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Bull. Soc. Photogr. Imag. Japan. (2017) Vol. 27 No. 2: 26–31

Original Paper

Analyzing the Components of Dark Circle by Nonlinear Estimation of Chromophore Concentrations and Shading
Rina Akaho, Misa Hirose, and Norimichi TsumuraAbstract: is paper aims to apply nonlinear estimation of chromophore concentrations: melanin, oxy-hemoglobin, deoxy-hemoglobin andThshading to the real hyperspectral image of skin. Skin reflectance is captured in the wavelengths between 400nm and 700nm by hyperspectral scanner. Five-band wavelengths data are selected from skin reflectance. By using the cubic function which obtained byMonte Carlo simulation of light transport in multi-layered tissue, chromophore concentrations and shading are determined by minimize residual sum of squares of reflectance. The dark circles are analyzed by the proposed method, and dominant component of thedark circles is found by the subjective evaluation for the modulated images.

Key words:

melanin volume, blood volume, Monte Carlo simulation, spectral reflectance

1. Introduction
Multispectral imaging has generated growing interest in various
fields, such as biomedical imaging, recording for digital archives, andsensing and controlling systems in the last few decades1-9). The main
aim of image sensing is to provide non-contact and non-invasive
sensing techniques.
Skin is a multi-layered tissue composed of the epidermis, dermis
and subcutaneous tissues and contains chromophores such as melanin, oxy-hemoglobin and deoxy-hemoglobin. Since diffuse reflectance of human skin is changed depending on the concentration ofthese chromophores, the analysis of diffuse reflectance can provide
information about tissue activities related to these chromophores.
This information is useful to be applied for early detection of skindisease and monitoring health.
Tsumura et al. discussed a method of extracting melanin and hemoglobin information by applying Independent Component Analysis (ICA) to skin color images1,5). Kikuchi et al. proposed imaging
of a hemoglobin oxygen saturation ratio of the face with a spectral
camera based on the multi regression analysis10). There are many discussions about estimating chromophore concentrations linearly
from skin color images and spectral images. On the other hand,
Kobayashi et al. analyzed the nonlinear relation between absorbanceand chromophores of skin based on Monte Carlo simulation and themodified Lambert-Beer's law11). Kobayashi et al. reported a methodof estimating the optical path length of each layer from absorbanceand the quantity of chromophores.
By using the estimated optical path length, the concentration ofchromophores can be analysed based on the modified Lambert-Beer's law. However, this method cannot estimate the optical
Received 11th, July 2017; Accepted 24th, October 2017.

Graduate School of Advanced Integration Science, Chiba University

address : 1-33, Yayoi-cho, Inage-ku, Chiba-shi, Chiba, 263-8522 Japan

path length if the concentration of chromophores is not provided.
Even if the concentration is supplied, the estimation accuracy is
not sufficient because the concentration is derived linearly by multiple regression analysis. Hirose et al. calculated the relationship between chromophore concentration and absorbance by creating the
combination of a chromophore concentration on the simulation12).
Estimation accuracy of the method by Hirose et al. was evaluated bynumerical skin phantom, they concluded that their method performed high accurate estimation. However it was not applied andevaluated by real skin images.

2. Nonlinear Estimation of Chromophore Concentrations and Shading from Five Band Images9)
2.1 Analysis of the Relation between Absorbance and Chromophore Concentration
First, we analyze the relation between absorbance and chromophore concentration by Monte Carlo simulation and define the absorbance as the cubic functions of chromophore concentration as it
was previously performed by minimizing11).
Diffuse reflectance data for skin is obtained by Monte Carlo simulation of light transport in multi-layered tissue (MCML)9). MCML
follows the propagation of photons in tissue.
As shown in Fig. 1, the two-layered skin model is used and iscomposed of the epidermis and dermis.
Five optical parameters are set at each layer: thickness t, reflectance index n, anisotropy factor g, scattering coefficient μs and absorption coefficient μa. The thickness t of epidermis and dermis are
0.006 and 0.40 cm respectively in this basic model13). The reflectanceindex n, scattering coefficient μs and anisotropy factor g of two layers

(a)where λ is the wavelength and the subscripts of the absorption
coefficient epi, der, mel, ohb, and hb indicate epidermis, dermis, melanin, oxy-hemoglobin, and deoxy-hemoglobin, respectively. Mel,
Ohb, Hb, Thb and StO indicate concentration of melanin, oxy-hemoglobin, deoxy-hemoglobin and oxygen saturation, respectively.
Chromophore concentrations are input to MCML to acquire diffuse reflectance of skin. Set melanin concentration Mel = 0.01, 0.02,
0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09 and 0.1; Thb = 0.002, 0.004,
0.006, 0.008 and 0.01; and StO = 0, 0.2, 0.4, 0.6, 0.8 and 1. 300 reflectance data are obtained from their combinations.
The diffuse reflectance obtained by MCML is converted to absorbance with logarithmic transformation, and the absorbance for eachwavelength is defined by a cubic function of chromophore concentration. The chromophore concentration is determined to minimize
the residual sum of squares of the reflectance as is described in next
section.
2.2 Estimation of Chromophore Concentrations and Shadingfrom Five Band Images
Four components, melanin, oxy-hemoglobin, deoxy-hemoglobin
and shading, are extracted from five band images of the skin by using
cubic functions. For this purpose, these four components are determined to minimize the residual sum of squares RSSest as follows.
RSSest = Σ[R(λ) − (exp( − (Z(λ) + k))]2,(2)where R(λ) is spectral reflectance of human skin and k indicate
bias value which is shading component. Z(λ) is absorbance definedby the cubic function of melanin concentration and absorption coefficient of dermis.
Z = aX 3+ bX 2Y + cXY 2+ dY 3+ eX 2+ fXY + gY 2+ hX + iY + j,(3)where a~j are absorption coefficient. X is absorption coefficient ofdermis and Y is percentage of melanin. Fig.2 shows Z(λ) in case thewavelength is 700nm. Estimation accuracy of the method by Hirose
et al. was evaluated by numerical skin phantom, they concluded that
their method performed high accurate estimation12). In the next sec-

(c)

(d)

Fig.2 Skin absorbance Z(λ). (a) shows skin absorbance at 400nm. (b) 500nm.
(c) 600nm. (d) 700nm.
MelaninBloodvolumeAbsorbance

μa.epi(λ) = Mel × 0.01 × μa.mel(λ),μa.der(λ)= {Ohb μa.ohb(λ) + Hb × μa.hb(λ)} × 0.01
(1)
= {Thb × StO × μa.ohb(λ) + Thb × (1-StO) × μa.hb(λ)} × 0.01,

Oxygensaturation

k:ShadeSimulated reflectanceZ (λ ) + k

400 Wavelength[nm] 700

Absorbanceare the same value, n = 1.4, μs and g is based on previously used data4).
The absorption coefficient μa is calculated by the absorption coefficients of chromophores such as melanin, oxy-hemoglobin and deoxy-hemoglobin as follows.

Z(λ ): AbsorbanceFig.1 Two-layered skin model is composed of the epidermis and dermis.

(b)Z( λ ): Absorbancen, µ a.der , µ s , gZ( λ ): Absorbancen, µ a.epi , µ s , gdermis

Iteration

thickness t
epidermis

27

Z( λ ): AbsorbanceAnalyzing the Components of Dark Circle by Nonlinear Estimation of Chromophore Concentrations and Shading

Z( λ ): AbsorbanceRina Akaho, Misa Hirose, and Norimichi Tsumura

Measured reflectance− log( R(λ ))400 Wavelength[nm] 700

Fig.3 Flow of estimation method.

tion, therefore, we apply this method to the real skin spectral image.

3. Estimation of Chromophore Concentrations andShading from Real Images
3.1 Experimental Environment and Selection of Wavelengths set
Fig.4 shows experimental set-up to capture hyperspectral imagesof skin. Hyperspectral images were captured using a hyperspectral
scanner( JFE ImSpector) in every 10nm between 400nm and 700nm
and using artificial solar(Seric Ltd.) as a light source in a dark room.
Surface reflectance is removed to improve the accuracy for estimation of chromophore concentrations and shading. In this experiment, Spectralon was used as a white checker. This white checker isclose to the perfectly diffusing surface and size is 300mm×40mm×10mm. First, we captured hyperspectral image of white checker.
Reflected spectral power of skin is divided by reflected spectral power of white checker to obtain spectral reflectance of skin. Fig.5 shows
the RGB images which is concerted from spectral reflectance ofskin. We used 10-degree color-matching function and standard illumination light D65 as a light source for conversion to RGB image.
We empirically selected 5 wavelengths from the obtained 31 wavelengths data, and estimation chromophore concentrations by using
the method describe in section 2.2. Appropriate wavelengths set are
determined to minimize the residual sum of squares RSSwav as fol-

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Bull. Soc. Photogr. Imag. Japan. Vol. 27 No. 2 (2017)

Artificial
sunlight
Polarizing
plate

(a)
0.6

0.18

Hyperspectral
scannerChinsupport

0.16

0.4

0.14

Fig.4 Experimental set-up.

Spot on the skin

0.2

0.12

Dark circles
under the eyes

0.1

0

0.08

-0.2

(b)

(c)
0.02

1
0.8

0.015

0.6
0.4

0.01

0.2

Fig.5 RGB Image of skin.

0.005

0

(d)

lows.
N

RSSest = Σ Σ [Rest(λ) − Rreal(λ)]2,(4)c=1 λwhere Rest(λ) is spectral reflectance calculated from estimated fivecomponents and Rreal(λ) is spectral reflectance captured using a hyperspectral scanner. N is the number of pixels in the image.
3.2 Results and Discussion
Appropriate wavelengths set were 470, 510, 570, 630, 700nm
from our results of evaluating using Eq.(3). Fig. 6 shows results of
estimation at images including pigmented spot on the skin. Melaninconcentration map is shown in Fig. 6(a). It is estimated that melaninconcentration is high density at pigmented spot area on the skin.
Fig. 8 shows the result of estimation on dark circles under the eyes.
It is also estimated that melanin concentration is high density at the
freckle area and the area of dark circles. Shading map is shown in
Fig. 8(b). From this result, it is observed that the shading components are estimated appropriately on the aspect of the shape trend in
the area. Fig. 8(c) shows oxygen saturation map. From this result, it
is observed that oxygen saturation is low at dark circles area underthe eyes. Fig. 7 and Fig. 9 show the result of estimation by using
conventional multiple regression analysis. Results of both area seemto be estimated appropriately, however, melanin concentration andblood volume are very low and oxygen saturation are very noisy13), 14).

(e)Fig.6 Concentration distribution of chromophore at spot on the skin byusing proposed method. (a) shows RGB image. (b) shows melaninmap. (c) shows shading map. (d) shows oxygen saturation map. (e)shows blood volume map.

(a)
2.7

0.95

2.5

0.85

2.3

0.75

2.1

0.65

1.9

0.55

×10-3

0.45

(b)

(c)
1

2

0.8

1

0.6

0

0.4

－1
－2

0.2

4. Modulating chromophore concentration
Estimated chromophore concentrations which are obtained fromprevious section are modulated. The modulated concentrations areused to calculate the spectral reflectance as in the Section 2.2. RGB
images are calculated from the spectral reflectance. Furthermore,
RGB images of dark circles are evaluated to determine dominant

－3

0

(d)

×10-4

(e)

Fig.7 Concentration distribution of chromophore at spot on the skin byusing conventional multiple regression analysis. (a) shows RGB image. (b) shows melanin map. (c) shows shading map. (d) shows oxygen
saturation map. (e) shows blood volume map.

Rina Akaho, Misa Hirose, and Norimichi Tsumura

Analyzing the Components of Dark Circle by Nonlinear Estimation of Chromophore Concentrations and Shading

Estimated

Melanin

(a)

0.1

29

RGB Image

0.2

0.1 0.12 0.14 0.16 0.18 0.2－0.2 0 0.2 0.4 0.6 0.8 1

(b)

(c)

Decreased Increased

Modulation

0.1

0.2

Fig.10 Modulation of melanin concentration and RGB image.

0

0.2

0.4

0.6

0.8

1

0.012 0.014 0.016 0.018 0.02 0.022

(d)

(e)

Fig.8 Concentration distribution of chromophore at dark circles under theeyes by using proposed method. (a) shows RGB image. (b) shows melanin map. (c) shows shading map. (d) shows oxygen saturation map.
(e) shows blood volume map.

2.2

2.6

3×10-3

0.4

0.8

1.4

(b)

－4

1.6

(c)

0

－2

2×10-4

0

0.2

(d)

0.4

Melcontrol = Mel + PMel × (Melmax − Melmin)(5)
StOcontrol = StO + PStO × (StOmax − StOmin)(6)
Thbcontrol = Thb + PThb × (Thbmax − Thbmin)(7)Shacontrol = Sha + PSha × (Shamax − Shamin)(8)where Mel, StO, Thb, Sha are estimated concentrations at the pixel
under the modulation. PMel, PStO, PThb, PSha are degree of modulation.
Melmax, StOmax, Thbmax, Shamax are maximum value in estimated areaand Melmin, StOmin, Thbmin, Shamin are minimum value. We use three
types about degree of modulation; unchanging, decreasing and increasing as Fig.10. Since there are four components in the images
and three types of modulation in the image processing, we obtained
81 images from combinations. Fig.11-13 shows example of modulated images.

(a)

1.8

oxygen saturation, if estimated concentration at one pixel is lower
than threshold, the component is modulated by image processing.
The concentrations are modulated as follows.

4.2 Generation of RGB image for evaluation
Absorbance of modulated chromophore concentrations is definedby concentrations using Eq.3. Absorbance is converted into reflectance using Eq.9. RGB image is obtained from reflectance and performed gamma correction for sRGB display.
0.6

0.8

1

(e)

Fig.9 Concentration distribution of chromophore at dark circles under theeyes by using conventional multiple regression analysis. (a) shows
RGB image. (b) shows melanin map. (c) shows shading map. (d)shows oxygen saturation map. (e) shows blood volume map.

components relating appearance of dark circles.
4.1 Modulation of estimated concentration valueFirst, threshold is set for each component; melanin, blood volume,
oxygen saturation and shading. In melanin and shading if the estimated concentration at one pixel is higher than threshold value, thecomponent is modulated by image processing. In blood volume andR(λ) = exp(−Z(λ) + k),(9)5. Removal of dark circles
5.1 Subjective evaluation experiment for finding dominant component of dark circles
Fig. 14(a) shows experimental setup of evaluation experiment.
Example of evaluated images are shown in Fig. 14(b). Left image isbefore modulation and right side is the image after modulation. The
observers are asked to evaluate the image after modulation compared with the image before modulation. The evaluation is performed by classification with five grades as Table 1.In the evaluatedimages, only the area in green rectangle is modulated in this paper.

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Bull. Soc. Photogr. Imag. Japan. Vol. 27 No. 2 (2017)

Bloodvolume(a)(b)

Fig.14 Subjective evaluation experiment.
Table. 1 The evaluation is performed by classification with five grades.

Melanin

Evaluation
value

Fig.11 Modulated image related to melanin and blood volume.

5

Improvement

3No-change

4

Oxygensaturation

Little improvement2

Little aggravation

1

Aggravation

Averageevaluation value

good 5

Melaninunchanged

Melanin concentration
decreased
increased

4
3
2

bad 1

Fig.12 Modulated image related to melanin and oxygen saturation.

Evaluated image number (eighty one)
Fig.15 Result of subjective evaluation experiment.

Shading

MelaninFig.13 Modulated image related to melanin and shading.

5.2 Result of subjective evaluation experiment
Result of experiment for subjective evaluation shown in Fig. 15.
Horizontal axis is number of evaluated image, it is sorted by modulation degree of melanin. Vertical axis is value in average evaluation.
When the one component is fixed, there are 27 combinations. Fig.
15 shows that melanin component is highly related to appearance ofdark circles in this experiment. Although the evaluation value ischanged by combination of other three components, it can be said
the difference in each groups; unchanged, decreased, increased, canbe ignored as seen in Fig. 15. Moreover, significant difference test by

(a)

(b)

Fig.16 Removal of dark circle by decreasing melanin. (a) shows RGB image
before modulation. (b) shows RGB image after decreasing melanin.

using variance analysis showed that only melanin affected the appearance.

6. Conclusion
We estimated chromophore concentrations from hyperspectral
image of skin by using nonlinear estimation method. As a result of
melanin concentration map, melanin was high concentration at pigmented spot, freckle and dark circles. At dark circle area, oxygen
saturation was low concentration. From these results, we can con-

Rina Akaho, Misa Hirose, and Norimichi Tsumura

Analyzing the Components of Dark Circle by Nonlinear Estimation of Chromophore Concentrations and Shading

clude that the method by Hirose et al. can be applied to real skin
images since physiologically valid results were obtained by our study.
Furthermore, we modulated estimated concentration and foundmelanin component is highly related to appearance of dark circles.
In future works, we will apply this method for many kinds of dark
circles.

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