Abstract

Light reflected from an object’s surface contains much information about its physical and chemical properties. Changes in the physical properties of an object are barely detectable in spectra. Conventional trichromatic systems, on the other hand, cannot detect most spectral features because spectral information is compressively represented as trichromatic signals forming a three-dimensional subspace. We propose a method for designing a filter that optically modulates a camera’s spectral sensitivity to find an alternative subspace highlighting an object’s spectral features more effectively than the original trichromatic space. We designed and developed a filter that detects cosmetic foundations on human face. Results confirmed that the filter can visualize and nondestructively inspect the foundation distribution.

© 2011 OSA

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References

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  1. K. Nishino, A. Kaarna, K. Miyazawa, and S. Nakauchi, “Spectral filtering for color discrimination enhancement,” in Proceedings of the 15th Color Imaging Conference (Albuquerque, New Mexico, USA), pp. 195–200 (2007).
  2. K. Nishino, A. Kaarna, K. Miyazawa, H. Oda, and S. Nakauchi, “Optical implementation of spectral filtering for the enhancement of skin color discrimination,” Color Res. Appl. (to be published).
  3. A. Kaarna, K. Nishino, K. Miyazawa, and S. Nakauchi, “Michromatic scope for enhancement of color difference,” Color Res. Appl. 35(2), 101–109 (2010).
  4. E. Angelopoulou, The reflectance spectrum of human skin, (Technical Report MS-CIS-99–29, GRASP Laboratory, Department of Computer and Information Science, University of Pennsylvania, USA, 1999).
  5. N. Tsumura, M. Kawabuchi, H. Haneishi, and Y. Miyake, “Mapping pigmentation in human skin by multi-visible-spectral imaging by inverse optical scattering technique,” J. Imag. Sci. Tech. 45(5), 444–450 (2001).
  6. I. V. Meglinski and S. J. Matcher, “Quantitative assessment of skin layers absorption and skin reflectance spectra simulation in the visible and near-infrared spectral regions,” Physiol. Meas. 23(4), 741–753 (2002).
    [CrossRef] [PubMed]
  7. G. N. Stamatas, B. Z. Zmudzka, N. Kollias, and J. Z. Beer, “Non-invasive measurements of skin pigmentation in situ,” Pigment Cell Res. 17(6), 618–626 (2004).
    [CrossRef] [PubMed]
  8. S. J. Preece and E. Claridge, “Spectral filter optimization for the recovery of parameters which describe human skin,” IEEE Trans. Pattern Anal. Mach. Intell. 26(7), 913–922 (2004).
    [CrossRef]
  9. M. Moncrieff, S. Cotton, E. Claridge, and P. Hall, “Spectrophotometric intracutaneous analysis: a new technique for imaging pigmented skin lesions,” Br. J. Dermatol. 146(3), 448–457 (2002).
    [CrossRef] [PubMed]
  10. J. K. Wagner, C. Jovel, H. L. Norton, E. J. Parra, and M. D. Shriver, “Comparing quantitative measures of erythema, pigmentation and skin response using reflectometry,” Pigment Cell Res. 15(5), 379–384 (2002).
    [CrossRef] [PubMed]
  11. G. N. Stamatas, M. Southall, and N. Kollias, “In vivo monitoring of cutaneous edema using spectral imaging in the visible and near infrared,” J. Invest. Dermatol. 126(8), 1753–1760 (2006).
    [CrossRef] [PubMed]
  12. G. N. Stamatas and N. Kollias, “In vivo documentation of cutaneous inflammation using spectral imaging,” J. Biomed. Opt. 12(5), 051603 (2007).
    [CrossRef] [PubMed]
  13. J. Shiozawa, K. Nishikata, and N. Nakamura, “Applications of optically-arranged metal-acrylic films for super-covering makeups,” J. SCCJ 27, 326–326 (1993).
  14. M. Doi, R. Ohtsuki, and S. Tominaga, “Spectral estimation of made-up skin color under various conditions,” in Proc. SPIE (San Jose, California, USA), pp. 606204 (2006).
  15. N. Matsushiro and N. Ohta, “Theoretical analysis of subtractive color mixture characteristics III-realistic colorants and single tristimulus dimension,” Color Res. Appl. 30(5), 354–362 (2005).
    [CrossRef]
  16. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
    [CrossRef] [PubMed]
  17. J. Serra, Image Analysis and Mathematical Morphology (Academic Press, London, UK, 1982).
  18. J. Serra, Image Analysis and Mathematical Morphology, Part II: Theoretical Advances (Academic Press, London, UK, 1988).
  19. J. Serra and L. Vincent, “7An overview of morphological filtering,” Circ. Sys. Sig. Proc. 11(1), 47–108 (1992).
    [CrossRef]
  20. R. S. Berns, Bilmeyer and Saltzman’s Principles of Color Technology Third Edition (Wiley-Interscience, 2000), Chap. 6.

2010

A. Kaarna, K. Nishino, K. Miyazawa, and S. Nakauchi, “Michromatic scope for enhancement of color difference,” Color Res. Appl. 35(2), 101–109 (2010).

2007

G. N. Stamatas and N. Kollias, “In vivo documentation of cutaneous inflammation using spectral imaging,” J. Biomed. Opt. 12(5), 051603 (2007).
[CrossRef] [PubMed]

2006

G. N. Stamatas, M. Southall, and N. Kollias, “In vivo monitoring of cutaneous edema using spectral imaging in the visible and near infrared,” J. Invest. Dermatol. 126(8), 1753–1760 (2006).
[CrossRef] [PubMed]

2005

N. Matsushiro and N. Ohta, “Theoretical analysis of subtractive color mixture characteristics III-realistic colorants and single tristimulus dimension,” Color Res. Appl. 30(5), 354–362 (2005).
[CrossRef]

2004

G. N. Stamatas, B. Z. Zmudzka, N. Kollias, and J. Z. Beer, “Non-invasive measurements of skin pigmentation in situ,” Pigment Cell Res. 17(6), 618–626 (2004).
[CrossRef] [PubMed]

S. J. Preece and E. Claridge, “Spectral filter optimization for the recovery of parameters which describe human skin,” IEEE Trans. Pattern Anal. Mach. Intell. 26(7), 913–922 (2004).
[CrossRef]

2002

M. Moncrieff, S. Cotton, E. Claridge, and P. Hall, “Spectrophotometric intracutaneous analysis: a new technique for imaging pigmented skin lesions,” Br. J. Dermatol. 146(3), 448–457 (2002).
[CrossRef] [PubMed]

J. K. Wagner, C. Jovel, H. L. Norton, E. J. Parra, and M. D. Shriver, “Comparing quantitative measures of erythema, pigmentation and skin response using reflectometry,” Pigment Cell Res. 15(5), 379–384 (2002).
[CrossRef] [PubMed]

I. V. Meglinski and S. J. Matcher, “Quantitative assessment of skin layers absorption and skin reflectance spectra simulation in the visible and near-infrared spectral regions,” Physiol. Meas. 23(4), 741–753 (2002).
[CrossRef] [PubMed]

2001

N. Tsumura, M. Kawabuchi, H. Haneishi, and Y. Miyake, “Mapping pigmentation in human skin by multi-visible-spectral imaging by inverse optical scattering technique,” J. Imag. Sci. Tech. 45(5), 444–450 (2001).

1993

J. Shiozawa, K. Nishikata, and N. Nakamura, “Applications of optically-arranged metal-acrylic films for super-covering makeups,” J. SCCJ 27, 326–326 (1993).

1992

J. Serra and L. Vincent, “7An overview of morphological filtering,” Circ. Sys. Sig. Proc. 11(1), 47–108 (1992).
[CrossRef]

1983

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[CrossRef] [PubMed]

Beer, J. Z.

G. N. Stamatas, B. Z. Zmudzka, N. Kollias, and J. Z. Beer, “Non-invasive measurements of skin pigmentation in situ,” Pigment Cell Res. 17(6), 618–626 (2004).
[CrossRef] [PubMed]

Claridge, E.

S. J. Preece and E. Claridge, “Spectral filter optimization for the recovery of parameters which describe human skin,” IEEE Trans. Pattern Anal. Mach. Intell. 26(7), 913–922 (2004).
[CrossRef]

M. Moncrieff, S. Cotton, E. Claridge, and P. Hall, “Spectrophotometric intracutaneous analysis: a new technique for imaging pigmented skin lesions,” Br. J. Dermatol. 146(3), 448–457 (2002).
[CrossRef] [PubMed]

Cotton, S.

M. Moncrieff, S. Cotton, E. Claridge, and P. Hall, “Spectrophotometric intracutaneous analysis: a new technique for imaging pigmented skin lesions,” Br. J. Dermatol. 146(3), 448–457 (2002).
[CrossRef] [PubMed]

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[CrossRef] [PubMed]

Hall, P.

M. Moncrieff, S. Cotton, E. Claridge, and P. Hall, “Spectrophotometric intracutaneous analysis: a new technique for imaging pigmented skin lesions,” Br. J. Dermatol. 146(3), 448–457 (2002).
[CrossRef] [PubMed]

Haneishi, H.

N. Tsumura, M. Kawabuchi, H. Haneishi, and Y. Miyake, “Mapping pigmentation in human skin by multi-visible-spectral imaging by inverse optical scattering technique,” J. Imag. Sci. Tech. 45(5), 444–450 (2001).

Jovel, C.

J. K. Wagner, C. Jovel, H. L. Norton, E. J. Parra, and M. D. Shriver, “Comparing quantitative measures of erythema, pigmentation and skin response using reflectometry,” Pigment Cell Res. 15(5), 379–384 (2002).
[CrossRef] [PubMed]

Kaarna, A.

A. Kaarna, K. Nishino, K. Miyazawa, and S. Nakauchi, “Michromatic scope for enhancement of color difference,” Color Res. Appl. 35(2), 101–109 (2010).

K. Nishino, A. Kaarna, K. Miyazawa, H. Oda, and S. Nakauchi, “Optical implementation of spectral filtering for the enhancement of skin color discrimination,” Color Res. Appl. (to be published).

Kawabuchi, M.

N. Tsumura, M. Kawabuchi, H. Haneishi, and Y. Miyake, “Mapping pigmentation in human skin by multi-visible-spectral imaging by inverse optical scattering technique,” J. Imag. Sci. Tech. 45(5), 444–450 (2001).

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[CrossRef] [PubMed]

Kollias, N.

G. N. Stamatas and N. Kollias, “In vivo documentation of cutaneous inflammation using spectral imaging,” J. Biomed. Opt. 12(5), 051603 (2007).
[CrossRef] [PubMed]

G. N. Stamatas, M. Southall, and N. Kollias, “In vivo monitoring of cutaneous edema using spectral imaging in the visible and near infrared,” J. Invest. Dermatol. 126(8), 1753–1760 (2006).
[CrossRef] [PubMed]

G. N. Stamatas, B. Z. Zmudzka, N. Kollias, and J. Z. Beer, “Non-invasive measurements of skin pigmentation in situ,” Pigment Cell Res. 17(6), 618–626 (2004).
[CrossRef] [PubMed]

Matcher, S. J.

I. V. Meglinski and S. J. Matcher, “Quantitative assessment of skin layers absorption and skin reflectance spectra simulation in the visible and near-infrared spectral regions,” Physiol. Meas. 23(4), 741–753 (2002).
[CrossRef] [PubMed]

Matsushiro, N.

N. Matsushiro and N. Ohta, “Theoretical analysis of subtractive color mixture characteristics III-realistic colorants and single tristimulus dimension,” Color Res. Appl. 30(5), 354–362 (2005).
[CrossRef]

Meglinski, I. V.

I. V. Meglinski and S. J. Matcher, “Quantitative assessment of skin layers absorption and skin reflectance spectra simulation in the visible and near-infrared spectral regions,” Physiol. Meas. 23(4), 741–753 (2002).
[CrossRef] [PubMed]

Miyake, Y.

N. Tsumura, M. Kawabuchi, H. Haneishi, and Y. Miyake, “Mapping pigmentation in human skin by multi-visible-spectral imaging by inverse optical scattering technique,” J. Imag. Sci. Tech. 45(5), 444–450 (2001).

Miyazawa, K.

A. Kaarna, K. Nishino, K. Miyazawa, and S. Nakauchi, “Michromatic scope for enhancement of color difference,” Color Res. Appl. 35(2), 101–109 (2010).

K. Nishino, A. Kaarna, K. Miyazawa, H. Oda, and S. Nakauchi, “Optical implementation of spectral filtering for the enhancement of skin color discrimination,” Color Res. Appl. (to be published).

Moncrieff, M.

M. Moncrieff, S. Cotton, E. Claridge, and P. Hall, “Spectrophotometric intracutaneous analysis: a new technique for imaging pigmented skin lesions,” Br. J. Dermatol. 146(3), 448–457 (2002).
[CrossRef] [PubMed]

Nakamura, N.

J. Shiozawa, K. Nishikata, and N. Nakamura, “Applications of optically-arranged metal-acrylic films for super-covering makeups,” J. SCCJ 27, 326–326 (1993).

Nakauchi, S.

A. Kaarna, K. Nishino, K. Miyazawa, and S. Nakauchi, “Michromatic scope for enhancement of color difference,” Color Res. Appl. 35(2), 101–109 (2010).

K. Nishino, A. Kaarna, K. Miyazawa, H. Oda, and S. Nakauchi, “Optical implementation of spectral filtering for the enhancement of skin color discrimination,” Color Res. Appl. (to be published).

Nishikata, K.

J. Shiozawa, K. Nishikata, and N. Nakamura, “Applications of optically-arranged metal-acrylic films for super-covering makeups,” J. SCCJ 27, 326–326 (1993).

Nishino, K.

A. Kaarna, K. Nishino, K. Miyazawa, and S. Nakauchi, “Michromatic scope for enhancement of color difference,” Color Res. Appl. 35(2), 101–109 (2010).

K. Nishino, A. Kaarna, K. Miyazawa, H. Oda, and S. Nakauchi, “Optical implementation of spectral filtering for the enhancement of skin color discrimination,” Color Res. Appl. (to be published).

Norton, H. L.

J. K. Wagner, C. Jovel, H. L. Norton, E. J. Parra, and M. D. Shriver, “Comparing quantitative measures of erythema, pigmentation and skin response using reflectometry,” Pigment Cell Res. 15(5), 379–384 (2002).
[CrossRef] [PubMed]

Oda, H.

K. Nishino, A. Kaarna, K. Miyazawa, H. Oda, and S. Nakauchi, “Optical implementation of spectral filtering for the enhancement of skin color discrimination,” Color Res. Appl. (to be published).

Ohta, N.

N. Matsushiro and N. Ohta, “Theoretical analysis of subtractive color mixture characteristics III-realistic colorants and single tristimulus dimension,” Color Res. Appl. 30(5), 354–362 (2005).
[CrossRef]

Parra, E. J.

J. K. Wagner, C. Jovel, H. L. Norton, E. J. Parra, and M. D. Shriver, “Comparing quantitative measures of erythema, pigmentation and skin response using reflectometry,” Pigment Cell Res. 15(5), 379–384 (2002).
[CrossRef] [PubMed]

Preece, S. J.

S. J. Preece and E. Claridge, “Spectral filter optimization for the recovery of parameters which describe human skin,” IEEE Trans. Pattern Anal. Mach. Intell. 26(7), 913–922 (2004).
[CrossRef]

Serra, J.

J. Serra and L. Vincent, “7An overview of morphological filtering,” Circ. Sys. Sig. Proc. 11(1), 47–108 (1992).
[CrossRef]

Shiozawa, J.

J. Shiozawa, K. Nishikata, and N. Nakamura, “Applications of optically-arranged metal-acrylic films for super-covering makeups,” J. SCCJ 27, 326–326 (1993).

Shriver, M. D.

J. K. Wagner, C. Jovel, H. L. Norton, E. J. Parra, and M. D. Shriver, “Comparing quantitative measures of erythema, pigmentation and skin response using reflectometry,” Pigment Cell Res. 15(5), 379–384 (2002).
[CrossRef] [PubMed]

Southall, M.

G. N. Stamatas, M. Southall, and N. Kollias, “In vivo monitoring of cutaneous edema using spectral imaging in the visible and near infrared,” J. Invest. Dermatol. 126(8), 1753–1760 (2006).
[CrossRef] [PubMed]

Stamatas, G. N.

G. N. Stamatas and N. Kollias, “In vivo documentation of cutaneous inflammation using spectral imaging,” J. Biomed. Opt. 12(5), 051603 (2007).
[CrossRef] [PubMed]

G. N. Stamatas, M. Southall, and N. Kollias, “In vivo monitoring of cutaneous edema using spectral imaging in the visible and near infrared,” J. Invest. Dermatol. 126(8), 1753–1760 (2006).
[CrossRef] [PubMed]

G. N. Stamatas, B. Z. Zmudzka, N. Kollias, and J. Z. Beer, “Non-invasive measurements of skin pigmentation in situ,” Pigment Cell Res. 17(6), 618–626 (2004).
[CrossRef] [PubMed]

Tsumura, N.

N. Tsumura, M. Kawabuchi, H. Haneishi, and Y. Miyake, “Mapping pigmentation in human skin by multi-visible-spectral imaging by inverse optical scattering technique,” J. Imag. Sci. Tech. 45(5), 444–450 (2001).

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[CrossRef] [PubMed]

Vincent, L.

J. Serra and L. Vincent, “7An overview of morphological filtering,” Circ. Sys. Sig. Proc. 11(1), 47–108 (1992).
[CrossRef]

Wagner, J. K.

J. K. Wagner, C. Jovel, H. L. Norton, E. J. Parra, and M. D. Shriver, “Comparing quantitative measures of erythema, pigmentation and skin response using reflectometry,” Pigment Cell Res. 15(5), 379–384 (2002).
[CrossRef] [PubMed]

Zmudzka, B. Z.

G. N. Stamatas, B. Z. Zmudzka, N. Kollias, and J. Z. Beer, “Non-invasive measurements of skin pigmentation in situ,” Pigment Cell Res. 17(6), 618–626 (2004).
[CrossRef] [PubMed]

Br. J. Dermatol.

M. Moncrieff, S. Cotton, E. Claridge, and P. Hall, “Spectrophotometric intracutaneous analysis: a new technique for imaging pigmented skin lesions,” Br. J. Dermatol. 146(3), 448–457 (2002).
[CrossRef] [PubMed]

Circ. Sys. Sig. Proc.

J. Serra and L. Vincent, “7An overview of morphological filtering,” Circ. Sys. Sig. Proc. 11(1), 47–108 (1992).
[CrossRef]

Color Res. Appl.

N. Matsushiro and N. Ohta, “Theoretical analysis of subtractive color mixture characteristics III-realistic colorants and single tristimulus dimension,” Color Res. Appl. 30(5), 354–362 (2005).
[CrossRef]

K. Nishino, A. Kaarna, K. Miyazawa, H. Oda, and S. Nakauchi, “Optical implementation of spectral filtering for the enhancement of skin color discrimination,” Color Res. Appl. (to be published).

A. Kaarna, K. Nishino, K. Miyazawa, and S. Nakauchi, “Michromatic scope for enhancement of color difference,” Color Res. Appl. 35(2), 101–109 (2010).

IEEE Trans. Pattern Anal. Mach. Intell.

S. J. Preece and E. Claridge, “Spectral filter optimization for the recovery of parameters which describe human skin,” IEEE Trans. Pattern Anal. Mach. Intell. 26(7), 913–922 (2004).
[CrossRef]

J. Biomed. Opt.

G. N. Stamatas and N. Kollias, “In vivo documentation of cutaneous inflammation using spectral imaging,” J. Biomed. Opt. 12(5), 051603 (2007).
[CrossRef] [PubMed]

J. Imag. Sci. Tech.

N. Tsumura, M. Kawabuchi, H. Haneishi, and Y. Miyake, “Mapping pigmentation in human skin by multi-visible-spectral imaging by inverse optical scattering technique,” J. Imag. Sci. Tech. 45(5), 444–450 (2001).

J. Invest. Dermatol.

G. N. Stamatas, M. Southall, and N. Kollias, “In vivo monitoring of cutaneous edema using spectral imaging in the visible and near infrared,” J. Invest. Dermatol. 126(8), 1753–1760 (2006).
[CrossRef] [PubMed]

J. SCCJ

J. Shiozawa, K. Nishikata, and N. Nakamura, “Applications of optically-arranged metal-acrylic films for super-covering makeups,” J. SCCJ 27, 326–326 (1993).

Physiol. Meas.

I. V. Meglinski and S. J. Matcher, “Quantitative assessment of skin layers absorption and skin reflectance spectra simulation in the visible and near-infrared spectral regions,” Physiol. Meas. 23(4), 741–753 (2002).
[CrossRef] [PubMed]

Pigment Cell Res.

G. N. Stamatas, B. Z. Zmudzka, N. Kollias, and J. Z. Beer, “Non-invasive measurements of skin pigmentation in situ,” Pigment Cell Res. 17(6), 618–626 (2004).
[CrossRef] [PubMed]

J. K. Wagner, C. Jovel, H. L. Norton, E. J. Parra, and M. D. Shriver, “Comparing quantitative measures of erythema, pigmentation and skin response using reflectometry,” Pigment Cell Res. 15(5), 379–384 (2002).
[CrossRef] [PubMed]

Science

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[CrossRef] [PubMed]

Other

J. Serra, Image Analysis and Mathematical Morphology (Academic Press, London, UK, 1982).

J. Serra, Image Analysis and Mathematical Morphology, Part II: Theoretical Advances (Academic Press, London, UK, 1988).

M. Doi, R. Ohtsuki, and S. Tominaga, “Spectral estimation of made-up skin color under various conditions,” in Proc. SPIE (San Jose, California, USA), pp. 606204 (2006).

R. S. Berns, Bilmeyer and Saltzman’s Principles of Color Technology Third Edition (Wiley-Interscience, 2000), Chap. 6.

K. Nishino, A. Kaarna, K. Miyazawa, and S. Nakauchi, “Spectral filtering for color discrimination enhancement,” in Proceedings of the 15th Color Imaging Conference (Albuquerque, New Mexico, USA), pp. 195–200 (2007).

E. Angelopoulou, The reflectance spectrum of human skin, (Technical Report MS-CIS-99–29, GRASP Laboratory, Department of Computer and Information Science, University of Pennsylvania, USA, 1999).

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Figures (8)

Fig. 1
Fig. 1

Filter design process flowchart. The solution of the transmittance function is formulated as a nonlinear optimization problem whose objective function is Eq. (1). The optimization consists of five steps.

Fig. 2
Fig. 2

Spectral sensitivities of the RGB color sensor for a Nikon D70 digital camera measured using a monochromator (Shimadzu, SPG-120) in the range of 380–780 nm in steps of 5 nm.

Fig. 3
Fig. 3

Average spectra of each data set. Slight spectral difference at wavelengths in the range 545–575 nm were caused by the spectral absorption characteristics of hemoglobin.

Fig. 4
Fig. 4

(a) Spectral transmittance of the theoretically designed and the optically realized filter. Transmittance function was theoretically designed by optimization process. The optical filter was realized by vacuum deposition technology. (b) Developed optical filter. The optical filter was made of a multilayer thin film, which was composed of 31 layers of SiO2 and TiO2.

Fig. 5
Fig. 5

Measurement geometry. The measurement device was a commercially available camera (Nikon D70) and a fluorescent light (Diva-Lite, 6300K) was selected as the illumination light source. Polarizing films were installed on both the camera and the illumination light source to eliminate specular light.

Fig. 6
Fig. 6

Color (chromaticity) distributions extracted from an RGB image taken with the digital camera. (a) Color distributions without filtering and (b) color distributions with filtering. The ellipses represent equiprobability ellipses whose shafts are defined by the standard deviations. Misclassification rates (a) 33.0% and (b) 5.97%.

Fig. 7
Fig. 7

Results of filtered images captured using a digital camera. Foundation was applied only on the left side of the face. (a) RGB color image without the filter. (b) Filtered color image. The image in the figure shows obvious enhancement. (c) Discriminant score computed according to Eq. (5).

Fig. 8
Fig. 8

Discrimination accuracy with and without luminance information. Trichromatic signals measured in Section 3.2 were used for this comparison and the discrimination accuracies were computed with leave-one-out cross validation. The left two bars show the discrimination accuracies when the optical filter was not equipped and the right two bars show the accuracies with the filter.

Equations (5)

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

P e ( I 1 ( λ ) , I 2 ( λ ) ) = p 1 P ( c a t e g o r y = 2 | I 1 ( λ ) ) + p 2 P ( c a t e g o r y = 1 | I 2 ( λ ) ) ,
C i k = λ T ( λ ) I i ( λ ) S k ( λ ) , i { 1 , 2 } , k { R , G , B } ,
C i = ( r i , g ) i = ( C i R C i R + C i G + C i B , C i G C i R + C i G + C i B ) .
T ( λ ) = k = 1 N D k B k ( λ ) , B k ( λ ) = { { ω 3 + 3 ω 2 ( ω | λ λ k | ) + 3 ω ( ω | λ λ k | ) 2 3 ( ω | λ λ k | ) 3 } / 6 ω 3 for | λ λ k | ω , ( 2 ω | λ λ k | ) 3 / 6 ω 3 for ω | λ λ k | 2 ω , 0 for 2 ω | λ λ k | ,
f d ( C ) = ( Σ 1 ( μ 1 μ 2 ) ) t ( C μ 1 + μ 2 2 ) log ( p 2 / p 1 ) ,

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