Abstract

We developed an optimization method of chromophore vectors for skin images in the modified Lambert-Beer law. In the proposed method, vectors are optimized to minimize intermixture between melanin, hemoglobin, and shading components. Using the proposed method, the vectors can be optimized appropriately and stably. The proposed method also optimizes shading images, which may contain useful information. The melanin component obtained using the proposed method has a good correlation with that obtained from the conventional method with a reflectance spectrum. The proposed method advances the capability of prompt action upon installation of new equipment and eliminates arbitrary judgment of acceptance or rejection of vectors for each test image, which improves objectivity.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. J. Yang, X. Sun, J. Liang, and P. L. Rosin, “Clinical Skin Lesion Diagnosis using Representations Inspired by Dermatologist Criteria,” Cvpr, 1258–1266 (2018).
  2. V. K. Shrivastava, N. D. Londhe, R. S. Sonawane, and J. S. Suri, “Computer-aided diagnosis of psoriasis skin images with HOS, texture and color features: A first comparative study of its kind,” Comput. Methods Programs Biomed. 126, 98–109 (2016).
    [Crossref]
  3. Z. Liu and J. Zerubia, “Skin image illumination modeling and chromophore identification for melanoma diagnosis,” Phys. Med. Biol. 60(9), 3415–3431 (2015).
    [Crossref]
  4. E. Claridge, S. Cotton, P. Hall, and M. Moncrieff, “From colour to tissue histology: Physics-based interpretation of images of pigmented skin lesions,” Med. Image Anal. 7(4), 489–502 (2003).
    [Crossref]
  5. G. Lu and B. Fei, “Medical hyperspectral imaging: a review,” J. Biomed. Opt. 19(1), 010901 (2014).
    [Crossref]
  6. Z. Liu and J. Zerubia, “Melanin and Hemoglobin Identification for Skin Disease Analysis,” in 2013 2nd IAPR Asian Conference on Pattern Recognition (IEEE, 2013), pp. 145–149.
  7. A. R. Matias, M. Ferreira, P. Costa, and P. Neto, “Skin colour, skin redness and melanin biometric measurements: Comparison study between Antera 3D, Mexameter and Colorimeter,” Ski. Res. Technol. 21(3), 346–362 (2015).
    [Crossref]
  8. R. Ranabhatt, K. Singh, R. Siddharth, S. Tripathi, and D. Arya, “Color matching in facial prosthetics: A systematic review,” J. Indian Prosthodont. Soc. 17(1), 3–7 (2017).
    [Crossref]
  9. Y. Takahashi, Y. Fukushima, K. Kondo, and M. Ichihashi, “Facial skin photo-aging and development of hyperpigmented spots from children to middle-aged Japanese woman,” Ski. Res. Technol. 23(4), 613–618 (2017).
    [Crossref]
  10. J. A. Iglesias-Guitian, C. Aliaga, A. Jarabo, and D. Gutierrez, “A Biophysically-Based Model of the Optical Properties of Skin Aging,” Comput. Graph. Forum 34(2), 45–55 (2015).
    [Crossref]
  11. T. Weyrich, H. W. Jensen, M. Gross, W. Matusik, H. Pfister, B. Bickel, C. Donner, C. Tu, J. McAndless, J. Lee, and A. Ngan, “Analysis of human faces using a measurement-based skin reflectance model,” ACM Trans. Graph. 25(3), 1013–1024 (2006).
    [Crossref]
  12. N. Tsumura, N. Ojima, K. Sato, M. Shiraishi, H. Shimizu, H. Nabeshima, S. Akazaki, K. Hori, and Y. Miyake, “Image-based skin color and texture analysis/synthesis by extracting hemoglobin and melanin information in the skin,” ACM Trans. Graph. 22(3), 770 (2003).
    [Crossref]
  13. S. Tanaka and N. Tsumura, “Improvement of analyzing method for human skin color separation by independent component analysis,” in Imaging, Manipulation, and Analysis of Biomolecules, Cells, and Tissues XVII, D. L. Farkas, J. F. Leary, and A. Tarnok, eds. (SPIE, 2019), p. 48.
  14. J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, and J. W. Feather, “A theoretical and experimental study of light absorption and scattering by in vivo skin,” Phys. Med. Biol. 25(4), 695–709 (1980).
    [Crossref]
  15. B. L. Diffey, R. J. Oliver, and P. M. Farr, “A portable instrument for quantifying erythema induced by ultraviolet radiation,” Br. J. Dermatol. 111(6), 663–672 (1984).
    [Crossref]
  16. J. W. Feather, M. Hajizadeh-Saffar, G. Leslie, and J. B. Dawson, “A portable scanning reflectance spectrophotometer using visible wavelengths for the rapid measurement of skin pigments,” Phys. Med. Biol. 34(7), 807–820 (1989).
    [Crossref]
  17. I. Nishidate, Y. Aizu, and H. Mishina, “Estimation of melanin and hemoglobin in skin tissue using multiple regression analysis aided by Monte Carlo simulation,” J. Biomed. Opt. 9(4), 700 (2004).
    [Crossref]
  18. M. Shimada, Y. Yamada, M. Itoh, and T. Yatagai, “Melanin and blood concentration in a human skin model studied by multiple regression analysis: assessment by Monte Carlo simulation,” Phys. Med. Biol. 46(9), 2397–2406 (2001).
    [Crossref]
  19. M. Shimada, Y. Yamada, M. Itoh, and T. Yatagai, “Melanin and blood concentration in human skin studied by multiple regression analysis: Experiments,” Phys. Med. Biol. 46(9), 2385–2395 (2001).
    [Crossref]
  20. I. Nishidate, K. Sasaoka, T. Yuasa, K. Niizeki, T. Maeda, and Y. Aizu, “Visualizing of skin chromophore concentrations by use of RGB images,” Opt. Lett. 33(19), 2263–2265 (2008).
    [Crossref]
  21. I. Nishidate, N. Tanaka, T. Kawase, T. Maeda, T. Yuasa, Y. Aizu, T. Yuasa, and K. Niizeki, “Noninvasive imaging of human skin hemodynamics using a digital red-green-blue camera,” J. Biomed. Opt. 16(8), 086012 (2011).
    [Crossref]
  22. A. Hyvärinen and E. Oja, “Independent component analysis: algorithms and applications,” Neural Networks 13(4-5), 411–430 (2000).
    [Crossref]
  23. M. Hirose, S. Toyota, N. Ojima, K. Ogawa-Ochiai, and N. Tsumura, “Principal component analysis for surface reflection components and structure in facial images and synthesis of facial images for various ages,” Opt. Rev. 24(4), 517–528 (2017).
    [Crossref]

2017 (3)

R. Ranabhatt, K. Singh, R. Siddharth, S. Tripathi, and D. Arya, “Color matching in facial prosthetics: A systematic review,” J. Indian Prosthodont. Soc. 17(1), 3–7 (2017).
[Crossref]

Y. Takahashi, Y. Fukushima, K. Kondo, and M. Ichihashi, “Facial skin photo-aging and development of hyperpigmented spots from children to middle-aged Japanese woman,” Ski. Res. Technol. 23(4), 613–618 (2017).
[Crossref]

M. Hirose, S. Toyota, N. Ojima, K. Ogawa-Ochiai, and N. Tsumura, “Principal component analysis for surface reflection components and structure in facial images and synthesis of facial images for various ages,” Opt. Rev. 24(4), 517–528 (2017).
[Crossref]

2016 (1)

V. K. Shrivastava, N. D. Londhe, R. S. Sonawane, and J. S. Suri, “Computer-aided diagnosis of psoriasis skin images with HOS, texture and color features: A first comparative study of its kind,” Comput. Methods Programs Biomed. 126, 98–109 (2016).
[Crossref]

2015 (3)

Z. Liu and J. Zerubia, “Skin image illumination modeling and chromophore identification for melanoma diagnosis,” Phys. Med. Biol. 60(9), 3415–3431 (2015).
[Crossref]

A. R. Matias, M. Ferreira, P. Costa, and P. Neto, “Skin colour, skin redness and melanin biometric measurements: Comparison study between Antera 3D, Mexameter and Colorimeter,” Ski. Res. Technol. 21(3), 346–362 (2015).
[Crossref]

J. A. Iglesias-Guitian, C. Aliaga, A. Jarabo, and D. Gutierrez, “A Biophysically-Based Model of the Optical Properties of Skin Aging,” Comput. Graph. Forum 34(2), 45–55 (2015).
[Crossref]

2014 (1)

G. Lu and B. Fei, “Medical hyperspectral imaging: a review,” J. Biomed. Opt. 19(1), 010901 (2014).
[Crossref]

2011 (1)

I. Nishidate, N. Tanaka, T. Kawase, T. Maeda, T. Yuasa, Y. Aizu, T. Yuasa, and K. Niizeki, “Noninvasive imaging of human skin hemodynamics using a digital red-green-blue camera,” J. Biomed. Opt. 16(8), 086012 (2011).
[Crossref]

2008 (1)

2006 (1)

T. Weyrich, H. W. Jensen, M. Gross, W. Matusik, H. Pfister, B. Bickel, C. Donner, C. Tu, J. McAndless, J. Lee, and A. Ngan, “Analysis of human faces using a measurement-based skin reflectance model,” ACM Trans. Graph. 25(3), 1013–1024 (2006).
[Crossref]

2004 (1)

I. Nishidate, Y. Aizu, and H. Mishina, “Estimation of melanin and hemoglobin in skin tissue using multiple regression analysis aided by Monte Carlo simulation,” J. Biomed. Opt. 9(4), 700 (2004).
[Crossref]

2003 (2)

N. Tsumura, N. Ojima, K. Sato, M. Shiraishi, H. Shimizu, H. Nabeshima, S. Akazaki, K. Hori, and Y. Miyake, “Image-based skin color and texture analysis/synthesis by extracting hemoglobin and melanin information in the skin,” ACM Trans. Graph. 22(3), 770 (2003).
[Crossref]

E. Claridge, S. Cotton, P. Hall, and M. Moncrieff, “From colour to tissue histology: Physics-based interpretation of images of pigmented skin lesions,” Med. Image Anal. 7(4), 489–502 (2003).
[Crossref]

2001 (2)

M. Shimada, Y. Yamada, M. Itoh, and T. Yatagai, “Melanin and blood concentration in a human skin model studied by multiple regression analysis: assessment by Monte Carlo simulation,” Phys. Med. Biol. 46(9), 2397–2406 (2001).
[Crossref]

M. Shimada, Y. Yamada, M. Itoh, and T. Yatagai, “Melanin and blood concentration in human skin studied by multiple regression analysis: Experiments,” Phys. Med. Biol. 46(9), 2385–2395 (2001).
[Crossref]

2000 (1)

A. Hyvärinen and E. Oja, “Independent component analysis: algorithms and applications,” Neural Networks 13(4-5), 411–430 (2000).
[Crossref]

1989 (1)

J. W. Feather, M. Hajizadeh-Saffar, G. Leslie, and J. B. Dawson, “A portable scanning reflectance spectrophotometer using visible wavelengths for the rapid measurement of skin pigments,” Phys. Med. Biol. 34(7), 807–820 (1989).
[Crossref]

1984 (1)

B. L. Diffey, R. J. Oliver, and P. M. Farr, “A portable instrument for quantifying erythema induced by ultraviolet radiation,” Br. J. Dermatol. 111(6), 663–672 (1984).
[Crossref]

1980 (1)

J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, and J. W. Feather, “A theoretical and experimental study of light absorption and scattering by in vivo skin,” Phys. Med. Biol. 25(4), 695–709 (1980).
[Crossref]

Aizu, Y.

I. Nishidate, N. Tanaka, T. Kawase, T. Maeda, T. Yuasa, Y. Aizu, T. Yuasa, and K. Niizeki, “Noninvasive imaging of human skin hemodynamics using a digital red-green-blue camera,” J. Biomed. Opt. 16(8), 086012 (2011).
[Crossref]

I. Nishidate, K. Sasaoka, T. Yuasa, K. Niizeki, T. Maeda, and Y. Aizu, “Visualizing of skin chromophore concentrations by use of RGB images,” Opt. Lett. 33(19), 2263–2265 (2008).
[Crossref]

I. Nishidate, Y. Aizu, and H. Mishina, “Estimation of melanin and hemoglobin in skin tissue using multiple regression analysis aided by Monte Carlo simulation,” J. Biomed. Opt. 9(4), 700 (2004).
[Crossref]

Akazaki, S.

N. Tsumura, N. Ojima, K. Sato, M. Shiraishi, H. Shimizu, H. Nabeshima, S. Akazaki, K. Hori, and Y. Miyake, “Image-based skin color and texture analysis/synthesis by extracting hemoglobin and melanin information in the skin,” ACM Trans. Graph. 22(3), 770 (2003).
[Crossref]

Aliaga, C.

J. A. Iglesias-Guitian, C. Aliaga, A. Jarabo, and D. Gutierrez, “A Biophysically-Based Model of the Optical Properties of Skin Aging,” Comput. Graph. Forum 34(2), 45–55 (2015).
[Crossref]

Arya, D.

R. Ranabhatt, K. Singh, R. Siddharth, S. Tripathi, and D. Arya, “Color matching in facial prosthetics: A systematic review,” J. Indian Prosthodont. Soc. 17(1), 3–7 (2017).
[Crossref]

Barker, D. J.

J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, and J. W. Feather, “A theoretical and experimental study of light absorption and scattering by in vivo skin,” Phys. Med. Biol. 25(4), 695–709 (1980).
[Crossref]

Bickel, B.

T. Weyrich, H. W. Jensen, M. Gross, W. Matusik, H. Pfister, B. Bickel, C. Donner, C. Tu, J. McAndless, J. Lee, and A. Ngan, “Analysis of human faces using a measurement-based skin reflectance model,” ACM Trans. Graph. 25(3), 1013–1024 (2006).
[Crossref]

Claridge, E.

E. Claridge, S. Cotton, P. Hall, and M. Moncrieff, “From colour to tissue histology: Physics-based interpretation of images of pigmented skin lesions,” Med. Image Anal. 7(4), 489–502 (2003).
[Crossref]

Costa, P.

A. R. Matias, M. Ferreira, P. Costa, and P. Neto, “Skin colour, skin redness and melanin biometric measurements: Comparison study between Antera 3D, Mexameter and Colorimeter,” Ski. Res. Technol. 21(3), 346–362 (2015).
[Crossref]

Cotterill, J. A.

J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, and J. W. Feather, “A theoretical and experimental study of light absorption and scattering by in vivo skin,” Phys. Med. Biol. 25(4), 695–709 (1980).
[Crossref]

Cotton, S.

E. Claridge, S. Cotton, P. Hall, and M. Moncrieff, “From colour to tissue histology: Physics-based interpretation of images of pigmented skin lesions,” Med. Image Anal. 7(4), 489–502 (2003).
[Crossref]

Dawson, J. B.

J. W. Feather, M. Hajizadeh-Saffar, G. Leslie, and J. B. Dawson, “A portable scanning reflectance spectrophotometer using visible wavelengths for the rapid measurement of skin pigments,” Phys. Med. Biol. 34(7), 807–820 (1989).
[Crossref]

J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, and J. W. Feather, “A theoretical and experimental study of light absorption and scattering by in vivo skin,” Phys. Med. Biol. 25(4), 695–709 (1980).
[Crossref]

Diffey, B. L.

B. L. Diffey, R. J. Oliver, and P. M. Farr, “A portable instrument for quantifying erythema induced by ultraviolet radiation,” Br. J. Dermatol. 111(6), 663–672 (1984).
[Crossref]

Donner, C.

T. Weyrich, H. W. Jensen, M. Gross, W. Matusik, H. Pfister, B. Bickel, C. Donner, C. Tu, J. McAndless, J. Lee, and A. Ngan, “Analysis of human faces using a measurement-based skin reflectance model,” ACM Trans. Graph. 25(3), 1013–1024 (2006).
[Crossref]

Ellis, D. J.

J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, and J. W. Feather, “A theoretical and experimental study of light absorption and scattering by in vivo skin,” Phys. Med. Biol. 25(4), 695–709 (1980).
[Crossref]

Farr, P. M.

B. L. Diffey, R. J. Oliver, and P. M. Farr, “A portable instrument for quantifying erythema induced by ultraviolet radiation,” Br. J. Dermatol. 111(6), 663–672 (1984).
[Crossref]

Feather, J. W.

J. W. Feather, M. Hajizadeh-Saffar, G. Leslie, and J. B. Dawson, “A portable scanning reflectance spectrophotometer using visible wavelengths for the rapid measurement of skin pigments,” Phys. Med. Biol. 34(7), 807–820 (1989).
[Crossref]

J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, and J. W. Feather, “A theoretical and experimental study of light absorption and scattering by in vivo skin,” Phys. Med. Biol. 25(4), 695–709 (1980).
[Crossref]

Fei, B.

G. Lu and B. Fei, “Medical hyperspectral imaging: a review,” J. Biomed. Opt. 19(1), 010901 (2014).
[Crossref]

Ferreira, M.

A. R. Matias, M. Ferreira, P. Costa, and P. Neto, “Skin colour, skin redness and melanin biometric measurements: Comparison study between Antera 3D, Mexameter and Colorimeter,” Ski. Res. Technol. 21(3), 346–362 (2015).
[Crossref]

Fisher, G. W.

J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, and J. W. Feather, “A theoretical and experimental study of light absorption and scattering by in vivo skin,” Phys. Med. Biol. 25(4), 695–709 (1980).
[Crossref]

Fukushima, Y.

Y. Takahashi, Y. Fukushima, K. Kondo, and M. Ichihashi, “Facial skin photo-aging and development of hyperpigmented spots from children to middle-aged Japanese woman,” Ski. Res. Technol. 23(4), 613–618 (2017).
[Crossref]

Grassam, E.

J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, and J. W. Feather, “A theoretical and experimental study of light absorption and scattering by in vivo skin,” Phys. Med. Biol. 25(4), 695–709 (1980).
[Crossref]

Gross, M.

T. Weyrich, H. W. Jensen, M. Gross, W. Matusik, H. Pfister, B. Bickel, C. Donner, C. Tu, J. McAndless, J. Lee, and A. Ngan, “Analysis of human faces using a measurement-based skin reflectance model,” ACM Trans. Graph. 25(3), 1013–1024 (2006).
[Crossref]

Gutierrez, D.

J. A. Iglesias-Guitian, C. Aliaga, A. Jarabo, and D. Gutierrez, “A Biophysically-Based Model of the Optical Properties of Skin Aging,” Comput. Graph. Forum 34(2), 45–55 (2015).
[Crossref]

Hajizadeh-Saffar, M.

J. W. Feather, M. Hajizadeh-Saffar, G. Leslie, and J. B. Dawson, “A portable scanning reflectance spectrophotometer using visible wavelengths for the rapid measurement of skin pigments,” Phys. Med. Biol. 34(7), 807–820 (1989).
[Crossref]

Hall, P.

E. Claridge, S. Cotton, P. Hall, and M. Moncrieff, “From colour to tissue histology: Physics-based interpretation of images of pigmented skin lesions,” Med. Image Anal. 7(4), 489–502 (2003).
[Crossref]

Hirose, M.

M. Hirose, S. Toyota, N. Ojima, K. Ogawa-Ochiai, and N. Tsumura, “Principal component analysis for surface reflection components and structure in facial images and synthesis of facial images for various ages,” Opt. Rev. 24(4), 517–528 (2017).
[Crossref]

Hori, K.

N. Tsumura, N. Ojima, K. Sato, M. Shiraishi, H. Shimizu, H. Nabeshima, S. Akazaki, K. Hori, and Y. Miyake, “Image-based skin color and texture analysis/synthesis by extracting hemoglobin and melanin information in the skin,” ACM Trans. Graph. 22(3), 770 (2003).
[Crossref]

Hyvärinen, A.

A. Hyvärinen and E. Oja, “Independent component analysis: algorithms and applications,” Neural Networks 13(4-5), 411–430 (2000).
[Crossref]

Ichihashi, M.

Y. Takahashi, Y. Fukushima, K. Kondo, and M. Ichihashi, “Facial skin photo-aging and development of hyperpigmented spots from children to middle-aged Japanese woman,” Ski. Res. Technol. 23(4), 613–618 (2017).
[Crossref]

Iglesias-Guitian, J. A.

J. A. Iglesias-Guitian, C. Aliaga, A. Jarabo, and D. Gutierrez, “A Biophysically-Based Model of the Optical Properties of Skin Aging,” Comput. Graph. Forum 34(2), 45–55 (2015).
[Crossref]

Itoh, M.

M. Shimada, Y. Yamada, M. Itoh, and T. Yatagai, “Melanin and blood concentration in a human skin model studied by multiple regression analysis: assessment by Monte Carlo simulation,” Phys. Med. Biol. 46(9), 2397–2406 (2001).
[Crossref]

M. Shimada, Y. Yamada, M. Itoh, and T. Yatagai, “Melanin and blood concentration in human skin studied by multiple regression analysis: Experiments,” Phys. Med. Biol. 46(9), 2385–2395 (2001).
[Crossref]

Jarabo, A.

J. A. Iglesias-Guitian, C. Aliaga, A. Jarabo, and D. Gutierrez, “A Biophysically-Based Model of the Optical Properties of Skin Aging,” Comput. Graph. Forum 34(2), 45–55 (2015).
[Crossref]

Jensen, H. W.

T. Weyrich, H. W. Jensen, M. Gross, W. Matusik, H. Pfister, B. Bickel, C. Donner, C. Tu, J. McAndless, J. Lee, and A. Ngan, “Analysis of human faces using a measurement-based skin reflectance model,” ACM Trans. Graph. 25(3), 1013–1024 (2006).
[Crossref]

Kawase, T.

I. Nishidate, N. Tanaka, T. Kawase, T. Maeda, T. Yuasa, Y. Aizu, T. Yuasa, and K. Niizeki, “Noninvasive imaging of human skin hemodynamics using a digital red-green-blue camera,” J. Biomed. Opt. 16(8), 086012 (2011).
[Crossref]

Kondo, K.

Y. Takahashi, Y. Fukushima, K. Kondo, and M. Ichihashi, “Facial skin photo-aging and development of hyperpigmented spots from children to middle-aged Japanese woman,” Ski. Res. Technol. 23(4), 613–618 (2017).
[Crossref]

Lee, J.

T. Weyrich, H. W. Jensen, M. Gross, W. Matusik, H. Pfister, B. Bickel, C. Donner, C. Tu, J. McAndless, J. Lee, and A. Ngan, “Analysis of human faces using a measurement-based skin reflectance model,” ACM Trans. Graph. 25(3), 1013–1024 (2006).
[Crossref]

Leslie, G.

J. W. Feather, M. Hajizadeh-Saffar, G. Leslie, and J. B. Dawson, “A portable scanning reflectance spectrophotometer using visible wavelengths for the rapid measurement of skin pigments,” Phys. Med. Biol. 34(7), 807–820 (1989).
[Crossref]

Liang, J.

J. Yang, X. Sun, J. Liang, and P. L. Rosin, “Clinical Skin Lesion Diagnosis using Representations Inspired by Dermatologist Criteria,” Cvpr, 1258–1266 (2018).

Liu, Z.

Z. Liu and J. Zerubia, “Skin image illumination modeling and chromophore identification for melanoma diagnosis,” Phys. Med. Biol. 60(9), 3415–3431 (2015).
[Crossref]

Z. Liu and J. Zerubia, “Melanin and Hemoglobin Identification for Skin Disease Analysis,” in 2013 2nd IAPR Asian Conference on Pattern Recognition (IEEE, 2013), pp. 145–149.

Londhe, N. D.

V. K. Shrivastava, N. D. Londhe, R. S. Sonawane, and J. S. Suri, “Computer-aided diagnosis of psoriasis skin images with HOS, texture and color features: A first comparative study of its kind,” Comput. Methods Programs Biomed. 126, 98–109 (2016).
[Crossref]

Lu, G.

G. Lu and B. Fei, “Medical hyperspectral imaging: a review,” J. Biomed. Opt. 19(1), 010901 (2014).
[Crossref]

Maeda, T.

I. Nishidate, N. Tanaka, T. Kawase, T. Maeda, T. Yuasa, Y. Aizu, T. Yuasa, and K. Niizeki, “Noninvasive imaging of human skin hemodynamics using a digital red-green-blue camera,” J. Biomed. Opt. 16(8), 086012 (2011).
[Crossref]

I. Nishidate, K. Sasaoka, T. Yuasa, K. Niizeki, T. Maeda, and Y. Aizu, “Visualizing of skin chromophore concentrations by use of RGB images,” Opt. Lett. 33(19), 2263–2265 (2008).
[Crossref]

Matias, A. R.

A. R. Matias, M. Ferreira, P. Costa, and P. Neto, “Skin colour, skin redness and melanin biometric measurements: Comparison study between Antera 3D, Mexameter and Colorimeter,” Ski. Res. Technol. 21(3), 346–362 (2015).
[Crossref]

Matusik, W.

T. Weyrich, H. W. Jensen, M. Gross, W. Matusik, H. Pfister, B. Bickel, C. Donner, C. Tu, J. McAndless, J. Lee, and A. Ngan, “Analysis of human faces using a measurement-based skin reflectance model,” ACM Trans. Graph. 25(3), 1013–1024 (2006).
[Crossref]

McAndless, J.

T. Weyrich, H. W. Jensen, M. Gross, W. Matusik, H. Pfister, B. Bickel, C. Donner, C. Tu, J. McAndless, J. Lee, and A. Ngan, “Analysis of human faces using a measurement-based skin reflectance model,” ACM Trans. Graph. 25(3), 1013–1024 (2006).
[Crossref]

Mishina, H.

I. Nishidate, Y. Aizu, and H. Mishina, “Estimation of melanin and hemoglobin in skin tissue using multiple regression analysis aided by Monte Carlo simulation,” J. Biomed. Opt. 9(4), 700 (2004).
[Crossref]

Miyake, Y.

N. Tsumura, N. Ojima, K. Sato, M. Shiraishi, H. Shimizu, H. Nabeshima, S. Akazaki, K. Hori, and Y. Miyake, “Image-based skin color and texture analysis/synthesis by extracting hemoglobin and melanin information in the skin,” ACM Trans. Graph. 22(3), 770 (2003).
[Crossref]

Moncrieff, M.

E. Claridge, S. Cotton, P. Hall, and M. Moncrieff, “From colour to tissue histology: Physics-based interpretation of images of pigmented skin lesions,” Med. Image Anal. 7(4), 489–502 (2003).
[Crossref]

Nabeshima, H.

N. Tsumura, N. Ojima, K. Sato, M. Shiraishi, H. Shimizu, H. Nabeshima, S. Akazaki, K. Hori, and Y. Miyake, “Image-based skin color and texture analysis/synthesis by extracting hemoglobin and melanin information in the skin,” ACM Trans. Graph. 22(3), 770 (2003).
[Crossref]

Neto, P.

A. R. Matias, M. Ferreira, P. Costa, and P. Neto, “Skin colour, skin redness and melanin biometric measurements: Comparison study between Antera 3D, Mexameter and Colorimeter,” Ski. Res. Technol. 21(3), 346–362 (2015).
[Crossref]

Ngan, A.

T. Weyrich, H. W. Jensen, M. Gross, W. Matusik, H. Pfister, B. Bickel, C. Donner, C. Tu, J. McAndless, J. Lee, and A. Ngan, “Analysis of human faces using a measurement-based skin reflectance model,” ACM Trans. Graph. 25(3), 1013–1024 (2006).
[Crossref]

Niizeki, K.

I. Nishidate, N. Tanaka, T. Kawase, T. Maeda, T. Yuasa, Y. Aizu, T. Yuasa, and K. Niizeki, “Noninvasive imaging of human skin hemodynamics using a digital red-green-blue camera,” J. Biomed. Opt. 16(8), 086012 (2011).
[Crossref]

I. Nishidate, K. Sasaoka, T. Yuasa, K. Niizeki, T. Maeda, and Y. Aizu, “Visualizing of skin chromophore concentrations by use of RGB images,” Opt. Lett. 33(19), 2263–2265 (2008).
[Crossref]

Nishidate, I.

I. Nishidate, N. Tanaka, T. Kawase, T. Maeda, T. Yuasa, Y. Aizu, T. Yuasa, and K. Niizeki, “Noninvasive imaging of human skin hemodynamics using a digital red-green-blue camera,” J. Biomed. Opt. 16(8), 086012 (2011).
[Crossref]

I. Nishidate, K. Sasaoka, T. Yuasa, K. Niizeki, T. Maeda, and Y. Aizu, “Visualizing of skin chromophore concentrations by use of RGB images,” Opt. Lett. 33(19), 2263–2265 (2008).
[Crossref]

I. Nishidate, Y. Aizu, and H. Mishina, “Estimation of melanin and hemoglobin in skin tissue using multiple regression analysis aided by Monte Carlo simulation,” J. Biomed. Opt. 9(4), 700 (2004).
[Crossref]

Ogawa-Ochiai, K.

M. Hirose, S. Toyota, N. Ojima, K. Ogawa-Ochiai, and N. Tsumura, “Principal component analysis for surface reflection components and structure in facial images and synthesis of facial images for various ages,” Opt. Rev. 24(4), 517–528 (2017).
[Crossref]

Oja, E.

A. Hyvärinen and E. Oja, “Independent component analysis: algorithms and applications,” Neural Networks 13(4-5), 411–430 (2000).
[Crossref]

Ojima, N.

M. Hirose, S. Toyota, N. Ojima, K. Ogawa-Ochiai, and N. Tsumura, “Principal component analysis for surface reflection components and structure in facial images and synthesis of facial images for various ages,” Opt. Rev. 24(4), 517–528 (2017).
[Crossref]

N. Tsumura, N. Ojima, K. Sato, M. Shiraishi, H. Shimizu, H. Nabeshima, S. Akazaki, K. Hori, and Y. Miyake, “Image-based skin color and texture analysis/synthesis by extracting hemoglobin and melanin information in the skin,” ACM Trans. Graph. 22(3), 770 (2003).
[Crossref]

Oliver, R. J.

B. L. Diffey, R. J. Oliver, and P. M. Farr, “A portable instrument for quantifying erythema induced by ultraviolet radiation,” Br. J. Dermatol. 111(6), 663–672 (1984).
[Crossref]

Pfister, H.

T. Weyrich, H. W. Jensen, M. Gross, W. Matusik, H. Pfister, B. Bickel, C. Donner, C. Tu, J. McAndless, J. Lee, and A. Ngan, “Analysis of human faces using a measurement-based skin reflectance model,” ACM Trans. Graph. 25(3), 1013–1024 (2006).
[Crossref]

Ranabhatt, R.

R. Ranabhatt, K. Singh, R. Siddharth, S. Tripathi, and D. Arya, “Color matching in facial prosthetics: A systematic review,” J. Indian Prosthodont. Soc. 17(1), 3–7 (2017).
[Crossref]

Rosin, P. L.

J. Yang, X. Sun, J. Liang, and P. L. Rosin, “Clinical Skin Lesion Diagnosis using Representations Inspired by Dermatologist Criteria,” Cvpr, 1258–1266 (2018).

Sasaoka, K.

Sato, K.

N. Tsumura, N. Ojima, K. Sato, M. Shiraishi, H. Shimizu, H. Nabeshima, S. Akazaki, K. Hori, and Y. Miyake, “Image-based skin color and texture analysis/synthesis by extracting hemoglobin and melanin information in the skin,” ACM Trans. Graph. 22(3), 770 (2003).
[Crossref]

Shimada, M.

M. Shimada, Y. Yamada, M. Itoh, and T. Yatagai, “Melanin and blood concentration in a human skin model studied by multiple regression analysis: assessment by Monte Carlo simulation,” Phys. Med. Biol. 46(9), 2397–2406 (2001).
[Crossref]

M. Shimada, Y. Yamada, M. Itoh, and T. Yatagai, “Melanin and blood concentration in human skin studied by multiple regression analysis: Experiments,” Phys. Med. Biol. 46(9), 2385–2395 (2001).
[Crossref]

Shimizu, H.

N. Tsumura, N. Ojima, K. Sato, M. Shiraishi, H. Shimizu, H. Nabeshima, S. Akazaki, K. Hori, and Y. Miyake, “Image-based skin color and texture analysis/synthesis by extracting hemoglobin and melanin information in the skin,” ACM Trans. Graph. 22(3), 770 (2003).
[Crossref]

Shiraishi, M.

N. Tsumura, N. Ojima, K. Sato, M. Shiraishi, H. Shimizu, H. Nabeshima, S. Akazaki, K. Hori, and Y. Miyake, “Image-based skin color and texture analysis/synthesis by extracting hemoglobin and melanin information in the skin,” ACM Trans. Graph. 22(3), 770 (2003).
[Crossref]

Shrivastava, V. K.

V. K. Shrivastava, N. D. Londhe, R. S. Sonawane, and J. S. Suri, “Computer-aided diagnosis of psoriasis skin images with HOS, texture and color features: A first comparative study of its kind,” Comput. Methods Programs Biomed. 126, 98–109 (2016).
[Crossref]

Siddharth, R.

R. Ranabhatt, K. Singh, R. Siddharth, S. Tripathi, and D. Arya, “Color matching in facial prosthetics: A systematic review,” J. Indian Prosthodont. Soc. 17(1), 3–7 (2017).
[Crossref]

Singh, K.

R. Ranabhatt, K. Singh, R. Siddharth, S. Tripathi, and D. Arya, “Color matching in facial prosthetics: A systematic review,” J. Indian Prosthodont. Soc. 17(1), 3–7 (2017).
[Crossref]

Sonawane, R. S.

V. K. Shrivastava, N. D. Londhe, R. S. Sonawane, and J. S. Suri, “Computer-aided diagnosis of psoriasis skin images with HOS, texture and color features: A first comparative study of its kind,” Comput. Methods Programs Biomed. 126, 98–109 (2016).
[Crossref]

Sun, X.

J. Yang, X. Sun, J. Liang, and P. L. Rosin, “Clinical Skin Lesion Diagnosis using Representations Inspired by Dermatologist Criteria,” Cvpr, 1258–1266 (2018).

Suri, J. S.

V. K. Shrivastava, N. D. Londhe, R. S. Sonawane, and J. S. Suri, “Computer-aided diagnosis of psoriasis skin images with HOS, texture and color features: A first comparative study of its kind,” Comput. Methods Programs Biomed. 126, 98–109 (2016).
[Crossref]

Takahashi, Y.

Y. Takahashi, Y. Fukushima, K. Kondo, and M. Ichihashi, “Facial skin photo-aging and development of hyperpigmented spots from children to middle-aged Japanese woman,” Ski. Res. Technol. 23(4), 613–618 (2017).
[Crossref]

Tanaka, N.

I. Nishidate, N. Tanaka, T. Kawase, T. Maeda, T. Yuasa, Y. Aizu, T. Yuasa, and K. Niizeki, “Noninvasive imaging of human skin hemodynamics using a digital red-green-blue camera,” J. Biomed. Opt. 16(8), 086012 (2011).
[Crossref]

Tanaka, S.

S. Tanaka and N. Tsumura, “Improvement of analyzing method for human skin color separation by independent component analysis,” in Imaging, Manipulation, and Analysis of Biomolecules, Cells, and Tissues XVII, D. L. Farkas, J. F. Leary, and A. Tarnok, eds. (SPIE, 2019), p. 48.

Toyota, S.

M. Hirose, S. Toyota, N. Ojima, K. Ogawa-Ochiai, and N. Tsumura, “Principal component analysis for surface reflection components and structure in facial images and synthesis of facial images for various ages,” Opt. Rev. 24(4), 517–528 (2017).
[Crossref]

Tripathi, S.

R. Ranabhatt, K. Singh, R. Siddharth, S. Tripathi, and D. Arya, “Color matching in facial prosthetics: A systematic review,” J. Indian Prosthodont. Soc. 17(1), 3–7 (2017).
[Crossref]

Tsumura, N.

M. Hirose, S. Toyota, N. Ojima, K. Ogawa-Ochiai, and N. Tsumura, “Principal component analysis for surface reflection components and structure in facial images and synthesis of facial images for various ages,” Opt. Rev. 24(4), 517–528 (2017).
[Crossref]

N. Tsumura, N. Ojima, K. Sato, M. Shiraishi, H. Shimizu, H. Nabeshima, S. Akazaki, K. Hori, and Y. Miyake, “Image-based skin color and texture analysis/synthesis by extracting hemoglobin and melanin information in the skin,” ACM Trans. Graph. 22(3), 770 (2003).
[Crossref]

S. Tanaka and N. Tsumura, “Improvement of analyzing method for human skin color separation by independent component analysis,” in Imaging, Manipulation, and Analysis of Biomolecules, Cells, and Tissues XVII, D. L. Farkas, J. F. Leary, and A. Tarnok, eds. (SPIE, 2019), p. 48.

Tu, C.

T. Weyrich, H. W. Jensen, M. Gross, W. Matusik, H. Pfister, B. Bickel, C. Donner, C. Tu, J. McAndless, J. Lee, and A. Ngan, “Analysis of human faces using a measurement-based skin reflectance model,” ACM Trans. Graph. 25(3), 1013–1024 (2006).
[Crossref]

Weyrich, T.

T. Weyrich, H. W. Jensen, M. Gross, W. Matusik, H. Pfister, B. Bickel, C. Donner, C. Tu, J. McAndless, J. Lee, and A. Ngan, “Analysis of human faces using a measurement-based skin reflectance model,” ACM Trans. Graph. 25(3), 1013–1024 (2006).
[Crossref]

Yamada, Y.

M. Shimada, Y. Yamada, M. Itoh, and T. Yatagai, “Melanin and blood concentration in a human skin model studied by multiple regression analysis: assessment by Monte Carlo simulation,” Phys. Med. Biol. 46(9), 2397–2406 (2001).
[Crossref]

M. Shimada, Y. Yamada, M. Itoh, and T. Yatagai, “Melanin and blood concentration in human skin studied by multiple regression analysis: Experiments,” Phys. Med. Biol. 46(9), 2385–2395 (2001).
[Crossref]

Yang, J.

J. Yang, X. Sun, J. Liang, and P. L. Rosin, “Clinical Skin Lesion Diagnosis using Representations Inspired by Dermatologist Criteria,” Cvpr, 1258–1266 (2018).

Yatagai, T.

M. Shimada, Y. Yamada, M. Itoh, and T. Yatagai, “Melanin and blood concentration in human skin studied by multiple regression analysis: Experiments,” Phys. Med. Biol. 46(9), 2385–2395 (2001).
[Crossref]

M. Shimada, Y. Yamada, M. Itoh, and T. Yatagai, “Melanin and blood concentration in a human skin model studied by multiple regression analysis: assessment by Monte Carlo simulation,” Phys. Med. Biol. 46(9), 2397–2406 (2001).
[Crossref]

Yuasa, T.

I. Nishidate, N. Tanaka, T. Kawase, T. Maeda, T. Yuasa, Y. Aizu, T. Yuasa, and K. Niizeki, “Noninvasive imaging of human skin hemodynamics using a digital red-green-blue camera,” J. Biomed. Opt. 16(8), 086012 (2011).
[Crossref]

I. Nishidate, N. Tanaka, T. Kawase, T. Maeda, T. Yuasa, Y. Aizu, T. Yuasa, and K. Niizeki, “Noninvasive imaging of human skin hemodynamics using a digital red-green-blue camera,” J. Biomed. Opt. 16(8), 086012 (2011).
[Crossref]

I. Nishidate, K. Sasaoka, T. Yuasa, K. Niizeki, T. Maeda, and Y. Aizu, “Visualizing of skin chromophore concentrations by use of RGB images,” Opt. Lett. 33(19), 2263–2265 (2008).
[Crossref]

Zerubia, J.

Z. Liu and J. Zerubia, “Skin image illumination modeling and chromophore identification for melanoma diagnosis,” Phys. Med. Biol. 60(9), 3415–3431 (2015).
[Crossref]

Z. Liu and J. Zerubia, “Melanin and Hemoglobin Identification for Skin Disease Analysis,” in 2013 2nd IAPR Asian Conference on Pattern Recognition (IEEE, 2013), pp. 145–149.

ACM Trans. Graph. (2)

T. Weyrich, H. W. Jensen, M. Gross, W. Matusik, H. Pfister, B. Bickel, C. Donner, C. Tu, J. McAndless, J. Lee, and A. Ngan, “Analysis of human faces using a measurement-based skin reflectance model,” ACM Trans. Graph. 25(3), 1013–1024 (2006).
[Crossref]

N. Tsumura, N. Ojima, K. Sato, M. Shiraishi, H. Shimizu, H. Nabeshima, S. Akazaki, K. Hori, and Y. Miyake, “Image-based skin color and texture analysis/synthesis by extracting hemoglobin and melanin information in the skin,” ACM Trans. Graph. 22(3), 770 (2003).
[Crossref]

Br. J. Dermatol. (1)

B. L. Diffey, R. J. Oliver, and P. M. Farr, “A portable instrument for quantifying erythema induced by ultraviolet radiation,” Br. J. Dermatol. 111(6), 663–672 (1984).
[Crossref]

Comput. Graph. Forum (1)

J. A. Iglesias-Guitian, C. Aliaga, A. Jarabo, and D. Gutierrez, “A Biophysically-Based Model of the Optical Properties of Skin Aging,” Comput. Graph. Forum 34(2), 45–55 (2015).
[Crossref]

Comput. Methods Programs Biomed. (1)

V. K. Shrivastava, N. D. Londhe, R. S. Sonawane, and J. S. Suri, “Computer-aided diagnosis of psoriasis skin images with HOS, texture and color features: A first comparative study of its kind,” Comput. Methods Programs Biomed. 126, 98–109 (2016).
[Crossref]

J. Biomed. Opt. (3)

G. Lu and B. Fei, “Medical hyperspectral imaging: a review,” J. Biomed. Opt. 19(1), 010901 (2014).
[Crossref]

I. Nishidate, Y. Aizu, and H. Mishina, “Estimation of melanin and hemoglobin in skin tissue using multiple regression analysis aided by Monte Carlo simulation,” J. Biomed. Opt. 9(4), 700 (2004).
[Crossref]

I. Nishidate, N. Tanaka, T. Kawase, T. Maeda, T. Yuasa, Y. Aizu, T. Yuasa, and K. Niizeki, “Noninvasive imaging of human skin hemodynamics using a digital red-green-blue camera,” J. Biomed. Opt. 16(8), 086012 (2011).
[Crossref]

J. Indian Prosthodont. Soc. (1)

R. Ranabhatt, K. Singh, R. Siddharth, S. Tripathi, and D. Arya, “Color matching in facial prosthetics: A systematic review,” J. Indian Prosthodont. Soc. 17(1), 3–7 (2017).
[Crossref]

Med. Image Anal. (1)

E. Claridge, S. Cotton, P. Hall, and M. Moncrieff, “From colour to tissue histology: Physics-based interpretation of images of pigmented skin lesions,” Med. Image Anal. 7(4), 489–502 (2003).
[Crossref]

Neural Networks (1)

A. Hyvärinen and E. Oja, “Independent component analysis: algorithms and applications,” Neural Networks 13(4-5), 411–430 (2000).
[Crossref]

Opt. Lett. (1)

Opt. Rev. (1)

M. Hirose, S. Toyota, N. Ojima, K. Ogawa-Ochiai, and N. Tsumura, “Principal component analysis for surface reflection components and structure in facial images and synthesis of facial images for various ages,” Opt. Rev. 24(4), 517–528 (2017).
[Crossref]

Phys. Med. Biol. (5)

J. B. Dawson, D. J. Barker, D. J. Ellis, E. Grassam, J. A. Cotterill, G. W. Fisher, and J. W. Feather, “A theoretical and experimental study of light absorption and scattering by in vivo skin,” Phys. Med. Biol. 25(4), 695–709 (1980).
[Crossref]

Z. Liu and J. Zerubia, “Skin image illumination modeling and chromophore identification for melanoma diagnosis,” Phys. Med. Biol. 60(9), 3415–3431 (2015).
[Crossref]

M. Shimada, Y. Yamada, M. Itoh, and T. Yatagai, “Melanin and blood concentration in a human skin model studied by multiple regression analysis: assessment by Monte Carlo simulation,” Phys. Med. Biol. 46(9), 2397–2406 (2001).
[Crossref]

M. Shimada, Y. Yamada, M. Itoh, and T. Yatagai, “Melanin and blood concentration in human skin studied by multiple regression analysis: Experiments,” Phys. Med. Biol. 46(9), 2385–2395 (2001).
[Crossref]

J. W. Feather, M. Hajizadeh-Saffar, G. Leslie, and J. B. Dawson, “A portable scanning reflectance spectrophotometer using visible wavelengths for the rapid measurement of skin pigments,” Phys. Med. Biol. 34(7), 807–820 (1989).
[Crossref]

Ski. Res. Technol. (2)

A. R. Matias, M. Ferreira, P. Costa, and P. Neto, “Skin colour, skin redness and melanin biometric measurements: Comparison study between Antera 3D, Mexameter and Colorimeter,” Ski. Res. Technol. 21(3), 346–362 (2015).
[Crossref]

Y. Takahashi, Y. Fukushima, K. Kondo, and M. Ichihashi, “Facial skin photo-aging and development of hyperpigmented spots from children to middle-aged Japanese woman,” Ski. Res. Technol. 23(4), 613–618 (2017).
[Crossref]

Other (3)

Z. Liu and J. Zerubia, “Melanin and Hemoglobin Identification for Skin Disease Analysis,” in 2013 2nd IAPR Asian Conference on Pattern Recognition (IEEE, 2013), pp. 145–149.

J. Yang, X. Sun, J. Liang, and P. L. Rosin, “Clinical Skin Lesion Diagnosis using Representations Inspired by Dermatologist Criteria,” Cvpr, 1258–1266 (2018).

S. Tanaka and N. Tsumura, “Improvement of analyzing method for human skin color separation by independent component analysis,” in Imaging, Manipulation, and Analysis of Biomolecules, Cells, and Tissues XVII, D. L. Farkas, J. F. Leary, and A. Tarnok, eds. (SPIE, 2019), p. 48.

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Figures (6)

Fig. 1.
Fig. 1. (a): Schematic view of procedure of SMI, and (b): visualization of the direction of adjustment. The symbol O in (b) represents the origin. The symbols “a” to “d” in (a) and (b) correspond to each other. The image (b) does not reflect the actual angles between the vectors.
Fig. 2.
Fig. 2. Demonstration of the effects of steps A and B. (a): Original RGB image. Under condition I: derived images of (b) melanin, (c) hemoglobin, and (d) shading. Under condition II: derived images of (e) melanin, (f) hemoglobin, and (g) shading. Under condition III: derived images of (h) melanin, (i) hemoglobin, and (j) shading. In condition I, the initial vectors (vectors determined to display the artifacts) are used as the vectors. In condition II, the vectors are optimized with step A. In condition III, the vectors are optimized with step B. For visibility, the pixel values of the results have been multiplied by (b) 0.75, (c) 3.0, (e) 0.5, (f) 3.0, and (h) 0.75.
Fig. 3.
Fig. 3. Schematic diagram of photographic instrument
Fig. 4.
Fig. 4. Examples of pictures (trimmed) and ROI of test images. A representative example of (a) transient redness and (b) a melanin spot. The ROIs are displayed with numbers that represent 1) a test image for the hemoglobin vector in SMI, 2) a test image for ICA, 3) an image for shading removal in ICA, and 4) a test image for the melanin vector in SMI.
Fig. 5.
Fig. 5. Representative example of (a) the original image and (b) images of components M, (c) H, and (d) S calculated with the vectors derived by SMI, and (e) M, (f) H, and (g) S obtained by ICA.
Fig. 6.
Fig. 6. Values from SMI vs. values from spectrum analysis of (a) M (${C_m}$) and (b) H (${C_{th}}$). Solid line: regression line, broken line: 95% confidence interval, dotted line: 95% prediction interval.

Tables (2)

Tables Icon

Table 1. Summary of the characteristics of each step in the sequence.

Tables Icon

Table 2. Averages and standard deviations (in parentheses) of vector values derived from test images by SMI with normal order (A→B→C→D), interchanged order (B→A→D→C), and ICA, and the RMS of SDs of r/g/b.

Equations (6)

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

( r g b ) = ( log e R log e G log e B ) ,
( r g b ) = X + ε , where X = M m + H h + S s = ( m h s ) ( M H S ) = A ( M H S ) ,
( M H S ) = A 1 ( r g b ) .
{ M = ( h × s ) p / ( h × s ) p ( h × s ) m ( h × s ) m H = ( s × m ) p / ( s × m ) p ( s × m ) h ( s × m ) h S = ( m × h ) p / ( m × h ) p ( m × h ) s ( m × h ) s .
C m = 6.428 × 10 1 + 1.692 × 10 4 a m 4.542 × 10 4 a t h + 7.356 × 10 0 a 0 + 2.172 × 10 10 a m 3 1.212 × 10 16 a t h 3 + 2.340 × 10 1 a 0 3 + 5.523 × 10 9 a m a t h a 0 1.647 × 10 11 a m 2 a t h + 5.766 × 10 7 a m 2 a 0 3.080 × 10 14 a t h 2 a m + 5.298 × 10 11 a t h 2 a 0 + 2.132 × 10 3 a 0 2 a m 6.203 × 10 6 a 0 2 a t h ,
C t h = 5.489 × 10 2 6.050 × 10 1 a m + 1.778 × 10 4 a t h + 5.264 × 10 1 a 0 + 1.015 × 10 9 a m 3 1.731 × 10 14 a t h 3 + 1.453 × 10 1 a 0 3 + 1.585 × 10 9 a m a t h a 0 6.486 × 10 11 a m 2 a t h + 2.952 × 10 6 a m 2 a 0 3.072 × 10 10 a t h 2 a m + 1.441 × 10 11 a t h 2 a 0 1.500 × 10 4 a 0 2 a m 1.682 × 10 6 a 0 2 a t h .

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