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†Louis D. Silverstein died on May 1, 2012, while working on the final revision of this paper at his home in Scottsdale, Arizona. Lou has been a long-time member of the Optical Society of America, and a contributor to JOSA A in particular, in addition to his commitment to the Society for Information Display (where he was a fellow and 2008 Otto Schade Award recipient), the Society for Imaging Science and Technology, and the Inter Society Color Council, which presented him its 2004 Macbeth Award.
Robert C. Carter and Louis D. Silverstein, "Perceiving color across scale: great and small, discrete and continuous," J. Opt. Soc. Am. A 29, 1346-1355 (2012)
We generalize, to images with continuously varying colors, our previously published model for comparing color differences of spatially discrete visual fields (icons, symbols) of disparate sizes. Our model is structural, including scattering of light by the intraocular media, followed by sparse retinal cone cell sampling of each physiological color primary. We use our model to show that small subtense of less than half a degree drastically reduces the number of discriminable colors available within a color gamut. The proposed generalization predicts and explains appearance of color fields having a wide range of subtenses (from to 44 deg in examples given).
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Multivariate Correlations of Cone Primary Attenuations Derived from Experiments of Jacobsen, Highnote, and Zhang–Wandell (for , , , and ; normalized to )
Cone Primary Attenuations
CS2010 Highnote
Zhang
dJacobsen
CS2010 Highnote
1.0000
0.9500
0.8885
Zhang
0.9500
1.0000
0.9050
dJacobsen
0.8885
0.9050
1.0000
Table 2.
Proportion of Target Contrast () That Is Lost to Scatteringa
Subtense (Arc Min)
Positive contrasts
0.059
0.108
0.175
0.256
0.346
Negative contrasts
0.055
0.103
0.171
0.252
0.341
Out of the target for positive contrasts, in for negative—based upon the van den Berg point spread function convolved with targets having specified subtenses.
Table 3.
Relation between Inverse Search Time () and CIEDE2000, as Mediated by Various Models of Effects of Subtense
Models of
Model
Proportion of Inverse Search Time Variance Explained by the Model,
Statistics Associated with Fig 3, Inverse Search Time versus CIEDE2000 Calculated from Tristimulus Values Preprocessed with the GM Using Zhang–Wandell Kernels and the van den Berg PSF
SSE
DFE
MSE
RMSE
12.357187449
117
0.105617
0.3249877
Parameter
Estimate
Approx. Std. Err.
Lower CL
Upper CL
Intercept
0.2838482652
0.10077022
0.0670307
0.49100222
RT
1.7924461538
0.04030976
1.71141942
1.87799599
Knee
14.028720798
0.86922935
12.1972424
16.6558905
Table 5.
Display Primary Tristimulus Values
R
84.65455
43.65
3.968182
G
71.725
143.45
23.90833
B
32.25
12.9
169.85
Table 6.
Example of Optimal Selection of Four Colors Corresponding to the 4-Color 2 Deg Result in Table 7
Color Number & Display Primary
Display Primary Intensity, Proportion of Maximum ()
Color 1 R
0
Color 1 G
1
Color 1 B
0
Color 2 R
0
Color 2 G
0.01052
Color 2 B
0
Color 3 R
1
Color 3 G
0.42987
Color 3 B
1
Color 4 R
0.00799
Color 4 G
0.02360
Color 4 B
0.57355
Table 7.
Maximized Minimum Color Difference (CIEDE2000) for 2 to 17 Colors
Contribution of the GM to Predicting Leeds Data Variance beyond Baseline
GM Correlation
GM
Baseline (Std. Tristimulus) Correlation
GM Contribution, Proportion of Variance Beyond Baseline
GM Contribution if 10% Errors of Measurement
44 deg standard
0.82
0.67
0.71
0.35
0.43
0.90
0.81
0.85
0.30
0.48
19 deg standard
0.74
0.55
0.47
0.42
0.48
0.92
0.85
0.86
0.39
0.65
2 deg standard
0.57
0.33
0.50
0.11
0.12
(boost 44 deg GM LD by 25%)
0.82
0.68
0.50
0.57
0.66
()
0.88
0.78
0.85
0.70
0.81
0.88
0.78
0.85
0.23
0.35
Tables (9)
Table 1.
Multivariate Correlations of Cone Primary Attenuations Derived from Experiments of Jacobsen, Highnote, and Zhang–Wandell (for , , , and ; normalized to )
Cone Primary Attenuations
CS2010 Highnote
Zhang
dJacobsen
CS2010 Highnote
1.0000
0.9500
0.8885
Zhang
0.9500
1.0000
0.9050
dJacobsen
0.8885
0.9050
1.0000
Table 2.
Proportion of Target Contrast () That Is Lost to Scatteringa
Subtense (Arc Min)
Positive contrasts
0.059
0.108
0.175
0.256
0.346
Negative contrasts
0.055
0.103
0.171
0.252
0.341
Out of the target for positive contrasts, in for negative—based upon the van den Berg point spread function convolved with targets having specified subtenses.
Table 3.
Relation between Inverse Search Time () and CIEDE2000, as Mediated by Various Models of Effects of Subtense
Models of
Model
Proportion of Inverse Search Time Variance Explained by the Model,
Statistics Associated with Fig 3, Inverse Search Time versus CIEDE2000 Calculated from Tristimulus Values Preprocessed with the GM Using Zhang–Wandell Kernels and the van den Berg PSF
SSE
DFE
MSE
RMSE
12.357187449
117
0.105617
0.3249877
Parameter
Estimate
Approx. Std. Err.
Lower CL
Upper CL
Intercept
0.2838482652
0.10077022
0.0670307
0.49100222
RT
1.7924461538
0.04030976
1.71141942
1.87799599
Knee
14.028720798
0.86922935
12.1972424
16.6558905
Table 5.
Display Primary Tristimulus Values
R
84.65455
43.65
3.968182
G
71.725
143.45
23.90833
B
32.25
12.9
169.85
Table 6.
Example of Optimal Selection of Four Colors Corresponding to the 4-Color 2 Deg Result in Table 7
Color Number & Display Primary
Display Primary Intensity, Proportion of Maximum ()
Color 1 R
0
Color 1 G
1
Color 1 B
0
Color 2 R
0
Color 2 G
0.01052
Color 2 B
0
Color 3 R
1
Color 3 G
0.42987
Color 3 B
1
Color 4 R
0.00799
Color 4 G
0.02360
Color 4 B
0.57355
Table 7.
Maximized Minimum Color Difference (CIEDE2000) for 2 to 17 Colors