David H. Brainard, Wendy A. Brunt, and Jon M. Speigle, "Color constancy in the nearly natural image. 1. Asymmetric matches," J. Opt. Soc. Am. A 14, 2091-2110 (1997)
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.
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The table provides the Munsell designations for the test surfaces, chromaticities and luminances of the test surfaces under the test illuminant, and chromaticities and luminances of the observers’ asymmetric matches. Since the data indicate that there is no effect of match surface on the observers’ matches (see Figs. 2, 3, and 5), data are collapsed across match surfaces. The final three columns of the table provide a color constancy prediction based on measurements of the light reflected from the test surface when it was placed at the match location (with the colorimeter turned off). Chromaticities are 1931 CIE and Luminances are
Table 2
Data for Experiment 2b, Observers JMS, ASH, and PBE
a
Observer
Test Panel
Test
Test
Test
Match
Match
Match
Const.
Const.
Const.
JMS
N 2.75/
0.351
0.353
1.20
0.434
0.392
3.02
0.458
0.389
5.22
N 3/
0.354
0.358
1.71
0.432
0.393
3.93
0.461
0.391
7.42
N 3.5/
0.356
0.354
1.83
0.435
0.391
4.57
0.460
0.392
7.93
N 5/
0.352
0.353
4.08
0.424
0.395
10.11
0.456
0.392
17.62
5 B
0.295
0.337
1.11
0.391
0.400
3.80
0.406
0.381
4.37
5 B
0.302
0.346
1.60
0.378
0.408
4.23
0.411
0.390
6.39
5 B
0.258
0.343
2.49
0.330
0.402
5.92
0.364
0.392
9.34
5 B
0.254
0.341
6.20
0.320
0.405
16.62
0.360
0.391
23.18
5 G
0.323
0.386
0.98
0.413
0.418
3.62
0.428
0.416
3.99
5 G
0.327
0.379
1.46
0.415
0.424
3.79
0.434
0.410
6.08
5 G
0.297
0.411
1.40
0.385
0.445
4.75
0.403
0.434
5.37
5 G
0.299
0.409
2.44
0.373
0.446
6.67
0.406
0.433
9.66
5 G
0.285
0.426
3.04
0.354
0.468
8.14
0.389
0.448
11.53
5 G
0.285
0.422
5.84
0.357
0.473
16.93
0.389
0.448
22.94
5 Y
0.380
0.374
1.40
0.451
0.398
3.36
0.480
0.401
6.23
5 Y
0.444
0.411
2.43
0.499
0.415
7.21
0.520
0.417
11.52
5 Y
0.462
0.420
3.99
0.508
0.420
10.77
0.529
0.420
19.15
5 Y
0.451
0.420
6.03
0.508
0.427
19.39
0.522
0.422
28.61
2.2 YR
0.433
0.363
7.75
0.501
0.392
24.13
0.525
0.381
35.61
3 YR
0.457
0.366
2.24
0.515
0.380
6.60
0.538
0.383
10.63
5 R
0.421
0.346
1.07
0.500
0.370
3.44
0.514
0.376
4.92
5 R
0.414
0.350
1.71
0.492
0.375
4.46
0.508
0.380
7.87
5 R
0.476
0.339
1.57
0.530
0.361
5.25
0.555
0.363
7.54
5 R
0.449
0.344
2.72
0.522
0.366
7.52
0.537
0.371
13.22
5 R
0.496
0.337
2.70
0.553
0.352
7.41
0.568
0.360
13.31
5 R
0.455
0.345
6.28
0.522
0.369
21.07
0.536
0.376
30.82
5 P
0.353
0.327
1.76
0.423
0.359
3.59
0.464
0.369
7.63
5 P
0.359
0.303
1.62
0.429
0.347
4.76
0.468
0.352
6.99
5 P
0.359
0.295
2.87
0.420
0.333
7.37
0.473
0.343
12.47
5 P
0.352
0.310
6.55
0.422
0.354
18.95
0.462
0.358
28.10
4.3 PB
0.274
0.309
3.99
0.329
0.351
9.78
0.383
0.369
15.87
ASH
N 2.75/
0.344
0.357
1.21
0.420
0.391
3.33
0.447
0.403
5.05
N 3/
0.350
0.356
1.77
0.420
0.393
5.13
0.450
0.401
7.37
N 3.5/
0.350
0.353
1.81
0.421
0.396
5.82
0.453
0.398
7.65
N 5/
0.348
0.353
4.01
0.421
0.401
12.86
0.451
0.398
16.94
5 B
0.297
0.348
1.63
0.357
0.405
4.70
0.402
0.399
6.33
5 B
0.258
0.340
2.51
0.313
0.400
7.27
0.358
0.399
9.24
5 B
0.251
0.342
6.05
0.307
0.405
21.03
0.353
0.402
22.29
5 G
0.323
0.383
1.42
0.401
0.431
4.07
0.423
0.424
5.65
5 G
0.294
0.407
2.49
0.360
0.458
7.19
0.396
0.444
9.68
5 G
0.283
0.427
3.01
0.345
0.478
8.88
0.381
0.458
11.01
5 G
0.278
0.432
5.98
0.344
0.484
19.73
0.376
0.468
23.12
5 Y
0.374
0.372
1.49
0.439
0.396
3.44
0.468
0.410
6.47
5 Y
0.441
0.410
2.37
0.506
0.422
8.31
0.511
0.425
10.95
5 Y
0.459
0.420
4.05
0.523
0.424
13.84
0.519
0.430
18.72
5 Y
0.453
0.417
5.95
0.515
0.432
22.11
0.516
0.429
27.46
3 YR
0.454
0.365
2.19
0.511
0.378
6.81
0.531
0.389
9.97
5 R
0.420
0.346
1.02
0.480
0.371
2.94
0.510
0.381
4.52
5 R
0.404
0.356
1.83
0.472
0.379
5.01
0.497
0.391
8.09
5 R
0.474
0.339
1.52
0.535
0.358
5.51
0.550
0.367
6.87
5 R
0.449
0.344
2.67
0.512
0.368
9.31
0.530
0.377
12.27
5 R
0.490
0.336
2.59
0.548
0.357
9.71
0.563
0.363
12.28
5 R
0.455
0.346
6.12
0.523
0.369
25.25
0.532
0.380
28.19
5 P
0.352
0.328
1.69
0.423
0.369
4.39
0.455
0.379
6.94
5 P
0.356
0.295
2.82
0.420
0.341
9.41
0.463
0.351
11.51
5 P
0.351
0.311
6.92
0.406
0.348
23.67
0.457
0.364
28.68
4.3 PB
0.271
0.308
3.95
0.340
0.354
11.88
0.376
0.376
15.05
PBE
N 2.75/
0.370
0.350
0.98
0.429
0.382
2.45
0.456
0.398
4.30
N 3/
0.374
0.359
1.41
0.428
0.393
3.56
0.458
0.404
6.22
N 3.5/
0.374
0.354
1.56
0.420
0.390
3.88
0.458
0.399
6.71
N 5/
0.373
0.355
3.65
0.423
0.393
8.11
0.459
0.400
16.51
5 B
0.321
0.354
1.35
0.383
0.399
3.56
0.412
0.403
5.49
5 B
0.274
0.345
2.15
0.334
0.386
4.79
0.366
0.404
8.71
5 B
0.236
0.331
2.19
0.306
0.381
5.95
0.324
0.389
7.92
5 B
0.269
0.347
5.23
0.303
0.384
11.50
0.359
0.405
20.30
5 G
0.349
0.383
1.24
0.410
0.415
3.25
0.435
0.423
5.47
5 G
0.317
0.407
2.12
0.381
0.432
5.21
0.404
0.444
8.68
5 G
0.306
0.426
2.52
0.368
0.455
6.10
0.393
0.458
10.10
5 G
0.299
0.422
4.73
0.350
0.458
11.38
0.387
0.460
19.60
5 Y
0.403
0.373
1.22
0.449
0.397
2.91
0.479
0.410
5.67
5 Y
0.466
0.405
2.02
0.490
0.415
4.51
0.517
0.425
9.65
5 Y
0.483
0.415
3.52
0.511
0.422
7.24
0.525
0.429
17.51
5 Y
0.476
0.411
5.09
0.492
0.418
13.50
0.520
0.428
23.84
2.2 YR
0.457
0.362
6.73
0.492
0.393
17.90
0.523
0.389
30.13
3 YR
0.479
0.359
1.91
0.510
0.383
4.57
0.537
0.387
8.88
5 R
0.444
0.347
0.96
0.468
0.372
2.62
0.515
0.384
4.51
5 R
0.435
0.351
1.57
0.493
0.377
3.91
0.508
0.387
7.12
5 R
0.497
0.336
1.41
0.515
0.362
3.67
0.555
0.365
6.36
5 R
0.472
0.343
2.36
0.498
0.366
5.42
0.535
0.376
10.88
5 R
0.516
0.335
2.49
0.545
0.356
6.27
0.568
0.363
12.13
5 R
0.476
0.344
5.43
0.514
0.371
12.72
0.537
0.378
25.78
5 P
0.376
0.316
5.93
0.409
0.345
14.63
0.466
0.368
26.39
4.3 PB
0.290
0.312
3.41
0.322
0.337
6.89
0.384
0.377
13.70
5 PB
0.240
0.268
2.63
0.264
0.292
5.24
0.328
0.333
9.50
5 PB
0.266
0.290
5.16
0.276
0.312
9.87
0.360
0.355
19.92
5 YR
0.562
0.375
8.11
0.587
0.381
17.71
0.584
0.389
40.21
5 YR
0.550
0.376
5.61
0.565
0.382
13.68
0.576
0.392
27.46
5 YR
0.534
0.375
3.97
0.552
0.383
9.99
0.567
0.394
20.27
5 G
0.282
0.446
3.82
0.322
0.487
7.68
0.368
0.476
14.71
5 G
0.296
0.437
7.41
0.340
0.476
18.11
0.384
0.471
31.29
5 Y
0.502
0.424
5.02
0.519
0.421
12.14
0.533
0.434
24.04
The table provides the Munsell designations for the test surfaces, chromaticities and luminances of the test surfaces under the test illuminant, and chromaticities and luminances of the observers’ asymmetric matches. Data are collapsed across match surfaces. The final three columns of the table provide a color constancy prediction based on the measurements and calculation described in the text (see Subsection 4.F). Chromaticities are 1931 CIE and Luminances are
Table 3
Experimental Illuminants, Equivalent Illuminants, and Constancy Indices for Experiments 2a and b
a
Illuminant
WAB
TES
JMS
ASH
PBE
Test
0.318
0.317
0.346
0.351
0.371
Test
0.352
0.353
0.367
0.354
0.353
Test
22.16
22.33
20.72
19.49
16.46
Match
0.435
0.434
0.450
0.452
0.456
Match
0.394
0.394
0.401
0.398
0.398
Match
83.23
83.32
88.36
81.60
71.96
Equiv.
0.391
0.388
0.421
0.422
0.416
Equiv.
0.399
0.393
0.404
0.393
0.384
Equiv.
59.29
69.69
57.61
63.78
38.86
Constancy index
0.59
0.63
0.64
0.70
0.48
Chromaticity only
0.57
0.57
0.68
0.69
0.52
Luminance only
0.60
0.78
0.55
0.71
0.40
The top portion of the table provides the chromaticities and luminances of the measured test and match illuminants for each observer. It also gives the chromaticity and luminance of the equivalent illuminant derived from each observer’s asymmetric matches. Chromaticities are 1931 CIE and Luminances are The bottom portion of the table gives the constancy indices computed for each observer. The overall constancy indices were computed by expressing the illuminants in the CIELAB uniform color space. The chromaticity indices were computed from the CIE chromaticities of the illuminants. The luminance indices were computed from the luminances of the illuminants. The mean values of the constancy, chromaticity, and luminance indices are 0.61, 0.60, and 0.61, respectively.
The table provides the Munsell designations for the test surfaces, chromaticities and luminances of the test surfaces under the test illuminant, and chromaticities and luminances of the observers’ asymmetric matches. Since the data indicate that there is no effect of match surface on the observers’ matches (see Figs. 2, 3, and 5), data are collapsed across match surfaces. The final three columns of the table provide a color constancy prediction based on measurements of the light reflected from the test surface when it was placed at the match location (with the colorimeter turned off). Chromaticities are 1931 CIE and Luminances are
Table 2
Data for Experiment 2b, Observers JMS, ASH, and PBE
a
Observer
Test Panel
Test
Test
Test
Match
Match
Match
Const.
Const.
Const.
JMS
N 2.75/
0.351
0.353
1.20
0.434
0.392
3.02
0.458
0.389
5.22
N 3/
0.354
0.358
1.71
0.432
0.393
3.93
0.461
0.391
7.42
N 3.5/
0.356
0.354
1.83
0.435
0.391
4.57
0.460
0.392
7.93
N 5/
0.352
0.353
4.08
0.424
0.395
10.11
0.456
0.392
17.62
5 B
0.295
0.337
1.11
0.391
0.400
3.80
0.406
0.381
4.37
5 B
0.302
0.346
1.60
0.378
0.408
4.23
0.411
0.390
6.39
5 B
0.258
0.343
2.49
0.330
0.402
5.92
0.364
0.392
9.34
5 B
0.254
0.341
6.20
0.320
0.405
16.62
0.360
0.391
23.18
5 G
0.323
0.386
0.98
0.413
0.418
3.62
0.428
0.416
3.99
5 G
0.327
0.379
1.46
0.415
0.424
3.79
0.434
0.410
6.08
5 G
0.297
0.411
1.40
0.385
0.445
4.75
0.403
0.434
5.37
5 G
0.299
0.409
2.44
0.373
0.446
6.67
0.406
0.433
9.66
5 G
0.285
0.426
3.04
0.354
0.468
8.14
0.389
0.448
11.53
5 G
0.285
0.422
5.84
0.357
0.473
16.93
0.389
0.448
22.94
5 Y
0.380
0.374
1.40
0.451
0.398
3.36
0.480
0.401
6.23
5 Y
0.444
0.411
2.43
0.499
0.415
7.21
0.520
0.417
11.52
5 Y
0.462
0.420
3.99
0.508
0.420
10.77
0.529
0.420
19.15
5 Y
0.451
0.420
6.03
0.508
0.427
19.39
0.522
0.422
28.61
2.2 YR
0.433
0.363
7.75
0.501
0.392
24.13
0.525
0.381
35.61
3 YR
0.457
0.366
2.24
0.515
0.380
6.60
0.538
0.383
10.63
5 R
0.421
0.346
1.07
0.500
0.370
3.44
0.514
0.376
4.92
5 R
0.414
0.350
1.71
0.492
0.375
4.46
0.508
0.380
7.87
5 R
0.476
0.339
1.57
0.530
0.361
5.25
0.555
0.363
7.54
5 R
0.449
0.344
2.72
0.522
0.366
7.52
0.537
0.371
13.22
5 R
0.496
0.337
2.70
0.553
0.352
7.41
0.568
0.360
13.31
5 R
0.455
0.345
6.28
0.522
0.369
21.07
0.536
0.376
30.82
5 P
0.353
0.327
1.76
0.423
0.359
3.59
0.464
0.369
7.63
5 P
0.359
0.303
1.62
0.429
0.347
4.76
0.468
0.352
6.99
5 P
0.359
0.295
2.87
0.420
0.333
7.37
0.473
0.343
12.47
5 P
0.352
0.310
6.55
0.422
0.354
18.95
0.462
0.358
28.10
4.3 PB
0.274
0.309
3.99
0.329
0.351
9.78
0.383
0.369
15.87
ASH
N 2.75/
0.344
0.357
1.21
0.420
0.391
3.33
0.447
0.403
5.05
N 3/
0.350
0.356
1.77
0.420
0.393
5.13
0.450
0.401
7.37
N 3.5/
0.350
0.353
1.81
0.421
0.396
5.82
0.453
0.398
7.65
N 5/
0.348
0.353
4.01
0.421
0.401
12.86
0.451
0.398
16.94
5 B
0.297
0.348
1.63
0.357
0.405
4.70
0.402
0.399
6.33
5 B
0.258
0.340
2.51
0.313
0.400
7.27
0.358
0.399
9.24
5 B
0.251
0.342
6.05
0.307
0.405
21.03
0.353
0.402
22.29
5 G
0.323
0.383
1.42
0.401
0.431
4.07
0.423
0.424
5.65
5 G
0.294
0.407
2.49
0.360
0.458
7.19
0.396
0.444
9.68
5 G
0.283
0.427
3.01
0.345
0.478
8.88
0.381
0.458
11.01
5 G
0.278
0.432
5.98
0.344
0.484
19.73
0.376
0.468
23.12
5 Y
0.374
0.372
1.49
0.439
0.396
3.44
0.468
0.410
6.47
5 Y
0.441
0.410
2.37
0.506
0.422
8.31
0.511
0.425
10.95
5 Y
0.459
0.420
4.05
0.523
0.424
13.84
0.519
0.430
18.72
5 Y
0.453
0.417
5.95
0.515
0.432
22.11
0.516
0.429
27.46
3 YR
0.454
0.365
2.19
0.511
0.378
6.81
0.531
0.389
9.97
5 R
0.420
0.346
1.02
0.480
0.371
2.94
0.510
0.381
4.52
5 R
0.404
0.356
1.83
0.472
0.379
5.01
0.497
0.391
8.09
5 R
0.474
0.339
1.52
0.535
0.358
5.51
0.550
0.367
6.87
5 R
0.449
0.344
2.67
0.512
0.368
9.31
0.530
0.377
12.27
5 R
0.490
0.336
2.59
0.548
0.357
9.71
0.563
0.363
12.28
5 R
0.455
0.346
6.12
0.523
0.369
25.25
0.532
0.380
28.19
5 P
0.352
0.328
1.69
0.423
0.369
4.39
0.455
0.379
6.94
5 P
0.356
0.295
2.82
0.420
0.341
9.41
0.463
0.351
11.51
5 P
0.351
0.311
6.92
0.406
0.348
23.67
0.457
0.364
28.68
4.3 PB
0.271
0.308
3.95
0.340
0.354
11.88
0.376
0.376
15.05
PBE
N 2.75/
0.370
0.350
0.98
0.429
0.382
2.45
0.456
0.398
4.30
N 3/
0.374
0.359
1.41
0.428
0.393
3.56
0.458
0.404
6.22
N 3.5/
0.374
0.354
1.56
0.420
0.390
3.88
0.458
0.399
6.71
N 5/
0.373
0.355
3.65
0.423
0.393
8.11
0.459
0.400
16.51
5 B
0.321
0.354
1.35
0.383
0.399
3.56
0.412
0.403
5.49
5 B
0.274
0.345
2.15
0.334
0.386
4.79
0.366
0.404
8.71
5 B
0.236
0.331
2.19
0.306
0.381
5.95
0.324
0.389
7.92
5 B
0.269
0.347
5.23
0.303
0.384
11.50
0.359
0.405
20.30
5 G
0.349
0.383
1.24
0.410
0.415
3.25
0.435
0.423
5.47
5 G
0.317
0.407
2.12
0.381
0.432
5.21
0.404
0.444
8.68
5 G
0.306
0.426
2.52
0.368
0.455
6.10
0.393
0.458
10.10
5 G
0.299
0.422
4.73
0.350
0.458
11.38
0.387
0.460
19.60
5 Y
0.403
0.373
1.22
0.449
0.397
2.91
0.479
0.410
5.67
5 Y
0.466
0.405
2.02
0.490
0.415
4.51
0.517
0.425
9.65
5 Y
0.483
0.415
3.52
0.511
0.422
7.24
0.525
0.429
17.51
5 Y
0.476
0.411
5.09
0.492
0.418
13.50
0.520
0.428
23.84
2.2 YR
0.457
0.362
6.73
0.492
0.393
17.90
0.523
0.389
30.13
3 YR
0.479
0.359
1.91
0.510
0.383
4.57
0.537
0.387
8.88
5 R
0.444
0.347
0.96
0.468
0.372
2.62
0.515
0.384
4.51
5 R
0.435
0.351
1.57
0.493
0.377
3.91
0.508
0.387
7.12
5 R
0.497
0.336
1.41
0.515
0.362
3.67
0.555
0.365
6.36
5 R
0.472
0.343
2.36
0.498
0.366
5.42
0.535
0.376
10.88
5 R
0.516
0.335
2.49
0.545
0.356
6.27
0.568
0.363
12.13
5 R
0.476
0.344
5.43
0.514
0.371
12.72
0.537
0.378
25.78
5 P
0.376
0.316
5.93
0.409
0.345
14.63
0.466
0.368
26.39
4.3 PB
0.290
0.312
3.41
0.322
0.337
6.89
0.384
0.377
13.70
5 PB
0.240
0.268
2.63
0.264
0.292
5.24
0.328
0.333
9.50
5 PB
0.266
0.290
5.16
0.276
0.312
9.87
0.360
0.355
19.92
5 YR
0.562
0.375
8.11
0.587
0.381
17.71
0.584
0.389
40.21
5 YR
0.550
0.376
5.61
0.565
0.382
13.68
0.576
0.392
27.46
5 YR
0.534
0.375
3.97
0.552
0.383
9.99
0.567
0.394
20.27
5 G
0.282
0.446
3.82
0.322
0.487
7.68
0.368
0.476
14.71
5 G
0.296
0.437
7.41
0.340
0.476
18.11
0.384
0.471
31.29
5 Y
0.502
0.424
5.02
0.519
0.421
12.14
0.533
0.434
24.04
The table provides the Munsell designations for the test surfaces, chromaticities and luminances of the test surfaces under the test illuminant, and chromaticities and luminances of the observers’ asymmetric matches. Data are collapsed across match surfaces. The final three columns of the table provide a color constancy prediction based on the measurements and calculation described in the text (see Subsection 4.F). Chromaticities are 1931 CIE and Luminances are
Table 3
Experimental Illuminants, Equivalent Illuminants, and Constancy Indices for Experiments 2a and b
a
Illuminant
WAB
TES
JMS
ASH
PBE
Test
0.318
0.317
0.346
0.351
0.371
Test
0.352
0.353
0.367
0.354
0.353
Test
22.16
22.33
20.72
19.49
16.46
Match
0.435
0.434
0.450
0.452
0.456
Match
0.394
0.394
0.401
0.398
0.398
Match
83.23
83.32
88.36
81.60
71.96
Equiv.
0.391
0.388
0.421
0.422
0.416
Equiv.
0.399
0.393
0.404
0.393
0.384
Equiv.
59.29
69.69
57.61
63.78
38.86
Constancy index
0.59
0.63
0.64
0.70
0.48
Chromaticity only
0.57
0.57
0.68
0.69
0.52
Luminance only
0.60
0.78
0.55
0.71
0.40
The top portion of the table provides the chromaticities and luminances of the measured test and match illuminants for each observer. It also gives the chromaticity and luminance of the equivalent illuminant derived from each observer’s asymmetric matches. Chromaticities are 1931 CIE and Luminances are The bottom portion of the table gives the constancy indices computed for each observer. The overall constancy indices were computed by expressing the illuminants in the CIELAB uniform color space. The chromaticity indices were computed from the CIE chromaticities of the illuminants. The luminance indices were computed from the luminances of the illuminants. The mean values of the constancy, chromaticity, and luminance indices are 0.61, 0.60, and 0.61, respectively.