Abstract

Classical approaches to transparency perception assume that transparency constitutes a perceptual dimension corresponding to the physical dimension of transmittance. Here I present an alternative theory, termed gamut relativity, that naturally explains key aspects of transparency perception. Rather than being computed as values along a perceptual dimension corresponding to transmittance, gamut relativity postulates that transparency is built directly into the fabric of the visual system’s representation of surface color. The theory, originally developed to explain properties of brightness and lightness perception, proposes how the relativity of the achromatic color gamut in a perceptual blackness–whiteness space underlies the representation of foreground and background surface layers. Whereas brightness and lightness perception were previously reanalyzed in terms of the relativity of the achromatic color gamut with respect to illumination level, transparency perception is here reinterpreted in terms of relativity with respect to physical transmittance. The relativity of the achromatic color gamut thus emerges as a fundamental computational principle underlying surface perception. A duality theorem relates the definition of transparency provided in gamut relativity with the classical definition underlying the physical blending models of computer graphics.

© 2013 Optical Society of America

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References

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  1. E. H. Adelson, “Perceptual organization and the judgment of brightness,” Science 262, 2042–2044 (1993).
    [CrossRef]
  2. E. H. Adelson, “Lightness perception and lightness illusions,” in The New Cognitive Neurosciences, M. Gazzaniga, ed. (MIT, 2000), pp. 339–352.
  3. B. L. Anderson, “A theory of illusory lightness and transparency in monocular and binocular images: the role of contour junctions,” Perception 26, 419–453 (1997).
    [CrossRef]
  4. B. L. Anderson, “Stereoscopic surface perception,” Neuron 24, 919–928 (1999).
    [CrossRef]
  5. B. L. Anderson, “The role of occlusion in the perception of depth, lightness, and opacity.” Psychol. Rev. 110, 785–801 (2003).
    [CrossRef]
  6. B. L. Anderson and J. Winawer, “Image segmentation and lightness perception,” Nature 434, 79–83 (2005).
    [CrossRef]
  7. B. L. Anderson and J. Winawer, “Layered image representations and the computation of surface lightness,” J. Vis. 8(7):18, 1–21 (2008).
    [CrossRef]
  8. F. Faul and V. Ekroll, “Psychophysical model of chromatic perceptual transparency based on substractive color mixture,” J. Opt. Soc. Am. A 19, 1084–1095 (2002).
    [CrossRef]
  9. F. Faul and V. Ekroll, “On the filter approach to perceptual transparency,” J. Vis. 11(7):7, 1–33 (2011).
    [CrossRef]
  10. F. Faul and V. Ekroll, “Transparent layer constancy,” J. Vis. 12(12):7, 1–26 (2012).
    [CrossRef]
  11. 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]
  12. F. Metelli, “An algebraic development of the theory of perceptual transparency,” Ergonomics 13, 59–66 (1970).
    [CrossRef]
  13. F. Metelli, “The perception of transparency,” Sci. Am. 230, 90–98 (1974).
    [CrossRef]
  14. F. Metelli, O. Da Pos, and A. Cavedon, “Balanced and unbalanced, complete and partial transparency,” Percept. Psychophys. 38, 354–366 (1985).
    [CrossRef]
  15. R. Robilotto, B.-G. Khang, and Q. Zaidi, “Sensory and physical determinants of perceived achromatic transparency,” J. Vis. 2(5):3 , 388–403 (2002).
    [CrossRef]
  16. R. Robilotto and Q. Zaidi, “Perceived transparency of neutral density filters across dissimilar backgrounds,” J. Vis. 4(3):5, 183–195 (2004).
    [CrossRef]
  17. M. Singh, “Lightness constancy through transparency: internal consistency in layered surface representations,” Vis. Res. 44, 1827–1842 (2004).
    [CrossRef]
  18. M. Singh and B. L. Anderson, “Photometric determinants of perceived transparency,” Vis. Res. 46, 879–894 (2006).
    [CrossRef]
  19. J. Beck, K. Prazdny, and R. Ivry, “The perception of transparency with achromatic colors,” Percept. Psychophys. 35, 407–422 (1984).
    [CrossRef]
  20. R. Kasrai and F. A. Kingdom, “Precision, accuracy, and range of perceived achromatic transparency,” J. Opt. Soc. Am. A 18, 1–11 (2001).
    [CrossRef]
  21. A. Kitaoka, “A new explanation of perceptual transparency connecting the X-junction contrast-polarity model with the luminance-based arithmetic model,” Jpn. Psychol. Res. 47, 175–187 (2005).
    [CrossRef]
  22. S. C. Masin, “A weighted-average model of achromatic transparency,” Percept. Psychophys. 49, 563–571 (1991).
    [CrossRef]
  23. S. C. Masin, “Color scission and phenomenal transparency,” Percept. Mot. Skills 89, 815–823 (1999).
    [CrossRef]
  24. S. C. Masin, “Effects of partial occlusion on perceived surface segregation,” Perception 32, 1189–1198 (2003).
    [CrossRef]
  25. S. C. Masin, “Test of models of achromatic transparency,” Perception 35, 1611–1624 (2006).
    [CrossRef]
  26. M. Singh and B. L. Anderson, “Perceptual assignment of opacity to translucent surfaces: the role of image blur,” Perception 31, 531–552 (2002).
    [CrossRef]
  27. M. Singh and B. L. Anderson, “Toward a perceptual theory of transparency,” Psychol. Rev. 109, 492–519 (2002).
    [CrossRef]
  28. A. L. Gilchrist, “Perceived lightness depends on perceived spatial arrangement,” Science 195, 185–187 (1977).
    [CrossRef]
  29. A. L. Gilchrist, “The perception of surface blacks and whites,” Sci. Am. 240, 112–124 (1979).
    [CrossRef]
  30. A. L. Gilchrist, S. Delman, and A. Jacobsen, “The classification and integration of edges as critical to the perception of reflectance and illumination,” Percept. Psychophys. 33, 425–436 (1983).
    [CrossRef]
  31. A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795–834 (1999).
    [CrossRef]
  32. A. L. Gilchrist, Seeing Black and White (Oxford University, 2006).
  33. E. H. Land and J. J. McCann, “Lightness and retinex theory,” J. Opt. Soc. Am. 61, 1–11 (1971).
    [CrossRef]
  34. A. D. Logvinenko and L. T. Maloney, “The proximity structure of achromatic surface colors and the impossibility of asymmetric lightness matching,” Percept. Psychophys. 68, 76–83 (2006).
    [CrossRef]
  35. M. E. Rudd and K. F. Arrington, “Darkness filling-in: a neural model of darkness induction,” Vis. Res. 41, 3649–3662 (2001).
    [CrossRef]
  36. M. E. Rudd and I. K. Zemach, “Quantitative properties of achromatic color induction: an edge integration analysis,” Vis. Res. 44, 971–981 (2004).
    [CrossRef]
  37. M. E. Rudd and I. K. Zemach, “The highest luminance anchoring rule in achromatic color perception: some counterexamples and an alternative theory,” J. Vis. 5(11):5, 983–1003 (2005).
    [CrossRef]
  38. M. E. Rudd and D. Popa, “Stevens’s brightness law, contrast gain control, and edge integration in achromatic color perception: a unified model,” J. Opt. Soc. Am. A 24, 2766–2782 (2007).
    [CrossRef]
  39. M. E. Rudd and I. K. Zemach, “Contrast polarity and edge integration in achromatic color perception,” J. Opt. Soc. Am. A 24, 2134–2156 (2007).
    [CrossRef]
  40. M. E. Rudd, “How attention and contrast gain control interact to regulate lightness contrast and assimilation: a computational neural model,” J. Vis. 10(14):40, 1–37 (2010).
    [CrossRef]
  41. M. Tommasi, “A ratio model of perceptual transparency,” Percept. Mot. Skills 89, 891–897 (1999).
    [CrossRef]
  42. T. Vladusich, M. P. Lucassen, and F. W. Cornelissen, “Edge integration and the perception of brightness and darkness,” J. Vis. 6(10):12, 1126–1147 (2006).
    [CrossRef]
  43. T. Vladusich, M. P. Lucassen, and F. W. Cornelissen, “Brightness and darkness as perceptual dimensions.,” PLoS Comput. Biol. 3, e179 (2007).
    [CrossRef]
  44. T. Vladusich, “Gamut relativity: a new computational approach to brightness and lightness perception,” J. Vis. 13(1):14, 1–21 (2013).
    [CrossRef]
  45. T. Vladusich, “Simultaneous contrast and gamut relativity in achromatic color perception,” Vis. Res. 69, 49–63 (2012).
    [CrossRef]
  46. H. Wallach, “Brightness constancy and the nature of achromatic colors,” J. Exp. Psychol. 38, 310–324 (1948).
    [CrossRef]
  47. A. D. Logvinenko and R. Tokunaga, “Lightness constancy and illumination discounting,” Atten. Percept. Psychophys. 73, 1886–1902 (2011).
    [CrossRef]
  48. M. Fukuda and S. C. Masin, “Test of balanced transparency,” Perception 23, 37–43 (1994).
    [CrossRef]

2013 (1)

T. Vladusich, “Gamut relativity: a new computational approach to brightness and lightness perception,” J. Vis. 13(1):14, 1–21 (2013).
[CrossRef]

2012 (2)

T. Vladusich, “Simultaneous contrast and gamut relativity in achromatic color perception,” Vis. Res. 69, 49–63 (2012).
[CrossRef]

F. Faul and V. Ekroll, “Transparent layer constancy,” J. Vis. 12(12):7, 1–26 (2012).
[CrossRef]

2011 (2)

F. Faul and V. Ekroll, “On the filter approach to perceptual transparency,” J. Vis. 11(7):7, 1–33 (2011).
[CrossRef]

A. D. Logvinenko and R. Tokunaga, “Lightness constancy and illumination discounting,” Atten. Percept. Psychophys. 73, 1886–1902 (2011).
[CrossRef]

2010 (1)

M. E. Rudd, “How attention and contrast gain control interact to regulate lightness contrast and assimilation: a computational neural model,” J. Vis. 10(14):40, 1–37 (2010).
[CrossRef]

2008 (1)

B. L. Anderson and J. Winawer, “Layered image representations and the computation of surface lightness,” J. Vis. 8(7):18, 1–21 (2008).
[CrossRef]

2007 (3)

2006 (4)

T. Vladusich, M. P. Lucassen, and F. W. Cornelissen, “Edge integration and the perception of brightness and darkness,” J. Vis. 6(10):12, 1126–1147 (2006).
[CrossRef]

A. D. Logvinenko and L. T. Maloney, “The proximity structure of achromatic surface colors and the impossibility of asymmetric lightness matching,” Percept. Psychophys. 68, 76–83 (2006).
[CrossRef]

M. Singh and B. L. Anderson, “Photometric determinants of perceived transparency,” Vis. Res. 46, 879–894 (2006).
[CrossRef]

S. C. Masin, “Test of models of achromatic transparency,” Perception 35, 1611–1624 (2006).
[CrossRef]

2005 (3)

A. Kitaoka, “A new explanation of perceptual transparency connecting the X-junction contrast-polarity model with the luminance-based arithmetic model,” Jpn. Psychol. Res. 47, 175–187 (2005).
[CrossRef]

B. L. Anderson and J. Winawer, “Image segmentation and lightness perception,” Nature 434, 79–83 (2005).
[CrossRef]

M. E. Rudd and I. K. Zemach, “The highest luminance anchoring rule in achromatic color perception: some counterexamples and an alternative theory,” J. Vis. 5(11):5, 983–1003 (2005).
[CrossRef]

2004 (3)

M. E. Rudd and I. K. Zemach, “Quantitative properties of achromatic color induction: an edge integration analysis,” Vis. Res. 44, 971–981 (2004).
[CrossRef]

R. Robilotto and Q. Zaidi, “Perceived transparency of neutral density filters across dissimilar backgrounds,” J. Vis. 4(3):5, 183–195 (2004).
[CrossRef]

M. Singh, “Lightness constancy through transparency: internal consistency in layered surface representations,” Vis. Res. 44, 1827–1842 (2004).
[CrossRef]

2003 (2)

B. L. Anderson, “The role of occlusion in the perception of depth, lightness, and opacity.” Psychol. Rev. 110, 785–801 (2003).
[CrossRef]

S. C. Masin, “Effects of partial occlusion on perceived surface segregation,” Perception 32, 1189–1198 (2003).
[CrossRef]

2002 (4)

R. Robilotto, B.-G. Khang, and Q. Zaidi, “Sensory and physical determinants of perceived achromatic transparency,” J. Vis. 2(5):3 , 388–403 (2002).
[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]

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

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

2001 (2)

R. Kasrai and F. A. Kingdom, “Precision, accuracy, and range of perceived achromatic transparency,” J. Opt. Soc. Am. A 18, 1–11 (2001).
[CrossRef]

M. E. Rudd and K. F. Arrington, “Darkness filling-in: a neural model of darkness induction,” Vis. Res. 41, 3649–3662 (2001).
[CrossRef]

1999 (4)

M. Tommasi, “A ratio model of perceptual transparency,” Percept. Mot. Skills 89, 891–897 (1999).
[CrossRef]

S. C. Masin, “Color scission and phenomenal transparency,” Percept. Mot. Skills 89, 815–823 (1999).
[CrossRef]

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795–834 (1999).
[CrossRef]

B. L. Anderson, “Stereoscopic surface perception,” Neuron 24, 919–928 (1999).
[CrossRef]

1997 (1)

B. L. Anderson, “A theory of illusory lightness and transparency in monocular and binocular images: the role of contour junctions,” Perception 26, 419–453 (1997).
[CrossRef]

1994 (1)

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

1993 (1)

E. H. Adelson, “Perceptual organization and the judgment of brightness,” Science 262, 2042–2044 (1993).
[CrossRef]

1991 (1)

S. C. Masin, “A weighted-average model of achromatic transparency,” Percept. Psychophys. 49, 563–571 (1991).
[CrossRef]

1990 (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]

1985 (1)

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

1984 (1)

J. Beck, K. Prazdny, and R. Ivry, “The perception of transparency with achromatic colors,” Percept. Psychophys. 35, 407–422 (1984).
[CrossRef]

1983 (1)

A. L. Gilchrist, S. Delman, and A. Jacobsen, “The classification and integration of edges as critical to the perception of reflectance and illumination,” Percept. Psychophys. 33, 425–436 (1983).
[CrossRef]

1979 (1)

A. L. Gilchrist, “The perception of surface blacks and whites,” Sci. Am. 240, 112–124 (1979).
[CrossRef]

1977 (1)

A. L. Gilchrist, “Perceived lightness depends on perceived spatial arrangement,” Science 195, 185–187 (1977).
[CrossRef]

1974 (1)

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

1971 (1)

1970 (1)

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

1948 (1)

H. Wallach, “Brightness constancy and the nature of achromatic colors,” J. Exp. Psychol. 38, 310–324 (1948).
[CrossRef]

Adelson, E. H.

E. H. Adelson, “Perceptual organization and the judgment of brightness,” Science 262, 2042–2044 (1993).
[CrossRef]

E. H. Adelson, “Lightness perception and lightness illusions,” in The New Cognitive Neurosciences, M. Gazzaniga, ed. (MIT, 2000), pp. 339–352.

Agostini, T.

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795–834 (1999).
[CrossRef]

Anderson, B. L.

B. L. Anderson and J. Winawer, “Layered image representations and the computation of surface lightness,” J. Vis. 8(7):18, 1–21 (2008).
[CrossRef]

M. Singh and B. L. Anderson, “Photometric determinants of perceived transparency,” Vis. Res. 46, 879–894 (2006).
[CrossRef]

B. L. Anderson and J. Winawer, “Image segmentation and lightness perception,” Nature 434, 79–83 (2005).
[CrossRef]

B. L. Anderson, “The role of occlusion in the perception of depth, lightness, and opacity.” Psychol. Rev. 110, 785–801 (2003).
[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]

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

B. L. Anderson, “Stereoscopic surface perception,” Neuron 24, 919–928 (1999).
[CrossRef]

B. L. Anderson, “A theory of illusory lightness and transparency in monocular and binocular images: the role of contour junctions,” Perception 26, 419–453 (1997).
[CrossRef]

Annan, V.

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795–834 (1999).
[CrossRef]

Arrington, K. F.

M. E. Rudd and K. F. Arrington, “Darkness filling-in: a neural model of darkness induction,” Vis. Res. 41, 3649–3662 (2001).
[CrossRef]

Beck, J.

J. Beck, K. Prazdny, and R. Ivry, “The perception of transparency with achromatic colors,” Percept. Psychophys. 35, 407–422 (1984).
[CrossRef]

Bonato, F.

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795–834 (1999).
[CrossRef]

Cataliotti, J.

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795–834 (1999).
[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]

Cornelissen, F. W.

T. Vladusich, M. P. Lucassen, and F. W. Cornelissen, “Brightness and darkness as perceptual dimensions.,” PLoS Comput. Biol. 3, e179 (2007).
[CrossRef]

T. Vladusich, M. P. Lucassen, and F. W. Cornelissen, “Edge integration and the perception of brightness and darkness,” J. Vis. 6(10):12, 1126–1147 (2006).
[CrossRef]

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]

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]

Delman, S.

A. L. Gilchrist, S. Delman, and A. Jacobsen, “The classification and integration of edges as critical to the perception of reflectance and illumination,” Percept. Psychophys. 33, 425–436 (1983).
[CrossRef]

Economou, E.

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795–834 (1999).
[CrossRef]

Ekroll, V.

F. Faul and V. Ekroll, “Transparent layer constancy,” J. Vis. 12(12):7, 1–26 (2012).
[CrossRef]

F. Faul and V. Ekroll, “On the filter approach to perceptual transparency,” J. Vis. 11(7):7, 1–33 (2011).
[CrossRef]

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

Faul, F.

F. Faul and V. Ekroll, “Transparent layer constancy,” J. Vis. 12(12):7, 1–26 (2012).
[CrossRef]

F. Faul and V. Ekroll, “On the filter approach to perceptual transparency,” J. Vis. 11(7):7, 1–33 (2011).
[CrossRef]

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

Fukuda, M.

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

Gazzaniga, M.

E. H. Adelson, “Lightness perception and lightness illusions,” in The New Cognitive Neurosciences, M. Gazzaniga, ed. (MIT, 2000), pp. 339–352.

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]

Gilchrist, A.

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795–834 (1999).
[CrossRef]

Gilchrist, A. L.

A. L. Gilchrist, S. Delman, and A. Jacobsen, “The classification and integration of edges as critical to the perception of reflectance and illumination,” Percept. Psychophys. 33, 425–436 (1983).
[CrossRef]

A. L. Gilchrist, “The perception of surface blacks and whites,” Sci. Am. 240, 112–124 (1979).
[CrossRef]

A. L. Gilchrist, “Perceived lightness depends on perceived spatial arrangement,” Science 195, 185–187 (1977).
[CrossRef]

A. L. Gilchrist, Seeing Black and White (Oxford University, 2006).

Ivry, R.

J. Beck, K. Prazdny, and R. Ivry, “The perception of transparency with achromatic colors,” Percept. Psychophys. 35, 407–422 (1984).
[CrossRef]

Jacobsen, A.

A. L. Gilchrist, S. Delman, and A. Jacobsen, “The classification and integration of edges as critical to the perception of reflectance and illumination,” Percept. Psychophys. 33, 425–436 (1983).
[CrossRef]

Kasrai, R.

Khang, B.-G.

R. Robilotto, B.-G. Khang, and Q. Zaidi, “Sensory and physical determinants of perceived achromatic transparency,” J. Vis. 2(5):3 , 388–403 (2002).
[CrossRef]

Kingdom, F. A.

Kitaoka, A.

A. Kitaoka, “A new explanation of perceptual transparency connecting the X-junction contrast-polarity model with the luminance-based arithmetic model,” Jpn. Psychol. Res. 47, 175–187 (2005).
[CrossRef]

Kossyfidis, C.

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795–834 (1999).
[CrossRef]

Land, E. H.

Li, X.

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795–834 (1999).
[CrossRef]

Logvinenko, A. D.

A. D. Logvinenko and R. Tokunaga, “Lightness constancy and illumination discounting,” Atten. Percept. Psychophys. 73, 1886–1902 (2011).
[CrossRef]

A. D. Logvinenko and L. T. Maloney, “The proximity structure of achromatic surface colors and the impossibility of asymmetric lightness matching,” Percept. Psychophys. 68, 76–83 (2006).
[CrossRef]

Lucassen, M. P.

T. Vladusich, M. P. Lucassen, and F. W. Cornelissen, “Brightness and darkness as perceptual dimensions.,” PLoS Comput. Biol. 3, e179 (2007).
[CrossRef]

T. Vladusich, M. P. Lucassen, and F. W. Cornelissen, “Edge integration and the perception of brightness and darkness,” J. Vis. 6(10):12, 1126–1147 (2006).
[CrossRef]

Maloney, L. T.

A. D. Logvinenko and L. T. Maloney, “The proximity structure of achromatic surface colors and the impossibility of asymmetric lightness matching,” Percept. Psychophys. 68, 76–83 (2006).
[CrossRef]

Masin, S. C.

S. C. Masin, “Test of models of achromatic transparency,” Perception 35, 1611–1624 (2006).
[CrossRef]

S. C. Masin, “Effects of partial occlusion on perceived surface segregation,” Perception 32, 1189–1198 (2003).
[CrossRef]

S. C. Masin, “Color scission and phenomenal transparency,” Percept. Mot. Skills 89, 815–823 (1999).
[CrossRef]

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

S. C. Masin, “A weighted-average model of achromatic transparency,” Percept. Psychophys. 49, 563–571 (1991).
[CrossRef]

McCann, J. J.

Metelli, F.

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

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

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

Popa, D.

Prazdny, K.

J. Beck, K. Prazdny, and R. Ivry, “The perception of transparency with achromatic colors,” Percept. Psychophys. 35, 407–422 (1984).
[CrossRef]

Robilotto, R.

R. Robilotto and Q. Zaidi, “Perceived transparency of neutral density filters across dissimilar backgrounds,” J. Vis. 4(3):5, 183–195 (2004).
[CrossRef]

R. Robilotto, B.-G. Khang, and Q. Zaidi, “Sensory and physical determinants of perceived achromatic transparency,” J. Vis. 2(5):3 , 388–403 (2002).
[CrossRef]

Rudd, M. E.

M. E. Rudd, “How attention and contrast gain control interact to regulate lightness contrast and assimilation: a computational neural model,” J. Vis. 10(14):40, 1–37 (2010).
[CrossRef]

M. E. Rudd and D. Popa, “Stevens’s brightness law, contrast gain control, and edge integration in achromatic color perception: a unified model,” J. Opt. Soc. Am. A 24, 2766–2782 (2007).
[CrossRef]

M. E. Rudd and I. K. Zemach, “Contrast polarity and edge integration in achromatic color perception,” J. Opt. Soc. Am. A 24, 2134–2156 (2007).
[CrossRef]

M. E. Rudd and I. K. Zemach, “The highest luminance anchoring rule in achromatic color perception: some counterexamples and an alternative theory,” J. Vis. 5(11):5, 983–1003 (2005).
[CrossRef]

M. E. Rudd and I. K. Zemach, “Quantitative properties of achromatic color induction: an edge integration analysis,” Vis. Res. 44, 971–981 (2004).
[CrossRef]

M. E. Rudd and K. F. Arrington, “Darkness filling-in: a neural model of darkness induction,” Vis. Res. 41, 3649–3662 (2001).
[CrossRef]

Singh, M.

M. Singh and B. L. Anderson, “Photometric determinants of perceived transparency,” Vis. Res. 46, 879–894 (2006).
[CrossRef]

M. Singh, “Lightness constancy through transparency: internal consistency in layered surface representations,” Vis. Res. 44, 1827–1842 (2004).
[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]

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

Spehar, B.

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795–834 (1999).
[CrossRef]

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]

Tokunaga, R.

A. D. Logvinenko and R. Tokunaga, “Lightness constancy and illumination discounting,” Atten. Percept. Psychophys. 73, 1886–1902 (2011).
[CrossRef]

Tommasi, M.

M. Tommasi, “A ratio model of perceptual transparency,” Percept. Mot. Skills 89, 891–897 (1999).
[CrossRef]

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]

Vladusich, T.

T. Vladusich, “Gamut relativity: a new computational approach to brightness and lightness perception,” J. Vis. 13(1):14, 1–21 (2013).
[CrossRef]

T. Vladusich, “Simultaneous contrast and gamut relativity in achromatic color perception,” Vis. Res. 69, 49–63 (2012).
[CrossRef]

T. Vladusich, M. P. Lucassen, and F. W. Cornelissen, “Brightness and darkness as perceptual dimensions.,” PLoS Comput. Biol. 3, e179 (2007).
[CrossRef]

T. Vladusich, M. P. Lucassen, and F. W. Cornelissen, “Edge integration and the perception of brightness and darkness,” J. Vis. 6(10):12, 1126–1147 (2006).
[CrossRef]

Wallach, H.

H. Wallach, “Brightness constancy and the nature of achromatic colors,” J. Exp. Psychol. 38, 310–324 (1948).
[CrossRef]

Winawer, J.

B. L. Anderson and J. Winawer, “Layered image representations and the computation of surface lightness,” J. Vis. 8(7):18, 1–21 (2008).
[CrossRef]

B. L. Anderson and J. Winawer, “Image segmentation and lightness perception,” Nature 434, 79–83 (2005).
[CrossRef]

Zaidi, Q.

R. Robilotto and Q. Zaidi, “Perceived transparency of neutral density filters across dissimilar backgrounds,” J. Vis. 4(3):5, 183–195 (2004).
[CrossRef]

R. Robilotto, B.-G. Khang, and Q. Zaidi, “Sensory and physical determinants of perceived achromatic transparency,” J. Vis. 2(5):3 , 388–403 (2002).
[CrossRef]

Zemach, I. K.

M. E. Rudd and I. K. Zemach, “Contrast polarity and edge integration in achromatic color perception,” J. Opt. Soc. Am. A 24, 2134–2156 (2007).
[CrossRef]

M. E. Rudd and I. K. Zemach, “The highest luminance anchoring rule in achromatic color perception: some counterexamples and an alternative theory,” J. Vis. 5(11):5, 983–1003 (2005).
[CrossRef]

M. E. Rudd and I. K. Zemach, “Quantitative properties of achromatic color induction: an edge integration analysis,” Vis. Res. 44, 971–981 (2004).
[CrossRef]

Atten. Percept. Psychophys. (1)

A. D. Logvinenko and R. Tokunaga, “Lightness constancy and illumination discounting,” Atten. Percept. Psychophys. 73, 1886–1902 (2011).
[CrossRef]

Ergonomics (1)

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

J. Exp. Psychol. (1)

H. Wallach, “Brightness constancy and the nature of achromatic colors,” J. Exp. Psychol. 38, 310–324 (1948).
[CrossRef]

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]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

J. Vis. (9)

M. E. Rudd and I. K. Zemach, “The highest luminance anchoring rule in achromatic color perception: some counterexamples and an alternative theory,” J. Vis. 5(11):5, 983–1003 (2005).
[CrossRef]

R. Robilotto, B.-G. Khang, and Q. Zaidi, “Sensory and physical determinants of perceived achromatic transparency,” J. Vis. 2(5):3 , 388–403 (2002).
[CrossRef]

R. Robilotto and Q. Zaidi, “Perceived transparency of neutral density filters across dissimilar backgrounds,” J. Vis. 4(3):5, 183–195 (2004).
[CrossRef]

B. L. Anderson and J. Winawer, “Layered image representations and the computation of surface lightness,” J. Vis. 8(7):18, 1–21 (2008).
[CrossRef]

F. Faul and V. Ekroll, “On the filter approach to perceptual transparency,” J. Vis. 11(7):7, 1–33 (2011).
[CrossRef]

F. Faul and V. Ekroll, “Transparent layer constancy,” J. Vis. 12(12):7, 1–26 (2012).
[CrossRef]

M. E. Rudd, “How attention and contrast gain control interact to regulate lightness contrast and assimilation: a computational neural model,” J. Vis. 10(14):40, 1–37 (2010).
[CrossRef]

T. Vladusich, M. P. Lucassen, and F. W. Cornelissen, “Edge integration and the perception of brightness and darkness,” J. Vis. 6(10):12, 1126–1147 (2006).
[CrossRef]

T. Vladusich, “Gamut relativity: a new computational approach to brightness and lightness perception,” J. Vis. 13(1):14, 1–21 (2013).
[CrossRef]

Jpn. Psychol. Res. (1)

A. Kitaoka, “A new explanation of perceptual transparency connecting the X-junction contrast-polarity model with the luminance-based arithmetic model,” Jpn. Psychol. Res. 47, 175–187 (2005).
[CrossRef]

Nature (1)

B. L. Anderson and J. Winawer, “Image segmentation and lightness perception,” Nature 434, 79–83 (2005).
[CrossRef]

Neuron (1)

B. L. Anderson, “Stereoscopic surface perception,” Neuron 24, 919–928 (1999).
[CrossRef]

Percept. Mot. Skills (2)

S. C. Masin, “Color scission and phenomenal transparency,” Percept. Mot. Skills 89, 815–823 (1999).
[CrossRef]

M. Tommasi, “A ratio model of perceptual transparency,” Percept. Mot. Skills 89, 891–897 (1999).
[CrossRef]

Percept. Psychophys. (5)

A. L. Gilchrist, S. Delman, and A. Jacobsen, “The classification and integration of edges as critical to the perception of reflectance and illumination,” Percept. Psychophys. 33, 425–436 (1983).
[CrossRef]

S. C. Masin, “A weighted-average model of achromatic transparency,” Percept. Psychophys. 49, 563–571 (1991).
[CrossRef]

J. Beck, K. Prazdny, and R. Ivry, “The perception of transparency with achromatic colors,” Percept. Psychophys. 35, 407–422 (1984).
[CrossRef]

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

A. D. Logvinenko and L. T. Maloney, “The proximity structure of achromatic surface colors and the impossibility of asymmetric lightness matching,” Percept. Psychophys. 68, 76–83 (2006).
[CrossRef]

Perception (5)

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

B. L. Anderson, “A theory of illusory lightness and transparency in monocular and binocular images: the role of contour junctions,” Perception 26, 419–453 (1997).
[CrossRef]

S. C. Masin, “Effects of partial occlusion on perceived surface segregation,” Perception 32, 1189–1198 (2003).
[CrossRef]

S. C. Masin, “Test of models of achromatic transparency,” Perception 35, 1611–1624 (2006).
[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]

PLoS Comput. Biol. (1)

T. Vladusich, M. P. Lucassen, and F. W. Cornelissen, “Brightness and darkness as perceptual dimensions.,” PLoS Comput. Biol. 3, e179 (2007).
[CrossRef]

Psychol. Rev. (3)

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795–834 (1999).
[CrossRef]

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

B. L. Anderson, “The role of occlusion in the perception of depth, lightness, and opacity.” Psychol. Rev. 110, 785–801 (2003).
[CrossRef]

Sci. Am. (2)

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

A. L. Gilchrist, “The perception of surface blacks and whites,” Sci. Am. 240, 112–124 (1979).
[CrossRef]

Science (2)

A. L. Gilchrist, “Perceived lightness depends on perceived spatial arrangement,” Science 195, 185–187 (1977).
[CrossRef]

E. H. Adelson, “Perceptual organization and the judgment of brightness,” Science 262, 2042–2044 (1993).
[CrossRef]

Vis. Res. (5)

M. Singh, “Lightness constancy through transparency: internal consistency in layered surface representations,” Vis. Res. 44, 1827–1842 (2004).
[CrossRef]

M. Singh and B. L. Anderson, “Photometric determinants of perceived transparency,” Vis. Res. 46, 879–894 (2006).
[CrossRef]

T. Vladusich, “Simultaneous contrast and gamut relativity in achromatic color perception,” Vis. Res. 69, 49–63 (2012).
[CrossRef]

M. E. Rudd and K. F. Arrington, “Darkness filling-in: a neural model of darkness induction,” Vis. Res. 41, 3649–3662 (2001).
[CrossRef]

M. E. Rudd and I. K. Zemach, “Quantitative properties of achromatic color induction: an edge integration analysis,” Vis. Res. 44, 971–981 (2004).
[CrossRef]

Other (2)

A. L. Gilchrist, Seeing Black and White (Oxford University, 2006).

E. H. Adelson, “Lightness perception and lightness illusions,” in The New Cognitive Neurosciences, M. Gazzaniga, ed. (MIT, 2000), pp. 339–352.

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Figures (7)

Fig. 1.
Fig. 1.

Examples of transparency perception. Top row: the sets of “squares” in the left and right panels are identical but appear as uniform white and black surface layers seen through black-and-white cloud layers varying in transparency across space, respectively. The effect was generated by smoothing the Fourier transform of a noise image to suppress high spatial frequencies, then computing the inverse transform [6,7]. The range of pixel values outside the borders of the squares was then compressed to produce the surrounding cloud contexts. To produce white squares, for example, the surrounding pixel values were compressed to lie between values appearing black and middle gray, respectively. Bottom row: a different type of transparency percept forms when the pixel range forming the squares is compressed relative to the surround. In this case, whitish and blackish squares with relatively uniform transparency are seen in front of a black-and-white cloud layer. A central aim of this article is to explain how these disparate transparency effects are computed by the human visual system.

Fig. 2.
Fig. 2.

Independence of achromatic color and transparency in the Metelli display. The Metelli display consists of four regions, labeled a, b, p, and q, with respective luminance values, a, b, p, and q. Transparency is perceived in the foreground (disk) surface layer, which is seen in front of a black-and-white background surface layer. The figure illustrates how achromatic color and transparency vary independently as a function of equal steps in mean log luminance and log luminance range (the log luminance difference, or ratio, of regions p and q), respectively. The scaling as a function of log luminance, rather than luminance, represents a key new aspect of the current theory (which can be quantitatively evaluated on calibrated displays). The independence of the achromatic color gamut and transparency finds a geometrical explanation in the current theory that departs radically from the conventional proposal that lightness and transparency correspond to perceptual dimensions.

Fig. 3.
Fig. 3.

Brightness and lightness perception according to gamut relativity. (a) Brightness perception is understood as the representation of achromatic surface colors under the assumption of a single illumination level: surface colors are represented as points falling on a negatively sloped “gamut” line (points in the sets X and Y) in blackness–whiteness space. (b) Lightness perception is understood as the representation of achromatic colors under the assumption of multiple illumination levels: surface colors are represented as points falling on more than one gamut line (points in the sets X and Z). Due to the asymmetric scaling of blackness–whiteness axes, a correspondence theorem proves that, under certain key assumptions, surface colors representing the same reflectance values, such as x1 and z1, lie perceptually closer to one another than surface colors representing different reflectance values, such as x1 and z2 or z3 [44]. Surface colors composing the set X are computationally treated as a “standard” set of surface colors to which the “comparison” surface colors composing the set Z are perceptually grouped for the purposes of generating surface color representations that are independent of illumination intensity. The vector q lying on the blackness axis represents shadow color, defined as the vector difference between the standard and comparison gamuts.

Fig. 4.
Fig. 4.

Transparency perception according to gamut relativity. (a), (c) Gamut relativity supports the computation of layered representations of transparent and opaque surfaces in the Metelli display, as a function of mean log luminance and log luminance range. High transparency (a), (b) is associated with high log luminance range, whereas low transparency is associated with low log luminance range (c), (d). Mathematical definitions are described in the text. (b), (d) Predictions of the episcotister model (α) and gamut relativity (λ). Gamut relativity predicts that different achromatic color gamuts—each representing a unique set of black, white, and gray surface colors—correspond to lines of constant transparency (λ). The episcotister model, by comparison, predicts that transparency is veridically related to physical transmittance (α), which is inconsistent with extant transparency matching data [27]. Note that the absolute scaling of blackness–whiteness space is not relevant to the current application of the theory.

Fig. 5.
Fig. 5.

Simulation of transparency level as a function of mean luminance. (a), (b) Luminance values plotted on the standard gamut (gray filled circles) correspond to a selection of pixels forming the squares in the bottom row of Fig. 1. Mathematical labels are analogous to those in the conventional Metelli display, with sb and sa representing the blackest and whitest standard colors of the background, sq and sp representing the blackest and whitest standard colors of the squares, and spq representing the geometric mean color within the squares. Comparison colors computed from below the geometric mean of the standard gamut (filled black circles) are grouped with the blackest standard color, whereas comparison colors computed from above the geometric mean of the standard gamut (empty black circles) are grouped to the whitest standard color. The blackish squares, denoted by cpq, appear more transparent than the whitish squares because they lie on a gamut line (fc) corresponding to a higher transparency level (λ). (c), (d) Due to the log luminance transformation, a region with constant luminance range but variable mean luminance is mapped to different transparency levels (λ). Transparency is plotted here as a function of increasing blackness (decreasing mean luminance).

Fig. 6.
Fig. 6.

Simulation of transparency matching. (a) Each open black circle represents the achromatic color setting corresponding to a given transparency match made to the relevant open gray triangle, representing the achromatic color of the reference target, lying on the same solid black gamut line of constant transparency (λ). Each dashed black curve indicates the range of achromatic colors that the subject could perceive by varying the test luminance range, for a given value of mean reference luminance. The dashed gray curves represent the curved gamuts corresponding to lines of constant transmittance (α), given the fixed background. (b) Simulated transparency matches corresponding to the points in (a). (c) Transparency matching data reprinted with permission from [27].

Fig. 7.
Fig. 7.

Simulation of spatial transparency gradients. (a), (b) Vector decomposition transforms the standard achromatic colors (filled gray circles) into pairs of comparison colors (open and filled black circles) subject to constraints supplied by the blackest and whitest standard colors. (b) The decomposed achromatic colors are then grouped with respect to the blackest and whitest standard colors to form black and white surface layers, respectively. (c), (d) Transparency level (λ) of the foreground cloud layer plotted as a function of blackness. Unlike many alternative approaches to transparency perception, gamut relativity naturally generalizes to explain gradients of transparency.

Equations (17)

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

p=αa+(1α)pq
q=αb+(1α)pq,
α=pqab.
ψ=logkψ,
ϕ=logkϕ,
|cpqspq||cabsab|=|spsq||sasb|.
hh=cc.
c=a2+b2.
c=(at)2+(bt)2=ta2+b2,
cc=1t.
h=abc,
h=abc=abt2ct=abtc,
hh=abccabt=1t.
λ=cc=|spsq||sasb|=(ϕpϕq)2+(ψpψq)2(ϕaϕb)2+(ψaψb)2,
λ=2(logplogq)22(logalogb)2=logplogqlogalogb.
logp=λloga+(1λ)logpq
logq=λlogb+(1λ)logpq,

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