Abstract

How accurately do human observers perceive the properties of an achromatic transparent filter with both reflective and transmissive components? To address this question, a novel six-luminance stimulus was employed, consisting of three transparent layer luminances set against three background luminances, which satisfied the conventional constraints of perceptual transparency. In one experiment, subjects adjusted one of the three layer luminances to complete the impression of a uniform transparent disk. It was found that the luminance-based formulation of Metelli’s episcotister model and a model based on ratios of Michelson contrasts best predicted the subjects’ settings, which were both accurate and precise. In another experiment, pairs of stimuli selected from a range with various values of the adjustable layer luminance were presented in a series of forced-choice trials. A modified implementation of the pair comparisons method was employed to recover the distribution that describes each subject’s preference pattern. Results showed that there exists a reasonably wide range of stimuli that give rise to at least some degree of perceived transparency.

© 2001 Optical Society of America

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References

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  1. H. von Helmholtz, Treatise on Physiological Optics (Dover, New York, 1866/1962).
  2. F. Metelli, “The perception of transparency,” Sci. Am. 230(4), 90–98 (1974).
    [CrossRef] [PubMed]
  3. F. Metelli, “An algebraic development of the theory of perceptual transparency,” Ergonomics 13, 59–66 (1970).
    [CrossRef] [PubMed]
  4. The terms “layer reflectance” and “layer luminance” are used throughout this paper to denote the absolute reflectance or luminance of the stimulus corresponding to the putative transparent layer, even though the variations in luminance would, in the physical case, be due to the background.
  5. W. Gerbino, “Achromatic transparency,” in Lightness, Brightness, and Transparency, A. L. Gilchrist, ed. (Erlbaum, Hove, UK, 1994), Chap. 5, pp. 215–255.
  6. A. L. Gilchrist, “Perceived lightness depends on perceived spatial arrangement,” Science 195, 185–187 (1977).
    [CrossRef] [PubMed]
  7. J. Beck, K. Prazdny, R. Ivry, “The perception of transparency with achromatic colors,” Percept. Psychophys. 35, 407–422 (1984).
    [CrossRef] [PubMed]
  8. W. Fuchs, “Experimentelle Untersuchungen über das simultane Hintereinandersehen auf derselben Sehrichtung,” Z. Psychol. 91, 145–235 (1923).
  9. S. C. Masin, “Transparent surfaces and illuminated holes,” Perception 24, 761–770 (1995).
    [CrossRef] [PubMed]
  10. W. Gerbino, C. I. Stultiens, J. M. Troost, C. M. de Weert, “Transparent layer constancy,” J. Exp. Psychol. Hum. Percept. Perform. 16, 3–20 (1990).
    [CrossRef] [PubMed]
  11. The principle of the six-luminance method has also been described by W. Gerbinoin a conference presentation, though it was not mentioned in the associated conference abstract: W. Gerbino, “Colour constraints and optimal transparency,” Perception (Suppl.) 22, 2 (1993).
  12. Additionally, in this display all the relevant luminances are in close proximity in central vision, such that no scanning of the image is required.
  13. M. Singh, B. L. Anderson, “Toward a perceptual theory of transparency,” manuscript available from Bart Anderson, Department of Brain and Cognitive Sciences, MIT NE20-447, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139; bart@psyche.mit.edu.
  14. There is disagreement in the literature over the usage of the term ‘forced-choice.’ Some maintain it should be used only if there is a correct answer on every trial, which is not the case in this experiment. The term forced choice is meant here to imply that there are two alternatives on each trial, from which one must be chosen. See N. A. Macmillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, New York, 1991) for a discussion of this issue.
  15. J. P. Guilford, Psychometric Methods (McGraw-Hill, New York, 1954).
  16. J. Beck, R. Ivry, “On the role of figural organization in perceptual transparency,” Percept. Psychophys. 44, 585–594 (1988).
    [CrossRef] [PubMed]
  17. M. Singh, D. Hoffman, “Part boundaries alter the perception of transparency,” Psychol. Sci. 9, 370–378 (1998).
    [CrossRef]
  18. D. G. Luenberger, Linear and Nonlinear Programming (Addison-Wesley, Reading, Mass., 1984).
  19. The minimization was performed by using the constr() function in the MATLAB optimization toolkit (The MathWorks, Inc., Natick, Mass).
  20. F. Metelli, O. Da Pos, A. Cavedon, “Balanced and unbalanced, complete and partial transparency,” Percept. Psychophys. 38, 354–366 (1985).
    [CrossRef] [PubMed]
  21. J. Beck, “Additive and subtractive color mixture in color transparency,” Percept. Psychophys. 23, 265–267 (1978).
    [CrossRef] [PubMed]
  22. D. Kersten, “Transparency and the cooperative computation of scene attributes,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), Chap. 15, pp. 209–228.
  23. T. Watanabe, P. Cavanagh, “Transparent surfaces defined by implicit X junctions,” Vision Res. 33, 2339–2346 (1993).
    [CrossRef] [PubMed]
  24. 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] [PubMed]
  25. M. D’Zmura, P. Colantoni, K. Knoblauch, B. Laget, “Color transparency,” Perception 26, 471–492 (1997).
    [CrossRef] [PubMed]
  26. S. Westland, C. Ripamonti, “Invariant cone-excitation ratios may predict transparency,” J. Opt. Soc. Am. A 17, 255–264 (2000).
    [CrossRef]

2000 (1)

1998 (1)

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

1997 (2)

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] [PubMed]

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

1995 (1)

S. C. Masin, “Transparent surfaces and illuminated holes,” Perception 24, 761–770 (1995).
[CrossRef] [PubMed]

1993 (2)

The principle of the six-luminance method has also been described by W. Gerbinoin a conference presentation, though it was not mentioned in the associated conference abstract: W. Gerbino, “Colour constraints and optimal transparency,” Perception (Suppl.) 22, 2 (1993).

The principle of the six-luminance method has also been described by W. Gerbinoin a conference presentation, though it was not mentioned in the associated conference abstract: W. Gerbino, “Colour constraints and optimal transparency,” Perception (Suppl.) 22, 2 (1993).

T. Watanabe, P. Cavanagh, “Transparent surfaces defined by implicit X junctions,” Vision Res. 33, 2339–2346 (1993).
[CrossRef] [PubMed]

1990 (1)

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

1988 (1)

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

1985 (1)

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

1984 (1)

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

1978 (1)

J. Beck, “Additive and subtractive color mixture in color transparency,” Percept. Psychophys. 23, 265–267 (1978).
[CrossRef] [PubMed]

1977 (1)

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

1974 (1)

F. Metelli, “The perception of transparency,” Sci. Am. 230(4), 90–98 (1974).
[CrossRef] [PubMed]

1970 (1)

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

1923 (1)

W. Fuchs, “Experimentelle Untersuchungen über das simultane Hintereinandersehen auf derselben Sehrichtung,” Z. Psychol. 91, 145–235 (1923).

Anderson, B. L.

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] [PubMed]

M. Singh, B. L. Anderson, “Toward a perceptual theory of transparency,” manuscript available from Bart Anderson, Department of Brain and Cognitive Sciences, MIT NE20-447, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139; bart@psyche.mit.edu.

Beck, J.

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

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

J. Beck, “Additive and subtractive color mixture in color transparency,” Percept. Psychophys. 23, 265–267 (1978).
[CrossRef] [PubMed]

Cavanagh, P.

T. Watanabe, P. Cavanagh, “Transparent surfaces defined by implicit X junctions,” Vision Res. 33, 2339–2346 (1993).
[CrossRef] [PubMed]

Cavedon, A.

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

Colantoni, P.

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

Creelman, C. D.

There is disagreement in the literature over the usage of the term ‘forced-choice.’ Some maintain it should be used only if there is a correct answer on every trial, which is not the case in this experiment. The term forced choice is meant here to imply that there are two alternatives on each trial, from which one must be chosen. See N. A. Macmillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, New York, 1991) for a discussion of this issue.

D’Zmura, M.

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

Da Pos, O.

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

de Weert, C. M.

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

Fuchs, W.

W. Fuchs, “Experimentelle Untersuchungen über das simultane Hintereinandersehen auf derselben Sehrichtung,” Z. Psychol. 91, 145–235 (1923).

Gerbino, W.

The principle of the six-luminance method has also been described by W. Gerbinoin a conference presentation, though it was not mentioned in the associated conference abstract: W. Gerbino, “Colour constraints and optimal transparency,” Perception (Suppl.) 22, 2 (1993).

The principle of the six-luminance method has also been described by W. Gerbinoin a conference presentation, though it was not mentioned in the associated conference abstract: W. Gerbino, “Colour constraints and optimal transparency,” Perception (Suppl.) 22, 2 (1993).

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

W. Gerbino, “Achromatic transparency,” in Lightness, Brightness, and Transparency, A. L. Gilchrist, ed. (Erlbaum, Hove, UK, 1994), Chap. 5, pp. 215–255.

Gilchrist, A. L.

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

Guilford, J. P.

J. P. Guilford, Psychometric Methods (McGraw-Hill, New York, 1954).

Hoffman, D.

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

Ivry, R.

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

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

Kersten, D.

D. Kersten, “Transparency and the cooperative computation of scene attributes,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), Chap. 15, pp. 209–228.

Knoblauch, K.

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

Laget, B.

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

Luenberger, D. G.

D. G. Luenberger, Linear and Nonlinear Programming (Addison-Wesley, Reading, Mass., 1984).

Macmillan, N. A.

There is disagreement in the literature over the usage of the term ‘forced-choice.’ Some maintain it should be used only if there is a correct answer on every trial, which is not the case in this experiment. The term forced choice is meant here to imply that there are two alternatives on each trial, from which one must be chosen. See N. A. Macmillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, New York, 1991) for a discussion of this issue.

Masin, S. C.

S. C. Masin, “Transparent surfaces and illuminated holes,” Perception 24, 761–770 (1995).
[CrossRef] [PubMed]

Metelli, F.

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

F. Metelli, “The perception of transparency,” Sci. Am. 230(4), 90–98 (1974).
[CrossRef] [PubMed]

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

Prazdny, K.

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

Ripamonti, C.

Singh, M.

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

M. Singh, B. L. Anderson, “Toward a perceptual theory of transparency,” manuscript available from Bart Anderson, Department of Brain and Cognitive Sciences, MIT NE20-447, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139; bart@psyche.mit.edu.

Stultiens, C. I.

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

von Helmholtz, H.

H. von Helmholtz, Treatise on Physiological Optics (Dover, New York, 1866/1962).

Watanabe, T.

T. Watanabe, P. Cavanagh, “Transparent surfaces defined by implicit X junctions,” Vision Res. 33, 2339–2346 (1993).
[CrossRef] [PubMed]

Westland, S.

Ergonomics (1)

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

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

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

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

Percept. Psychophys. (4)

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

J. Beck, “Additive and subtractive color mixture in color transparency,” Percept. Psychophys. 23, 265–267 (1978).
[CrossRef] [PubMed]

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

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

Perception (3)

S. C. Masin, “Transparent surfaces and illuminated holes,” Perception 24, 761–770 (1995).
[CrossRef] [PubMed]

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] [PubMed]

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

Perception (Suppl.) (1)

The principle of the six-luminance method has also been described by W. Gerbinoin a conference presentation, though it was not mentioned in the associated conference abstract: W. Gerbino, “Colour constraints and optimal transparency,” Perception (Suppl.) 22, 2 (1993).

Psychol. Sci. (1)

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

Sci. Am. (1)

F. Metelli, “The perception of transparency,” Sci. Am. 230(4), 90–98 (1974).
[CrossRef] [PubMed]

Science (1)

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

Vision Res. (1)

T. Watanabe, P. Cavanagh, “Transparent surfaces defined by implicit X junctions,” Vision Res. 33, 2339–2346 (1993).
[CrossRef] [PubMed]

Z. Psychol. (1)

W. Fuchs, “Experimentelle Untersuchungen über das simultane Hintereinandersehen auf derselben Sehrichtung,” Z. Psychol. 91, 145–235 (1923).

Other (10)

H. von Helmholtz, Treatise on Physiological Optics (Dover, New York, 1866/1962).

The terms “layer reflectance” and “layer luminance” are used throughout this paper to denote the absolute reflectance or luminance of the stimulus corresponding to the putative transparent layer, even though the variations in luminance would, in the physical case, be due to the background.

W. Gerbino, “Achromatic transparency,” in Lightness, Brightness, and Transparency, A. L. Gilchrist, ed. (Erlbaum, Hove, UK, 1994), Chap. 5, pp. 215–255.

D. G. Luenberger, Linear and Nonlinear Programming (Addison-Wesley, Reading, Mass., 1984).

The minimization was performed by using the constr() function in the MATLAB optimization toolkit (The MathWorks, Inc., Natick, Mass).

Additionally, in this display all the relevant luminances are in close proximity in central vision, such that no scanning of the image is required.

M. Singh, B. L. Anderson, “Toward a perceptual theory of transparency,” manuscript available from Bart Anderson, Department of Brain and Cognitive Sciences, MIT NE20-447, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139; bart@psyche.mit.edu.

There is disagreement in the literature over the usage of the term ‘forced-choice.’ Some maintain it should be used only if there is a correct answer on every trial, which is not the case in this experiment. The term forced choice is meant here to imply that there are two alternatives on each trial, from which one must be chosen. See N. A. Macmillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, New York, 1991) for a discussion of this issue.

J. P. Guilford, Psychometric Methods (McGraw-Hill, New York, 1954).

D. Kersten, “Transparency and the cooperative computation of scene attributes,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), Chap. 15, pp. 209–228.

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Figures (8)

Fig. 1
Fig. 1

Transparency stimuli: (a) two-luminance stimulus (does not provide a strong transparent percept), (b) four luminances simulating an episcotister in the classical bipartite display, (c) six-luminance stimulus with mid-gray background.

Fig. 2
Fig. 2

Optic array describing the episcotister luminance model. Note that the background is illuminated only directly and not through the layer.

Fig. 3
Fig. 3

Range of possible test patch settings. The correct image, according to the luminance episcotister (LE) model, is in the center.

Fig. 4
Fig. 4

The left column [(a)–(c)] shows adjustment settings for three subjects (along with solid line depicting a linear regression) compared with the expected episcotister luminance settings (dashed 45° line). The right column [(d)–(g)] shows the data from one subject (KW) compared with predictions according to alternative models: (d) filter model, (e) Michelson contrast model, (f) arithmetic mean model, (g) average brightness model. The performance of the subject (KW) matches the first three models [(c), (d), and (e)] the most closely.

Fig. 5
Fig. 5

Simulated example of underlying a priori probabilities (squares) and tally scores (triangles).

Fig. 6
Fig. 6

Forced-choice results for subject KW. Each plot shows the results from the luminance perturbation of one part (P, Q, and S, respectively, from top to bottom) of the stimulus around the value according to the LE model (solid vertical line). The original tally data are shown by triangles. The squares show the recovered a priori probabilities q. The dotted–dashed curve joining the triangles shows a check of the solution by substituting qi back into Eq. (9) to compare with the observed tallies p. The vertical dotted–dashed line is the first moment (average) of the a priori data, and the vertical dashed line is the average of three adjustment settings made by the subject.

Fig. 7
Fig. 7

Forced-choice results for subject FK.

Fig. 8
Fig. 8

Examples of modifications to the six-luminance stimulus for investigating figural conditions in transparency.

Tables (2)

Tables Icon

Table 1 Raw Forced-Choice Results a

Tables Icon

Table 2 Summary of Forced-Choice Results a

Equations (15)

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

p=ta+(1-t)r,q=tb+(1-t)r,
P=taI+(1-t)rI=tA+(1-t)rhI=tA+F
Q=tB+F,
t=P-QA-B,F=AQ-BPA-B,
tf=[(A-B)(P-Q)(I2-AQ)(I2-BP)]1/2A(I2-BP)-B(I2-AQ),
Ff=I2(AQ-BP)A(I2-BP)-B(I2-AQ),
Sf=tf2I2I2-FC C+Ff,
tM=P-SP+S/A-CA+C=P-QP+Q/A-BA+B.
SM=P A(AQ-BP)+C(AP-BQ)A(AP-BQ)+C(AQ-BP).
logSC=12logPA+logQBor S=CPAQB1/2.
S=P+Q2
pi=1C2Nj=1jiNqiqi+qj,
CkN=N!k!(N-k)!
i=1Npi-1C2Nj=1jiNqiqi+qj2
i=1Nqi=1,0qi1,|qi-qi+1|<0.3.

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