Wei-Feng Zhang and Dao-Qing Dai, "Spectral reflectance estimation from camera responses by support vector regression and a composite model," J. Opt. Soc. Am. A 25, 2286-2296 (2008)
Regression methods are widely used to estimate the spectral reflectance of object surfaces from camera responses. These methods are under the same problem setting as that to build an estimation function for each sampled wavelength separately, which means that the accuracy of the spectral estimation will be reduced when the training set is small. To improve the spectral estimation accuracy, we propose a novel estimating approach based on the support vector regression method. The proposed approach utilizes a composite modeling scheme, which formulates the RGB values and the sampled wavelength together as the input term to make the most use of the information from the training samples. Experimental results show that the proposed method can improve the recovery accuracy when the training set is small.
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Training, Validation, and Test Sets in the Experiment
Parameter
Training Set
Validation Set
Test Set
Data set
Munsell Matte
Agfa IT8.7/2
Paper, Macbeth CDC
Sample number
100, 200, 300, 600
288
426, 24
Table 2
Estimation Errors of Different Methods on the Test Seta
Error Terms
SNR
Wiener Estimation
Traditional setting
SVR
P-reg
P-kernel
G-kernel
D-kernel
P-kernel
G-kernel
RMSE
∞
Mean
0.0498
0.0476
0.0474
0.0465
0.0462
0.0476
0.0452
Std
0.0098
0.0106
0.0105
0.0102
0.0100
0.0104
0.0096
Max
0.0607
0.0592
0.0585
0.0574
0.0562
0.0581
0.0543
40
Mean
0.0552
0.0537
0.0534
0.0524
0.0529
0.0541
0.0513
Std
0.0118
0.0118
0.0121
0.0115
0.0119
0.0125
0.0110
Max
0.0719
0.0692
0.0686
0.0675
0.0666
0.0703
0.0645
30
Mean
0.0675
0.0659
0.0660
0.0655
0.0657
0.0667
0.0649
Std
0.0121
0.0129
0.0131
0.0117
0.0119
0.0136
0.0123
Max
0.0823
0.0816
0.0819
0.0799
0.0821
0.0827
0.0781
∞
Mean
1.681
1.727
1.647
1.679
1.634
1.680
1.619
Std
0.184
0.191
0.182
0.170
0.167
0.194
0.176
Max
2.181
2.233
2.220
2.119
2.133
2.342
2.106
40
Mean
6.055
6.566
6.474
5.886
6.328
6.423
5.675
Std
0.832
0.847
0.852
0.842
0.829
0.880
0.817
Max
7.558
8.011
7.897
7.348
7.610
8.325
7.191
30
Mean
10.62
11.14
10.90
10.57
11.02
10.77
10.23
Std
1.139
1.135
1.119
1.089
1.093
1.131
1.119
Max
13.27
13.87
13.24
12.74
12.74
13.11
12.56
The results are summarized over 10 trials with a training size of 100 samples. In every row the best result is labeled in bold type. P-reg, regularized polynomial models; G-kernel, Gaussian kernel with KRLS or SVR; P-kernel, polynomial kernel with KRLS or SVR; D-kernel, Dochon spline kernel with KRLS.
Table 3
Estimation Errors of Different Methods on the Test Seta
Error Trems
SNR
Wiener Estimation
Traditional Setting
SVR
P-reg
P-kernel
G-kernel
D-kernel
P-kernel
G-kernel
RMSE
∞
Mean
0.0499
0.0431
0.0429
0.0427
0.0428
0.0440
0.0432
Std
0.0083
0.0081
0.0078
0.0077
0.0080
0.0086
0.0083
Max
0.0589
0.0537
0.0528
0.0507
0.0511
0.0558
0.0521
40
Mean
0.0552
0.0507
0.0506
0.0502
0.0495
0.0510
0.0498
Std
0.0092
0.0098
0.0097
0.0093
0.0089
0.0109
0.0100
Max
0.0631
0.0618
0.0609
0.0604
0.0597
0.0625
0.0609
30
Mean
0.0682
0.0646
0.0642
0.0634
0.0634
0.0656
0.0631
Std
0.0104
0.0110
0.0112
0.0105
0.0103
0.0121
0.0117
Max
0.0797
0.0756
0.0753
0.0749
0.0742
0.0781
0.0756
∞
Mean
1.656
1.611
1.582
1.593
1.589
1.627
1.591
Std
0.179
0.183
0.176
0.168
0.166
0.193
0.175
Max
2.167
2.131
2.120
2.076
2.061
2.214
2.153
40
Mean
5.879
5.521
5.502
5.345
5.411
5.549
5.576
Std
0.824
0.819
0.816
0.817
0.804
0.831
0.813
Max
7.468
7.275
7.152
7.096
7.139
7.813
7.354
30
Mean
10.65
9.416
9.374
9.135
9.276
9.998
9.581
Std
1.094
0.982
0.971
0.924
0.933
1.136
0.0964
Max
12.78
11.92
11.48
11.37
11.40
12.41
11.56
The results are summarized over 10 trials with a training size of 600 samples. In every row the best result is labeled in bold type. P-reg, regularized polynomial models; G-kernel, Gaussian kernel with KRLS or SVR; P-kernel, polynomial kernel with KRLS or SVR; D-kernel, Dochon spline kernel with KRLS.
Tables (3)
Table 1
Training, Validation, and Test Sets in the Experiment
Parameter
Training Set
Validation Set
Test Set
Data set
Munsell Matte
Agfa IT8.7/2
Paper, Macbeth CDC
Sample number
100, 200, 300, 600
288
426, 24
Table 2
Estimation Errors of Different Methods on the Test Seta
Error Terms
SNR
Wiener Estimation
Traditional setting
SVR
P-reg
P-kernel
G-kernel
D-kernel
P-kernel
G-kernel
RMSE
∞
Mean
0.0498
0.0476
0.0474
0.0465
0.0462
0.0476
0.0452
Std
0.0098
0.0106
0.0105
0.0102
0.0100
0.0104
0.0096
Max
0.0607
0.0592
0.0585
0.0574
0.0562
0.0581
0.0543
40
Mean
0.0552
0.0537
0.0534
0.0524
0.0529
0.0541
0.0513
Std
0.0118
0.0118
0.0121
0.0115
0.0119
0.0125
0.0110
Max
0.0719
0.0692
0.0686
0.0675
0.0666
0.0703
0.0645
30
Mean
0.0675
0.0659
0.0660
0.0655
0.0657
0.0667
0.0649
Std
0.0121
0.0129
0.0131
0.0117
0.0119
0.0136
0.0123
Max
0.0823
0.0816
0.0819
0.0799
0.0821
0.0827
0.0781
∞
Mean
1.681
1.727
1.647
1.679
1.634
1.680
1.619
Std
0.184
0.191
0.182
0.170
0.167
0.194
0.176
Max
2.181
2.233
2.220
2.119
2.133
2.342
2.106
40
Mean
6.055
6.566
6.474
5.886
6.328
6.423
5.675
Std
0.832
0.847
0.852
0.842
0.829
0.880
0.817
Max
7.558
8.011
7.897
7.348
7.610
8.325
7.191
30
Mean
10.62
11.14
10.90
10.57
11.02
10.77
10.23
Std
1.139
1.135
1.119
1.089
1.093
1.131
1.119
Max
13.27
13.87
13.24
12.74
12.74
13.11
12.56
The results are summarized over 10 trials with a training size of 100 samples. In every row the best result is labeled in bold type. P-reg, regularized polynomial models; G-kernel, Gaussian kernel with KRLS or SVR; P-kernel, polynomial kernel with KRLS or SVR; D-kernel, Dochon spline kernel with KRLS.
Table 3
Estimation Errors of Different Methods on the Test Seta
Error Trems
SNR
Wiener Estimation
Traditional Setting
SVR
P-reg
P-kernel
G-kernel
D-kernel
P-kernel
G-kernel
RMSE
∞
Mean
0.0499
0.0431
0.0429
0.0427
0.0428
0.0440
0.0432
Std
0.0083
0.0081
0.0078
0.0077
0.0080
0.0086
0.0083
Max
0.0589
0.0537
0.0528
0.0507
0.0511
0.0558
0.0521
40
Mean
0.0552
0.0507
0.0506
0.0502
0.0495
0.0510
0.0498
Std
0.0092
0.0098
0.0097
0.0093
0.0089
0.0109
0.0100
Max
0.0631
0.0618
0.0609
0.0604
0.0597
0.0625
0.0609
30
Mean
0.0682
0.0646
0.0642
0.0634
0.0634
0.0656
0.0631
Std
0.0104
0.0110
0.0112
0.0105
0.0103
0.0121
0.0117
Max
0.0797
0.0756
0.0753
0.0749
0.0742
0.0781
0.0756
∞
Mean
1.656
1.611
1.582
1.593
1.589
1.627
1.591
Std
0.179
0.183
0.176
0.168
0.166
0.193
0.175
Max
2.167
2.131
2.120
2.076
2.061
2.214
2.153
40
Mean
5.879
5.521
5.502
5.345
5.411
5.549
5.576
Std
0.824
0.819
0.816
0.817
0.804
0.831
0.813
Max
7.468
7.275
7.152
7.096
7.139
7.813
7.354
30
Mean
10.65
9.416
9.374
9.135
9.276
9.998
9.581
Std
1.094
0.982
0.971
0.924
0.933
1.136
0.0964
Max
12.78
11.92
11.48
11.37
11.40
12.41
11.56
The results are summarized over 10 trials with a training size of 600 samples. In every row the best result is labeled in bold type. P-reg, regularized polynomial models; G-kernel, Gaussian kernel with KRLS or SVR; P-kernel, polynomial kernel with KRLS or SVR; D-kernel, Dochon spline kernel with KRLS.