Abstract

Human observers use the information offered by various visual cues when evaluating the glossiness of a surface. Several studies have demonstrated the effect of each single cue to glossiness, but little has been reported on how multiple cues are integrated for the perception of surface gloss. This paper reports on a psychophysical study with real stimuli that are different regarding multiple visual gloss criteria. Four samples were presented to 15 observers under different conditions of illumination in a light booth, resulting in a series of 16 stimuli. Through pairwise comparisons, an overall gloss scale was derived, from which it could be concluded that both differences in the distinctness of the reflected image and differences in luminance affect gloss perception. However, an investigation of the observers’ strategy to evaluate gloss indicated a dichotomy among observers. One group of observers used the distinctness-of-image as a principal cue to glossiness, while the second group evaluated gloss primarily from differences in luminance of both the specular highlight and the diffuse background. It could therefore be questioned whether surface gloss can be characterized with one single quantity, or that a set of quantities is necessary to describe the gloss differences between objects.

© 2012 Optical Society of America

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    [CrossRef]

2011 (3)

J. Kim, P. Marlow, and B. L. Anderson, “The perception of gloss depends on highlight congruence with surface shading,” J. Vision 11(9):4, 1–19 (2011).
[CrossRef]

P. Marlow, J. Kim, and B. L. Anderson, “The role of brightness and orientation congruence in the perception of surface gloss,” J. Vision 11(9):16, 1–12 (2011).
[CrossRef]

F. B. Leloup, M. R. Pointer, P. Dutré, and P. Hanselaer, “Luminance-based specular gloss characterization,” J. Opt. Soc. Am. A 28, 1322–1330 (2011).
[CrossRef]

2010 (8)

Y. Sakano and H. Ando, “Effects of head motion and stereo viewing on perceived glossiness,” J. Vision 10(9):15, 1–14 (2010).
[CrossRef]

J. Kim and B. L. Anderson, “Image statistics and the perception of surface gloss and lightness,” J. Vision 10(9):3, 1–17 (2010).
[CrossRef]

D. A. Wismeijer, C. J. Erkelens, R. van Ee, and M. Wexler, “Depth cue combination in spontaneous eye movements,” J. Vision 10(6):25, 1–15 (2010).
[CrossRef]

M. Giesel and K. R. Gegenfurtner, “Color appearance of real objects varying in material, hue, and shape,” J. Vision 10(9):10, 1–21 (2010).
[CrossRef]

J. B. Phillips, J. A. Ferwerda, and A. Nunziata, “Gloss discrimination and eye movement,” Proc. SPIE 7527, 75270Z (2010).
[CrossRef]

G. Ged, G. Obein, Z. Silvestri, J. Le Rohellec, and F. Viénot, “Recognizing real materials from their glossy appearance,” J. Vision 10(9):18, 1–17 (2010).
[CrossRef]

M. W. A. Wijntjes and S. C. Pont, “Illusory gloss on Lambertian surfaces,” J. Vision 10(9):13, 1–12 (2010).
[CrossRef]

G. Wendt, F. Faul, V. Ekroll, and R. Mausfeld, “Disparity, motion, and color information improve gloss constancy performance,” J. Vision 10(9):7, 1–17 (2010).
[CrossRef]

2009 (2)

B. L. Anderson and J. Kim, “Image statistics do not explain the perception of gloss and lightness,” J. Vision 9(11):10, 1–17 (2009).
[CrossRef]

J. Wills, S. Agarwal, D. Kriegman, and S. Belongie, “Toward a perceptual space for gloss,” ACM Trans. Graph. 28, 1–15 (2009).
[CrossRef]

2008 (4)

2007 (3)

D. C. Knill, “Robust cue integration: a Bayesian model and evidence from cue-conflict studies with stereoscopic and figure cues to slant,” J. Vision 7(7):5, 1–24 (2007).
[CrossRef]

P. Vangorp, J. Laurijssen, and P. Dutré, “The influence of shape on the perception of material reflectance,” ACM Trans. Graph. 26, 77:1–77:9 (2007).
[CrossRef]

I. Motoyoshi, S. Nishida, L. Sharan, and E. H. Adelson, “Image statistics and the perception of surface qualities,” Nature 447, 206–209 (2007).
[CrossRef]

2006 (1)

2004 (3)

G. Obein, K. Knoblauch, and F. Viénot, “Difference scaling of gloss: Nonlinearity, binocularity, and constancy,” J. Vision 4(9):4, 711–720 (2004).
[CrossRef]

R. W. Fleming, A. Torralba, and E. H. Adelson, “Specular reflections and the perception of shape,” J. Vision 4(9):10, 798–820 (2004).
[CrossRef]

J. F. Norman, J. T. Todd, and G. A. Orban, “Perception of three-dimensional shape from specular highlights, deformations of shading, and other types of visual information,” Psychol. Sci. 15, 565–570 (2004).

2003 (2)

M. Mikula, M. Ceppan, and K. Vasco, “Gloss and goniocolorimetry of printed materials,” Color Res. Appl. 28 (5), 335–342 (2003).
[CrossRef]

R. van Ee, W. J. Adams, and P. Mamassian, “Bayesian modeling of cue interaction: bistability in stereoscopic slant perception,” J. Opt. Soc. Am. A 20, 1398–1406 (2003).
[CrossRef]

2002 (1)

B. Hartung and D. Kersten, “Distinguishing shiny from matte,” J. Vision 2(7):551 (2002).
[CrossRef]

1998 (1)

1995 (1)

J. F. Norman and J. T. Todd, “The perception of 3-D structure from contradictory optical patterns,” Percept. Psychophys. 57, 826–834 (1995).
[CrossRef]

1994 (1)

K. Uomori and S. Nishida, “The dynamics of the visual system in combining conflicting KDE and binocular stereopsis cues,” Percept. Psychophys. 55, 526–536 (1994).
[CrossRef]

1987 (2)

H. R. Flock and Steven Nusinowitz, “Specularity, brightness, achromatic color—and orthogonality,” Percept. Psychophys. 42, 439–456 (1987).
[CrossRef]

F. W. Billmeyer and F. X. D. O’Donnell, “Visual gloss scaling and multidimensional scaling analysis of painted specimens,” Color Res. Appl. 12, 315–326 (1987).
[CrossRef]

1952 (1)

H. Scheffé, “An analysis of variance for paired comparisons,” J. Am. Stat. Assoc. 47, 381–400 (1952).

1946 (1)

W. J. Dixon and A. M. Mood, “The statistical sign test,” J. Am. Stat. Assoc. 41, 557–566 (1946).

1943 (1)

E. S. Pearson and H. O. Hartley, “Tables of the probability integral of the studentized range,” Biometrika 33, 89–99(1943).

1940 (1)

M. G. Kendall and B. Babington Smith, “On the method of paired comparisons,” Biometrika 31, 324–345 (1940).

Adams, W. J.

Adelson, E. H.

L. Sharan, Y. Li, I. Motoyoshi, S. Nishida, and E. H. Adelson, “Image statistics for surface reflectance perception,” J. Opt. Soc. Am. A 25, 846–865 (2008).
[CrossRef]

I. Motoyoshi, S. Nishida, L. Sharan, and E. H. Adelson, “Image statistics and the perception of surface qualities,” Nature 447, 206–209 (2007).
[CrossRef]

R. W. Fleming, A. Torralba, and E. H. Adelson, “Specular reflections and the perception of shape,” J. Vision 4(9):10, 798–820 (2004).
[CrossRef]

Agarwal, S.

J. Wills, S. Agarwal, D. Kriegman, and S. Belongie, “Toward a perceptual space for gloss,” ACM Trans. Graph. 28, 1–15 (2009).
[CrossRef]

Agresti, A.

A. Agresti, Categorical Data Analysis (Wiley, 2002).

Anderson, B. L.

J. Kim, P. Marlow, and B. L. Anderson, “The perception of gloss depends on highlight congruence with surface shading,” J. Vision 11(9):4, 1–19 (2011).
[CrossRef]

P. Marlow, J. Kim, and B. L. Anderson, “The role of brightness and orientation congruence in the perception of surface gloss,” J. Vision 11(9):16, 1–12 (2011).
[CrossRef]

J. Kim and B. L. Anderson, “Image statistics and the perception of surface gloss and lightness,” J. Vision 10(9):3, 1–17 (2010).
[CrossRef]

B. L. Anderson and J. Kim, “Image statistics do not explain the perception of gloss and lightness,” J. Vision 9(11):10, 1–17 (2009).
[CrossRef]

Ando, H.

Y. Sakano and H. Ando, “Effects of head motion and stereo viewing on perceived glossiness,” J. Vision 10(9):15, 1–14 (2010).
[CrossRef]

Belongie, S.

J. Wills, S. Agarwal, D. Kriegman, and S. Belongie, “Toward a perceptual space for gloss,” ACM Trans. Graph. 28, 1–15 (2009).
[CrossRef]

Billmeyer, F. W.

F. W. Billmeyer and F. X. D. O’Donnell, “Visual gloss scaling and multidimensional scaling analysis of painted specimens,” Color Res. Appl. 12, 315–326 (1987).
[CrossRef]

Brainard, D. H.

B. Xiao and D. H. Brainard, “Surface gloss and color perception of 3D objects,” Vis. Neurosci. 25, 371–385 (2008).
[CrossRef]

Ceppan, M.

M. Mikula, M. Ceppan, and K. Vasco, “Gloss and goniocolorimetry of printed materials,” Color Res. Appl. 28 (5), 335–342 (2003).
[CrossRef]

Dakin, J.

Dixon, W. J.

W. J. Dixon and A. M. Mood, “The statistical sign test,” J. Am. Stat. Assoc. 41, 557–566 (1946).

Dutré, P.

Ekroll, V.

G. Wendt, F. Faul, V. Ekroll, and R. Mausfeld, “Disparity, motion, and color information improve gloss constancy performance,” J. Vision 10(9):7, 1–17 (2010).
[CrossRef]

Erkelens, C. J.

D. A. Wismeijer, C. J. Erkelens, R. van Ee, and M. Wexler, “Depth cue combination in spontaneous eye movements,” J. Vision 10(6):25, 1–15 (2010).
[CrossRef]

Faul, F.

G. Wendt, F. Faul, V. Ekroll, and R. Mausfeld, “Disparity, motion, and color information improve gloss constancy performance,” J. Vision 10(9):7, 1–17 (2010).
[CrossRef]

Ferwerda, J. A.

J. B. Phillips, J. A. Ferwerda, and A. Nunziata, “Gloss discrimination and eye movement,” Proc. SPIE 7527, 75270Z (2010).
[CrossRef]

F. Pellacini, J. A. Ferwerda, and D. P. Greenberg, “Toward a psychophysically-based light reflection model for image synthesis,” in Proceedings of SIGGRAPH’00 (ACM, 2000), pp. 55–64.

Fleming, R. W.

R. W. Fleming, A. Torralba, and E. H. Adelson, “Specular reflections and the perception of shape,” J. Vision 4(9):10, 798–820 (2004).
[CrossRef]

Flock, H. R.

H. R. Flock and Steven Nusinowitz, “Specularity, brightness, achromatic color—and orthogonality,” Percept. Psychophys. 42, 439–456 (1987).
[CrossRef]

Forment, S.

Ged, G.

G. Ged, G. Obein, Z. Silvestri, J. Le Rohellec, and F. Viénot, “Recognizing real materials from their glossy appearance,” J. Vision 10(9):18, 1–17 (2010).
[CrossRef]

Gegenfurtner, K. R.

M. Giesel and K. R. Gegenfurtner, “Color appearance of real objects varying in material, hue, and shape,” J. Vision 10(9):10, 1–21 (2010).
[CrossRef]

Gibbons, J. D.

M. Kendall and J. D. Gibbons, Rank Correlation Methods(Griffin Ltd, 1975).

Giesel, M.

M. Giesel and K. R. Gegenfurtner, “Color appearance of real objects varying in material, hue, and shape,” J. Vision 10(9):10, 1–21 (2010).
[CrossRef]

Greenberg, D. P.

F. Pellacini, J. A. Ferwerda, and D. P. Greenberg, “Toward a psychophysically-based light reflection model for image synthesis,” in Proceedings of SIGGRAPH’00 (ACM, 2000), pp. 55–64.

Hanselaer, P.

Hartley, H. O.

E. S. Pearson and H. O. Hartley, “Tables of the probability integral of the studentized range,” Biometrika 33, 89–99(1943).

Hartung, B.

B. Hartung and D. Kersten, “Distinguishing shiny from matte,” J. Vision 2(7):551 (2002).
[CrossRef]

Ho, Y.-H.

Y.-H. Ho, M. S. Landy, and L. T. Maloney, “Conjoint measurement of gloss and surface texture,” Psychol. Sci. 19, 196–204 (2008).

Howard, I. P.

I. P. Howard and B. J. Rogers, Seeing in Depth: Vol. II. Depth Perception (Porteus, 2002).

Hunter, R. S.

R. S. Hunter, “Methods of determining gloss,” Natl. Bur. Stand. Research Paper RP958, J. Res. Natl. Bur. Stand.18, 19–39 (1937).

Ji, W.

Kendall, M.

M. Kendall and J. D. Gibbons, Rank Correlation Methods(Griffin Ltd, 1975).

Kendall, M. G.

M. G. Kendall and B. Babington Smith, “On the method of paired comparisons,” Biometrika 31, 324–345 (1940).

Kersten, D.

B. Hartung and D. Kersten, “Distinguishing shiny from matte,” J. Vision 2(7):551 (2002).
[CrossRef]

Kim, J.

J. Kim, P. Marlow, and B. L. Anderson, “The perception of gloss depends on highlight congruence with surface shading,” J. Vision 11(9):4, 1–19 (2011).
[CrossRef]

P. Marlow, J. Kim, and B. L. Anderson, “The role of brightness and orientation congruence in the perception of surface gloss,” J. Vision 11(9):16, 1–12 (2011).
[CrossRef]

J. Kim and B. L. Anderson, “Image statistics and the perception of surface gloss and lightness,” J. Vision 10(9):3, 1–17 (2010).
[CrossRef]

B. L. Anderson and J. Kim, “Image statistics do not explain the perception of gloss and lightness,” J. Vision 9(11):10, 1–17 (2009).
[CrossRef]

Knill, D. C.

D. C. Knill, “Robust cue integration: a Bayesian model and evidence from cue-conflict studies with stereoscopic and figure cues to slant,” J. Vision 7(7):5, 1–24 (2007).
[CrossRef]

Knoblauch, K.

G. Obein, K. Knoblauch, and F. Viénot, “Difference scaling of gloss: Nonlinearity, binocularity, and constancy,” J. Vision 4(9):4, 711–720 (2004).
[CrossRef]

Kriegman, D.

J. Wills, S. Agarwal, D. Kriegman, and S. Belongie, “Toward a perceptual space for gloss,” ACM Trans. Graph. 28, 1–15 (2009).
[CrossRef]

Landy, M. S.

Y.-H. Ho, M. S. Landy, and L. T. Maloney, “Conjoint measurement of gloss and surface texture,” Psychol. Sci. 19, 196–204 (2008).

Laurijssen, J.

P. Vangorp, J. Laurijssen, and P. Dutré, “The influence of shape on the perception of material reflectance,” ACM Trans. Graph. 26, 77:1–77:9 (2007).
[CrossRef]

Le Rohellec, J.

G. Ged, G. Obein, Z. Silvestri, J. Le Rohellec, and F. Viénot, “Recognizing real materials from their glossy appearance,” J. Vision 10(9):18, 1–17 (2010).
[CrossRef]

Leloup, F. B.

Li, Y.

Luo, R. M.

Maloney, L. T.

Y.-H. Ho, M. S. Landy, and L. T. Maloney, “Conjoint measurement of gloss and surface texture,” Psychol. Sci. 19, 196–204 (2008).

Mamassian, P.

Marlow, P.

J. Kim, P. Marlow, and B. L. Anderson, “The perception of gloss depends on highlight congruence with surface shading,” J. Vision 11(9):4, 1–19 (2011).
[CrossRef]

P. Marlow, J. Kim, and B. L. Anderson, “The role of brightness and orientation congruence in the perception of surface gloss,” J. Vision 11(9):16, 1–12 (2011).
[CrossRef]

Mausfeld, R.

G. Wendt, F. Faul, V. Ekroll, and R. Mausfeld, “Disparity, motion, and color information improve gloss constancy performance,” J. Vision 10(9):7, 1–17 (2010).
[CrossRef]

Mikula, M.

M. Mikula, M. Ceppan, and K. Vasco, “Gloss and goniocolorimetry of printed materials,” Color Res. Appl. 28 (5), 335–342 (2003).
[CrossRef]

Mood, A. M.

W. J. Dixon and A. M. Mood, “The statistical sign test,” J. Am. Stat. Assoc. 41, 557–566 (1946).

Motoyoshi, I.

L. Sharan, Y. Li, I. Motoyoshi, S. Nishida, and E. H. Adelson, “Image statistics for surface reflectance perception,” J. Opt. Soc. Am. A 25, 846–865 (2008).
[CrossRef]

I. Motoyoshi, S. Nishida, L. Sharan, and E. H. Adelson, “Image statistics and the perception of surface qualities,” Nature 447, 206–209 (2007).
[CrossRef]

Nishida, S.

L. Sharan, Y. Li, I. Motoyoshi, S. Nishida, and E. H. Adelson, “Image statistics for surface reflectance perception,” J. Opt. Soc. Am. A 25, 846–865 (2008).
[CrossRef]

I. Motoyoshi, S. Nishida, L. Sharan, and E. H. Adelson, “Image statistics and the perception of surface qualities,” Nature 447, 206–209 (2007).
[CrossRef]

S. Nishida and M. Shinya, “Use of image-based information in judgments of surface-reflectance properties,” J. Opt. Soc. Am. A 15, 2951–2965 (1998).
[CrossRef]

K. Uomori and S. Nishida, “The dynamics of the visual system in combining conflicting KDE and binocular stereopsis cues,” Percept. Psychophys. 55, 526–536 (1994).
[CrossRef]

Norman, J. F.

J. F. Norman, J. T. Todd, and G. A. Orban, “Perception of three-dimensional shape from specular highlights, deformations of shading, and other types of visual information,” Psychol. Sci. 15, 565–570 (2004).

J. F. Norman and J. T. Todd, “The perception of 3-D structure from contradictory optical patterns,” Percept. Psychophys. 57, 826–834 (1995).
[CrossRef]

Nunziata, A.

J. B. Phillips, J. A. Ferwerda, and A. Nunziata, “Gloss discrimination and eye movement,” Proc. SPIE 7527, 75270Z (2010).
[CrossRef]

Nusinowitz, Steven

H. R. Flock and Steven Nusinowitz, “Specularity, brightness, achromatic color—and orthogonality,” Percept. Psychophys. 42, 439–456 (1987).
[CrossRef]

O’Donnell, F. X. D.

F. W. Billmeyer and F. X. D. O’Donnell, “Visual gloss scaling and multidimensional scaling analysis of painted specimens,” Color Res. Appl. 12, 315–326 (1987).
[CrossRef]

Obein, G.

G. Ged, G. Obein, Z. Silvestri, J. Le Rohellec, and F. Viénot, “Recognizing real materials from their glossy appearance,” J. Vision 10(9):18, 1–17 (2010).
[CrossRef]

G. Obein, K. Knoblauch, and F. Viénot, “Difference scaling of gloss: Nonlinearity, binocularity, and constancy,” J. Vision 4(9):4, 711–720 (2004).
[CrossRef]

Orban, G. A.

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Appl. Opt. (1)

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M. Mikula, M. Ceppan, and K. Vasco, “Gloss and goniocolorimetry of printed materials,” Color Res. Appl. 28 (5), 335–342 (2003).
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M. Giesel and K. R. Gegenfurtner, “Color appearance of real objects varying in material, hue, and shape,” J. Vision 10(9):10, 1–21 (2010).
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Nature (1)

I. Motoyoshi, S. Nishida, L. Sharan, and E. H. Adelson, “Image statistics and the perception of surface qualities,” Nature 447, 206–209 (2007).
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Percept. Psychophys. (3)

K. Uomori and S. Nishida, “The dynamics of the visual system in combining conflicting KDE and binocular stereopsis cues,” Percept. Psychophys. 55, 526–536 (1994).
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[CrossRef]

Proc. SPIE (1)

J. B. Phillips, J. A. Ferwerda, and A. Nunziata, “Gloss discrimination and eye movement,” Proc. SPIE 7527, 75270Z (2010).
[CrossRef]

Psychol. Sci. (2)

J. F. Norman, J. T. Todd, and G. A. Orban, “Perception of three-dimensional shape from specular highlights, deformations of shading, and other types of visual information,” Psychol. Sci. 15, 565–570 (2004).

Y.-H. Ho, M. S. Landy, and L. T. Maloney, “Conjoint measurement of gloss and surface texture,” Psychol. Sci. 19, 196–204 (2008).

Vis. Neurosci. (1)

B. Xiao and D. H. Brainard, “Surface gloss and color perception of 3D objects,” Vis. Neurosci. 25, 371–385 (2008).
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A. Agresti, Categorical Data Analysis (Wiley, 2002).

http://www.eldim.fr/products/uniformity-series/muratest-16m .

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Figures (9)

Fig. 1.
Fig. 1.

Side view of the light booth with the two specular light sources and the ambient light source. The intensity of both specular sources is regulated separately. A close-up of two employed stimuli with differences in specular gloss, contrast gloss, and DOI, is presented in the enclosed picture.

Fig. 2.
Fig. 2.

BRDF functions at an angle of incidence of 60° and at wavelength of 589 nm. The viewing angle ranges from 0° to 80° in the opposite half-plane. Each sample is denoted by a different symbol and color.

Fig. 3.
Fig. 3.

Gray scale images of the four stimuli (a) A4, (b) B4, (c) C4, and (d) D4. Images are acquired with the MURATest absolute luminance camera. In each image, the 80% threshold delimiting the highlight region, from which the average Lim is calculated, is indicated in red.

Fig. 4.
Fig. 4.

Glossiness estimates α^i plotted against specular gloss values in the 60° geometry, expressed in SGU. Each stimulus is represented by a symbol/color combination, resp. representing the sample and the luminance of the specular highlight. Diamonds, circles, squares, and triangles resp. apply to samples A, B, C, and D. The colors red, green, blue, and yellow (bottom mark to upper mark for each symbol) resp. apply to a low, medium-low, medium-high, and high luminance of the specular highlight.

Fig. 5.
Fig. 5.

Overall glossiness estimates α^i plotted against visual gloss predictions VG for all 16 stimuli. Both the values of α^i and VG are rescaled between 0 and 100. Each stimulus is represented by a symbol/color combination, resp. representing the sample and the luminance of the specular highlight. Diamonds, circles, squares, and triangles resp. apply to samples A, B, C, and D. The colors red, green, blue, and yellow (from left to right for each symbol) resp. apply to a low, medium-low, medium-high, and high luminance of the specular highlight.

Fig. 6.
Fig. 6.

Preference probability matrix P, in which is indicated the average number of times pij that stimulus i is rated to be glossier than stimulus j.

Fig. 7.
Fig. 7.

2D plot of the observer positions in (PC1, PC2)-space.

Fig. 8.
Fig. 8.

Representation of the components scores of the 16 stimuli for PC1 and PC2, resp. denoted by red squares and green triangles.

Fig. 9.
Fig. 9.

Overall glossiness estimates α^i derived from visual assessments of the second group of observers only, plotted against visual gloss predictions VG for all 16 stimuli. Both the values of α^i and VG are rescaled between 0 and 100. Each stimulus is represented by a symbol/color combination, resp. representing the sample and the luminance of the specular highlight. Diamonds, circles, squares, and triangles resp. apply to samples A, B, C, and D. The colors red, green, blue, and yellow (from left to right for each symbol) resp. apply to a low, medium-low, medium-high, and high luminance of the specular highlight.

Tables (6)

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Table 1. Average Specular Gloss Values Obtained in Three Basic Geometries (20°, 60°, 85°), Expressed in SGU

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Table 2. Description of Each Stimulus, Together with the Calculated Average Lim and Lb (cd·m2)

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Table 3. Computed Values of the Coefficient of Consistency for Each Observer in Both Orders of Presentation, Respectively Denoted by ζ1 and ζ2, Listed Together with the Observers’ Average Coefficient of Consistency ζavg

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Table 4. Glossiness Estimates α^i of All 16 Stimuli, Listed Together with the Calculated Value of Y0.05 and the Glossiness Range

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Table 5. The Covariance Matrix Eigenvalues, Together with the Explained Variance of Each PC, for the Input Matrix Consisting of the Glossiness Estimates α^i Attributed by all 15 Observers to the 16 Stimuli

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Table 6. Stimulus Loadings for the First Two PCs

Equations (8)

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

u^ij=1/rk=1rxijk,
π^ij=1/2(u^iju^ji).
α^i=1nj=1nπ^ij.
πij=αiαj.
Y0.05=q0.95((Se/4N(r2r)n)1/2.
Se=i=1nj=1nk=1r(xijku^ij)2.
ζ=1[24d/(n34n)].
VG=28Lim1/321Lb1/3.

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