Juan L. Nieves, Javier Hernández-Andrés, Eva Valero, and Javier Romero, "Spectral-reflectance linear models for optical color-pattern recognition," Appl. Opt. 43, 1880-1891 (2004)
We propose a new method of color-pattern recognition by optical correlation that uses a linear description of spectral reflectance functions and the spectral power distribution of illuminants that contains few parameters. We report on a method of preprocessing color input scenes in which the spectral functions are derived from linear models based on principal-component analysis. This multichannel algorithm transforms the red-green-blue (RGB) components into a new set of components that permit a generalization of the matched filter operations that are usually applied in optical pattern recognition with more-stable results under changes in illumination in the source images. The correlation is made in the subspace spanned by the coefficients that describe all reflectances according to a suitable basis for linear representation. First we illustrate the method in a control experiment in which the scenes are captured under known conditions of illumination. The discrimination capability of the algorithm improves upon the conventional RGB multichannel decomposition used in optical correlators when scenes are captured under different illuminant conditions and is slightly better than color recognition based on uniform color spaces (e.g., the CIELab system). Then we test the coefficient method in situations in which the target is captured under a reference illuminant and the scene that contains the target under an unknown spectrally different illuminant. We show that the method prevents false alarms caused by changes in the illuminant and that only two coefficients suffice to discriminate polychromatic objects.
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RGB Components of the Six Color Areas of Objects O1–O4 under the D65 Illuminanta
Object
R
G
B
O1
64
96
29
70
137
97
126
42
37
104
125
78
130
22
74
53
56
78
O2
28
30
29
78
137
97
68
73
37
29
125
78
41
107
74
35
56
78
O3
70
57
112
60
80
97
104
14
73
68
37
78
53
16
34
102
65
78
O4
64
96
64
70
137
28
126
42
126
104
125
68
130
22
130
53
56
41
From left to right for each R, G, and B component, the column values correspond to each of the six color areas that compose objects O1–O4.
Table 2
RGB Color Difference ΔRGB between Color Object O1 Captured under the D65 Illuminant and Objects O2–O4 Captured under Each of the Test Illuminants
Test Illuminant
Color Difference ΔRGB
Object O2
Object O3
Object O4
D65
23
26
15
A
61
62
43
10,000K
57
57
40
Orange
22
32
21
Table 3
Correlation and Discrimination Results Obtained from Conventional RGB Multichannel Decomposition under Known Illuminant Conditionsa
Illuminant
Channel
Object
50% Threshold
O1
O2
O3
O4
D65
R
3.647 × 1014
2.517 × 1014
2.360 × 1014
2.793 × 1014
1.824 × 1014
G
4.311 × 1014
2.323 × 1014
1.917 × 1014
4.760 × 1014
2.380 × 1014
B
2.127 × 1014
9.851 × 1013
1.026 × 1014
2.165 × 1014
1.083 × 1014
Recognized
and
Yes
No
No
Yes
A
R
3.096 × 1014
2.099 × 1014
2.058 × 1014
2.319 × 1014
1.548 × 1014
G
1.616 × 1014
8.748 × 1013
7.114 × 1013
1.770 × 1014
8.852 × 1013
B
4.906 × 1013
2.426 × 1013
2.735 × 1013
5.305 × 1013
2.652 × 1013
Recognized
and
Yes
No
No
Yes
10,000K
R
1.413 × 1014
9.979 × 1013
9.440 × 1013
1.082 × 1014
7.065 × 1013
G
2.058 × 1014
1.108 × 1014
9.405 × 1013
2.260 × 1014
1.130 × 1014
B
1.252 × 1014
6.094 × 1013
6.322 × 1013
1.318 × 1014
6.590 × 1013
Recognized
and
Yes
No
No
Yes
Orange
R
5.252 × 1014
3.531 × 1014
3.274 × 1014
4.036 × 1014
2.626 × 1014
G
4.672 × 1014
2.523 × 1014
2.588 × 1015
5.175 × 1014
2.588 × 1014
B
1.344 × 1014
6.656 × 1013
7.272 × 1013
1.481 × 1014
5.740 × 1013
Recognized
and
Yes
No
Yes
Yes
The target is object O1 under illuminant D65.
Table 4
Correlation and Discrimination Results Obtained from Multichannel Decomposition Based on the CIELab Color Transformation under Known Illuminant Conditionsa
Illuminant
Channel
Object
50% Threshold
O1
O2
O3
O4
D65
L*
1.246 × 1011
8.977 × 1010
7.685 × 1010
1.320 × 1011
6.814 × 1010
a*
5.564 × 1012
1.251 × 1012
1.538 × 1012
4.219 × 1012
2.782 × 1012
b*
2.969 × 108
7.672 × 107
1.157 × 108
1.004 × 108
1.485 × 108
Recognized
and
Yes
No
No
No
A
L*
1.313 × 1013
1.072 × 1013
9.742 × 1012
1.279 × 1013
6.566 × 1012
a*
1.430 × 1014
2.984 × 1013
3.490 × 1013
1.098 × 1014
7.149 × 1013
b*
6.505 × 109
2.627 × 109
3.485 × 109
3.262 × 108
3.253 × 109
Recognized
and
Yes
No
No
Yes
10,000K
L*
9.757 × 103
9.896 × 103
9.963 × 103
9.768 × 103
5.228 × 103
a*
5.705 × 102
1.279 × 102
2.000 × 102
4.517 × 102
2.852 × 102
b*
3.800 × 102
1.510 × 102
8.100 × 103
1.250 × 102
1.900 × 102
Recognized
and
Yes
No
No
No
Orange
L*
1.234 × 1013
1.003 × 1013
9.408 × 1012
1.212 × 1013
6.169 × 1012
a*
1.333 × 1014
2.669 × 1013
3.652 × 1013
9.997 × 1013
6.664 × 1013
b*
6.294 × 109
2.140 × 109
3.382 × 109
2.144 × 109
3.147 × 109
Recognized
and
Yes
No
No
No
The target is object O1 under illuminant D65.
Table 5
Correlation and Discrimination Results Obtained from Multichannel Decomposition Expressed as Three Coefficients under Known Illuminant Conditionsa
Illuminant
Channel
Object
50% Threshold
O1
O2
O3
O4
D65
Coefficient 1
7.880 × 10-2
5.710 × 10-2
6.157 × 10-2
5.828 × 10-2
3.940 × 10-2
Coefficient 2
2.196 × 10-3
1.142 × 10-5
1.071 × 10-5
2.400 × 10-3
1.200 × 10-3
Coefficient 3
3.050 × 10-4
4.342 × 10-5
6.078 × 10-5
1.103 × 10-4
1.525 × 10-4
Recognized
and
Yes
No
No
No
A
Coefficient 1
8.020 × 10-2
5.896 × 10-2
6.356 × 10-2
5.997 × 10-2
4.010 × 10-2
Coefficient 2
2.110 × 10-3
1.064 × 10-5
1.274 × 10-4
2.291 × 10-3
1.150 × 10-3
Coefficient 3
2.663 × 10-4
3.140 × 10-5
6.910 × 10-5
9.648 × 10-5
1.332 × 10-4
Recognized
and
Yes
No
No
No
10,000K
Coefficient 1
7.690 × 10-2
5.516 × 10-2
6.013 × 10-2
5.674 × 10-2
3.845 × 10-2
Coefficient 2
2.400 × 10-3
1.164 × 10-5
9.621 × 10-5
2.401 × 10-3
1.200 × 10-3
Coefficient 3
2.995 × 10-4
4.133 × 10-5
6.622 × 10-5
1.011 × 10-4
1.497 × 10-4
Recognized
and
Yes
No
No
No
Orange
Coefficient 1
8.060 × 10-2
5.863 × 10-2
6.270 × 10-2
5.987 × 10-2
4.030 × 10-2
Coefficient 2
2.180 × 10-3
1.049 × 10-5
1.122 × 10-4
2.400 × 10-3
1.200 × 10-3
Coefficient 3
2.838 × 10-4
3.820 × 10-5
5.989 × 10-5
1.029 × 10-4
1.419 × 10-4
Recognized
and
Yes
No
No
No
The target is object O1 under illuminant D65.
Table 6
GFC and Root-Mean-Square Error Obtained for the Four Test Illuminants
Illuminant
GFC
Root-Mean-Square Error
1
0.9746
0.1685
2
0.9896
0.0964
3
0.9945
0.1087
4
0.9962
0.0567
Table 7
Correlation and Discrimination Results Obtained from Conventional RGB Multichannel Decomposition under Several Unknown Illuminant Conditionsa
Illuminant
Channel
Object
50% Threshold
O1
O2
O3
O4
Test 1
R
5.356 × 1014
3.583 × 1014
3.286 × 1014
4.093 × 1014
2.678 × 1014
G
3.506 × 1014
1.893 × 1014
1.513 × 1014
3.882 × 1014
1.941 × 1014
B
8.047 × 1013
3.983 × 1013
4.351 × 1013
9.074 × 1013
4.537 × 1013
Recognized
and
Yes
No
No
Yes
Test 2
R
1.573 × 1014
1.106 × 1014
1.026 × 1014
1.211 × 1014
7.865 × 1013
G
2.614 × 1014
1.408 × 1014
1.179 × 1014
2.888 × 1014
1.444 × 1014
B
1.609 × 1014
7.847 × 1013
8.069 × 1013
1.698 × 1014
8.490 × 1013
Recognized
and
Yes
No
No
Yes
Test 3
R
5.074 × 1014
3.422 × 1014
3.195 × 1014
3.879 × 1014
2.537 × 1014
G
5.098 × 1014
2.741 × 1014
2.233 × 1014
5.644 × 1014
2.822 × 1014
B
1.825 × 1014
8.900 × 1013
9.556 × 1013
2.007 × 1014
1.004 × 1014
Recognized
and
Yes
No
No
Yes
Test 4
R
2.626 × 1014
1.759 × 1014
1.755 × 1014
1.966 × 1014
1.131 × 1014
G
9.639 × 1013
5.274 × 1013
4.263 × 1013
1.059 × 1014
5.296 × 1013
B
1.777 × 1013
9.175 × 1012
1.060 × 1013
1.976 × 1013
9.875 × 1012
Recognized
and
Yes
No
No
Yes
The target is object O1 under illuminant D65.
Table 8
Correlation and Discrimination Results Obtained from Multichannel Decomposition Based on the CIELab Color Transformation under Several Unknown Illuminant Conditionsa
Illuminant
Channel
Object
50% Threshold
O1
O2
O3
O4
Test 1
L*
1.534 × 1013
1.249 × 1013
1.190 × 1013
1.359 × 1013
7.669 × 1012
a*
1.121 × 1014
1.666 × 1013
5.042 × 1013
8.032 × 1013
6.060 × 1013
b*
7.522 × 109
2.991 × 109
4.368 × 109
3.332 × 109
3.771 × 109
Recognized
and
Yes
No
No
No
Test 2
L*
1.412 × 1013
1.159 × 1013
1.064 × 1013
1.348 × 1013
7.062 × 1012
a*
1.973 × 1014
5.428 × 1013
2.569 × 1013
1.458 × 1014
9.866 × 1013
b*
8.708 × 109
3.164 × 109
3.705 × 109
3.646 × 109
4.354 × 109
Recognized
and
Yes
No
No
No
Test 3
L*
1.300 × 1013
1.059 × 1013
9.963 × 1012
1.281 × 1013
6.502 × 1012
a*
1.505 × 1014
3.383 × 1013
3.096 × 1013
1.116 × 1014
7.524 × 1013
b*
7.274 × 109
2.719 × 109
3.668 × 109
3.329 × 109
3.637 × 109
Recognized
and
Yes
No
No
No
Test 4
L*
1.492 × 1013
1.217 × 1013
1.216 × 1013
1.435 × 1013
7.461 × 1012
a*
5.331 × 1013
5.466 × 1013
5.270 × 1013
3.458 × 1013
2.733 × 1013
b*
6.154 × 109
3.056 × 109
3.785 × 109
3.370 × 109
3.077 × 109
Recognized
and
Yes
No
Yes
Yes
The target is object O1 under the illuminant D65.
Table 9
Correlation and Discrimination Results Obtained from Multichannel Decomposition Expressed as Three Coefficients under Several Unknown Illuminant Conditionsa
Illuminant
Channel
Object
50% Threshold
O1
O2
O3
O4
Test 1
Coefficient 1
1.105 × 10-1
8.050 × 10-2
8.261 × 10-2
8.371 × 10-2
5.525 × 10-2
Coefficient 2
2.870 × 10-3
2.135 × 10-5
4.405 × 10-5
3.110 × 10-3
1.550 × 10-3
Coefficient 3
4.646 × 10-4
6.796 × 10-5
6.240 × 10-5
1.853 × 10-4
2.320 × 10-4
Recognized
and
Yes
No
No
No
Test 2
Coefficient 1
9.854 × 10-2
6.897 × 10-2
7.295 × 10-2
7.393 × 10-2
4.925 × 10-2
Coefficient 2
2.740 × 10-3
1.858 × 10-5
1.104 × 10-4
2.951 × 10-3
1.500 × 10-3
Coefficient 3
4.230 × 10-4
5.746 × 10-5
5.595 × 10-5
1.459 × 10-4
2.115 × 10-4
Recognized
and
Yes
No
No
No
Test 3
Coefficient 1
7.586 × 10-2
5.408 × 10-2
5.766 × 10-2
5.656 × 10-2
3.795 × 10-2
Coefficient 2
2.014 × 10-3
1.462 × 10-5
1.112 × 10-4
2.172 × 10-3
1.100 × 10-3
Coefficient 3
3.099 × 10-4
4.198 × 10-5
4.116 × 10-5
1.137 × 10-4
1.549 × 10-4
Recognized
and
Yes
No
No
No
Test 4
Coefficient 1
9.616 × 10-2
7.111 × 10-2
7.481 × 10-2
7.331 × 10-2
4.810 × 10-2
Coefficient 2
2.418 × 10-3
1.264 × 10-5
1.552 × 10-4
2.604 × 10-3
1.300 × 10-3
Coefficient 3
3.621 × 10-4
3.820 × 10-5
5.628 × 10-5
1.416 × 10-4
1.810 × 10-4
Recognized
and
Yes
No
No
No
The target is object O1 under illuminant D65.
Tables (9)
Table 1
RGB Components of the Six Color Areas of Objects O1–O4 under the D65 Illuminanta
Object
R
G
B
O1
64
96
29
70
137
97
126
42
37
104
125
78
130
22
74
53
56
78
O2
28
30
29
78
137
97
68
73
37
29
125
78
41
107
74
35
56
78
O3
70
57
112
60
80
97
104
14
73
68
37
78
53
16
34
102
65
78
O4
64
96
64
70
137
28
126
42
126
104
125
68
130
22
130
53
56
41
From left to right for each R, G, and B component, the column values correspond to each of the six color areas that compose objects O1–O4.
Table 2
RGB Color Difference ΔRGB between Color Object O1 Captured under the D65 Illuminant and Objects O2–O4 Captured under Each of the Test Illuminants
Test Illuminant
Color Difference ΔRGB
Object O2
Object O3
Object O4
D65
23
26
15
A
61
62
43
10,000K
57
57
40
Orange
22
32
21
Table 3
Correlation and Discrimination Results Obtained from Conventional RGB Multichannel Decomposition under Known Illuminant Conditionsa
Illuminant
Channel
Object
50% Threshold
O1
O2
O3
O4
D65
R
3.647 × 1014
2.517 × 1014
2.360 × 1014
2.793 × 1014
1.824 × 1014
G
4.311 × 1014
2.323 × 1014
1.917 × 1014
4.760 × 1014
2.380 × 1014
B
2.127 × 1014
9.851 × 1013
1.026 × 1014
2.165 × 1014
1.083 × 1014
Recognized
and
Yes
No
No
Yes
A
R
3.096 × 1014
2.099 × 1014
2.058 × 1014
2.319 × 1014
1.548 × 1014
G
1.616 × 1014
8.748 × 1013
7.114 × 1013
1.770 × 1014
8.852 × 1013
B
4.906 × 1013
2.426 × 1013
2.735 × 1013
5.305 × 1013
2.652 × 1013
Recognized
and
Yes
No
No
Yes
10,000K
R
1.413 × 1014
9.979 × 1013
9.440 × 1013
1.082 × 1014
7.065 × 1013
G
2.058 × 1014
1.108 × 1014
9.405 × 1013
2.260 × 1014
1.130 × 1014
B
1.252 × 1014
6.094 × 1013
6.322 × 1013
1.318 × 1014
6.590 × 1013
Recognized
and
Yes
No
No
Yes
Orange
R
5.252 × 1014
3.531 × 1014
3.274 × 1014
4.036 × 1014
2.626 × 1014
G
4.672 × 1014
2.523 × 1014
2.588 × 1015
5.175 × 1014
2.588 × 1014
B
1.344 × 1014
6.656 × 1013
7.272 × 1013
1.481 × 1014
5.740 × 1013
Recognized
and
Yes
No
Yes
Yes
The target is object O1 under illuminant D65.
Table 4
Correlation and Discrimination Results Obtained from Multichannel Decomposition Based on the CIELab Color Transformation under Known Illuminant Conditionsa
Illuminant
Channel
Object
50% Threshold
O1
O2
O3
O4
D65
L*
1.246 × 1011
8.977 × 1010
7.685 × 1010
1.320 × 1011
6.814 × 1010
a*
5.564 × 1012
1.251 × 1012
1.538 × 1012
4.219 × 1012
2.782 × 1012
b*
2.969 × 108
7.672 × 107
1.157 × 108
1.004 × 108
1.485 × 108
Recognized
and
Yes
No
No
No
A
L*
1.313 × 1013
1.072 × 1013
9.742 × 1012
1.279 × 1013
6.566 × 1012
a*
1.430 × 1014
2.984 × 1013
3.490 × 1013
1.098 × 1014
7.149 × 1013
b*
6.505 × 109
2.627 × 109
3.485 × 109
3.262 × 108
3.253 × 109
Recognized
and
Yes
No
No
Yes
10,000K
L*
9.757 × 103
9.896 × 103
9.963 × 103
9.768 × 103
5.228 × 103
a*
5.705 × 102
1.279 × 102
2.000 × 102
4.517 × 102
2.852 × 102
b*
3.800 × 102
1.510 × 102
8.100 × 103
1.250 × 102
1.900 × 102
Recognized
and
Yes
No
No
No
Orange
L*
1.234 × 1013
1.003 × 1013
9.408 × 1012
1.212 × 1013
6.169 × 1012
a*
1.333 × 1014
2.669 × 1013
3.652 × 1013
9.997 × 1013
6.664 × 1013
b*
6.294 × 109
2.140 × 109
3.382 × 109
2.144 × 109
3.147 × 109
Recognized
and
Yes
No
No
No
The target is object O1 under illuminant D65.
Table 5
Correlation and Discrimination Results Obtained from Multichannel Decomposition Expressed as Three Coefficients under Known Illuminant Conditionsa
Illuminant
Channel
Object
50% Threshold
O1
O2
O3
O4
D65
Coefficient 1
7.880 × 10-2
5.710 × 10-2
6.157 × 10-2
5.828 × 10-2
3.940 × 10-2
Coefficient 2
2.196 × 10-3
1.142 × 10-5
1.071 × 10-5
2.400 × 10-3
1.200 × 10-3
Coefficient 3
3.050 × 10-4
4.342 × 10-5
6.078 × 10-5
1.103 × 10-4
1.525 × 10-4
Recognized
and
Yes
No
No
No
A
Coefficient 1
8.020 × 10-2
5.896 × 10-2
6.356 × 10-2
5.997 × 10-2
4.010 × 10-2
Coefficient 2
2.110 × 10-3
1.064 × 10-5
1.274 × 10-4
2.291 × 10-3
1.150 × 10-3
Coefficient 3
2.663 × 10-4
3.140 × 10-5
6.910 × 10-5
9.648 × 10-5
1.332 × 10-4
Recognized
and
Yes
No
No
No
10,000K
Coefficient 1
7.690 × 10-2
5.516 × 10-2
6.013 × 10-2
5.674 × 10-2
3.845 × 10-2
Coefficient 2
2.400 × 10-3
1.164 × 10-5
9.621 × 10-5
2.401 × 10-3
1.200 × 10-3
Coefficient 3
2.995 × 10-4
4.133 × 10-5
6.622 × 10-5
1.011 × 10-4
1.497 × 10-4
Recognized
and
Yes
No
No
No
Orange
Coefficient 1
8.060 × 10-2
5.863 × 10-2
6.270 × 10-2
5.987 × 10-2
4.030 × 10-2
Coefficient 2
2.180 × 10-3
1.049 × 10-5
1.122 × 10-4
2.400 × 10-3
1.200 × 10-3
Coefficient 3
2.838 × 10-4
3.820 × 10-5
5.989 × 10-5
1.029 × 10-4
1.419 × 10-4
Recognized
and
Yes
No
No
No
The target is object O1 under illuminant D65.
Table 6
GFC and Root-Mean-Square Error Obtained for the Four Test Illuminants
Illuminant
GFC
Root-Mean-Square Error
1
0.9746
0.1685
2
0.9896
0.0964
3
0.9945
0.1087
4
0.9962
0.0567
Table 7
Correlation and Discrimination Results Obtained from Conventional RGB Multichannel Decomposition under Several Unknown Illuminant Conditionsa
Illuminant
Channel
Object
50% Threshold
O1
O2
O3
O4
Test 1
R
5.356 × 1014
3.583 × 1014
3.286 × 1014
4.093 × 1014
2.678 × 1014
G
3.506 × 1014
1.893 × 1014
1.513 × 1014
3.882 × 1014
1.941 × 1014
B
8.047 × 1013
3.983 × 1013
4.351 × 1013
9.074 × 1013
4.537 × 1013
Recognized
and
Yes
No
No
Yes
Test 2
R
1.573 × 1014
1.106 × 1014
1.026 × 1014
1.211 × 1014
7.865 × 1013
G
2.614 × 1014
1.408 × 1014
1.179 × 1014
2.888 × 1014
1.444 × 1014
B
1.609 × 1014
7.847 × 1013
8.069 × 1013
1.698 × 1014
8.490 × 1013
Recognized
and
Yes
No
No
Yes
Test 3
R
5.074 × 1014
3.422 × 1014
3.195 × 1014
3.879 × 1014
2.537 × 1014
G
5.098 × 1014
2.741 × 1014
2.233 × 1014
5.644 × 1014
2.822 × 1014
B
1.825 × 1014
8.900 × 1013
9.556 × 1013
2.007 × 1014
1.004 × 1014
Recognized
and
Yes
No
No
Yes
Test 4
R
2.626 × 1014
1.759 × 1014
1.755 × 1014
1.966 × 1014
1.131 × 1014
G
9.639 × 1013
5.274 × 1013
4.263 × 1013
1.059 × 1014
5.296 × 1013
B
1.777 × 1013
9.175 × 1012
1.060 × 1013
1.976 × 1013
9.875 × 1012
Recognized
and
Yes
No
No
Yes
The target is object O1 under illuminant D65.
Table 8
Correlation and Discrimination Results Obtained from Multichannel Decomposition Based on the CIELab Color Transformation under Several Unknown Illuminant Conditionsa
Illuminant
Channel
Object
50% Threshold
O1
O2
O3
O4
Test 1
L*
1.534 × 1013
1.249 × 1013
1.190 × 1013
1.359 × 1013
7.669 × 1012
a*
1.121 × 1014
1.666 × 1013
5.042 × 1013
8.032 × 1013
6.060 × 1013
b*
7.522 × 109
2.991 × 109
4.368 × 109
3.332 × 109
3.771 × 109
Recognized
and
Yes
No
No
No
Test 2
L*
1.412 × 1013
1.159 × 1013
1.064 × 1013
1.348 × 1013
7.062 × 1012
a*
1.973 × 1014
5.428 × 1013
2.569 × 1013
1.458 × 1014
9.866 × 1013
b*
8.708 × 109
3.164 × 109
3.705 × 109
3.646 × 109
4.354 × 109
Recognized
and
Yes
No
No
No
Test 3
L*
1.300 × 1013
1.059 × 1013
9.963 × 1012
1.281 × 1013
6.502 × 1012
a*
1.505 × 1014
3.383 × 1013
3.096 × 1013
1.116 × 1014
7.524 × 1013
b*
7.274 × 109
2.719 × 109
3.668 × 109
3.329 × 109
3.637 × 109
Recognized
and
Yes
No
No
No
Test 4
L*
1.492 × 1013
1.217 × 1013
1.216 × 1013
1.435 × 1013
7.461 × 1012
a*
5.331 × 1013
5.466 × 1013
5.270 × 1013
3.458 × 1013
2.733 × 1013
b*
6.154 × 109
3.056 × 109
3.785 × 109
3.370 × 109
3.077 × 109
Recognized
and
Yes
No
Yes
Yes
The target is object O1 under the illuminant D65.
Table 9
Correlation and Discrimination Results Obtained from Multichannel Decomposition Expressed as Three Coefficients under Several Unknown Illuminant Conditionsa
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