In order to study color constancy, the color appearance of the center of a center–surround paradigm was measured by using multiple-alternative forced-response matching. The center was presented with (1) no surround, (2) an adjacent chromatic surround, or (3) a chromatic surround separated from the center by an achromatic gap. The center and the surrounds were presented under various simulated illuminants ranging from illuminant A to illuminant D75. We found that when no surround is present, color constancy fails; however, when surrounds are present, some degree of color constancy is displayed. We also found that color constancy is poor when chromatic induction is minimal. In addition, it was determined that, if the ratios of R, G, and B of the center to R, G, and B of the surround remain constant as the illuminant changes, color constancy results. (R, G, and B correspond to the outputs of the retinal color mechanisms.)
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Used with blue-green center.
Used with yellow center.
Table 2
Means and Standard Deviations (SD’s) of Chromaticity Coordinates u′ and v′ of Matching Colors Chosen for a Blue-Green Center under Various Illuminants and with Various Green-Surround Configurations
Illuminant
Surround
u′
υ′
Number of Trials
Mean
SD
Mean
SD
A
none
0.157
0.003
0.532
0.007
33
adjacent
0.158
0.003
0.505
0.012
33
distant
0.154
0.006
0.513
0.013
33
F2
none
0.147
0.003
0.516
0.008
27
adjacent
0.152
0.006
0.496
0.009
27
distant
0.147
0.005
0.499
0.009
27
B
none
0.132
0.004
0.495
0.006
24
adjacent
0.138
0.005
0.472
0.012
24
distant
0.134
0.005
0.482
0.007
24
D55
none
0.131
0.004
0.491
0.006
24
adjacent
0.134
0.006
0.466
0.007
24
distant
0.128
0.001
0.482
0.005
24
D65
none
0.130
0.004
0.480
0.008
24
adjacent
0.132
0.004
0.465
0.006
24
distant
0.131
0.005
0.473
0.007
24
C
none
0.129
0.003
0.473
0.005
66
adjacent
0.133
0.004
0.461
0.006
66
distant
0.130
0.003
0.469
0.007
66
Table 3
Measure of Difference between Perceived Colors of Blue-Green Centers with Green Surround under Various Illuminantsa
Illuminant Pair
Euclidean Distance for the Following Surround Condition
None
Adjacent
Distant
A, C
0.059
0.048
0.046
A, F2
0.018
0.011
0.016
F2, B
0.026
0.028
0.021
B, D55
0.004
0.007
0.006
D55, D65
0.011
0.002
0.009
D65, C
0.007
0.004
0.004
The Euclidean distance [Eq. (2)] was computed for matched colors for pairs of illuminants. Distances are given for no-surround, adjacent-surround, and distant-surround conditions. Separation between the colors of the most distant pair (A, C) is smaller when a surround is present, indicating the importance of surrounds in color constancy.
Table 4
Groups of Matched Colors for Which Tukey’s HSD Test Did Not Show a Statistically Significant Differencea
Center, Surround Colors
Surround Configuration
None
Adjacent
Distant
Blue-green, green
D55, D65
C, D65
C, D65
Blue-green, blue
A, F2
B, D55
D55, D65
C, D65
C, D65
Yellow, green
D65, D75
B, D55
B, D55
D55, C
D55, C
D65, D75
Yellow, blue
D55, C, D65
D55, C
Each row under each column lists two or three colors among which no significant difference could be demonstrated. For example, with a blue-green center and a green adjacent surround, Tukey’s HSD test showed no significant difference (α = 0.05) between matched colors for illuminants D55 and D65 (first row), nor did it demonstrate a significant difference between matched colors for illuminants C and D65 (second row). ANOVA was performed for each surround configuration to determine whether there was a significant difference between the matched colors for the different illuminants. If a significant difference was found, then Tukey’s HSD test was performed to compare the matched colors in a pairwise fashion.
Table 5
Data Collected for Experiments with a Blue-Green Center and Various Blue-Surround Configurationsa
Illuminant
Surround
u′
υ′
Number of Trials
Mean
SD
Mean
SD
A
none
0.156
0.004
0.526
0.006
33
adjacent
0.145
0.001
0.549
0.005
33
distant
0.151
0.006
0.523
0.012
33
F2
none
0.147
0.006
0.511
0.007
21
adjacent
0.145
0.002
0.545
0.010
21
distant
0.146
0.005
0.510
0.012
21
B
none
0.135
0.004
0.493
0.005
21
adjacent
0.130
0.006
0.511
0.010
21
distant
0.132
0.004
0.492
0.007
21
D55
none
0.130
0.004
0.494
0.005
21
adjacent
0.132
0.004
0.403
0.011
21
distant
0.131
0.005
0.493
0.008
21
D65
none
0.129
0.003
0.481
0.005
21
adjacent
0.134
0.004
0.500
0.010
21
distant
0.129
0.003
0.483
0.008
21
C
none
0.129
0.003
0.474
0.006
72
adjacent
0.132
0.005
0.496
0.012
72
distant
0.130
0.004
0.479
0.007
72
SD, standard deviation.
Table 6
Euclidean Distances between Matched Colors for a Blue-Green Center with Blue Surround under Pairs of Illuminants
Illuminant Pair
Euclidean Distance for the Following Surround Condition
None
Adjacent
Distant
A, C
0.059
0.050
0.046
A, F2
0.021
0.004
0.014
F2, B
0.024
0.037
0.023
B, D55
0.005
0.007
0.001
D55, D65
0.013
0.004
0.010
D65, C
0.007
0.005
0.004
Table 7
Data Collected for Experiments with Yellow Center with Various Green-Surround Configurations
Illuminant
Surround
u′
υ′
Number of Trials
Mean
SD
Mean
SD
B
none
0.242
0.003
0.545
0.002
12
adjacent
0.242
0.003
0.544
0.003
12
distant
0.240
0.003
0.544
0.003
12
D55
none
0.236
0.005
0.542
0.005
12
adjacent
0.238
0.002
0.541
0.004
12
distant
0.237
0.006
0.541
0.005
12
C
none
0.232
0.003
0.543
0.005
24
adjacent
0.236
0.006
0.538
0.005
24
distant
0.234
0.004
0.540
0.004
24
D65
none
0.227
0.004
0.543
0.005
12
adjacent
0.230
0.005
0.539
0.006
12
distant
0.228
0.004
0.543
0.006
12
D75
none
0.225
0.004
0.539
0.005
12
adjacent
0.230
0.004
0.539
0.006
12
distant
0.224
0.003
0.542
0.006
12
Table 8
Euclidean Distances between Matched Colors for a Yellow Center with Green Surround under Pairs of Illuminants
Illuminant Pair
Euclidean Distance for the Following Surround Configuration
None
Adjacent
Distant
B, D75
0.018
0.013
0.016
B, D55
0.006
0.005
0.004
D55, C
0.004
0.004
0.003
C, D65
0.005
0.005
0.007
D65, D75
0.005
0.000
0.004
Table 9
Data Collected for Experiments with a Yellow Center and Various Blue-Surround Configurations
Illuminant
Surround
u′
υ′
Number of Trials
Mean
SD
Mean
SD
B
none
0.242
0.003
0.545
0.003
12
adjacent
0.241
0.003
0.542
0.004
12
distant
0.241
0.003
0.543
0.004
12
D55
none
0.237
0.005
0.544
0.004
12
adjacent
0.236
0.005
0.539
0.004
12
distant
0.233
0.004
0.541
0.005
12
C
none
0.233
0.004
0.541
0.005
21
adjacent
0.236
0.007
0.539
0.005
21
distant
0.234
0.004
0.542
0.004
21
D65
none
0.228
0.001
0.543
0.004
9
adjacent
0.233
0.005
0.541
0.004
9
distant
0.228
0.002
0.538
0.004
9
D75
none
0.223
0.004
0.542
0.005
9
adjacent
0.227
0.004
0.536
0.005
9
distant
0.225
0.004
0.542
0.004
9
Table 10
Euclidean Distances between Matched Colors for a Yellow Center with Blue Surround under Pairs of Illuminants
Illuminant Pair
Euclidean Distance for the Following Surround Configuration
None
Adjacent
Distant
B, D75
0.019
0.015
0.016
B, D55
0.004
0.005
0.007
D55, C
0.006
0.000
0.010
C, D65
0.005
0.004
0.007
D65, D75
0.005
0.008
0.007
Table 11
Center-to-Surround Ratios for R, G, and B and R, G, and B Values for Matched Colors
The first column lists the designations of the center color, the surround color; and the illuminant, respectively (e.g., in the first row BG, G, and A indicate blue-green center, green surround, and illuminant A). In the second set of three columns are listed the R, G, and B values of the corresponding matched color. When the center-to-surround ratios of R, G, and B are the same (less than 2% difference) for two different illuminants, the R, G, and B values of the matched colors are quite similar.
Tables (11)
Table 1
Colorimetric Coordinates (u′, v′) of Center, Surround, and Achromatic-Gap Reflectances under Various Illuminants
Used with blue-green center.
Used with yellow center.
Table 2
Means and Standard Deviations (SD’s) of Chromaticity Coordinates u′ and v′ of Matching Colors Chosen for a Blue-Green Center under Various Illuminants and with Various Green-Surround Configurations
Illuminant
Surround
u′
υ′
Number of Trials
Mean
SD
Mean
SD
A
none
0.157
0.003
0.532
0.007
33
adjacent
0.158
0.003
0.505
0.012
33
distant
0.154
0.006
0.513
0.013
33
F2
none
0.147
0.003
0.516
0.008
27
adjacent
0.152
0.006
0.496
0.009
27
distant
0.147
0.005
0.499
0.009
27
B
none
0.132
0.004
0.495
0.006
24
adjacent
0.138
0.005
0.472
0.012
24
distant
0.134
0.005
0.482
0.007
24
D55
none
0.131
0.004
0.491
0.006
24
adjacent
0.134
0.006
0.466
0.007
24
distant
0.128
0.001
0.482
0.005
24
D65
none
0.130
0.004
0.480
0.008
24
adjacent
0.132
0.004
0.465
0.006
24
distant
0.131
0.005
0.473
0.007
24
C
none
0.129
0.003
0.473
0.005
66
adjacent
0.133
0.004
0.461
0.006
66
distant
0.130
0.003
0.469
0.007
66
Table 3
Measure of Difference between Perceived Colors of Blue-Green Centers with Green Surround under Various Illuminantsa
Illuminant Pair
Euclidean Distance for the Following Surround Condition
None
Adjacent
Distant
A, C
0.059
0.048
0.046
A, F2
0.018
0.011
0.016
F2, B
0.026
0.028
0.021
B, D55
0.004
0.007
0.006
D55, D65
0.011
0.002
0.009
D65, C
0.007
0.004
0.004
The Euclidean distance [Eq. (2)] was computed for matched colors for pairs of illuminants. Distances are given for no-surround, adjacent-surround, and distant-surround conditions. Separation between the colors of the most distant pair (A, C) is smaller when a surround is present, indicating the importance of surrounds in color constancy.
Table 4
Groups of Matched Colors for Which Tukey’s HSD Test Did Not Show a Statistically Significant Differencea
Center, Surround Colors
Surround Configuration
None
Adjacent
Distant
Blue-green, green
D55, D65
C, D65
C, D65
Blue-green, blue
A, F2
B, D55
D55, D65
C, D65
C, D65
Yellow, green
D65, D75
B, D55
B, D55
D55, C
D55, C
D65, D75
Yellow, blue
D55, C, D65
D55, C
Each row under each column lists two or three colors among which no significant difference could be demonstrated. For example, with a blue-green center and a green adjacent surround, Tukey’s HSD test showed no significant difference (α = 0.05) between matched colors for illuminants D55 and D65 (first row), nor did it demonstrate a significant difference between matched colors for illuminants C and D65 (second row). ANOVA was performed for each surround configuration to determine whether there was a significant difference between the matched colors for the different illuminants. If a significant difference was found, then Tukey’s HSD test was performed to compare the matched colors in a pairwise fashion.
Table 5
Data Collected for Experiments with a Blue-Green Center and Various Blue-Surround Configurationsa
Illuminant
Surround
u′
υ′
Number of Trials
Mean
SD
Mean
SD
A
none
0.156
0.004
0.526
0.006
33
adjacent
0.145
0.001
0.549
0.005
33
distant
0.151
0.006
0.523
0.012
33
F2
none
0.147
0.006
0.511
0.007
21
adjacent
0.145
0.002
0.545
0.010
21
distant
0.146
0.005
0.510
0.012
21
B
none
0.135
0.004
0.493
0.005
21
adjacent
0.130
0.006
0.511
0.010
21
distant
0.132
0.004
0.492
0.007
21
D55
none
0.130
0.004
0.494
0.005
21
adjacent
0.132
0.004
0.403
0.011
21
distant
0.131
0.005
0.493
0.008
21
D65
none
0.129
0.003
0.481
0.005
21
adjacent
0.134
0.004
0.500
0.010
21
distant
0.129
0.003
0.483
0.008
21
C
none
0.129
0.003
0.474
0.006
72
adjacent
0.132
0.005
0.496
0.012
72
distant
0.130
0.004
0.479
0.007
72
SD, standard deviation.
Table 6
Euclidean Distances between Matched Colors for a Blue-Green Center with Blue Surround under Pairs of Illuminants
Illuminant Pair
Euclidean Distance for the Following Surround Condition
None
Adjacent
Distant
A, C
0.059
0.050
0.046
A, F2
0.021
0.004
0.014
F2, B
0.024
0.037
0.023
B, D55
0.005
0.007
0.001
D55, D65
0.013
0.004
0.010
D65, C
0.007
0.005
0.004
Table 7
Data Collected for Experiments with Yellow Center with Various Green-Surround Configurations
Illuminant
Surround
u′
υ′
Number of Trials
Mean
SD
Mean
SD
B
none
0.242
0.003
0.545
0.002
12
adjacent
0.242
0.003
0.544
0.003
12
distant
0.240
0.003
0.544
0.003
12
D55
none
0.236
0.005
0.542
0.005
12
adjacent
0.238
0.002
0.541
0.004
12
distant
0.237
0.006
0.541
0.005
12
C
none
0.232
0.003
0.543
0.005
24
adjacent
0.236
0.006
0.538
0.005
24
distant
0.234
0.004
0.540
0.004
24
D65
none
0.227
0.004
0.543
0.005
12
adjacent
0.230
0.005
0.539
0.006
12
distant
0.228
0.004
0.543
0.006
12
D75
none
0.225
0.004
0.539
0.005
12
adjacent
0.230
0.004
0.539
0.006
12
distant
0.224
0.003
0.542
0.006
12
Table 8
Euclidean Distances between Matched Colors for a Yellow Center with Green Surround under Pairs of Illuminants
Illuminant Pair
Euclidean Distance for the Following Surround Configuration
None
Adjacent
Distant
B, D75
0.018
0.013
0.016
B, D55
0.006
0.005
0.004
D55, C
0.004
0.004
0.003
C, D65
0.005
0.005
0.007
D65, D75
0.005
0.000
0.004
Table 9
Data Collected for Experiments with a Yellow Center and Various Blue-Surround Configurations
Illuminant
Surround
u′
υ′
Number of Trials
Mean
SD
Mean
SD
B
none
0.242
0.003
0.545
0.003
12
adjacent
0.241
0.003
0.542
0.004
12
distant
0.241
0.003
0.543
0.004
12
D55
none
0.237
0.005
0.544
0.004
12
adjacent
0.236
0.005
0.539
0.004
12
distant
0.233
0.004
0.541
0.005
12
C
none
0.233
0.004
0.541
0.005
21
adjacent
0.236
0.007
0.539
0.005
21
distant
0.234
0.004
0.542
0.004
21
D65
none
0.228
0.001
0.543
0.004
9
adjacent
0.233
0.005
0.541
0.004
9
distant
0.228
0.002
0.538
0.004
9
D75
none
0.223
0.004
0.542
0.005
9
adjacent
0.227
0.004
0.536
0.005
9
distant
0.225
0.004
0.542
0.004
9
Table 10
Euclidean Distances between Matched Colors for a Yellow Center with Blue Surround under Pairs of Illuminants
Illuminant Pair
Euclidean Distance for the Following Surround Configuration
None
Adjacent
Distant
B, D75
0.019
0.015
0.016
B, D55
0.004
0.005
0.007
D55, C
0.006
0.000
0.010
C, D65
0.005
0.004
0.007
D65, D75
0.005
0.008
0.007
Table 11
Center-to-Surround Ratios for R, G, and B and R, G, and B Values for Matched Colors
The first column lists the designations of the center color, the surround color; and the illuminant, respectively (e.g., in the first row BG, G, and A indicate blue-green center, green surround, and illuminant A). In the second set of three columns are listed the R, G, and B values of the corresponding matched color. When the center-to-surround ratios of R, G, and B are the same (less than 2% difference) for two different illuminants, the R, G, and B values of the matched colors are quite similar.