Abstract

Phenomenal transparency is commonly studied by using a stimulus configuration introduced by Metelli: a bipartite patch, divided into equal left and right halves is overlaid with a smaller, concentric bipartite patch, divided along the same line. Observers are instructed to report either a transparent patch over an opaque bipartite field or a mosaic of four opaque patches. We show theoretically and empirically that these are only two of five generic perceptual categories, namely, transparent patch, transparent annulus (hole), mosaic, partial transparency, and multiple transparency (ambiguous) cases. Thus Gestalt factors complicate the interpretation “phenomenal transparency.” We propose a framework that avoids this complication. There is excellent agreement between predictions and results.

© 2008 Optical Society of America

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  1. W. Metzger, Gesetze des Sehens (Waldemar Kramer, 1975).
  2. Laws of Seeing [Gesetze des Sehens], L. Spillmann, M. Wertheimer, and S. Lehar, translators (MIT Press, 2006).
  3. F. Metelli, "Zur Analyse der phänomenalen Durchsichtigkeitserscheinungen," in Gestalt und Wirklichkeit, R.Müller and J.Fischl, eds. (Duncker & Humblot, 1967), pp. 258-304.
  4. F. Metelli, "An algebraic development of the theory of perceptual transparency," Ergonomics 13, 59-66 (1970).
    [CrossRef] [PubMed]
  5. F. Metelli, "Achromatic colour conditions in the perception of transparency," in Perception: Essays in Honor of James J. Gibson, R.B.MacLeod and H.L.Pick, eds. (Cornell U. Press, 1974), pp. 95-116.
  6. F. Metelli, "The perception of transparency," Sci. Am. 230(4), 91-98 (1974).
    [CrossRef]
  7. In the literature, called "partial transparency." The concept was introduced by Beck in 1984 [J. Beck, K. Prazdny, and R. Ivry, "The perception of transparency with achromatic colors," Percept. Psychophys. 35, 407-422 (1984)]. See also . The concept of "partial transparency" is not very well defined; we believe it to correspond to our Left or Right overlay categories.
  8. J. Beck and R. Ivry, "On the role of figural organization in perceptual transparency," Percept. Psychophys. 44, 585-594 (1988).
    [CrossRef] [PubMed]
  9. F. Metelli, O. da Pos, and A. Cavedon, "Balanced and unbalanced, complete and partial transparency," Percept. Psychophys. 38, 354-366 (1985).
    [CrossRef] [PubMed]
  10. 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]
  11. W. Gerbino, C. I. F. H. J. Stultiens, J. M. Troost, and Ch. M. M. de Weert, "Transparent layer constancy," J. Exp. Psychol. 16, 3-20 (1990).
  12. S. C. Masin, "The luminance conditions of transparency," Perception 26, 39-50 (1997).
    [CrossRef] [PubMed]
  13. M. Singh and D. D. Hoffman, "Part boundaries alter the perception of transparency," Psychol. Sci. 9, 370-378 (1998).
    [CrossRef]
  14. M. Singh and B. L. Anderson, "Towards a perceptual theory of transparency," Psychol. Rev. 109, 492-519 (2002).
    [CrossRef] [PubMed]
  15. R. W. Fleming and B. L. Anderson, "The perceptual organization of depth," in The Visual Neurosciences, L.Chalupa and J.S.Werner, eds. (MIT Press, 2003), pp. 1284-1299.
  16. P. Kubelka and F. Munk, "Ein Beitrag Zur Optik der Farbanstriche," Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).
  17. K. Koffka, Principles of Gestalt Psychology (Lund Humphries, 1935).
  18. M. Wertheimer, "Über Gestalttheorie," an address before the Kant Society, Berlin, 7th December, 1924, Erlangen, 1925, translation by W.D.Ellis in Source Book of Gestalt Psychology (Harcourt, Brace, 1938).
  19. R. Arnheim, Visual Thinking (U. California Press, 1969).
  20. W. Kohler, Gestalt Psychology (Liveright, 1947).
  21. G. Kanizsa, Organization in Vision: Essays on Gestalt Perception (Praeger, 1979).
  22. F. Metelli, "Oggettualità stratificazione e risalto nell'organizzazione (percettiva) di figura e sfondo," Arch. Psicol Neurol. Psichiatr II(4), 831-841 (1941).
  23. F. Metelli, "Morfologia dei fenomeni di completamento nella percezione visiva," in Gestalthaftes Sehen, E.von Ehrenfels and F.Weinhandl, eds. (Wissenschaftliche Buchgesellschaft, 1960), pp. 266-278.
  24. F. Metelli, "On the visual perception of transparency," inStudies in Perception: Festschrift for Fabio Metelli, G.B. F.D'Arcais, ed. (Martello Giunti, 1975), pp. 488-496.
  25. F. Metelli, "Shadows without penumbra," in Gestalttheorie in der modernen Psychologie (Metzger Festschrift), S.Ertal, L.Kemmier, and S.Michael, eds. (Steinkopff, 1975), pp. 200-209.
    [CrossRef]
  26. F. Metelli, "What does 'more transparent' mean? A paradox," in Vision and Artifact, M.Henle, ed. (Springer, 1976), pp. 19-24.
  27. F. Metelli, O. da Pos, and A. Cavedon, "Some conditions regarding localization and mode of appearance of achromatic colors," Atti Mem. Accad. Pata. Sci. Lett. Arti 89, 213-221 (1976-1977).
  28. F. Metelli, S. C. Masin and A. M. Manganelli, "Partial transparency," Atti Accad. Patav. Sci. Lett. Arti 1979-1980, Cl. Sci. morali, Lett. Arti XVII (Parte III), 115-169 (1981).
  29. F. Metelli, "Stimulation and perception of transparency," Psychol. Res. 47, 185-202 (1985).
    [CrossRef] [PubMed]
  30. F. Metelli, "Osservazioni sull'articolo di Marco Sambin: trasparenza con superfici indotte'," G. Ital. Psicolo. XI, 393-398 (1984).
  31. F. Metelli, "Su alcune condizioni spazio-figurali della trasparenza," in Conoscenza e Struttura, W.Gerbino, ed. (Il Mulino, 1985), pp. 303-331.
  32. D. Hoffman, Visual Intelligence: How We Create What We See (Norton, 1998).
  33. M. Albert, D. Hoffman, "Genericity in spatial vision," in Geometric Representations of Perceptual Phenomena: Articles in Honor of Tarow Indows on His 70th Birthday, R.D.Luce, M.D.D'Zmura, D.Hoffman, G.J.Iverson, and A.K.Romney, eds. (Erlbaum, 1995), pp. 95-112.
  34. D. B. Gauld, Differential Topology: An Introduction (Marcel Dekker, 1982).
  35. Metelli, who was an acute visual observer, remarks on our Hole category in a footnote: "In questo caso [namely ∣u−v∣>∣x−y∣] si determina un effetto curioso .... Invece delle regioni centrali diventano trasparenti, e cioè assumono le funzioni di U e V, le regioni laterali, e quindi si restaura la condizione necessaria [∣u−v∣<∣x−y∣" [expressions in our notation] but does not appear to have used this insight in the way we did. See footnote 21, p. 171 in F. Metelli, "Stimolazione e percezione della trasparenza con tonalità acromatiche," Ric. Psicol. 26, 159-180 (1983). Percepts related to holes have been more widely studied in binocular vision, e.g., see .
  36. B. L. Anderson and B. Julesz, "A theoretical analysis of illusory contour formation in stereopsis," Psychol. Rev. 102, 705-743 (1995).
    [CrossRef]
  37. B. L. Anderson, M. Singh, and J. Meng, "The perceived transmittance of inhomogeneous surfaces and media," Vision Res. 46, 1982-1995 (2006).
    [CrossRef] [PubMed]
  38. R. Robilotto and Q. Zaidi, "Perceived transparency of neutral density filters across dissimilar backgrounds," J. Vision 4(3), 183-195 (2004).
    [CrossRef]
  39. R. Kasrai and F. A. A. Kingdom, "Precision, accuracy, and range of perceived achromatic transparency," J. Opt. Soc. Am. A 18, 1-11 (2001).
    [CrossRef]

2006 (2)

Laws of Seeing [Gesetze des Sehens], L. Spillmann, M. Wertheimer, and S. Lehar, translators (MIT Press, 2006).

B. L. Anderson, M. Singh, and J. Meng, "The perceived transmittance of inhomogeneous surfaces and media," Vision Res. 46, 1982-1995 (2006).
[CrossRef] [PubMed]

2005 (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]

2004 (1)

R. Robilotto and Q. Zaidi, "Perceived transparency of neutral density filters across dissimilar backgrounds," J. Vision 4(3), 183-195 (2004).
[CrossRef]

2003 (1)

R. W. Fleming and B. L. Anderson, "The perceptual organization of depth," in The Visual Neurosciences, L.Chalupa and J.S.Werner, eds. (MIT Press, 2003), pp. 1284-1299.

2002 (1)

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

2001 (1)

1998 (2)

M. Singh and D. D. Hoffman, "Part boundaries alter the perception of transparency," Psychol. Sci. 9, 370-378 (1998).
[CrossRef]

D. Hoffman, Visual Intelligence: How We Create What We See (Norton, 1998).

1997 (1)

S. C. Masin, "The luminance conditions of transparency," Perception 26, 39-50 (1997).
[CrossRef] [PubMed]

1995 (2)

M. Albert, D. Hoffman, "Genericity in spatial vision," in Geometric Representations of Perceptual Phenomena: Articles in Honor of Tarow Indows on His 70th Birthday, R.D.Luce, M.D.D'Zmura, D.Hoffman, G.J.Iverson, and A.K.Romney, eds. (Erlbaum, 1995), pp. 95-112.

B. L. Anderson and B. Julesz, "A theoretical analysis of illusory contour formation in stereopsis," Psychol. Rev. 102, 705-743 (1995).
[CrossRef]

1990 (1)

W. Gerbino, C. I. F. H. J. Stultiens, J. M. Troost, and Ch. M. M. de Weert, "Transparent layer constancy," J. Exp. Psychol. 16, 3-20 (1990).

1988 (1)

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

1985 (3)

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, "Su alcune condizioni spazio-figurali della trasparenza," in Conoscenza e Struttura, W.Gerbino, ed. (Il Mulino, 1985), pp. 303-331.

F. Metelli, "Stimulation and perception of transparency," Psychol. Res. 47, 185-202 (1985).
[CrossRef] [PubMed]

1984 (2)

F. Metelli, "Osservazioni sull'articolo di Marco Sambin: trasparenza con superfici indotte'," G. Ital. Psicolo. XI, 393-398 (1984).

In the literature, called "partial transparency." The concept was introduced by Beck in 1984 [J. Beck, K. Prazdny, and R. Ivry, "The perception of transparency with achromatic colors," Percept. Psychophys. 35, 407-422 (1984)]. See also . The concept of "partial transparency" is not very well defined; we believe it to correspond to our Left or Right overlay categories.

1983 (1)

Metelli, who was an acute visual observer, remarks on our Hole category in a footnote: "In questo caso [namely ∣u−v∣>∣x−y∣] si determina un effetto curioso .... Invece delle regioni centrali diventano trasparenti, e cioè assumono le funzioni di U e V, le regioni laterali, e quindi si restaura la condizione necessaria [∣u−v∣<∣x−y∣" [expressions in our notation] but does not appear to have used this insight in the way we did. See footnote 21, p. 171 in F. Metelli, "Stimolazione e percezione della trasparenza con tonalità acromatiche," Ric. Psicol. 26, 159-180 (1983). Percepts related to holes have been more widely studied in binocular vision, e.g., see .

1982 (1)

D. B. Gauld, Differential Topology: An Introduction (Marcel Dekker, 1982).

1981 (1)

F. Metelli, S. C. Masin and A. M. Manganelli, "Partial transparency," Atti Accad. Patav. Sci. Lett. Arti 1979-1980, Cl. Sci. morali, Lett. Arti XVII (Parte III), 115-169 (1981).

1979 (1)

G. Kanizsa, Organization in Vision: Essays on Gestalt Perception (Praeger, 1979).

1976 (1)

F. Metelli, "What does 'more transparent' mean? A paradox," in Vision and Artifact, M.Henle, ed. (Springer, 1976), pp. 19-24.

1975 (3)

F. Metelli, "On the visual perception of transparency," inStudies in Perception: Festschrift for Fabio Metelli, G.B. F.D'Arcais, ed. (Martello Giunti, 1975), pp. 488-496.

F. Metelli, "Shadows without penumbra," in Gestalttheorie in der modernen Psychologie (Metzger Festschrift), S.Ertal, L.Kemmier, and S.Michael, eds. (Steinkopff, 1975), pp. 200-209.
[CrossRef]

W. Metzger, Gesetze des Sehens (Waldemar Kramer, 1975).

1974 (2)

F. Metelli, "Achromatic colour conditions in the perception of transparency," in Perception: Essays in Honor of James J. Gibson, R.B.MacLeod and H.L.Pick, eds. (Cornell U. Press, 1974), pp. 95-116.

F. Metelli, "The perception of transparency," Sci. Am. 230(4), 91-98 (1974).
[CrossRef]

1970 (1)

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

1969 (1)

R. Arnheim, Visual Thinking (U. California Press, 1969).

1967 (1)

F. Metelli, "Zur Analyse der phänomenalen Durchsichtigkeitserscheinungen," in Gestalt und Wirklichkeit, R.Müller and J.Fischl, eds. (Duncker & Humblot, 1967), pp. 258-304.

1960 (1)

F. Metelli, "Morfologia dei fenomeni di completamento nella percezione visiva," in Gestalthaftes Sehen, E.von Ehrenfels and F.Weinhandl, eds. (Wissenschaftliche Buchgesellschaft, 1960), pp. 266-278.

1947 (1)

W. Kohler, Gestalt Psychology (Liveright, 1947).

1941 (1)

F. Metelli, "Oggettualità stratificazione e risalto nell'organizzazione (percettiva) di figura e sfondo," Arch. Psicol Neurol. Psichiatr II(4), 831-841 (1941).

1938 (1)

M. Wertheimer, "Über Gestalttheorie," an address before the Kant Society, Berlin, 7th December, 1924, Erlangen, 1925, translation by W.D.Ellis in Source Book of Gestalt Psychology (Harcourt, Brace, 1938).

1935 (1)

K. Koffka, Principles of Gestalt Psychology (Lund Humphries, 1935).

1931 (1)

P. Kubelka and F. Munk, "Ein Beitrag Zur Optik der Farbanstriche," Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

Albert, M.

M. Albert, D. Hoffman, "Genericity in spatial vision," in Geometric Representations of Perceptual Phenomena: Articles in Honor of Tarow Indows on His 70th Birthday, R.D.Luce, M.D.D'Zmura, D.Hoffman, G.J.Iverson, and A.K.Romney, eds. (Erlbaum, 1995), pp. 95-112.

Anderson, B. L.

B. L. Anderson, M. Singh, and J. Meng, "The perceived transmittance of inhomogeneous surfaces and media," Vision Res. 46, 1982-1995 (2006).
[CrossRef] [PubMed]

R. W. Fleming and B. L. Anderson, "The perceptual organization of depth," in The Visual Neurosciences, L.Chalupa and J.S.Werner, eds. (MIT Press, 2003), pp. 1284-1299.

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

B. L. Anderson and B. Julesz, "A theoretical analysis of illusory contour formation in stereopsis," Psychol. Rev. 102, 705-743 (1995).
[CrossRef]

Arnheim, R.

R. Arnheim, Visual Thinking (U. California Press, 1969).

Beck, J.

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

In the literature, called "partial transparency." The concept was introduced by Beck in 1984 [J. Beck, K. Prazdny, and R. Ivry, "The perception of transparency with achromatic colors," Percept. Psychophys. 35, 407-422 (1984)]. See also . The concept of "partial transparency" is not very well defined; we believe it to correspond to our Left or Right overlay categories.

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]

F. Metelli, O. da Pos, and A. Cavedon, "Some conditions regarding localization and mode of appearance of achromatic colors," Atti Mem. Accad. Pata. Sci. Lett. Arti 89, 213-221 (1976-1977).

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]

F. Metelli, O. da Pos, and A. Cavedon, "Some conditions regarding localization and mode of appearance of achromatic colors," Atti Mem. Accad. Pata. Sci. Lett. Arti 89, 213-221 (1976-1977).

de Weert, Ch. M. M.

W. Gerbino, C. I. F. H. J. Stultiens, J. M. Troost, and Ch. M. M. de Weert, "Transparent layer constancy," J. Exp. Psychol. 16, 3-20 (1990).

Fleming, R. W.

R. W. Fleming and B. L. Anderson, "The perceptual organization of depth," in The Visual Neurosciences, L.Chalupa and J.S.Werner, eds. (MIT Press, 2003), pp. 1284-1299.

Gauld, D. B.

D. B. Gauld, Differential Topology: An Introduction (Marcel Dekker, 1982).

Gerbino, W.

W. Gerbino, C. I. F. H. J. Stultiens, J. M. Troost, and Ch. M. M. de Weert, "Transparent layer constancy," J. Exp. Psychol. 16, 3-20 (1990).

Hoffman, D.

D. Hoffman, Visual Intelligence: How We Create What We See (Norton, 1998).

M. Albert, D. Hoffman, "Genericity in spatial vision," in Geometric Representations of Perceptual Phenomena: Articles in Honor of Tarow Indows on His 70th Birthday, R.D.Luce, M.D.D'Zmura, D.Hoffman, G.J.Iverson, and A.K.Romney, eds. (Erlbaum, 1995), pp. 95-112.

Hoffman, D. D.

M. Singh and D. D. Hoffman, "Part boundaries alter the perception of transparency," Psychol. Sci. 9, 370-378 (1998).
[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]

In the literature, called "partial transparency." The concept was introduced by Beck in 1984 [J. Beck, K. Prazdny, and R. Ivry, "The perception of transparency with achromatic colors," Percept. Psychophys. 35, 407-422 (1984)]. See also . The concept of "partial transparency" is not very well defined; we believe it to correspond to our Left or Right overlay categories.

Julesz, B.

B. L. Anderson and B. Julesz, "A theoretical analysis of illusory contour formation in stereopsis," Psychol. Rev. 102, 705-743 (1995).
[CrossRef]

Kanizsa, G.

G. Kanizsa, Organization in Vision: Essays on Gestalt Perception (Praeger, 1979).

Kasrai, R.

Kingdom, F. A. 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]

Koffka, K.

K. Koffka, Principles of Gestalt Psychology (Lund Humphries, 1935).

Kohler, W.

W. Kohler, Gestalt Psychology (Liveright, 1947).

Kubelka, P.

P. Kubelka and F. Munk, "Ein Beitrag Zur Optik der Farbanstriche," Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

Manganelli, A. M.

F. Metelli, S. C. Masin and A. M. Manganelli, "Partial transparency," Atti Accad. Patav. Sci. Lett. Arti 1979-1980, Cl. Sci. morali, Lett. Arti XVII (Parte III), 115-169 (1981).

Masin, S. C.

S. C. Masin, "The luminance conditions of transparency," Perception 26, 39-50 (1997).
[CrossRef] [PubMed]

F. Metelli, S. C. Masin and A. M. Manganelli, "Partial transparency," Atti Accad. Patav. Sci. Lett. Arti 1979-1980, Cl. Sci. morali, Lett. Arti XVII (Parte III), 115-169 (1981).

Meng, J.

B. L. Anderson, M. Singh, and J. Meng, "The perceived transmittance of inhomogeneous surfaces and media," Vision Res. 46, 1982-1995 (2006).
[CrossRef] [PubMed]

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, "Stimulation and perception of transparency," Psychol. Res. 47, 185-202 (1985).
[CrossRef] [PubMed]

F. Metelli, "Su alcune condizioni spazio-figurali della trasparenza," in Conoscenza e Struttura, W.Gerbino, ed. (Il Mulino, 1985), pp. 303-331.

F. Metelli, "Osservazioni sull'articolo di Marco Sambin: trasparenza con superfici indotte'," G. Ital. Psicolo. XI, 393-398 (1984).

Metelli, who was an acute visual observer, remarks on our Hole category in a footnote: "In questo caso [namely ∣u−v∣>∣x−y∣] si determina un effetto curioso .... Invece delle regioni centrali diventano trasparenti, e cioè assumono le funzioni di U e V, le regioni laterali, e quindi si restaura la condizione necessaria [∣u−v∣<∣x−y∣" [expressions in our notation] but does not appear to have used this insight in the way we did. See footnote 21, p. 171 in F. Metelli, "Stimolazione e percezione della trasparenza con tonalità acromatiche," Ric. Psicol. 26, 159-180 (1983). Percepts related to holes have been more widely studied in binocular vision, e.g., see .

F. Metelli, S. C. Masin and A. M. Manganelli, "Partial transparency," Atti Accad. Patav. Sci. Lett. Arti 1979-1980, Cl. Sci. morali, Lett. Arti XVII (Parte III), 115-169 (1981).

F. Metelli, O. da Pos, and A. Cavedon, "Some conditions regarding localization and mode of appearance of achromatic colors," Atti Mem. Accad. Pata. Sci. Lett. Arti 89, 213-221 (1976-1977).

F. Metelli, "What does 'more transparent' mean? A paradox," in Vision and Artifact, M.Henle, ed. (Springer, 1976), pp. 19-24.

F. Metelli, "On the visual perception of transparency," inStudies in Perception: Festschrift for Fabio Metelli, G.B. F.D'Arcais, ed. (Martello Giunti, 1975), pp. 488-496.

F. Metelli, "Shadows without penumbra," in Gestalttheorie in der modernen Psychologie (Metzger Festschrift), S.Ertal, L.Kemmier, and S.Michael, eds. (Steinkopff, 1975), pp. 200-209.
[CrossRef]

F. Metelli, "The perception of transparency," Sci. Am. 230(4), 91-98 (1974).
[CrossRef]

F. Metelli, "Achromatic colour conditions in the perception of transparency," in Perception: Essays in Honor of James J. Gibson, R.B.MacLeod and H.L.Pick, eds. (Cornell U. Press, 1974), pp. 95-116.

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

F. Metelli, "Zur Analyse der phänomenalen Durchsichtigkeitserscheinungen," in Gestalt und Wirklichkeit, R.Müller and J.Fischl, eds. (Duncker & Humblot, 1967), pp. 258-304.

F. Metelli, "Morfologia dei fenomeni di completamento nella percezione visiva," in Gestalthaftes Sehen, E.von Ehrenfels and F.Weinhandl, eds. (Wissenschaftliche Buchgesellschaft, 1960), pp. 266-278.

F. Metelli, "Oggettualità stratificazione e risalto nell'organizzazione (percettiva) di figura e sfondo," Arch. Psicol Neurol. Psichiatr II(4), 831-841 (1941).

Metzger, W.

W. Metzger, Gesetze des Sehens (Waldemar Kramer, 1975).

Munk, F.

P. Kubelka and F. Munk, "Ein Beitrag Zur Optik der Farbanstriche," Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

Prazdny, K.

In the literature, called "partial transparency." The concept was introduced by Beck in 1984 [J. Beck, K. Prazdny, and R. Ivry, "The perception of transparency with achromatic colors," Percept. Psychophys. 35, 407-422 (1984)]. See also . The concept of "partial transparency" is not very well defined; we believe it to correspond to our Left or Right overlay categories.

Robilotto, R.

R. Robilotto and Q. Zaidi, "Perceived transparency of neutral density filters across dissimilar backgrounds," J. Vision 4(3), 183-195 (2004).
[CrossRef]

Singh, M.

B. L. Anderson, M. Singh, and J. Meng, "The perceived transmittance of inhomogeneous surfaces and media," Vision Res. 46, 1982-1995 (2006).
[CrossRef] [PubMed]

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

M. Singh and D. D. Hoffman, "Part boundaries alter the perception of transparency," Psychol. Sci. 9, 370-378 (1998).
[CrossRef]

Stultiens, C. I. F. H. J.

W. Gerbino, C. I. F. H. J. Stultiens, J. M. Troost, and Ch. M. M. de Weert, "Transparent layer constancy," J. Exp. Psychol. 16, 3-20 (1990).

Troost, J. M.

W. Gerbino, C. I. F. H. J. Stultiens, J. M. Troost, and Ch. M. M. de Weert, "Transparent layer constancy," J. Exp. Psychol. 16, 3-20 (1990).

Wertheimer, M.

M. Wertheimer, "Über Gestalttheorie," an address before the Kant Society, Berlin, 7th December, 1924, Erlangen, 1925, translation by W.D.Ellis in Source Book of Gestalt Psychology (Harcourt, Brace, 1938).

Zaidi, Q.

R. Robilotto and Q. Zaidi, "Perceived transparency of neutral density filters across dissimilar backgrounds," J. Vision 4(3), 183-195 (2004).
[CrossRef]

Arch. Psicol Neurol. Psichiatr (1)

F. Metelli, "Oggettualità stratificazione e risalto nell'organizzazione (percettiva) di figura e sfondo," Arch. Psicol Neurol. Psichiatr II(4), 831-841 (1941).

Atti Mem. Accad. Pata. Sci. Lett. Arti (1)

F. Metelli, O. da Pos, and A. Cavedon, "Some conditions regarding localization and mode of appearance of achromatic colors," Atti Mem. Accad. Pata. Sci. Lett. Arti 89, 213-221 (1976-1977).

Ergonomics (1)

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

G. Ital. Psicolo. (1)

F. Metelli, "Osservazioni sull'articolo di Marco Sambin: trasparenza con superfici indotte'," G. Ital. Psicolo. XI, 393-398 (1984).

J. Exp. Psychol. (1)

W. Gerbino, C. I. F. H. J. Stultiens, J. M. Troost, and Ch. M. M. de Weert, "Transparent layer constancy," J. Exp. Psychol. 16, 3-20 (1990).

J. Opt. Soc. Am. A (1)

J. Vision (1)

R. Robilotto and Q. Zaidi, "Perceived transparency of neutral density filters across dissimilar backgrounds," J. Vision 4(3), 183-195 (2004).
[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]

Percept. Psychophys. (2)

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 (1)

S. C. Masin, "The luminance conditions of transparency," Perception 26, 39-50 (1997).
[CrossRef] [PubMed]

Psychol. Res. (1)

F. Metelli, "Stimulation and perception of transparency," Psychol. Res. 47, 185-202 (1985).
[CrossRef] [PubMed]

Psychol. Rev. (2)

B. L. Anderson and B. Julesz, "A theoretical analysis of illusory contour formation in stereopsis," Psychol. Rev. 102, 705-743 (1995).
[CrossRef]

M. Singh and B. L. Anderson, "Towards 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 (1998).
[CrossRef]

Ric. Psicol. (1)

Metelli, who was an acute visual observer, remarks on our Hole category in a footnote: "In questo caso [namely ∣u−v∣>∣x−y∣] si determina un effetto curioso .... Invece delle regioni centrali diventano trasparenti, e cioè assumono le funzioni di U e V, le regioni laterali, e quindi si restaura la condizione necessaria [∣u−v∣<∣x−y∣" [expressions in our notation] but does not appear to have used this insight in the way we did. See footnote 21, p. 171 in F. Metelli, "Stimolazione e percezione della trasparenza con tonalità acromatiche," Ric. Psicol. 26, 159-180 (1983). Percepts related to holes have been more widely studied in binocular vision, e.g., see .

Sci. Am. (1)

F. Metelli, "The perception of transparency," Sci. Am. 230(4), 91-98 (1974).
[CrossRef]

Vision Res. (1)

B. L. Anderson, M. Singh, and J. Meng, "The perceived transmittance of inhomogeneous surfaces and media," Vision Res. 46, 1982-1995 (2006).
[CrossRef] [PubMed]

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

P. Kubelka and F. Munk, "Ein Beitrag Zur Optik der Farbanstriche," Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

Other (20)

K. Koffka, Principles of Gestalt Psychology (Lund Humphries, 1935).

M. Wertheimer, "Über Gestalttheorie," an address before the Kant Society, Berlin, 7th December, 1924, Erlangen, 1925, translation by W.D.Ellis in Source Book of Gestalt Psychology (Harcourt, Brace, 1938).

R. Arnheim, Visual Thinking (U. California Press, 1969).

W. Kohler, Gestalt Psychology (Liveright, 1947).

G. Kanizsa, Organization in Vision: Essays on Gestalt Perception (Praeger, 1979).

R. W. Fleming and B. L. Anderson, "The perceptual organization of depth," in The Visual Neurosciences, L.Chalupa and J.S.Werner, eds. (MIT Press, 2003), pp. 1284-1299.

In the literature, called "partial transparency." The concept was introduced by Beck in 1984 [J. Beck, K. Prazdny, and R. Ivry, "The perception of transparency with achromatic colors," Percept. Psychophys. 35, 407-422 (1984)]. See also . The concept of "partial transparency" is not very well defined; we believe it to correspond to our Left or Right overlay categories.

F. Metelli, "Achromatic colour conditions in the perception of transparency," in Perception: Essays in Honor of James J. Gibson, R.B.MacLeod and H.L.Pick, eds. (Cornell U. Press, 1974), pp. 95-116.

W. Metzger, Gesetze des Sehens (Waldemar Kramer, 1975).

Laws of Seeing [Gesetze des Sehens], L. Spillmann, M. Wertheimer, and S. Lehar, translators (MIT Press, 2006).

F. Metelli, "Zur Analyse der phänomenalen Durchsichtigkeitserscheinungen," in Gestalt und Wirklichkeit, R.Müller and J.Fischl, eds. (Duncker & Humblot, 1967), pp. 258-304.

F. Metelli, "Su alcune condizioni spazio-figurali della trasparenza," in Conoscenza e Struttura, W.Gerbino, ed. (Il Mulino, 1985), pp. 303-331.

D. Hoffman, Visual Intelligence: How We Create What We See (Norton, 1998).

M. Albert, D. Hoffman, "Genericity in spatial vision," in Geometric Representations of Perceptual Phenomena: Articles in Honor of Tarow Indows on His 70th Birthday, R.D.Luce, M.D.D'Zmura, D.Hoffman, G.J.Iverson, and A.K.Romney, eds. (Erlbaum, 1995), pp. 95-112.

D. B. Gauld, Differential Topology: An Introduction (Marcel Dekker, 1982).

F. Metelli, S. C. Masin and A. M. Manganelli, "Partial transparency," Atti Accad. Patav. Sci. Lett. Arti 1979-1980, Cl. Sci. morali, Lett. Arti XVII (Parte III), 115-169 (1981).

F. Metelli, "Morfologia dei fenomeni di completamento nella percezione visiva," in Gestalthaftes Sehen, E.von Ehrenfels and F.Weinhandl, eds. (Wissenschaftliche Buchgesellschaft, 1960), pp. 266-278.

F. Metelli, "On the visual perception of transparency," inStudies in Perception: Festschrift for Fabio Metelli, G.B. F.D'Arcais, ed. (Martello Giunti, 1975), pp. 488-496.

F. Metelli, "Shadows without penumbra," in Gestalttheorie in der modernen Psychologie (Metzger Festschrift), S.Ertal, L.Kemmier, and S.Michael, eds. (Steinkopff, 1975), pp. 200-209.
[CrossRef]

F. Metelli, "What does 'more transparent' mean? A paradox," in Vision and Artifact, M.Henle, ed. (Springer, 1976), pp. 19-24.

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Figures (10)

Fig. 1
Fig. 1

Example of a stimulus as used in the experiment. The background serves to anchor the basic Metelli figure. The observer selects a category by clicking the corresponding button with the mouse. Immediately after the selection the next stimulus appears.

Fig. 2
Fig. 2

Generic interpretations of the Metelli figure involving a translucent layer.

Fig. 3
Fig. 3

Cross sections through the X Y U V hypercube. In the array of cross sections you have x = 0.1 , 0.3 , 0.5 , 0.7 , 0.9 from left to right and y = 0.1 , 0.3 , 0.5 , 0.7 , 0.9 from bottom to top. In each cross section u runs horizontally, and v vertically from zero to one. The gray tones signify (from lightest to darkest) Square (white), Square or Right, Square or Left, Right, Mosaic, Left, Hole, or Right, Hole or Left, and Hole (black).

Fig. 4
Fig. 4

Designations of X, Y, U and V regions for the Square, Hole, Right and Left translucency case (from left to right).

Fig. 5
Fig. 5

Examples of cases (from left to right, top to bottom) a translucent Square, overlay with Hole, Right overlay, ambiguous Square or Left overlay, ambiguous Hole or Left overlay, and—finally—a Mosaic, that is to say, a configuration that does not admit of a translucency interpretation. (The omitted cases of ambiguous Square with Right overlay, ambiguous Hole with Right overlay, and the left overlay, are of course simply obtained by holding the page upside down.)

Fig. 6
Fig. 6

Collapsed counts of observers (left to right) AD, JK, and SP.

Fig. 7
Fig. 7

In a simulation the actual stimuli used in the experiment were perturbed 100 times and the perturbed instance categorized. This yields a probability of miscategorization plotted as the “Sim” bars. The stimuli have been sorted by this probability. The empirical probability of miscategorization by the three observers AD, JK, and SP has also been plotted in the same sequence (here the resolution is only 1 3 because there were only three repeated trials per stimulus). We show the simulated and empirical frequencies for the miscategorization of Mosaic stimuli. Notice that sensitive stimuli in the simulation are frequently miscategorized by the observers, and robust instances hardly ever. The stimuli that were never miscategorized in the simulation were never confused by the observers, either.

Fig. 8
Fig. 8

Left to right, Mosaic, an Upper, and ambiguous Lower and Left case for the X-crossing configuration.

Fig. 9
Fig. 9

Left, unit square of color pairs { X , Y } and { P , Q } . The indicated points are the black point { K , K } = { 0 , 0 } , the white point { W , W } = { 1 , 1 } , and the back ground { X , Y } . The shaded region indicates the region where the overlay pair has a valid Metelli interpretation; the shades indicate partial constraints. Right, the opaque overlay limit lies on a diagonal point { T , T } . We picked many such diagonal points and interpolated with the background via the parameter α, thus generating the (straight) orbits. Notice that the orbits sweep out the convex hull of the diagonal and the background.

Fig. 10
Fig. 10

The orbits in the bicolor diagram for the Kubelka–Munk approximation are curved. They do not exhaust the convex region covered in the Metelli model; in the shaded region one has a valid Metelli interpretation but no Kubelka–Munk interpretation.

Tables (9)

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Table 1 Probabilities of Various Gestalt Configurations for Random, Uniform Distribution of Image Intensities

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Table 2 Frequencies (Times 100) of Various Gestalt Configurations with Perturbation a

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Table 3 Percentages of Correct Categorization for Basic Categories for Three Observers

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Table 4 Responses of Observer AD

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Table 5 Responses of Observer JK

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Table 6 Responses of Observer SP

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Table 7 Collapsed Responses for Observer AD

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Table 8 Collapsed Responses for Observer JK

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Table 9 Collapsed Responses for Observer SP

Equations (21)

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

r = ( 1 α ) ϱ + α t ,
H = r 1 r 0 r 1 + r 0 = α 2 σ + α
0 r , r 0 , r 1 , σ , α 1 .
u = σ + α x , v = σ + α y ,
α = v u y x , σ = u y v x y x .
0 u y v x y x 1 , 0 u y v x y x + v u y x 1 .
( ( x > y ) ( u > v ) P ) ( ( x < y ) ( u < v ) Q ) ,
P = ( ( ( u < x ) ( u x < y v ) ) ( x + y u + v > y + u + x v x ) ) ,
Q = ( ( ( u < x ) ( u x > v y ) ) ( u x + y u + v < y + u + x v ) ) .
P = α X + ( 1 α ) T ,
Q = α Y + ( 1 α ) T ,
P = α X + β T ,
Q = α Y + β T ,
T = X Q Y P ( X Y ) ( P Q ) ,
α = P Q X Y .
( P Q ) ( Q X P Y ) ( P + Q X + Y Q + X + P Y ) ( X < P ) ,
( P > Q ) ( X < P ) ( Y < Q ) ( P + Q X + Y < Q + X + P Y ) .
X ξ 1 X , Y ξ 1 Y , P ξ 1 P , Q ξ 1 Q ,
ξ > Q X P Y ( X Y ) ( Q P ) > 1 .
P = X T T T ( X 1 T ) exp [ α ( 1 T T ) ] X T ( X 1 T ) exp [ α ( 1 T T ) ] ,
Q = Y T T T ( Y 1 T ) exp [ α ( 1 T T ) ] Y T ( Y 1 T ) exp [ α ( 1 T T ) ] ,

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