The 1257 reflectance spectra of the chips in the Munsell Book of Color—Matte Finish Collection (Munsell Color, Baltimore, Md., 1976) were measured with a rapid acousto-optic spectrophotometer. Measured spectra were sampled from 400 to 700 nm at 5-nm intervals. The correlation matrix of this sample set was formed, and the characteristic vectors of this matrix were computed. It is shown, contradictory to earlier recommendations [
Psychon. Sci. 1,
369 (
1964)], that as many as eight characteristic spectra are needed to achieve good representation for all spectra.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
Eight Characteristic Vectors and Corresponding Eigenvalues for Munsell Colorsa
Normalized Amplitude of the Following Eigenvector
Wavelength (nm)
First
Second
Third
Fourth
Fifth
Sixth
Seventh
Eighth
400
0.1673
−0.0479
0.2434
−0.8923
0.2769
0.1513
−0.1091
−0.0392
0.1474
−0.0863
0.2267
−0.1868
−0.3863
−0.6154
0.5428
−0.2004
0.1369
−0.0974
0.1742
−0.011
−0.1933
−0.148
−0.0789
0.5319
0.1298
−0.1035
0.1646
0.0038
−0.1627
0.0098
−0.1436
0.3421
0.1264
−0.1068
0.1702
0.0285
−0.1663
0.0201
−0.1216
0.1184
0.1245
−0.1188
0.1666
0.0417
−0.1395
0.0455
−0.132
0.0289
0.1234
−0.1184
0.1556
0.0623
−0.1225
0.0548
−0.1136
−0.0101
0.1235
−0.1234
0.1495
0.073
−0.1187
0.0771
−0.1266
−0.0389
0.1237
−0.1302
0.1445
0.0787
−0.1064
0.0936
−0.1107
−0.0488
0.1228
−0.1348
0.1376
0.0829
−0.0937
0.1067
−0.0986
−0.0733
0.1228
−0.1406
0.1272
0.0823
−0.0739
0.1169
−0.0806
−0.0982
0.1232
−0.1468
0.1132
0.0837
−0.0466
0.1221
−0.0444
−0.1127
0.1236
−0.1514
0.0948
0.0823
−0.0089
0.1243
−0.0065
−0.114
0.1241
−0.1572
0.0806
0.0819
0.0216
0.1174
0.0256
−0.1291
0.1248
−0.1613
0.0657
0.0816
0.0488
0.1112
0.0499
−0.1285
0.1248
−0.1665
0.0406
0.0789
0.0924
0.0945
0.0823
−0.123
0.1256
−0.1717
0.0082
0.0755
0.1419
0.0626
0.1217
−0.0919
0.1254
−0.1722
−0.0203
0.0689
0.183
0.0363
0.1481
−0.0616
0.1251
−0.1681
−0.0472
0.0627
0.1981
0.0053
0.1571
−0.0228
0.1252
−0.1648
−0.0632
0.0568
0.2029
−0.014
0.1575
0.0055
500
0.1256
−0.1588
−0.0773
0.0494
0.2039
−0.025
0.1481
0.0297
0.1261
−0.1498
−0.1001
0.0373
0.1895
−0.045
0.1238
0.0569
0.1263
−0.1346
−0.1287
0.0198
0.1599
−0.0739
0.0774
0.0885
0.1266
−0.1219
−0.1542
0.0049
0.1313
−0.0945
0.0262
0.1002
0.1261
−0.1098
−0.1726
−0.0077
0.1022
−0.1141
−0.0188
0.1113
0.125
−0.0954
−0.1885
−0.0196
0.0633
−0.1281
−0.0685
0.1163
0.1244
−0.0788
−0.1999
−0.032
0.0226
−0.1357
−0.1133
0.1185
0.1245
−0.0663
−0.2056
−0.0392
−0.009
−0.1294
−0.1376
0.1085
0.1244
−0.0511
−0.2045
−0.0448
−0.0382
−0.1139
−0.1462
0.0914
0.1244
−0.0338
−0.2029
−0.0483
−0.0683
−0.0892
−0.1401
0.0454
0.125
−0.015
−0.1992
−0.0519
−0.0971
−0.0557
−0.1226
−0.017
0.1259
0.0002
−0.1977
−0.0552
−0.1186
−0.0282
−0.1122
−0.0656
0.1263
0.0115
−0.1945
−0.0565
−0.1324
−0.0076
−0.0995
−0.1002
0.1266
0.0236
−0.1892
−0.0577
−0.1461
0.0117
−0.0798
−0.1322
0.127
0.0359
−0.1815
−0.0567
−0.1561
0.0383
−0.0632
−0.1525
0.1277
0.0512
−0.1652
−0.0541
−0.1607
0.0713
−0.0227
−0.1553
0.1287
0.0693
−0.1441
−0.05
−0.1589
0.108
0.0193
−0.1381
0.1296
0.0838
−0.1224
−0.0422
−0.1518
0.1348
0.0606
−0.1112
0.1301
0.0961
−0.1023
−0.0355
−0.1378
0.1526
0.0897
−0.0787
0.1304
0.1113
−0.0773
−0.0256
−0.1154
0.1624
0.1182
−0.0258
600
0.1301
0.1256
−0.0495
−0.0146
−0.0829
0.1611
0.1394
0.024
0.1301
0.1359
−0.0279
−0.0035
−0.0573
0.1508
0.1498
0.0563
0.1297
0.1422
−0.0116
0.0058
−0.03
0.1336
0.1451
0.0889
0.1298
0.1463
−0.0041
0.0103
−0.0139
0.1204
0.1446
0.111
0.1291
0.1482
0.0032
0.0129
−0.0033
0.1129
0.1392
0.1219
0.1288
0.1507
0.0129
0.0206
0.0117
0.0971
0.1282
0.1282
0.1283
0.1524
0.0248
0.0263
0.0287
0.0791
0.1173
0.1328
0.1284
0.1538
0.0363
0.0321
0.0412
0.0553
0.0964
0.1292
0.1284
0.1539
0.0435
0.0371
0.051
0.0329
0.0736
0.1158
0.1283
0.1552
0.0512
0.0422
0.0596
0.0192
0.055
0.1031
0.1282
0.1544
0.0584
0.0463
0.0635
0.0019
0.0353
0.0828
0.1282
0.1547
0.0661
0.0508
0.0683
−0.0213
0.0108
0.0564
0.1281
0.1533
0.0709
0.0541
0.0778
−0.0414
−0.0169
0.0266
0.1284
0.1533
0.0779
0.0599
0.0834
−0.0657
−0.0472
−0.0005
0.1282
0.1535
0.0835
0.0639
0.0908
−0.0888
−0.0716
−0.0423
0.1284
0.153
0.0859
0.0655
0.099
−0.1103
−0.0976
−0.0694
0.1285
0.1529
0.0876
0.0674
0.1078
−0.1327
−0.1193
−0.1014
0.1283
0.1519
0.0876
0.0699
0.1131
−0.1502
−0.1344
−0.1221
0.1284
0.1524
0.087
0.0703
0.1158
−0.1643
−0.1532
−0.1463
0.1277
0.1481
0.0855
0.0722
0.1197
−0.1711
−0.1686
−0.1637
700
0.1267
0.1413
0.0808
0.07
0.1193
−0.175
−0.1697
−0.1772
Eigenvalues for the first, second, third, fourth, fifth, sixth, seventh, and eighth eigenvectors are 1129.2, 72.7, 28.8, 12.7, 5.0, 3.4, 2.2, and 0.8, respectively.
Table 2
xy Color Coordinates of Two Munsell Samples and Their Reconstructions with Two, Four, Six, and Eight Eigenvectorsa
Sample Coordinate
Original Spectrum
Two Vectors
Four Vectors
Six Vectors
Eight Vectors
Reconstruction
Error
Reconstruction
Error
Reconstruction
Error
Reconstruction
Error
5 B 7/8
x
0.226
0.231
0.005
0.226
−0.000
0.225
−0.001
0.226
0.000
y
0.260
0.278
0.018
0.259
−0.001
0.259
−0.001
0.260
0.000
5R 6/14
x
0.508
0.538
0.029
0.504
−0.005
0.516
0.008
0.520
0.012
y
0.317
0.429
0.111
0.285
−0.033
0.318
0.001
0.322
0.005
The spectra of the sample are shown in Figs. 2 and 3.
Table 3
Maximum and Average Errors of xy Color Coordinates
The error limit is defined as the difference between the original and the reconstructed spectral reflectances averaged over the wavelength band.
Tables (4)
Table 1
Eight Characteristic Vectors and Corresponding Eigenvalues for Munsell Colorsa
Normalized Amplitude of the Following Eigenvector
Wavelength (nm)
First
Second
Third
Fourth
Fifth
Sixth
Seventh
Eighth
400
0.1673
−0.0479
0.2434
−0.8923
0.2769
0.1513
−0.1091
−0.0392
0.1474
−0.0863
0.2267
−0.1868
−0.3863
−0.6154
0.5428
−0.2004
0.1369
−0.0974
0.1742
−0.011
−0.1933
−0.148
−0.0789
0.5319
0.1298
−0.1035
0.1646
0.0038
−0.1627
0.0098
−0.1436
0.3421
0.1264
−0.1068
0.1702
0.0285
−0.1663
0.0201
−0.1216
0.1184
0.1245
−0.1188
0.1666
0.0417
−0.1395
0.0455
−0.132
0.0289
0.1234
−0.1184
0.1556
0.0623
−0.1225
0.0548
−0.1136
−0.0101
0.1235
−0.1234
0.1495
0.073
−0.1187
0.0771
−0.1266
−0.0389
0.1237
−0.1302
0.1445
0.0787
−0.1064
0.0936
−0.1107
−0.0488
0.1228
−0.1348
0.1376
0.0829
−0.0937
0.1067
−0.0986
−0.0733
0.1228
−0.1406
0.1272
0.0823
−0.0739
0.1169
−0.0806
−0.0982
0.1232
−0.1468
0.1132
0.0837
−0.0466
0.1221
−0.0444
−0.1127
0.1236
−0.1514
0.0948
0.0823
−0.0089
0.1243
−0.0065
−0.114
0.1241
−0.1572
0.0806
0.0819
0.0216
0.1174
0.0256
−0.1291
0.1248
−0.1613
0.0657
0.0816
0.0488
0.1112
0.0499
−0.1285
0.1248
−0.1665
0.0406
0.0789
0.0924
0.0945
0.0823
−0.123
0.1256
−0.1717
0.0082
0.0755
0.1419
0.0626
0.1217
−0.0919
0.1254
−0.1722
−0.0203
0.0689
0.183
0.0363
0.1481
−0.0616
0.1251
−0.1681
−0.0472
0.0627
0.1981
0.0053
0.1571
−0.0228
0.1252
−0.1648
−0.0632
0.0568
0.2029
−0.014
0.1575
0.0055
500
0.1256
−0.1588
−0.0773
0.0494
0.2039
−0.025
0.1481
0.0297
0.1261
−0.1498
−0.1001
0.0373
0.1895
−0.045
0.1238
0.0569
0.1263
−0.1346
−0.1287
0.0198
0.1599
−0.0739
0.0774
0.0885
0.1266
−0.1219
−0.1542
0.0049
0.1313
−0.0945
0.0262
0.1002
0.1261
−0.1098
−0.1726
−0.0077
0.1022
−0.1141
−0.0188
0.1113
0.125
−0.0954
−0.1885
−0.0196
0.0633
−0.1281
−0.0685
0.1163
0.1244
−0.0788
−0.1999
−0.032
0.0226
−0.1357
−0.1133
0.1185
0.1245
−0.0663
−0.2056
−0.0392
−0.009
−0.1294
−0.1376
0.1085
0.1244
−0.0511
−0.2045
−0.0448
−0.0382
−0.1139
−0.1462
0.0914
0.1244
−0.0338
−0.2029
−0.0483
−0.0683
−0.0892
−0.1401
0.0454
0.125
−0.015
−0.1992
−0.0519
−0.0971
−0.0557
−0.1226
−0.017
0.1259
0.0002
−0.1977
−0.0552
−0.1186
−0.0282
−0.1122
−0.0656
0.1263
0.0115
−0.1945
−0.0565
−0.1324
−0.0076
−0.0995
−0.1002
0.1266
0.0236
−0.1892
−0.0577
−0.1461
0.0117
−0.0798
−0.1322
0.127
0.0359
−0.1815
−0.0567
−0.1561
0.0383
−0.0632
−0.1525
0.1277
0.0512
−0.1652
−0.0541
−0.1607
0.0713
−0.0227
−0.1553
0.1287
0.0693
−0.1441
−0.05
−0.1589
0.108
0.0193
−0.1381
0.1296
0.0838
−0.1224
−0.0422
−0.1518
0.1348
0.0606
−0.1112
0.1301
0.0961
−0.1023
−0.0355
−0.1378
0.1526
0.0897
−0.0787
0.1304
0.1113
−0.0773
−0.0256
−0.1154
0.1624
0.1182
−0.0258
600
0.1301
0.1256
−0.0495
−0.0146
−0.0829
0.1611
0.1394
0.024
0.1301
0.1359
−0.0279
−0.0035
−0.0573
0.1508
0.1498
0.0563
0.1297
0.1422
−0.0116
0.0058
−0.03
0.1336
0.1451
0.0889
0.1298
0.1463
−0.0041
0.0103
−0.0139
0.1204
0.1446
0.111
0.1291
0.1482
0.0032
0.0129
−0.0033
0.1129
0.1392
0.1219
0.1288
0.1507
0.0129
0.0206
0.0117
0.0971
0.1282
0.1282
0.1283
0.1524
0.0248
0.0263
0.0287
0.0791
0.1173
0.1328
0.1284
0.1538
0.0363
0.0321
0.0412
0.0553
0.0964
0.1292
0.1284
0.1539
0.0435
0.0371
0.051
0.0329
0.0736
0.1158
0.1283
0.1552
0.0512
0.0422
0.0596
0.0192
0.055
0.1031
0.1282
0.1544
0.0584
0.0463
0.0635
0.0019
0.0353
0.0828
0.1282
0.1547
0.0661
0.0508
0.0683
−0.0213
0.0108
0.0564
0.1281
0.1533
0.0709
0.0541
0.0778
−0.0414
−0.0169
0.0266
0.1284
0.1533
0.0779
0.0599
0.0834
−0.0657
−0.0472
−0.0005
0.1282
0.1535
0.0835
0.0639
0.0908
−0.0888
−0.0716
−0.0423
0.1284
0.153
0.0859
0.0655
0.099
−0.1103
−0.0976
−0.0694
0.1285
0.1529
0.0876
0.0674
0.1078
−0.1327
−0.1193
−0.1014
0.1283
0.1519
0.0876
0.0699
0.1131
−0.1502
−0.1344
−0.1221
0.1284
0.1524
0.087
0.0703
0.1158
−0.1643
−0.1532
−0.1463
0.1277
0.1481
0.0855
0.0722
0.1197
−0.1711
−0.1686
−0.1637
700
0.1267
0.1413
0.0808
0.07
0.1193
−0.175
−0.1697
−0.1772
Eigenvalues for the first, second, third, fourth, fifth, sixth, seventh, and eighth eigenvectors are 1129.2, 72.7, 28.8, 12.7, 5.0, 3.4, 2.2, and 0.8, respectively.
Table 2
xy Color Coordinates of Two Munsell Samples and Their Reconstructions with Two, Four, Six, and Eight Eigenvectorsa
Sample Coordinate
Original Spectrum
Two Vectors
Four Vectors
Six Vectors
Eight Vectors
Reconstruction
Error
Reconstruction
Error
Reconstruction
Error
Reconstruction
Error
5 B 7/8
x
0.226
0.231
0.005
0.226
−0.000
0.225
−0.001
0.226
0.000
y
0.260
0.278
0.018
0.259
−0.001
0.259
−0.001
0.260
0.000
5R 6/14
x
0.508
0.538
0.029
0.504
−0.005
0.516
0.008
0.520
0.012
y
0.317
0.429
0.111
0.285
−0.033
0.318
0.001
0.322
0.005
The spectra of the sample are shown in Figs. 2 and 3.
Table 3
Maximum and Average Errors of xy Color Coordinates