Abstract

A improved spectral reflectance reconstruction method is developed to transform camera RGB to spectral reflectance for skin images. Rather than using conventional direct or two-step processes, we transform camera RGB to skin reflectance directly using a principal component analysis (PCA) approach. The novelty in our direct method (RGB to spectra) is the use of a skin-specific colour characterisation chart with spectra closer to human skin spectra, and a new database of skin reflectances to derive the PCA bases. The experimental results using the facial images of 17 subjects demonstrate that our new direct method gives a significantly better performance than conventional, two-step methods and direct methods with traditional characterization charts. This new spectral reconstruction algorithm is sufficiently precise to reconstruct spectral properites relating to chromophores and its performance is within the acceptable range for maxillofacial soft tissue prostheses (error < 3 ΔE*ab units).

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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2015 (1)

2014 (2)

K. Xiao, F. Zardawi, R. van Noort, and J. M. Yates, “Developing a 3D colour image reproduction system for additive manufacturing of facial prostheses,” Int. J. Adv. Manuf. Technol. 70(9-12), 2043–2049 (2014).
[Crossref]

R. Shrestha, R. Pillay, S. George, and J. Y. Hardeberg, “Quality evaluation in spectral imaging - Quality factors and metrics,” J. Int. Colour Assoc. 10, 22–35 (2014).

2013 (3)

J. Tian and Y. Tang, “Wavelength-sensitive-function controlled reflectance reconstruction,” Opt. Lett. 38(15), 2818–2820 (2013).
[Crossref] [PubMed]

I. Nishidate, T. Maeda, K. Niizeki, and Y. Aizu, “Estimation of Melanin and Hemoglobin Using Spectral Reflectance Images Reconstructed from a Digital RGB Image by the Wiener Estimation Method,” Sensors (Basel) 13(6), 7902–7915 (2013).
[Crossref] [PubMed]

K. Kikuchi, Y. Masuda, and T. Hirao, “Imaging of hemoglobin oxygen saturation ratio in the face by spectral camera and its application to evaluate dark circles,” Skin Res. Technol. 19(4), 499–507 (2013).
[PubMed]

2012 (1)

S. Chen and Q. Liu, “Modified Wiener estimation of diffuse reflectance spectra from RGB values by the synthesis of new colors for tissue measurements,” J. Biomed. Opt. 17(3), 030501 (2012).
[Crossref] [PubMed]

2009 (1)

R. D. Paravina, G. Majkic, M. Del Mar Perez, and S. Kiat-Amnuay, “Color difference thresholds of maxillofacial skin replications,” J. Prosthodont. 18(7), 618–625 (2009).
[Crossref] [PubMed]

2008 (1)

A. Leonardi, S. Buonaccorsi, V. Pellacchia, L. M. Moricca, E. Indrizzi, and G. Fini, “Maxillofacial prosthetic rehabilitation using extraoral implants,” J. Craniofac. Surg. 19(2), 398–405 (2008).
[Crossref] [PubMed]

2007 (2)

2006 (2)

M. A. Changizi, Q. Zhang, and S. Shimojo, “Bare skin, blood and the evolution of primate colour vision,” Biol. Lett. 2(2), 217–221 (2006).
[Crossref] [PubMed]

H.-L. Shen and J. H. Xin, “Spectral characterization of a color scanner based on optimized adaptive estimation,” J. Opt. Soc. Am. A 23(7), 1566–1569 (2006).
[Crossref] [PubMed]

2005 (1)

2002 (3)

M. Shi and G. Healey, “Using reflectance models for color scanner calibration,” J. Opt. Soc. Am. A 19(4), 645–656 (2002).
[Crossref] [PubMed]

K. Barnard and B. Funt, “Camera characterization for color research,” Color Res. Appl. 27(3), 152–163 (2002).
[Crossref]

Q. Sun and M. D. Fairchild, “Statistical characterization of face spectral reflectances and its application to human portraiture spectral estimation,” J. Imaging Sci. Technol. 46, 498–506 (2002).

2000 (1)

1996 (1)

F. H. Imai, N. Tsumura, H. Haneishi, and Y. Miyake, “Principal component analysis of skin color and its application to colorimetric color reproduction on CRT display and hardcopy,” J. Imaging Sci. Technol. 40, 422–430 (1996).

Aizu, Y.

I. Nishidate, T. Maeda, K. Niizeki, and Y. Aizu, “Estimation of Melanin and Hemoglobin Using Spectral Reflectance Images Reconstructed from a Digital RGB Image by the Wiener Estimation Method,” Sensors (Basel) 13(6), 7902–7915 (2013).
[Crossref] [PubMed]

Barnard, K.

K. Barnard and B. Funt, “Camera characterization for color research,” Color Res. Appl. 27(3), 152–163 (2002).
[Crossref]

Buonaccorsi, S.

A. Leonardi, S. Buonaccorsi, V. Pellacchia, L. M. Moricca, E. Indrizzi, and G. Fini, “Maxillofacial prosthetic rehabilitation using extraoral implants,” J. Craniofac. Surg. 19(2), 398–405 (2008).
[Crossref] [PubMed]

Cai, P.-Q.

Changizi, M. A.

M. A. Changizi, Q. Zhang, and S. Shimojo, “Bare skin, blood and the evolution of primate colour vision,” Biol. Lett. 2(2), 217–221 (2006).
[Crossref] [PubMed]

Chen, S.

S. Chen and Q. Liu, “Modified Wiener estimation of diffuse reflectance spectra from RGB values by the synthesis of new colors for tissue measurements,” J. Biomed. Opt. 17(3), 030501 (2012).
[Crossref] [PubMed]

Cheung, V.

Connah, D.

Cui, G.

C. Li, G. Cui, and M. R. Luo, “The accuracy of polynomial models for characterizing digital cameras,” in Proceedings of AIC2003 Bangkok: Color Communication and Management (2003), pp. 166–170.

Del Mar Perez, M.

R. D. Paravina, G. Majkic, M. Del Mar Perez, and S. Kiat-Amnuay, “Color difference thresholds of maxillofacial skin replications,” J. Prosthodont. 18(7), 618–625 (2009).
[Crossref] [PubMed]

Fairchild, M. D.

Q. Sun and M. D. Fairchild, “Statistical characterization of face spectral reflectances and its application to human portraiture spectral estimation,” J. Imaging Sci. Technol. 46, 498–506 (2002).

Fini, G.

A. Leonardi, S. Buonaccorsi, V. Pellacchia, L. M. Moricca, E. Indrizzi, and G. Fini, “Maxillofacial prosthetic rehabilitation using extraoral implants,” J. Craniofac. Surg. 19(2), 398–405 (2008).
[Crossref] [PubMed]

Funt, B.

K. Barnard and B. Funt, “Camera characterization for color research,” Color Res. Appl. 27(3), 152–163 (2002).
[Crossref]

George, S.

R. Shrestha, R. Pillay, S. George, and J. Y. Hardeberg, “Quality evaluation in spectral imaging - Quality factors and metrics,” J. Int. Colour Assoc. 10, 22–35 (2014).

Gill, L.

K. Xiao, J. M. Yates, F. Zardawi, S. Sueeprasan, N. Liao, L. Gill, C. Li, and S. Wuerger, “Characterising the variations in ethnic skin colours: a new calibrated data base for human skin,” Skin Res. Technol. in press (2016).

Haneishi, H.

H. Haneishi, T. Hasegawa, A. Hosoi, Y. Yokoyama, N. Tsumura, and Y. Miyake, “System design for accurately estimating the spectral reflectance of art paintings,” Appl. Opt. 39(35), 6621–6632 (2000).
[Crossref] [PubMed]

F. H. Imai, N. Tsumura, H. Haneishi, and Y. Miyake, “Principal component analysis of skin color and its application to colorimetric color reproduction on CRT display and hardcopy,” J. Imaging Sci. Technol. 40, 422–430 (1996).

Hardeberg, J.

Hardeberg, J. Y.

R. Shrestha, R. Pillay, S. George, and J. Y. Hardeberg, “Quality evaluation in spectral imaging - Quality factors and metrics,” J. Int. Colour Assoc. 10, 22–35 (2014).

Hasegawa, T.

Healey, G.

Hirao, T.

K. Kikuchi, Y. Masuda, and T. Hirao, “Imaging of hemoglobin oxygen saturation ratio in the face by spectral camera and its application to evaluate dark circles,” Skin Res. Technol. 19(4), 499–507 (2013).
[PubMed]

Hosoi, A.

Imai, F. H.

F. H. Imai, N. Tsumura, H. Haneishi, and Y. Miyake, “Principal component analysis of skin color and its application to colorimetric color reproduction on CRT display and hardcopy,” J. Imaging Sci. Technol. 40, 422–430 (1996).

Indrizzi, E.

A. Leonardi, S. Buonaccorsi, V. Pellacchia, L. M. Moricca, E. Indrizzi, and G. Fini, “Maxillofacial prosthetic rehabilitation using extraoral implants,” J. Craniofac. Surg. 19(2), 398–405 (2008).
[Crossref] [PubMed]

Kiat-Amnuay, S.

R. D. Paravina, G. Majkic, M. Del Mar Perez, and S. Kiat-Amnuay, “Color difference thresholds of maxillofacial skin replications,” J. Prosthodont. 18(7), 618–625 (2009).
[Crossref] [PubMed]

Kikuchi, K.

K. Kikuchi, Y. Masuda, and T. Hirao, “Imaging of hemoglobin oxygen saturation ratio in the face by spectral camera and its application to evaluate dark circles,” Skin Res. Technol. 19(4), 499–507 (2013).
[PubMed]

Leonardi, A.

A. Leonardi, S. Buonaccorsi, V. Pellacchia, L. M. Moricca, E. Indrizzi, and G. Fini, “Maxillofacial prosthetic rehabilitation using extraoral implants,” J. Craniofac. Surg. 19(2), 398–405 (2008).
[Crossref] [PubMed]

Li, C.

V. Cheung, S. Westland, C. Li, J. Hardeberg, and D. Connah, “Characterization of trichromatic color cameras by using a new multispectral imaging technique,” J. Opt. Soc. Am. A 22(7), 1231–1240 (2005).
[Crossref] [PubMed]

K. Xiao, J. M. Yates, F. Zardawi, S. Sueeprasan, N. Liao, L. Gill, C. Li, and S. Wuerger, “Characterising the variations in ethnic skin colours: a new calibrated data base for human skin,” Skin Res. Technol. in press (2016).

C. Li, G. Cui, and M. R. Luo, “The accuracy of polynomial models for characterizing digital cameras,” in Proceedings of AIC2003 Bangkok: Color Communication and Management (2003), pp. 166–170.

Li, J.

X. Zhang, Q. Wang, J. Li, X. Zhou, Y. Yang, and H. Xu, “Estimating spectral reflectance from camera responses based on CIEXYZ tristimulus values under multi-illuminants,” Color Res. Appl. in press (2016).

Liao, N.

K. Xiao, J. M. Yates, F. Zardawi, S. Sueeprasan, N. Liao, L. Gill, C. Li, and S. Wuerger, “Characterising the variations in ethnic skin colours: a new calibrated data base for human skin,” Skin Res. Technol. in press (2016).

Liu, Q.

S. Chen and Q. Liu, “Modified Wiener estimation of diffuse reflectance spectra from RGB values by the synthesis of new colors for tissue measurements,” J. Biomed. Opt. 17(3), 030501 (2012).
[Crossref] [PubMed]

Luo, M. R.

C. Li, G. Cui, and M. R. Luo, “The accuracy of polynomial models for characterizing digital cameras,” in Proceedings of AIC2003 Bangkok: Color Communication and Management (2003), pp. 166–170.

Maeda, T.

I. Nishidate, T. Maeda, K. Niizeki, and Y. Aizu, “Estimation of Melanin and Hemoglobin Using Spectral Reflectance Images Reconstructed from a Digital RGB Image by the Wiener Estimation Method,” Sensors (Basel) 13(6), 7902–7915 (2013).
[Crossref] [PubMed]

Mahmood, A.

Majkic, G.

R. D. Paravina, G. Majkic, M. Del Mar Perez, and S. Kiat-Amnuay, “Color difference thresholds of maxillofacial skin replications,” J. Prosthodont. 18(7), 618–625 (2009).
[Crossref] [PubMed]

Masuda, Y.

K. Kikuchi, Y. Masuda, and T. Hirao, “Imaging of hemoglobin oxygen saturation ratio in the face by spectral camera and its application to evaluate dark circles,” Skin Res. Technol. 19(4), 499–507 (2013).
[PubMed]

Mian, A.

Miyake, Y.

H. Haneishi, T. Hasegawa, A. Hosoi, Y. Yokoyama, N. Tsumura, and Y. Miyake, “System design for accurately estimating the spectral reflectance of art paintings,” Appl. Opt. 39(35), 6621–6632 (2000).
[Crossref] [PubMed]

F. H. Imai, N. Tsumura, H. Haneishi, and Y. Miyake, “Principal component analysis of skin color and its application to colorimetric color reproduction on CRT display and hardcopy,” J. Imaging Sci. Technol. 40, 422–430 (1996).

Moricca, L. M.

A. Leonardi, S. Buonaccorsi, V. Pellacchia, L. M. Moricca, E. Indrizzi, and G. Fini, “Maxillofacial prosthetic rehabilitation using extraoral implants,” J. Craniofac. Surg. 19(2), 398–405 (2008).
[Crossref] [PubMed]

Nansen, C.

Niizeki, K.

I. Nishidate, T. Maeda, K. Niizeki, and Y. Aizu, “Estimation of Melanin and Hemoglobin Using Spectral Reflectance Images Reconstructed from a Digital RGB Image by the Wiener Estimation Method,” Sensors (Basel) 13(6), 7902–7915 (2013).
[Crossref] [PubMed]

Nishidate, I.

I. Nishidate, T. Maeda, K. Niizeki, and Y. Aizu, “Estimation of Melanin and Hemoglobin Using Spectral Reflectance Images Reconstructed from a Digital RGB Image by the Wiener Estimation Method,” Sensors (Basel) 13(6), 7902–7915 (2013).
[Crossref] [PubMed]

Paravina, R. D.

R. D. Paravina, G. Majkic, M. Del Mar Perez, and S. Kiat-Amnuay, “Color difference thresholds of maxillofacial skin replications,” J. Prosthodont. 18(7), 618–625 (2009).
[Crossref] [PubMed]

Pellacchia, V.

A. Leonardi, S. Buonaccorsi, V. Pellacchia, L. M. Moricca, E. Indrizzi, and G. Fini, “Maxillofacial prosthetic rehabilitation using extraoral implants,” J. Craniofac. Surg. 19(2), 398–405 (2008).
[Crossref] [PubMed]

Pillay, R.

R. Shrestha, R. Pillay, S. George, and J. Y. Hardeberg, “Quality evaluation in spectral imaging - Quality factors and metrics,” J. Int. Colour Assoc. 10, 22–35 (2014).

Shafait, F.

Shao, S.-J.

Shen, H.-L.

Shi, M.

Shimojo, S.

M. A. Changizi, Q. Zhang, and S. Shimojo, “Bare skin, blood and the evolution of primate colour vision,” Biol. Lett. 2(2), 217–221 (2006).
[Crossref] [PubMed]

Shrestha, R.

R. Shrestha, R. Pillay, S. George, and J. Y. Hardeberg, “Quality evaluation in spectral imaging - Quality factors and metrics,” J. Int. Colour Assoc. 10, 22–35 (2014).

Sueeprasan, S.

K. Xiao, J. M. Yates, F. Zardawi, S. Sueeprasan, N. Liao, L. Gill, C. Li, and S. Wuerger, “Characterising the variations in ethnic skin colours: a new calibrated data base for human skin,” Skin Res. Technol. in press (2016).

Sun, Q.

Q. Sun and M. D. Fairchild, “Statistical characterization of face spectral reflectances and its application to human portraiture spectral estimation,” J. Imaging Sci. Technol. 46, 498–506 (2002).

Tang, Y.

Tian, J.

Tsumura, N.

H. Haneishi, T. Hasegawa, A. Hosoi, Y. Yokoyama, N. Tsumura, and Y. Miyake, “System design for accurately estimating the spectral reflectance of art paintings,” Appl. Opt. 39(35), 6621–6632 (2000).
[Crossref] [PubMed]

F. H. Imai, N. Tsumura, H. Haneishi, and Y. Miyake, “Principal component analysis of skin color and its application to colorimetric color reproduction on CRT display and hardcopy,” J. Imaging Sci. Technol. 40, 422–430 (1996).

Uzair, M.

van Noort, R.

K. Xiao, F. Zardawi, R. van Noort, and J. M. Yates, “Developing a 3D colour image reproduction system for additive manufacturing of facial prostheses,” Int. J. Adv. Manuf. Technol. 70(9-12), 2043–2049 (2014).
[Crossref]

Wang, Q.

X. Zhang, Q. Wang, J. Li, X. Zhou, Y. Yang, and H. Xu, “Estimating spectral reflectance from camera responses based on CIEXYZ tristimulus values under multi-illuminants,” Color Res. Appl. in press (2016).

Westland, S.

Wuerger, S.

K. Xiao, J. M. Yates, F. Zardawi, S. Sueeprasan, N. Liao, L. Gill, C. Li, and S. Wuerger, “Characterising the variations in ethnic skin colours: a new calibrated data base for human skin,” Skin Res. Technol. in press (2016).

Xiao, K.

K. Xiao, F. Zardawi, R. van Noort, and J. M. Yates, “Developing a 3D colour image reproduction system for additive manufacturing of facial prostheses,” Int. J. Adv. Manuf. Technol. 70(9-12), 2043–2049 (2014).
[Crossref]

K. Xiao, J. M. Yates, F. Zardawi, S. Sueeprasan, N. Liao, L. Gill, C. Li, and S. Wuerger, “Characterising the variations in ethnic skin colours: a new calibrated data base for human skin,” Skin Res. Technol. in press (2016).

Xin, J. H.

Xu, H.

X. Zhang, Q. Wang, J. Li, X. Zhou, Y. Yang, and H. Xu, “Estimating spectral reflectance from camera responses based on CIEXYZ tristimulus values under multi-illuminants,” Color Res. Appl. in press (2016).

Yang, Y.

X. Zhang, Q. Wang, J. Li, X. Zhou, Y. Yang, and H. Xu, “Estimating spectral reflectance from camera responses based on CIEXYZ tristimulus values under multi-illuminants,” Color Res. Appl. in press (2016).

Yates, J. M.

K. Xiao, F. Zardawi, R. van Noort, and J. M. Yates, “Developing a 3D colour image reproduction system for additive manufacturing of facial prostheses,” Int. J. Adv. Manuf. Technol. 70(9-12), 2043–2049 (2014).
[Crossref]

K. Xiao, J. M. Yates, F. Zardawi, S. Sueeprasan, N. Liao, L. Gill, C. Li, and S. Wuerger, “Characterising the variations in ethnic skin colours: a new calibrated data base for human skin,” Skin Res. Technol. in press (2016).

Yokoyama, Y.

Zardawi, F.

K. Xiao, F. Zardawi, R. van Noort, and J. M. Yates, “Developing a 3D colour image reproduction system for additive manufacturing of facial prostheses,” Int. J. Adv. Manuf. Technol. 70(9-12), 2043–2049 (2014).
[Crossref]

K. Xiao, J. M. Yates, F. Zardawi, S. Sueeprasan, N. Liao, L. Gill, C. Li, and S. Wuerger, “Characterising the variations in ethnic skin colours: a new calibrated data base for human skin,” Skin Res. Technol. in press (2016).

Zhang, Q.

M. A. Changizi, Q. Zhang, and S. Shimojo, “Bare skin, blood and the evolution of primate colour vision,” Biol. Lett. 2(2), 217–221 (2006).
[Crossref] [PubMed]

Zhang, X.

X. Zhang, Q. Wang, J. Li, X. Zhou, Y. Yang, and H. Xu, “Estimating spectral reflectance from camera responses based on CIEXYZ tristimulus values under multi-illuminants,” Color Res. Appl. in press (2016).

Zhou, X.

X. Zhang, Q. Wang, J. Li, X. Zhou, Y. Yang, and H. Xu, “Estimating spectral reflectance from camera responses based on CIEXYZ tristimulus values under multi-illuminants,” Color Res. Appl. in press (2016).

Appl. Opt. (1)

Biol. Lett. (1)

M. A. Changizi, Q. Zhang, and S. Shimojo, “Bare skin, blood and the evolution of primate colour vision,” Biol. Lett. 2(2), 217–221 (2006).
[Crossref] [PubMed]

Color Res. Appl. (1)

K. Barnard and B. Funt, “Camera characterization for color research,” Color Res. Appl. 27(3), 152–163 (2002).
[Crossref]

Int. J. Adv. Manuf. Technol. (1)

K. Xiao, F. Zardawi, R. van Noort, and J. M. Yates, “Developing a 3D colour image reproduction system for additive manufacturing of facial prostheses,” Int. J. Adv. Manuf. Technol. 70(9-12), 2043–2049 (2014).
[Crossref]

J. Biomed. Opt. (1)

S. Chen and Q. Liu, “Modified Wiener estimation of diffuse reflectance spectra from RGB values by the synthesis of new colors for tissue measurements,” J. Biomed. Opt. 17(3), 030501 (2012).
[Crossref] [PubMed]

J. Craniofac. Surg. (1)

A. Leonardi, S. Buonaccorsi, V. Pellacchia, L. M. Moricca, E. Indrizzi, and G. Fini, “Maxillofacial prosthetic rehabilitation using extraoral implants,” J. Craniofac. Surg. 19(2), 398–405 (2008).
[Crossref] [PubMed]

J. Imaging Sci. Technol. (2)

Q. Sun and M. D. Fairchild, “Statistical characterization of face spectral reflectances and its application to human portraiture spectral estimation,” J. Imaging Sci. Technol. 46, 498–506 (2002).

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Figures (10)

Fig. 1
Fig. 1

Colour specifications in CIELAB of the two different colour charts used for calibration. (a) on the left: the 140 X-Rite SG colour samples, (b) in the middle, the 90 Silicon skin chart (Spectromatch Ltd), and (c) on the right, a subset (100) of typical human skin colours. Please note that the scales are different between (a) and (b)/(c) to visualize the subtle but important differences between the Silicon and the human skin colours.

Fig. 2
Fig. 2

Spectra of Silicon skin charts (SS), provided by Spectromatch Ltd.

Fig. 3
Fig. 3

Direct recovery method using the skin database (DB) and the silicon skin chart (SS)

Fig. 4
Fig. 4

(a) On the left the capture of the facial camera image is shown while subjects are seated in the viewing cabinet. Spectral reflectances are obtained using a CM700d spectrophotometer. (b) 34 Test skin spectra (forehead and cheek) for 17 individuals

Fig. 5
Fig. 5

Representative sample of reconstructed spectra. Upper row: two spectra (#7, #26) with errors close to the mean error of 2.7 (cf Table 1) for direct reconstruction (DIRECT SS/DB) as indicated by a solid line (spectrum #7 with a perceptual error of 2.35 and spectrum #26 with a perceptual error of 2.87). Lower left panel: spectrum #8 with the lowest perceptual error of 0.63 for the best performing method ‘DIRECT SS/DB’. Lower right panel: worst reconstruction; spectrum #20 with a perceptual error of 8.5. In all cases the ‘W’ feature at around 560nm is recovered if present in the original spectrum.

Fig. 6
Fig. 6

Correlation between the RMSE based on spectral information and the perceptual error reflecting the visible differences between the original and the reconstructed spectra. The highest correlation between these two measures is obtained for the best-performing method (DIRECT SS/DB).

Fig. 7
Fig. 7

On the left the absorbance as a function of wavelength is shown for the oxygenated (red line) and the de-oxygenated haemoglobin (green line). On the right panel, the inverse of the absorbance is plotted to show that the ‘W’ feature in the skin reflectance spectra (e.g. Figure 5, upper left panel) is a reflection of the oxygenation saturation of haemoglobin. Thin vertical lines indicate the location of the peak sensitivities of the cones in the human retina.

Fig. 8
Fig. 8

Reconstructed skin spectra #1-9 with associated reconstruction error (RMSE and Perceptual Error) using each of the four methods: TWO-STEP SG/DB, TWO-STEP SS/DB, DIRECT SS/SS, DIRECT SS/DB together with the original spectra

Fig. 9
Fig. 9

Reconstructed skin spectra #10-21 with associated reconstruction error (RMSE and Perceptual Error) using each of the four methods: TWO-STEP SG/DB, TWO-STEP SS/DB, DIRECT SS/SS, DIRECT SS/DB together with the original spectra

Fig. 10
Fig. 10

Reconstructed skin spectra #22-34 with associated reconstruction error (RMSE and Perceptual Error) using each of the four methods: TWO-STEP SG/DB, TWO-STEP SS/DB, DIRECT SS/SS, DIRECT SS/DB together with the original spectra

Tables (6)

Tables Icon

Table 1 A summary of the properties of the four methods

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Table 2 Performance of the four reconstruction methods across different illuminations

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Table 3 Spectral shape differences in terms of RMSE for each method in the full spectral range between 400 nm and 700 nm at 10 nm intervals)

Tables Icon

Table 4 Spectral shape differences in terms of SSV for each method in the full spectral range (between 400 nm and 700 nm at 10 nm intervals)

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Table 5 Spectral shape differences in terms of RMSE for each method in the W shape range (between 500 nm and 600 nm at 10 nm intervals)

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Table 6 Spectral shape differences in terms of SSV for each method in the W shape range (between 500 nm and 600 nm at 10 nm intervals)

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

X= 0 j 1 + j 2 + j 3 m a X, j 1 , j 2 , j 3 R j 1 G j 2 B j 3 Y= 0 j 1 + j 2 + j 3 m a Y, j 1 , j 2 , j 3 R j 1 G j 2 B j 3 Z= 0 j 1 + j 2 + j 3 m a Z, j 1 , j 2 , j 3 R j 1 G j 2 B j 3
u= W T r
u= W T U 3 α
α= ( W T U 3 ) 1 u and r= U 3 α
β= ( U K ) T r
β ^ i = 0 j 1 + j 2 + j 3 m a β i , j 1 , j 2 , j 3 R j 1 G j 2 B j 3
r= U K β
RMSE= 1 n k=1 n ( r k (o) r k (o) ) 2
SSV= RMSE 2 + S 2
S 2 =1 {[ 1 n k=1 n ( r k (o) μ (o) )( r k (c) μ (c) ) ]/( σ (o) σ (c) )} 2

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