Wei Dong, Hui-Liang Shen, Xin Du, Si-Jie Shao, and John H. Xin, "Spectral bidirectional texture function reconstruction by fusing multiple-color and spectral images," Appl. Opt. 55, 10400-10408 (2016)
Spectral bidirectional texture function (BTF) is essential for accurate reproduction of material appearance due to its nature of conveying both spatial and spectral information. A practical issue is that the acquisition of raw spectral BTFs is time-consuming. To resolve the limitation, this paper proposes a novel framework for efficient spectral BTF acquisition and reconstruction. The framework acquires red-green-blue (RGB) BTF images and just one spectral image. The full spectral BTFs are reconstructed by fusing the RGB and spectral images based on nonnegative matrix factorization (NMF). Experimental results indicate that the accuracy of spectral reflectance reconstruction is higher than that of existing algorithms. With the reconstructed spectral BTFs, the material appearance can be reproduced with high fidelity under various illumination conditions.
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Average Responses (Relative Error) of the Mean BTF Images, with The BTF Images Simulated from the Sandpaper and Cylinder Surfaces, and Rendered by Six MERL BRDF Materialsa
Yellow-Paint
Pink-Fabric
Green-Latex
Blue-Rubber
Red-Plastic
Delrin
Sandpaper
Densely sampled
50.01
75.68
32.18
29.79
37.57
90.06
50.21 (0.40%)
75.51 (0.23%)
31.91 (0.85%)
29.77 (0.09%)
37.48 (0.24%)
89.80 (0.29%)
50.21 (0.40%)
75.51 (0.23%)
31.91 (0.85%)
29.77 (0.09%)
37.48 (0.24%)
89.80 (0.29%)
50.22 (0.43%)
75.51 (0.23%)
31.92 (0.83%)
29.78 (0.05%)
37.48 (0.24%)
89.80 (0.29%)
Cylinder
Densely sampled
50.82
76.20
33.94
30.83
39.22
95.44
50.71 (0.23%)
75.93 (0.35%)
33.75 (0.57%)
30.54 (0.93%)
38.94 (0.71%)
94.05 (1.46%)
50.71 (0.23%)
75.93 (0.35%)
33.75 (0.57%)
30.54 (0.93%)
38.94 (0.71%)
94.05 (1.46%)
50.71 (0.23%)
75.97 (0.30%)
33.76 (0.54%)
30.55 (0.90%)
38.96 (0.67%)
94.01 (1.49%)
The number of lighting directions, , is determined by rotation interval .
Table 2.
Colorimetric Errors Produced by Spectral Reflectance Reconstruction Algorithmsa
(D65)
(F2)
(A)
WE
PCA
NNPCA
Proposed
WE
PCA
NNPCA
Proposed
WE
PCA
NNPCA
Proposed
Red-fabric
(0°, 0°)
1.16
1.03
1.06
0.65
1.12
0.90
0.91
0.69
1.21
1.06
1.07
0.62
(15°, 0°)
1.67
1.11
1.16
0.92
1.68
1.11
1.12
0.89
1.64
1.15
1.17
0.84
(45°, 120°)
1.93
1.26
1.31
1.03
1.97
1.27
1.29
0.98
1.79
1.23
1.26
0.90
(75°, 240°)
1.82
1.27
1.32
1.07
2.06
1.33
1.34
1.13
1.80
1.24
1.25
0.91
Lego-brick
(0°, 0°)
1.09
1.02
1.02
0.94
1.15
1.12
1.12
0.99
1.00
1.12
1.12
0.97
(15°, 0°)
1.54
1.35
1.35
1.23
1.56
1.41
1.41
1.20
1.47
1.43
1.43
1.17
(45°, 120°)
1.49
1.33
1.33
1.21
1.50
1.39
1.39
1.19
1.41
1.41
1.41
1.16
(75°, 240°)
1.49
1.34
1.34
1.23
1.48
1.40
1.40
1.20
1.35
1.40
1.40
1.16
The viewing direction is for training, and the other three directions are for testing.
Table 3.
Spectral RMS Errors Produced by the Spectral Reflectance Reconstruction Algorithmsa
Spectral RMS
WE
PCA
NNPCA
Proposed
Red-fabric
(0°, 0°)
0.0025
0.0023
0.0024
0.0018
(15°, 0°)
0.0036
0.0042
0.0045
0.0032
(45°, 120°)
0.0042
0.0050
0.0054
0.0038
(75°, 240°)
0.0070
0.0074
0.0079
0.0065
Lego-brick
(0°, 0°)
0.0059
0.0062
0.0062
0.0054
(15°, 0°)
0.0060
0.0059
0.0059
0.0056
(45°, 120°)
0.0069
0.0066
0.0066
0.0062
(75°, 240°)
0.0086
0.0082
0.0082
0.0079
The viewing direction is for training, and the other three directions are for testing.
Table 4.
Colorimetric and Spectral Errors (Mean and Maximum) Produced by Spectral Reflectance Reconstruction Algorithms on 19 Real Materials
(D65)
(F2)
(A)
Spectral RMS
Mean
Max.
Mean
Max.
Mean
Max.
Mean
Max.
WE
1.33
3.15
1.29
2.80
1.33
4.02
0.017
0.049
PCA
3.10
5.89
3.39
7.82
2.95
5.62
0.071
0.255
NNPCA
2.94
5.62
2.92
7.84
1.81
3.26
0.067
0.209
Proposed
0.95
1.82
0.96
1.81
0.95
1.81
0.013
0.032
Table 5.
Time (Unit: Hours) Required for Spectral BTF Acquisition when Using the Traditional Full Measurement Technique and the Proposed Method
Full Measurement
Proposed Method
Capturing
61.6
5.25
Reconstruction
–
0.83
Total
61.6
6.08
Tables (5)
Table 1.
Average Responses (Relative Error) of the Mean BTF Images, with The BTF Images Simulated from the Sandpaper and Cylinder Surfaces, and Rendered by Six MERL BRDF Materialsa
Yellow-Paint
Pink-Fabric
Green-Latex
Blue-Rubber
Red-Plastic
Delrin
Sandpaper
Densely sampled
50.01
75.68
32.18
29.79
37.57
90.06
50.21 (0.40%)
75.51 (0.23%)
31.91 (0.85%)
29.77 (0.09%)
37.48 (0.24%)
89.80 (0.29%)
50.21 (0.40%)
75.51 (0.23%)
31.91 (0.85%)
29.77 (0.09%)
37.48 (0.24%)
89.80 (0.29%)
50.22 (0.43%)
75.51 (0.23%)
31.92 (0.83%)
29.78 (0.05%)
37.48 (0.24%)
89.80 (0.29%)
Cylinder
Densely sampled
50.82
76.20
33.94
30.83
39.22
95.44
50.71 (0.23%)
75.93 (0.35%)
33.75 (0.57%)
30.54 (0.93%)
38.94 (0.71%)
94.05 (1.46%)
50.71 (0.23%)
75.93 (0.35%)
33.75 (0.57%)
30.54 (0.93%)
38.94 (0.71%)
94.05 (1.46%)
50.71 (0.23%)
75.97 (0.30%)
33.76 (0.54%)
30.55 (0.90%)
38.96 (0.67%)
94.01 (1.49%)
The number of lighting directions, , is determined by rotation interval .
Table 2.
Colorimetric Errors Produced by Spectral Reflectance Reconstruction Algorithmsa
(D65)
(F2)
(A)
WE
PCA
NNPCA
Proposed
WE
PCA
NNPCA
Proposed
WE
PCA
NNPCA
Proposed
Red-fabric
(0°, 0°)
1.16
1.03
1.06
0.65
1.12
0.90
0.91
0.69
1.21
1.06
1.07
0.62
(15°, 0°)
1.67
1.11
1.16
0.92
1.68
1.11
1.12
0.89
1.64
1.15
1.17
0.84
(45°, 120°)
1.93
1.26
1.31
1.03
1.97
1.27
1.29
0.98
1.79
1.23
1.26
0.90
(75°, 240°)
1.82
1.27
1.32
1.07
2.06
1.33
1.34
1.13
1.80
1.24
1.25
0.91
Lego-brick
(0°, 0°)
1.09
1.02
1.02
0.94
1.15
1.12
1.12
0.99
1.00
1.12
1.12
0.97
(15°, 0°)
1.54
1.35
1.35
1.23
1.56
1.41
1.41
1.20
1.47
1.43
1.43
1.17
(45°, 120°)
1.49
1.33
1.33
1.21
1.50
1.39
1.39
1.19
1.41
1.41
1.41
1.16
(75°, 240°)
1.49
1.34
1.34
1.23
1.48
1.40
1.40
1.20
1.35
1.40
1.40
1.16
The viewing direction is for training, and the other three directions are for testing.
Table 3.
Spectral RMS Errors Produced by the Spectral Reflectance Reconstruction Algorithmsa
Spectral RMS
WE
PCA
NNPCA
Proposed
Red-fabric
(0°, 0°)
0.0025
0.0023
0.0024
0.0018
(15°, 0°)
0.0036
0.0042
0.0045
0.0032
(45°, 120°)
0.0042
0.0050
0.0054
0.0038
(75°, 240°)
0.0070
0.0074
0.0079
0.0065
Lego-brick
(0°, 0°)
0.0059
0.0062
0.0062
0.0054
(15°, 0°)
0.0060
0.0059
0.0059
0.0056
(45°, 120°)
0.0069
0.0066
0.0066
0.0062
(75°, 240°)
0.0086
0.0082
0.0082
0.0079
The viewing direction is for training, and the other three directions are for testing.
Table 4.
Colorimetric and Spectral Errors (Mean and Maximum) Produced by Spectral Reflectance Reconstruction Algorithms on 19 Real Materials
(D65)
(F2)
(A)
Spectral RMS
Mean
Max.
Mean
Max.
Mean
Max.
Mean
Max.
WE
1.33
3.15
1.29
2.80
1.33
4.02
0.017
0.049
PCA
3.10
5.89
3.39
7.82
2.95
5.62
0.071
0.255
NNPCA
2.94
5.62
2.92
7.84
1.81
3.26
0.067
0.209
Proposed
0.95
1.82
0.96
1.81
0.95
1.81
0.013
0.032
Table 5.
Time (Unit: Hours) Required for Spectral BTF Acquisition when Using the Traditional Full Measurement Technique and the Proposed Method
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