Fig. 1. Schematic diagram of the observation model for the imaging system using an RGB camera. 

Fig. 2. Example of the luminance distribution captured by a mobile phone camera under an LED light source. 

Fig. 3. Estimation errors of the surface-spectral reflectance as a function of the g and a parameters, where an X-rite Color Checker, an iPhone 6s, and seven LED light sources were used (refer to Section 5 for the details). Points A and B represent the estimation errors when using the L1 and L2 minimum parameter values, respectively. Point C represents the minimum error by the entire search of g and a. 

Fig. 4. Relative RGB spectral sensitivity functions of the three mobile phone cameras: (1) Apple iPhone 6s, (2) Apple iPhone 8, and (3) Huawei P10 lite, where the red, green, and blue curves correspond to (1), (2), and (3) cameras, respectively. 

Fig. 5. Spectral power distributions of seven LED light sources used in experiments. 

Fig. 6. Data set of spectral reflectances used to obtain the statistical quantities of the surface-spectral reflectance x. 

Fig. 7. Color checkers used for reflectance estimation validation. (a) Imaging targets comprising 24 color-checkers and the white reference standard (Spectralon). (b) Spectral reflectances of the 24 color-checkers and the white reference standard measured by the spectral colorimeter. 

Fig. 8. Estimation results of the spectral reflectances for the 24 color-checkers when applying the LMMSE, Wiener, and PCA methods to the image data using the iPhone 6s. The parameters used were g _L1 and a_L1 for the LMMSE and Wiener methods and were only g _L1 for the PCA method. In the figures, the broken curves in bold red, bold green curves, and thin blue curves depict the spectral reflectances estimated by the LMMSE,Wiener, and PCAmethods, respectively; the black dotted curves depict themeasured spectral reflectances. 

Fig. 9. Estimation results of the spectral reflectances for the 24 color-checkers when applying the LMMSE, Wiener, and PCA methods to the image data using the iPhone 8 camera. The parameters used were g _L1 and a_L1 for the LMMSE and Wiener methods and were only g _L1 for the PCA method. In the figures, the broken curves in bold red, bold green curves, and thin blue curves depict the spectral reflectances estimated by the LMMSE,Wiener, and PCA methods, respectively; the dotted black curves indicate the measured spectral reflectances. 

Fig. 10. Estimation results of the spectral reflectances for the 24 color-checkers when applying the LMMSE, Wiener, and PCA methods to the image data using the Huawei P10 lite camera. The parameters used were g _L1 and aL1 for the LMMSE and Wiener methods and only g L1 for the PCA method. In the figures, the broken curves in bold red, bold green curves, and thin blue curves depict the spectral reflectances estimated by the LMMSE,Wiener, and PCA methods, respectively; the dotted black curves indicate the measured spectral reflectances. 

Fig. 11. Estimation results of the spectral reflectances for the 24 color-checkers when the observations were normalized with the reference standard sample (Spectralon) in using the iPhone 6s camera. The only parameter used was a_L1 for the LMMSE andWiener methods. The PCA methods used no parameters. In the figures, the broken curves in bold red, bold green curves, thin blue curves, and dotted black curves correspond to the spectral reflectances estimated by the LMMSE,Wiener, and PCAmethods and themeasured spectral reflectances, respectively. 

Fig. 12. Estimation results of the spectral reflectances for the 24 color-checkers when the observations were normalized using the reference standard sample (Spectralon) when applying the iPhone 8 camera. The only parameter used was a_L1 for the LMMSE andWiener methods. The PCA methods applied no parameters. In the figures, the broken curves in bold red, bold green curves, thin blue curves, and dotted black curves correspond to the spectral reflectances estimated by the LMMSE,Wiener, and PCA methods, and the measured spectral reflectances, respectively. 

Fig. 13. Estimation results of the spectral reflectances for the 24 color-checkers when the observations were normalized using the reference standard sample (Spectralon) when applying the Huawei P10 lite camera. The only parameter used was a_L1 for the LMMSE andWiener methods. The PCA methods used no parameters. In the figures, the broken curves in bold red, bold green curves, thin blue curves, and dotted black curves correspond to the spectral reflectances estimated by the LMMSE,Wiener, and PCA methods and the measured spectral reflectances, respectively. 

Fig. 14. Illuminant spectral power distribution of the incandescent lamp used in an experiment on the single RGB-based spectral estimation. 

Fig. 15. Variations in the estimation error and the percent variance as a function of the number of principal components. The error values are computed under three different parameter conditions for each of the three mobile phone cameras shown in Tables 1 and 2. The percent variance and the error values are plotted using the left and right scales, respectively.