Abstract

Most empirical work on color constancy is based on simple laboratory models of natural viewing conditions. These typically consist of spots seen against uniform backgrounds or computer simulations of flat surfaces seen under spatially uniform illumination. We report measurements made under more natural viewing conditions. The experiments were conducted in a room where the illumination was under computer control. Observers used a projection colorimeter to set asymmetric color matches across a spatial illumination gradient. Observers’ matches can be described by either of two simple models. One model posits gain control in cone-specific pathways. This diagonal model may be linked to ideas about the action of early visual mechanisms. The other model posits that the observer estimates and corrects for changes in illumination but does so imperfectly. This equivalent illuminant model provides a link between human performance and computational models of color constancy.

© 1997 Optical Society of America

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1997 (2)

D. H. Brainard, W. T. Freeman, “Bayesian color constancy,” J. Opt. Soc. Am. A 14, 1393–1411 (1997).
[CrossRef]

D. H. Brainard, M. D. Rutherford, J. M. Kraft, “Color constancy compared: experiments with real image and color monitors,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S476 (1997).

1996 (7)

D. H. Brainard, W. A. Brunt, “The equivalent illuminant,” Invest. Ophthalmol. Visual Sci. Suppl. 37, S648 (1996).

J. M. Speigle, W. A. Brunt, D. H. Brainard, “Color constancy measured using three tasks,” Invest. Ophthalmol. Visual Sci. Suppl. 37, S1064 (1996).

I. Kuriki, K. Uchikawa, “Limitations of surface-color and apparent-color constancy,” J. Opt. Soc. Am. A 13, 1622–1636 (1996).
[CrossRef]

J. M. Speigle, D. H. Brainard, “Luminosity thresholds: effects of test chromaticity and ambient illumination,” J. Opt. Soc. Am. A 13, 436–451 (1996).
[CrossRef]

M. P. Lucassen, J. Walraven, “Color constancy under natural and artificial illumination,” Vision Res. 36, 2699–2711 (1996).
[CrossRef] [PubMed]

E. J. Chichilnisky, B. A. Wandell, “Seeing gray through the on and off pathways,” Visual Neurosi. 13, 591–596 (1996).
[PubMed]

E. W. Jin, S. K. Shevell, “Color memory and color constancy,” J. Opt. Soc. Am. A 13, 1981–1991 (1996).
[CrossRef]

1995 (2)

K. H. Bauml, “Illuminant changes under different surface collections: examining some principles of color appearance,” J. Opt. Soc. Am. A 12, 261–271 (1995).
[CrossRef]

E. J. Chichilnisky, B. A. Wandell, “Photoreceptor sensitivity changes explain color appearance shifts induced by large uniform backgrounds in dichoptic matching,” Vision Res. 35, 239–254 (1995).
[CrossRef] [PubMed]

1994 (1)

1993 (10)

D. H. Brainard, B. A. Wandell, E.-J. Chichilnisky, “Color constancy: from physics to appearance,” Curr. Direc. Psychol. Sci. 2, 165–170 (1993).

L. E. Arend, “How much does illuminant color affect unattributed colors?” J. Opt. Soc. Am. A 10, 2134–2147 (1993).
[CrossRef]

M. P. Lucassen, J. Walraven, “Quantifying color constancy: evidence for nonlinear processing of cone-specific contrast,” Vision Res. 33, 739–757 (1993).
[CrossRef] [PubMed]

M. D. Fairchild, R. S. Berns, “Image color-appearance specification through extension of CIELAB,” Color Res. Appl. 18, 178–190 (1993).
[CrossRef]

A. B. Poirson, B. A. Wandell, “Appearance of colored patterns—pattern–color separability,” J. Opt. Soc. Am. A 10, 2458–2470 (1993).
[CrossRef]

B. V. Funt, M. S. Drew, “Color space analysis of mutual illumination,” IEEE Trans. Pattern. Anal. Mach. Intell. 15, 1319–1326 (1993).
[CrossRef]

R. Mausfeld, R. Niederee, “An inquiry into relational concepts of colour, based on incremental principles of colour coding for minimal relational stimuli,” Perception 22, 427–462 (1993).
[PubMed]

M. D’Zmura, G. Iverson, “Color constancy. I. Basic theory of two-stage linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 10, 2148–2165 (1993).
[CrossRef]

M. D’Zmura, G. Iverson, “Color constancy. II. Results for two-stage linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 10, 2166–2180 (1993).
[CrossRef]

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

1992 (3)

1991 (3)

L. E. Arend, A. Reeves, J. Schirillo, R. Goldstein, “Simultaneous color constancy: papers with diverse Munsell values,” J. Opt. Soc. Am. A 8, 661–672 (1991).
[CrossRef] [PubMed]

J. M. Troost, C. M. de Weert, “Naming versus matching in color constancy,” Percept. Psychophys. 50, 591–602 (1991).
[CrossRef] [PubMed]

R. W. G. Hunt, “Revised colour-appearance model for related and unrelated colours,” Color Res. Appl. 16, 146–165 (1991).
[CrossRef]

1990 (3)

A. Valberg, B. Lange-Malecki, “‘Color constancy’ in Mondrian patterns: a partial cancellation of physical chromaticity shifts by simultaneous contrast,” Vision Res. 30, 371–380 (1990).
[CrossRef]

Y. Nayatani, K. Takahama, H. Sobagaki, K. Hashimoto, “Color-appearance model and chromatic adaptation transform,” Color Res. Appl. 15, 210–221 (1990).
[CrossRef]

D. A. Forsyth, “A novel algorithm for color constancy,” Int. J. Comput. Vis. 5, 5–36 (1990).
[CrossRef]

1989 (1)

D. Jameson, L. Hurvich, “Essay concerning color constancy,” Annu. Rev. Psychol. 40, 1–22 (1989).
[CrossRef] [PubMed]

1988 (1)

B. V. Funt, M. S. Drew, “Color constancy computation in near-Mondrian scenes using a finite dimensional linear model,” IEEE Trans. Comput. Vis. Pattern Recog. (1988).

1987 (1)

1986 (3)

1984 (1)

A. Gilchrist, A. Jacobsen, “Perception of lightness and illumination in a world of one reflectance,” Perception 13, 5–19 (1984).
[PubMed]

1983 (1)

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

1982 (1)

J. S. Werner, J. Walraven, “Effect of chromatic adaptation on the achromatic locus: the role of contrast, luminance and background color,” Vision Res. 22, 929–944 (1982).
[CrossRef] [PubMed]

1980 (2)

A. L. Gilchrist, “When does perceived lightness depend on perceived spatial arrangements?” Percept. Psychophys. 28, 527–538 (1980).
[CrossRef] [PubMed]

G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
[CrossRef]

1978 (1)

S. K. Shevell, “The dual role of chromatic backgrounds in color perception,” Vision Res. 18, 1649–1661 (1978).
[CrossRef] [PubMed]

1977 (1)

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

1976 (2)

J. J. McCann, S. P. McKee, T. H. Taylor, “Quantitative studies in retinex theory: a comparison between theoretical predictions and observer responses to the ‘color Mondrian’ experiments,” Vision Res. 16, 445–458 (1976).
[CrossRef]

J. Walraven, “Discounting the background: the missing link in the explanation of chromatic induction,” Vision Res. 16, 289–295 (1976).
[CrossRef]

1975 (1)

V. Smith, J. Pokorny, “ Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

1967 (1)

W. S. Stiles, “Mechanism concepts in colour theory,” J. Colour Group 11, 106–123 (1967).

1964 (2)

R. M. Evans, “Variables of perceived color,” J. Opt. Soc. Am. 54, 1467–1474 (1964).
[CrossRef] [PubMed]

D. Jameson, L. M. Hurvich, “Theory of brightness and color contrast in human vision,” Vision Res. 4, 135–154 (1964).
[CrossRef] [PubMed]

1957 (2)

1952 (1)

1950 (1)

D. Nickerson, D. H. Wilson, “Munsell reference colors now specified for nine illuminants,” Illum. Eng. 45, 507–517 (1950).

1943 (1)

1940 (2)

H. Helson, V. B. Jeffers, “Fundamental problems in color vision. II. Hue, lightness, and saturation of selective samples in chromatic illumination,” J. Exp. Psychol. 26, 1–27 (1940).
[CrossRef]

D. B. Judd, “Hue saturation and lightness of surface colors with chromatic illumination,” J. Opt. Soc. Am. 30, 2–32 (1940).
[CrossRef]

1938 (1)

H. Helson, “Fundamental problems in color vision. I. The principle governing changes in hue, saturation and lightness of non-selective samples in chromatic illumination,” J. Exp. Psychol. 23, 439–476 (1938).
[CrossRef]

Adelson, E. H.

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

E. H. Adelson, A. P. Pentland, “The perception of shading and reflectance,” in Visual Perception: Computation and Psychophysics, D. Knill, W. Richards eds. (Cambridge U. Press, New York, 1996).

Arend, L. E.

Bauml, K. H.

K. H. Bauml, “Illuminant changes under different surface collections: examining some principles of color appearance,” J. Opt. Soc. Am. A 12, 261–271 (1995).
[CrossRef]

K. H. Bauml, “Color appearance: effects of illumant changes under different surface collections,” J. Opt. Soc. Am. A 11, 531–542 (1994).
[CrossRef]

K. H. Bauml, “Color constancy in a Mondrian world,” presented at the conference “From Genes to Perception,”Tübingen, Germany, September 5–7, 1996.

K. H. Bauml, Institut fur Psychologie, Universität Regensburg, Regensburg, Germany, 1996 (personal communication).

Berns, R. S.

M. D. Fairchild, R. S. Berns, “Image color-appearance specification through extension of CIELAB,” Color Res. Appl. 18, 178–190 (1993).
[CrossRef]

Boring, E. G.

E. G. Boring, Sensation and Perception in the History of Experimental Psychology (D. Appleton Century, New York, 1942).

Boynton, R. M.

P. K. Kaiser, R. M. Boynton, Human Color Vision, 2nd ed. (Optical Society of America, Washington, D.C., 1996).

Brainard, D. H.

D. H. Brainard, W. T. Freeman, “Bayesian color constancy,” J. Opt. Soc. Am. A 14, 1393–1411 (1997).
[CrossRef]

D. H. Brainard, M. D. Rutherford, J. M. Kraft, “Color constancy compared: experiments with real image and color monitors,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S476 (1997).

J. M. Speigle, D. H. Brainard, “Luminosity thresholds: effects of test chromaticity and ambient illumination,” J. Opt. Soc. Am. A 13, 436–451 (1996).
[CrossRef]

D. H. Brainard, W. A. Brunt, “The equivalent illuminant,” Invest. Ophthalmol. Visual Sci. Suppl. 37, S648 (1996).

J. M. Speigle, W. A. Brunt, D. H. Brainard, “Color constancy measured using three tasks,” Invest. Ophthalmol. Visual Sci. Suppl. 37, S1064 (1996).

D. H. Brainard, B. A. Wandell, E.-J. Chichilnisky, “Color constancy: from physics to appearance,” Curr. Direc. Psychol. Sci. 2, 165–170 (1993).

D. H. Brainard, B. A. Wandell, “Asymmetric color-matching: how color appearance depends on the illuminant,” J. Opt. Soc. Am. A 9, 1433–1448 (1992).
[CrossRef] [PubMed]

D. H. Brainard, B. A. Wandell, “A bilinear model of the illuminant’s effect on color appearance,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon eds. (MIT Press, Cambridge, Mass., 1991).

J. M. Speigle, D. H. Brainard, “Is color constancy task independent?” in Proceedings of the 4th Information Science and Technology/Society for Information Display Color Imaging Conference: Color Science, Systems, and Applications (Society for Imaging Science and Technology, Springfield, Va., 1996), pp. 167–172.

W. T. Freeman, D. H. Brainard, “Bayesian decision theory, the maximum local mass estimate, and color constancy,” in Proceedings of the 5th International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1995), pp. 210–217.

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Y. Nayatani, K. Takahama, H. Sobagaki, K. Hashimoto, “Color-appearance model and chromatic adaptation transform,” Color Res. Appl. 15, 210–221 (1990).
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R. W. G. Hunt, “Revised colour-appearance model for related and unrelated colours,” Color Res. Appl. 16, 146–165 (1991).
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Curr. Direc. Psychol. Sci. (1)

D. H. Brainard, B. A. Wandell, E.-J. Chichilnisky, “Color constancy: from physics to appearance,” Curr. Direc. Psychol. Sci. 2, 165–170 (1993).

IEEE Trans. Comput. Vis. Pattern Recog. (1)

B. V. Funt, M. S. Drew, “Color constancy computation in near-Mondrian scenes using a finite dimensional linear model,” IEEE Trans. Comput. Vis. Pattern Recog. (1988).

IEEE Trans. Pattern. Anal. Mach. Intell. (1)

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D. A. Forsyth, “A novel algorithm for color constancy,” Int. J. Comput. Vis. 5, 5–36 (1990).
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Invest. Ophthalmol. Visual Sci. Suppl. (3)

D. H. Brainard, M. D. Rutherford, J. M. Kraft, “Color constancy compared: experiments with real image and color monitors,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S476 (1997).

D. H. Brainard, W. A. Brunt, “The equivalent illuminant,” Invest. Ophthalmol. Visual Sci. Suppl. 37, S648 (1996).

J. M. Speigle, W. A. Brunt, D. H. Brainard, “Color constancy measured using three tasks,” Invest. Ophthalmol. Visual Sci. Suppl. 37, S1064 (1996).

J. Colour Group (1)

W. S. Stiles, “Mechanism concepts in colour theory,” J. Colour Group 11, 106–123 (1967).

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H. Helson, V. B. Jeffers, “Fundamental problems in color vision. II. Hue, lightness, and saturation of selective samples in chromatic illumination,” J. Exp. Psychol. 26, 1–27 (1940).
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J. Franklin Inst. (1)

G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
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J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (17)

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E. W. Jin, S. K. Shevell, “Color memory and color constancy,” J. Opt. Soc. Am. A 13, 1981–1991 (1996).
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M. D’Zmura, G. Iverson, “Color constancy. II. Results for two-stage linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 10, 2166–2180 (1993).
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I. Kuriki, K. Uchikawa, “Limitations of surface-color and apparent-color constancy,” J. Opt. Soc. Am. A 13, 1622–1636 (1996).
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[CrossRef] [PubMed]

D. H. Brainard, W. T. Freeman, “Bayesian color constancy,” J. Opt. Soc. Am. A 14, 1393–1411 (1997).
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P. DeMarco, J. Pokorny, V. C. Smith, “Full-spectrum cone sensitivity functions for X-chromosome-linked anomalous trichromats,” J. Opt. Soc. Am. A 9, 1465–1476 (1992).
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Percept. Psychophys. (3)

A. L. Gilchrist, “When does perceived lightness depend on perceived spatial arrangements?” Percept. Psychophys. 28, 527–538 (1980).
[CrossRef] [PubMed]

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

J. M. Troost, C. M. de Weert, “Naming versus matching in color constancy,” Percept. Psychophys. 50, 591–602 (1991).
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Perception (2)

A. Gilchrist, A. Jacobsen, “Perception of lightness and illumination in a world of one reflectance,” Perception 13, 5–19 (1984).
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For the perceived-surface-color task, which we do not believe our observers were performing, the mean constancy index from Arend et al.27 was 0.44, still lower than ours. In recent experiments, however, Bauml51 has found a mean constancy index of 0.78 for a perceived-surface-color task.

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Figures (12)

Fig. 1
Fig. 1

Experimental room. The room is 89×114. Its walls and ceiling were painted a matte gray of roughly 50% reflectance; its floor was covered with a gray carpet. Other objects in the room were visible to the observer, including a brown metal bookcase and a white table. Ambient illumination was provided by 12 theater stage lamps, labeled R, G, and B, arranged in four triads. Gradients of illumination were provided by an additional lamp, indicated by the rectangle labeled 1. The observer viewed test and match surfaces located on the far wall of the room. The match surface was spot illuminated by a projection colorimeter. Both test and match surfaces were surrounded by a 1/4 black felt border. The background for the surfaces was a 48×72 sheet of particle board painted the same gray as the room. Locations indicated by the figure are approximate.

Fig. 2
Fig. 2

Typical results from Experiment 1. (a) CIE xy chromaticity plot, (b) luminance versus x chromaticity. Open squares, coordinates of two test surfaces; solid squares, coordinates of matches made with different match surfaces. Each plotted point is the mean over replications for the same match surface.

Fig. 3
Fig. 3

Effect of match surface, Experiment 1. The data show that changing the identity of the match surface does not affect observers’ matches. See description in text. (a) CIE x chromaticities of the comparison matches plotted against the CIE x chromaticity of the standard match; (b) CIE y chromaticities of the comparison matches plotted against the CIE y chromaticity of the standard match; (c) luminances of the comparison matches plotted against the luminance of the standard match. The data are collapsed across observers WAB and TES.

Fig. 4
Fig. 4

Results from Experiment 2a. (a), (b) Results for observer WAB; (c), (d) results for observer TES. Open squares, test surface coordinates; solid squares, match surface coordinates. Each corresponding pair of test and match surfaces is connected by a solid line. For each test surface, each plotted point was obtained by taking the mean match over replications and over match surfaces. Where visible, the error bars represent ±1 standard error of the mean. Error bars not visible are smaller than the plotted points.

Fig. 5
Fig. 5

Effect of match surface, Experiment 2a. The data again show that changing the identity of the match surface does not affect observers’ matches. See description in text. The format and observers are the same as for Fig. 3.

Fig. 6
Fig. 6

Results from Experiment 2b. To avoid overwhelming the plots, only a subset of the data for observer JMS is shown. The format is as for Fig. 4.

Fig. 7
Fig. 7

Color constancy, Experiment 2a: comparison of WAB’s asymmetric matches from Experiment 2a with physical measurements of the light reflected from the test surface when the surface is viewed under the match illuminant. Open squares, test surface coordinates; solid squares, match surface coordinates; solid circles, coordinates of the test surfaces under the match illuminant. If the observer were color constant, the solid squares and the solid circles would coincide. To avoid overwhelming the plot, results are shown only for a few typical test surfaces.

Fig. 8
Fig. 8

Experiment 2 model fit. Each bar in the histograms gives the mean CIELAB ΔE* prediction error for one model and observer. (a) Fits for Experiment 2a for observers WAB and TES; (b) fit for Experiment 2b for observers JMS, ASH, and PBE. Precision: each individual match is fitted with the mean match for the corresponding test surface, giving a bound on how well any model can fit the data. In (a) we show the precision both for Experiment 2a and for the symmetric matching conditions of Experiment 1. Affine: each individual match is predicted by the affine model applied to the cone coordinates of the corresponding test surface. Linear: each individual match is predicted by the linear model. Diagonal: diagonal model predictions. Equiv. Illum.: equivalent illuminant model predictions. Constancy: each individual match is predicted by the measurement of the corresponding color constancy prediction (see Subsection 4.F). No effect: each individual match is predicted by the cone excitation coordinates of the corresponding test surface, giving an estimate of the size of the effect of changing the illuminant. The CIELAB coordinates of the matches and predictions were computed with respect to a white point defined by the illuminant at the match location. Note that this illuminant differed between Experiments 1 and 2. Direct comparisons of CIELAB ΔE* values across different white points are less meaningful than comparisons of values computed for the same white point, since the accuracy of across-white-point comparisons depends critically on the adaptation model incorporated in the CIELAB calculation. The apparently lower match precision in Experiment 1 in comparison with that of Experiment 2 is probably not significant. The key comparisons in the figure are all of CIELAB ΔE* values computed for a single white point.

Fig. 9
Fig. 9

Scatterplots of model fits. Each subplot shows a scatterplot of predicted versus observed match cone coordinates. Each column shows data for L, M, or S cones. Top row, each individual match is predicted by the mean match for its test surface; next four rows, affine, linear, diagonal, and equivalent illuminant models. The model fitting procedure minimized CIELAB ΔE* predictive error. Data are for all five observers in Experiments 2a and 2b. Each observer’s data was fitted separately.

Fig. 10
Fig. 10

Scatterplots of model fits. Each subplot shows a scatterplot of predicted versus observed match cone coordinates. Each column shows data for L, M, or S cones. Top row, linear model; bottom row, diagonal model. The model fitting procedure minimized the squared predictive error in cone excitation space. Data are for all five observers in Experiments 2a and 2b. Each observer’s data was fitted separately.

Fig. 11
Fig. 11

Model fit: comparison of WAB’s asymmetric matches from Experiment 2a with the predictions of the diagonal and equivalent illuminant models. Open squares, test surface coordinates; solid squares, match surface coordinates; open circles, diagonal model; open triangles, equivalent illuminant model. To avoid overwhelming the plot, results are shown only for a few typical test surfaces.

Fig. 12
Fig. 12

Equivalent illuminants. Each row shows the coordinates of the equivalent illuminant (solid circles) for one observer. For comparison, the coordinates of the test illuminants (open squares) and match illuminants (solid squares) are also shown. If the observer were perfectly color constant, the solid circles would superpose on the closed squares. Top row, Experiment 2a, observer WAB; middle row, Experiment 2b, observer ASH; bottom row, Experiment 2b, observer PBE.

Tables (3)

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Table 1 Data for Experiment 2a, Observers WAB and TES a

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Table 2 Data for Experiment 2b, Observers JMS, ASH, and PBE a

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Table 3 Experimental Illuminants, Equivalent Illuminants, and Constancy Indices for Experiments 2a and b a

Equations (8)

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

rm=Art+a,
rm=Art.
CI=1-|em-e^em||em-et|,
s=Bsws,
e=Bewe,
r=T diag(Bewe)Bsws,
w^s=[T diag(Bew^et)Bs]-1rt.
rm=T diag(Bew^em)Bsw^s=T diag(Bew^em)Bs[T diag(Bew^et)Bs]-1rt=A(w^et,w^em)rt,

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