1DISCo-Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Viale Sarca 336, Edificio U14, 20126 Milano, Italy (simone.bianco@disco.unimib.it)
Simone Bianco, "Reflectance spectra recovery from tristimulus values by adaptive estimation with metameric shape correction," J. Opt. Soc. Am. A 27, 1868-1877 (2010)
In this work a local optimization-based method that is able to recover the reflectance spectra with the desired tristimulus values, choosing the metamer with the most similar shape to the reflectances available in the training set, is proposed. Four different datasets of reflectance spectra and three different error metrics have been used in this study. According to all the error metrics considered, the proposed algorithm was able to recover the spectral reflectances with a higher accuracy than all the state of the art methods considered.
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Compute the final recovered spectra using Eq. (17)
End
End
Table 2
Algorithm Performances on All the Datasets Considered: Average, 95% Percentile, and Standard Deviation (std) of the Colorimetric Error under the CIE D65, A, and F2 Illuminants; Percentages of Reconstructed Spectra with Poor, Accurate, and Good Reconstructions Judged by PSNR; Percentages of Reconstructed Spectra with Poor, Accurate, Good, and Excellent Reconstructions Judged by GFC
WST Scores, Evaluated on the Error Distributions, Obtained by the Algorithms Subdivided for Each Dataset and Illuminant Considereda
Method
Scores
MUNtr
MUNte
VHRELte
MCCte
MDCte
D65
A
F2
D65
A
F2
D65
A
F2
D65
A
F2
D65
A
F2
PINV
1
0
2
1
0
1
1
3
3
0
0
0
1
0
0
PINV-PCA
2
0
2
2
0
1
2
3
4
1
0
0
0
0
0
HAW
3
3
0
3
3
0
2
0
0
3
0
0
3
0
0
adaPCA
6
5
5
3
4
5
2
3
6
3
6
6
6
6
5
PCAemRe
0
4
0
0
4
1
0
0
0
2
0
0
1
4
0
PCAmuBa
3
6
6
3
6
6
6
0
0
3
0
0
3
6
5
ZSS
3
0
2
3
0
1
2
3
4
3
0
0
3
0
0
Proposed
6
7
7
3
7
7
6
7
7
3
7
7
6
7
7
The best score for each dataset–illuminant combination is reported in bold font. The score is representative of the number of algorithms with respect to which the considered algorithm gives statistically better or equivalent results.
Table 5
Sensitivity Analysis of the Optimization Function with Respect to the Colorimetric Error Term , i.e., the Weight α
Dataset
[0,100,100,1]
[1,100,100,1]
[1,0,0,0]
GFC
GFC
GFC
GFC
GFC
GFC
GFC
GFC
GFC
MUNStr
19.8029
0.9965
0.0181
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9972
MUNSte
20.1850
0.9961
0.0106
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9965
VHRELte
24.5944
0.9782
0.5200
0.9832
0.0000
0.9854
0.0000
0.9854
0.0000
0.9854
0.0000
0.9854
0.0000
0.9854
0.0000
0.9854
0.0000
0.9843
MCCte
23.0726
0.9933
0.3170
0.9943
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9954
MDCte
21.7940
0.9957
0.0745
0.9964
0.0073
0.9964
0.0000
0.9964
0.0000
0.9964
0.0000
0.9964
0.0000
0.9964
0.0000
0.9964
0.0000
0.9959
Table 6
Sensitivity Analysis of the Optimization Function with Respect to the Shape Feasibility Terms, i.e., the Weights
Dataset
[1,0,0,1]
[1,1,1,1]
[0,1,1,0]
GFC
GFC
GFC
GFC
GFC
GFC
GFC
GFC
GFC
MUNStr
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9972
MUNSte
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0002
0.9967
VHRELte
0.0000
0.9851
0.0000
0.9851
0.0000
0.9852
0.0001
0.9854
0.0000
0.9854
0.0000
0.9854
0.0000
0.9854
0.0000
0.9854
0.0036
0.9851
MCCte
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9946
MDCte
0.0000
0.9964
0.0000
0.9964
0.0000
0.9964
0.0000
0.9964
0.0000
0.9964
0.0000
0.9964
0.0000
0.9964
0.0000
0.9964
0.0008
0.9962
Table 7
Sensitivity Analysis of the Optimization Function with Respect to the Spectral Error Term GFC, i.e., the Weight δ
Dataset
[1,100,100,0]
[1,100,100,1]
[0,0,0,1]
GFC
GFC
GFC
GFC
GFC
GFC
GFC
GFC
GFC
MUNStr
0.0000
0.9972
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0181
0.9974
22.0189
0.9964
MUNSte
0.0000
0.9965
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0106
0.9967
21.5030
0.9960
VHRELte
0.0000
0.9844
0.0000
0.9854
0.0000
0.9854
0.0000
0.9854
0.0000
0.9854
0.0000
0.9854
0.0000
0.9854
0.4280
0.9845
24.6220
0.9763
MCCte
0.0000
0.9954
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.3170
0.9943
22.4140
0.9933
MDCte
0.0088
0.9959
0.0089
0.9964
0.0088
0.9964
0.0088
0.9964
0.0000
0.9964
0.0000
0.9964
0.0074
0.9964
0.0746
0.9964
20.7156
0.9958
Tables (7)
Table 1
Pseudo-Code of the Proposed Algorithm
Begin
Derive a basis for the whole training set
Estimate the recovered spectra
Calculate the spectral residuals between the recovered
and the training set spectra
Derive a basis B for the spectral residuals
Use the basis to give an initial estimate of the recovered
spectra using Eq. (5) for each initial estimate of the
recovered spectra
Do
Calculate the GFC with the spectra in the training set
Compute the final recovered spectra using Eq. (17)
End
End
Table 2
Algorithm Performances on All the Datasets Considered: Average, 95% Percentile, and Standard Deviation (std) of the Colorimetric Error under the CIE D65, A, and F2 Illuminants; Percentages of Reconstructed Spectra with Poor, Accurate, and Good Reconstructions Judged by PSNR; Percentages of Reconstructed Spectra with Poor, Accurate, Good, and Excellent Reconstructions Judged by GFC
WST Scores, Evaluated on the Error Distributions, Obtained by the Algorithms Subdivided for Each Dataset and Illuminant Considereda
Method
Scores
MUNtr
MUNte
VHRELte
MCCte
MDCte
D65
A
F2
D65
A
F2
D65
A
F2
D65
A
F2
D65
A
F2
PINV
1
0
2
1
0
1
1
3
3
0
0
0
1
0
0
PINV-PCA
2
0
2
2
0
1
2
3
4
1
0
0
0
0
0
HAW
3
3
0
3
3
0
2
0
0
3
0
0
3
0
0
adaPCA
6
5
5
3
4
5
2
3
6
3
6
6
6
6
5
PCAemRe
0
4
0
0
4
1
0
0
0
2
0
0
1
4
0
PCAmuBa
3
6
6
3
6
6
6
0
0
3
0
0
3
6
5
ZSS
3
0
2
3
0
1
2
3
4
3
0
0
3
0
0
Proposed
6
7
7
3
7
7
6
7
7
3
7
7
6
7
7
The best score for each dataset–illuminant combination is reported in bold font. The score is representative of the number of algorithms with respect to which the considered algorithm gives statistically better or equivalent results.
Table 5
Sensitivity Analysis of the Optimization Function with Respect to the Colorimetric Error Term , i.e., the Weight α
Dataset
[0,100,100,1]
[1,100,100,1]
[1,0,0,0]
GFC
GFC
GFC
GFC
GFC
GFC
GFC
GFC
GFC
MUNStr
19.8029
0.9965
0.0181
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9972
MUNSte
20.1850
0.9961
0.0106
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9965
VHRELte
24.5944
0.9782
0.5200
0.9832
0.0000
0.9854
0.0000
0.9854
0.0000
0.9854
0.0000
0.9854
0.0000
0.9854
0.0000
0.9854
0.0000
0.9843
MCCte
23.0726
0.9933
0.3170
0.9943
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9954
MDCte
21.7940
0.9957
0.0745
0.9964
0.0073
0.9964
0.0000
0.9964
0.0000
0.9964
0.0000
0.9964
0.0000
0.9964
0.0000
0.9964
0.0000
0.9959
Table 6
Sensitivity Analysis of the Optimization Function with Respect to the Shape Feasibility Terms, i.e., the Weights
Dataset
[1,0,0,1]
[1,1,1,1]
[0,1,1,0]
GFC
GFC
GFC
GFC
GFC
GFC
GFC
GFC
GFC
MUNStr
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9974
0.0000
0.9972
MUNSte
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0000
0.9967
0.0002
0.9967
VHRELte
0.0000
0.9851
0.0000
0.9851
0.0000
0.9852
0.0001
0.9854
0.0000
0.9854
0.0000
0.9854
0.0000
0.9854
0.0000
0.9854
0.0036
0.9851
MCCte
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9947
0.0000
0.9946
MDCte
0.0000
0.9964
0.0000
0.9964
0.0000
0.9964
0.0000
0.9964
0.0000
0.9964
0.0000
0.9964
0.0000
0.9964
0.0000
0.9964
0.0008
0.9962
Table 7
Sensitivity Analysis of the Optimization Function with Respect to the Spectral Error Term GFC, i.e., the Weight δ