Tech. Phys. (Leipzig) 12, 593 (1934).

Anderson, B.

M. Singh and B. Anderson, “Photometric determinants of perceived transparency,” Vision Res. 46, 897-894 (2006).
[CrossRef]

Anderson, B. L.

B. L. Anderson, “The role of occlusion in the perception of depth, lightness and opacity,” Psychol. Rev. 110, 762-784 (2003).
[CrossRef]

M. Singh and B. L. Anderson, “Toward a perceptual theory of transparency,” Psychol. Rev. 109, 492-519 (2002).
[CrossRef] [PubMed]

M. Singh and B. L. Anderson, “Perceptual assignment of opacity to translucent surfaces: the role of image blur,” Perception 31, 531-552 (2002).
[CrossRef] [PubMed]

B. L. Anderson, “A theory of illusory lightness and transparency in monocular and binocular images,” Perception 26, 419-453 (1997).
[CrossRef] [PubMed]

Beck, J.

J. Beck and R. Ivry, “On the role of figural organization in perceptual transparency,” Percept. Psychophys. 44, 585-594 (1988).
[CrossRef] [PubMed]

J. Beck, “Additive and subtractive mixture in color transparency,” Percept. Psychophys. 23, 256-267 (1978).
[CrossRef]

Birnkrant, R.

J. Wolfe, R. Birnkrant, M. Kunar, and T. Horowitz, “Visual search for transparencies and opacity: attentional guidance by cue combination?” J. Vision 5, 257-274 (2005).
[CrossRef]

Brill, M.

M. Brill, “Physical and informational constraints on the perception of transparency and translucency,” Comput. Vis. Graph. Image Process. 28, 356-362 (1984).
[CrossRef]

Cavedon, A.

F. Metelli, O. da Pos, and A. Cavedon, “Balanced and unbalanced, complete and partial transparency,” Percept. Psychophys. 38, 354-366 (1985).
[CrossRef] [PubMed]

Chen, V. J.

V. J. Chen and M. D'Zmura, “Test of a convergence model for color transparency perception,” Perception 27, 595-608 (1988).
[CrossRef]

Colantoni, P.

M. D'Zmura, P. Colantoni, K. Knoblauch, and B. Laget, “Color transparency,” Perception 26, 471-492 (1997).
[CrossRef] [PubMed]

da Pos, O.

F. Metelli, O. da Pos, and A. Cavedon, “Balanced and unbalanced, complete and partial transparency,” Percept. Psychophys. 38, 354-366 (1985).
[CrossRef] [PubMed]

O. da Pos, Trasparenze (Icone, 1989).

de Weert, C. M.

W. Gerbino, C. I. Stultiens, J. M. Troost, and C. M. de Weert, “Transparent layer constancy,” J. Exp. Psychol. Hum. Percept. Perform. 16, 3-20 (1990).
[CrossRef] [PubMed]

D'Zmura, M.

J. Hagedorn and M. D'Zmura, “Color appearance of surfaces viewed through fog,” Perception 29, 1169-1184 (2000).
[CrossRef]

M. D'Zmura, P. Colantoni, K. Knoblauch, and B. Laget, “Color transparency,” Perception 26, 471-492 (1997).
[CrossRef] [PubMed]

V. J. Chen and M. D'Zmura, “Test of a convergence model for color transparency perception,” Perception 27, 595-608 (1988).
[CrossRef]

Ekroll, V.

Faul, F.

Fukuda, M.

M. Fukuda and S. C. Masin, “Test of balanced transparency,” Perception 23, 37-43 (1994).
[CrossRef] [PubMed]

T. Kozaki, M. Fukuda, Y. Nakano, and N. Masuda, “Phenomenal transparency and other related phenomena,” Hiyoshi Rev. of Natural Science (Keio University) 6, 68-81 (1989).

Fulvio, J. M.

J. M. Fulvio, M. Singh, and L. T. Maloney, “Combining achromatic and chromatic cues to transparency,” J. Vision 6, 760-776 (2006).
[CrossRef]

Gerbino, W.

W. Gerbino, C. I. Stultiens, J. M. Troost, and C. M. de Weert, “Transparent layer constancy,” J. Exp. Psychol. Hum. Percept. Perform. 16, 3-20 (1990).
[CrossRef] [PubMed]

Hagedorn, J.

J. Hagedorn and M. D'Zmura, “Color appearance of surfaces viewed through fog,” Perception 29, 1169-1184 (2000).
[CrossRef]

Hoffman, D. D.

M. Singh and D. D. Hoffman, “Part boundaries alter the perception of transparency,” Psychol. Sci. 9, 370-378 (1988).
[CrossRef]

Horowitz, T.

J. Wolfe, R. Birnkrant, M. Kunar, and T. Horowitz, “Visual search for transparencies and opacity: attentional guidance by cue combination?” J. Vision 5, 257-274 (2005).
[CrossRef]

Ivry, R.

J. Beck and R. Ivry, “On the role of figural organization in perceptual transparency,” Percept. Psychophys. 44, 585-594 (1988).
[CrossRef] [PubMed]

Khang, B. G.

B. G. Khang and Q. Zaidi, “Accuracy of color scission for spectral transparencies,” J. Vision 2, 451-466 (2002).
[CrossRef]

Knoblauch, K.

M. D'Zmura, P. Colantoni, K. Knoblauch, and B. Laget, “Color transparency,” Perception 26, 471-492 (1997).
[CrossRef] [PubMed]

Koenderink, J.

Koenderink, J. J.

J. J. Koenderink, Color for the Sciences (MIT Press, 2009).

Kozaki, T.

T. Kozaki, M. Fukuda, Y. Nakano, and N. Masuda, “Phenomenal transparency and other related phenomena,” Hiyoshi Rev. of Natural Science (Keio University) 6, 68-81 (1989).

Kubelka, P.

Kunar, M.

J. Wolfe, R. Birnkrant, M. Kunar, and T. Horowitz, “Visual search for transparencies and opacity: attentional guidance by cue combination?” J. Vision 5, 257-274 (2005).
[CrossRef]

Laget, B.

M. D'Zmura, P. Colantoni, K. Knoblauch, and B. Laget, “Color transparency,” Perception 26, 471-492 (1997).
[CrossRef] [PubMed]

Maloney, L. T.

J. M. Fulvio, M. Singh, and L. T. Maloney, “Combining achromatic and chromatic cues to transparency,” J. Vision 6, 760-776 (2006).
[CrossRef]

Manganelli, M.

F. Metelli, S. C. Masin, and M. Manganelli, “Partial transparency,” Atti dell' accademie Patavina di Scienze Lettere ed Arti 92, 115-169 (1981).

Masin, S.

S. Masin, “The luminance conditions for transparency,” Perception 26, 39-50 (1997).
[CrossRef] [PubMed]

Masin, S. C.

M. Fukuda and S. C. Masin, “Test of balanced transparency,” Perception 23, 37-43 (1994).
[CrossRef] [PubMed]

F. Metelli, S. C. Masin, and M. Manganelli, “Partial transparency,” Atti dell' accademie Patavina di Scienze Lettere ed Arti 92, 115-169 (1981).

Masuda, N.

T. Kozaki, M. Fukuda, Y. Nakano, and N. Masuda, “Phenomenal transparency and other related phenomena,” Hiyoshi Rev. of Natural Science (Keio University) 6, 68-81 (1989).

Metelli, F.

F. Metelli, O. da Pos, and A. Cavedon, “Balanced and unbalanced, complete and partial transparency,” Percept. Psychophys. 38, 354-366 (1985).
[CrossRef] [PubMed]

F. Metelli, S. C. Masin, and M. Manganelli, “Partial transparency,” Atti dell' accademie Patavina di Scienze Lettere ed Arti 92, 115-169 (1981).

F. Metelli, “The perception of transparency,” Sci. Am. 230, 90-98 (1974).
[CrossRef] [PubMed]

F. Metelli, “An algebraic development of the theory of transparency,” Ergonomics 13, 59-66 (1970).
[CrossRef] [PubMed]

F. Metelli, “Achromatic color conditions in the perception of transparency,” in Perceptions: Essays in Honor of J J. Gibson, R.B.MacLeod and H.L.Pick, eds. (Cornell University Press, 1974), pp. 96-116.

Metzger, W.

W. Metzger, “Ueber Durchsichtigkeits-Erscheinungen,” Rivista di Psicologia. Fascicolo Giubilare 49, 187-189 (1955).

Munk, F.

P. Kubelka and F. Munk, “Ein Beitrag zur Optik des Farbenstriche,” Z. Tech. Phys. (Leipzig) 12, 593 (1934).

Nakano, Y.

T. Kozaki, M. Fukuda, Y. Nakano, and N. Masuda, “Phenomenal transparency and other related phenomena,” Hiyoshi Rev. of Natural Science (Keio University) 6, 68-81 (1989).

Nakauchi, S.

Nakayama, K.

K. Nakayama and S. Shimojo, “Experiencing and perceiving visual surfaces,” Science 257, 1357-1363, (1992).
[CrossRef] [PubMed]

K. Nakayama, S. Shimojo, and V. S. Ramachandran, “Transparency: relations to depth, subjective contours, luminance and neon color spreading,” Perception 19, 497-513 (1990).
[CrossRef] [PubMed]

Parkkinen, J.

Pont, S.

Ramachandran, V. S.

K. Nakayama, S. Shimojo, and V. S. Ramachandran, “Transparency: relations to depth, subjective contours, luminance and neon color spreading,” Perception 19, 497-513 (1990).
[CrossRef] [PubMed]

Richards, W.

J. Koenderink, A. van Doorn, S. Pont, and W. Richards, “Gestalt and phenomenal transparency,” J. Opt. Soc. Am. A 25, 190-202 (2008).
[CrossRef]

R. Van Ee and W. Richards, “A planar and volumetric test for stereoanomaly,” Perception 31, 51-64 (2002).
[CrossRef] [PubMed]

W. Richards, “Anomalous stereoscopic depth perception,” J. Opt. Soc. Am. 61, 410-414 (1971).
[CrossRef] [PubMed]

W. Richards and A. Witkin, “Transparency. Part II in efficient computations and representations of visible surfaces,” W. Richards and K. Stevens, Final Report AFOSR Contract 79-0020, pp. 46-72, MIT Artificial Intelligence Laboratory (1979).

Shimojo, S.

K. Nakayama and S. Shimojo, “Experiencing and perceiving visual surfaces,” Science 257, 1357-1363, (1992).
[CrossRef] [PubMed]

K. Nakayama, S. Shimojo, and V. S. Ramachandran, “Transparency: relations to depth, subjective contours, luminance and neon color spreading,” Perception 19, 497-513 (1990).
[CrossRef] [PubMed]

Silfsten, P.

Singh, M.

M. Singh and B. Anderson, “Photometric determinants of perceived transparency,” Vision Res. 46, 897-894 (2006).
[CrossRef]

J. M. Fulvio, M. Singh, and L. T. Maloney, “Combining achromatic and chromatic cues to transparency,” J. Vision 6, 760-776 (2006).
[CrossRef]

M. Singh and B. L. Anderson, “Toward a perceptual theory of transparency,” Psychol. Rev. 109, 492-519 (2002).
[CrossRef] [PubMed]

M. Singh and B. L. Anderson, “Perceptual assignment of opacity to translucent surfaces: the role of image blur,” Perception 31, 531-552 (2002).
[CrossRef] [PubMed]

M. Singh and D. D. Hoffman, “Part boundaries alter the perception of transparency,” Psychol. Sci. 9, 370-378 (1988).
[CrossRef]

Stiles, W. S.

G. Wysecki and W. S. Stiles, Color Science (Wiley, 1967).

Stultiens, C. I.

W. Gerbino, C. I. Stultiens, J. M. Troost, and C. M. de Weert, “Transparent layer constancy,” J. Exp. Psychol. Hum. Percept. Perform. 16, 3-20 (1990).
[CrossRef] [PubMed]

Troost, J. M.

W. Gerbino, C. I. Stultiens, J. M. Troost, and C. M. de Weert, “Transparent layer constancy,” J. Exp. Psychol. Hum. Percept. Perform. 16, 3-20 (1990).
[CrossRef] [PubMed]

Ussui, S.

van Doorn, A.

Van Ee, R.

R. Van Ee and W. Richards, “A planar and volumetric test for stereoanomaly,” Perception 31, 51-64 (2002).
[CrossRef] [PubMed]

Witkin, A.

W. Richards and A. Witkin, “Transparency. Part II in efficient computations and representations of visible surfaces,” W. Richards and K. Stevens, Final Report AFOSR Contract 79-0020, pp. 46-72, MIT Artificial Intelligence Laboratory (1979).

Wolfe, J.

J. Wolfe, R. Birnkrant, M. Kunar, and T. Horowitz, “Visual search for transparencies and opacity: attentional guidance by cue combination?” J. Vision 5, 257-274 (2005).
[CrossRef]

Wysecki, G.

G. Wysecki and W. S. Stiles, Color Science (Wiley, 1967).

Zaidi, Q.

B. G. Khang and Q. Zaidi, “Accuracy of color scission for spectral transparencies,” J. Vision 2, 451-466 (2002).
[CrossRef]

Atti dell' accademie Patavina di Scienze Lettere ed Arti (1)

F. Metelli, S. C. Masin, and M. Manganelli, “Partial transparency,” Atti dell' accademie Patavina di Scienze Lettere ed Arti 92, 115-169 (1981).

Comput. Vis. Graph. Image Process. (1)

M. Brill, “Physical and informational constraints on the perception of transparency and translucency,” Comput. Vis. Graph. Image Process. 28, 356-362 (1984).
[CrossRef]

Ergonomics (1)

F. Metelli, “An algebraic development of the theory of transparency,” Ergonomics 13, 59-66 (1970).
[CrossRef] [PubMed]

Hiyoshi Rev. of Natural Science (Keio University) (1)

T. Kozaki, M. Fukuda, Y. Nakano, and N. Masuda, “Phenomenal transparency and other related phenomena,” Hiyoshi Rev. of Natural Science (Keio University) 6, 68-81 (1989).

J. Exp. Psychol. Hum. Percept. Perform. (1)

W. Gerbino, C. I. Stultiens, J. M. Troost, and C. M. de Weert, “Transparent layer constancy,” J. Exp. Psychol. Hum. Percept. Perform. 16, 3-20 (1990).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

J. Vision (3)

B. G. Khang and Q. Zaidi, “Accuracy of color scission for spectral transparencies,” J. Vision 2, 451-466 (2002).
[CrossRef]

J. Wolfe, R. Birnkrant, M. Kunar, and T. Horowitz, “Visual search for transparencies and opacity: attentional guidance by cue combination?” J. Vision 5, 257-274 (2005).
[CrossRef]

J. M. Fulvio, M. Singh, and L. T. Maloney, “Combining achromatic and chromatic cues to transparency,” J. Vision 6, 760-776 (2006).
[CrossRef]

Percept. Psychophys. (3)

J. Beck, “Additive and subtractive mixture in color transparency,” Percept. Psychophys. 23, 256-267 (1978).
[CrossRef]

J. Beck and R. Ivry, “On the role of figural organization in perceptual transparency,” Percept. Psychophys. 44, 585-594 (1988).
[CrossRef] [PubMed]

F. Metelli, O. da Pos, and A. Cavedon, “Balanced and unbalanced, complete and partial transparency,” Percept. Psychophys. 38, 354-366 (1985).
[CrossRef] [PubMed]

Perception (9)

M. Fukuda and S. C. Masin, “Test of balanced transparency,” Perception 23, 37-43 (1994).
[CrossRef] [PubMed]

S. Masin, “The luminance conditions for transparency,” Perception 26, 39-50 (1997).
[CrossRef] [PubMed]

J. Hagedorn and M. D'Zmura, “Color appearance of surfaces viewed through fog,” Perception 29, 1169-1184 (2000).
[CrossRef]

K. Nakayama, S. Shimojo, and V. S. Ramachandran, “Transparency: relations to depth, subjective contours, luminance and neon color spreading,” Perception 19, 497-513 (1990).
[CrossRef] [PubMed]

M. D'Zmura, P. Colantoni, K. Knoblauch, and B. Laget, “Color transparency,” Perception 26, 471-492 (1997).
[CrossRef] [PubMed]

R. Van Ee and W. Richards, “A planar and volumetric test for stereoanomaly,” Perception 31, 51-64 (2002).
[CrossRef] [PubMed]

B. L. Anderson, “A theory of illusory lightness and transparency in monocular and binocular images,” Perception 26, 419-453 (1997).
[CrossRef] [PubMed]

V. J. Chen and M. D'Zmura, “Test of a convergence model for color transparency perception,” Perception 27, 595-608 (1988).
[CrossRef]

M. Singh and B. L. Anderson, “Perceptual assignment of opacity to translucent surfaces: the role of image blur,” Perception 31, 531-552 (2002).
[CrossRef] [PubMed]

Psychol. Rev. (2)

B. L. Anderson, “The role of occlusion in the perception of depth, lightness and opacity,” Psychol. Rev. 110, 762-784 (2003).
[CrossRef]

M. Singh and B. L. Anderson, “Toward a perceptual theory of transparency,” Psychol. Rev. 109, 492-519 (2002).
[CrossRef] [PubMed]

Psychol. Sci. (1)

M. Singh and D. D. Hoffman, “Part boundaries alter the perception of transparency,” Psychol. Sci. 9, 370-378 (1988).
[CrossRef]

Rivista di Psicologia. Fascicolo Giubilare (1)

W. Metzger, “Ueber Durchsichtigkeits-Erscheinungen,” Rivista di Psicologia. Fascicolo Giubilare 49, 187-189 (1955).

Sci. Am. (1)

F. Metelli, “The perception of transparency,” Sci. Am. 230, 90-98 (1974).
[CrossRef] [PubMed]

Science (1)

K. Nakayama and S. Shimojo, “Experiencing and perceiving visual surfaces,” Science 257, 1357-1363, (1992).
[CrossRef] [PubMed]

Vision Res. (1)

M. Singh and B. Anderson, “Photometric determinants of perceived transparency,” Vision Res. 46, 897-894 (2006).
[CrossRef]

Z. Tech. Phys. (Leipzig) (1)

P. Kubelka and F. Munk, “Ein Beitrag zur Optik des Farbenstriche,” Z. Tech. Phys. (Leipzig) 12, 593 (1934).

Other (5)

F. Metelli, “Achromatic color conditions in the perception of transparency,” in Perceptions: Essays in Honor of J J. Gibson, R.B.MacLeod and H.L.Pick, eds. (Cornell University Press, 1974), pp. 96-116.

G. Wysecki and W. S. Stiles, Color Science (Wiley, 1967).

J. J. Koenderink, Color for the Sciences (MIT Press, 2009).

W. Richards and A. Witkin, “Transparency. Part II in efficient computations and representations of visible surfaces,” W. Richards and K. Stevens, Final Report AFOSR Contract 79-0020, pp. 46-72, MIT Artificial Intelligence Laboratory (1979).

O. da Pos, Trasparenze (Icone, 1989).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Example transparency. The RGB values are: A = = { 0.50 , 0.50 , 0.70 } ; B = = { 0.50 , 0.50 , 0.30 } ; P = = { 0.20 , 0.20 , 0.40 ) and Q = = { 0.20 , 0.20 , 0.05 } . Using Metelli Eqs. (1), a reflectance and transmittance of the overlay can be calculated for each RGB tristimulus value. For this example, the inferred reflectance and transmittance for the B tristimulus values were, respectively, 0.63 and 0.73. The negative value indicates a Metelli violation requiring an unrealizable or “imaginary” spectral surface color (see Fig. 2).

Fig. 2
Fig. 2

Slice at the RGB color space showing a violation of the Metelli conditions (left) and another example that is physically realizable (right).

Fig. 3
Fig. 3

Depiction of the experimental conditions. The parallelogram is part of a plane in RGB space defined by the points, A, B, and an anchor point max - P Q . Points are chosen along the line through C joining max - P Q and min - P Q . The boundary of the parallelogram indicates the limiting P Q settings for the Metelli conditions. In the lower panel, we show averaged settings for task 8 (Fig. 4). Note that observers accept settings that lie outside the parallelogram.

Fig. 4
Fig. 4

Averaged values of transmittance τ λ (top) and reflectance α λ (lower) for the upper bounds of transparency settings of eight subjects for task 8 (see Table 1 in Appendix A). The dashed curves indicate values if both of Metelli’s conditions were met at the same time (the ideal step function for the lower panel has been smoothed slightly). The L and H vertical lines give approximate boundaries for grayish tones to the overlay (below L, very dark; above H, very light). Note that although reflectance is mostly within the [0,1] interval over the grayish range, most of the transmittances exceed one. Similarly, the reverse is true outside this gray interval. (Points greater than 1.5 or less than 0.7 are plotted on the upper and lower boundaries of the panel. Arrows indicate very large values for standard deviations that exceeded the range indicated on the left).

Fig. 5
Fig. 5

Inferred transmittance (top) and reflectance (bottom) for task 21, where the P Q loci are shifted to the red. The left two panels are data from two subjects, the right panels are data from three subjects, all of whom provided similar data for task 8 (Fig. 4). The P Q values of the overlay vary from pinkish to dark purple, with max - P Q = { 1 , 0.7 , 0.7 } . The background panels are A = { 0.8 , 0.5 , 0.7 } , B = { 0.8 , 0.5 , 0.3 } . See Appendix A for further details.

Fig. 6
Fig. 6

Inferred transmittance (top) and reflectance (bottom) for task 13 for three subjects used also for task 21 (right panels of Fig. 5). For task 13 the P Q loci are shifted away from the achromatic locus to the green. The P Q values of the overlaid region vary from light blue-green (5BG8/5) to red-purple (2.5RP3/8), moving through a greenish gray. max - P Q = { 0.4 , 1 , 0.4 } . The background panels are A = { 0.2 , 0.3 , 0.7 } , B = { 0.5 , 1 , 0.01 } . The transmittances for all three channels are the same; the open circles show the compressed reflectance values inferred from the B tristimulus values; the solid circles show those inferred from the G tristimulus values. See Appendix A and text for further detail.

Tables (1)

Tables Icon

Table 1 Experimental Parameters and Violations

Equations (13)

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

P λ = τ λ A λ + ( 1 τ λ ) α λ ,
Q λ = τ λ B λ + ( 1 τ λ ) α λ .
( 0 τ λ 1 ) 0 ( P λ Q λ ) ( A λ B λ ) 1 ,
( 0 α λ 1 ) 0 ( P λ B λ + A λ Q λ ) ( A λ B λ P λ + Q λ ) 1 .
F ( A , B ; P , Q ) = ( ( ( P > Q ) ( A > B ) ) ( ( ( ( ( Q + A + P B ) > ( P + Q A + B ) ) ( P > A ) ) ( ( P < A ) ( P B < Q A ) ) ) ) ( ( P < Q ) ( A < B ) ( ( ( P B > Q A ) ( P < A ) ) ( ( P < A ) ( Q + A + P B ) < ( A B + Q A + B ) ) ) ) ) .
C 1 = F ( A 1 , B 1 ; P 1 , Q 1 ) ,
C 2 = F ( A 2 , B 2 ; P 2 , Q 2 ) ,
C 1 + 2 = F ( ( A 1 + A 2 ) 2 , ( B 1 + B 2 ) 2 ; ( P 1 + P 2 ) 2 , ( Q 1 + Q 2 ) 2 ) ,
H = ( C 1 C 2 ) ¬ C 1 + 2
F ( K + L 2 , K L 2 ; S + T 2 , S T 2 ) .
L K > T S ,
G ( K , S ) H ( L , T ) ,
( L T > 0 ) ( T < L ) .

Metrics