Quantitative Analysis of Skin using Diffuse Reﬂectance for Non-invasive

Pigments Detection

Shiwei Li

1 a

, Mohsen Ardabilian

1 b

and Abdelmalek Zine

2 c

Ecole Centrale de Lyon, LIRIS CNRS, France

Ecole Centrale de Lyon, ICJ CNRS, France

Keywords:

Artiﬁcial Neural Networks, Biomedical Engineering, Bioinformatics, Biomedical Signal Processing.

Abstract:

Skin diagnosis has become a signiﬁcant part of research topics in biomedical engineering and informatics,

since many conditions or symptoms of diseases, such as melanoma and jaundice, are indicated by skin appear-

ance. In the past, an invasive method (i.e. Biopsy) is widely used for pathological diagnosis by removing a

small amount of living tissue. Recently, non-invasive methods have been studied based on diffuse reﬂectance

for detecting skin inner information. With the development of machine learning techniques, non-invasive

methods can be further improved in many aspects, such as the speed and accuracy. Our research focuses on

analyzing and improving non-invasive skin pigments detection using neural networks. The relation between

skin pigments content and skin diffuse reﬂectance has been studied. Moreover, the computational time has

been accelerated signiﬁcantly after using the inverse mapping neural network instead of the forward mapping

one. The results show that our proposed method can obtain favorable results in estimating melanin content,

blood content, and oxygen saturation from synthetic skin diffuse reﬂectance for all lightly, moderately, and

darkly pigmented skin types compared to Monte Carlo simulations. And it turns out that our method works

well when using a measured skin reﬂectance database from National Institute of Standards and Technology

for the second validation.

1 INTRODUCTION

Skin, one of the most important human body or-

gans, protects us from external invasion, keeps us

warm, and regulates the balance of water. Skin

health has become a signiﬁcant issue. For exam-

ple, there have been many computer vision-based

tasks which focus on analyzing different facial fea-

tures (Leo et al., 2020). Some diseases reﬂect the

abnormal content of the pigment inside the skin, for

instance, melanoma is caused by a large amount of

melanin produced by exposure to sunlight. To give an

intuitive and quantitative expression, evaluating pig-

ments content is required. Traditional method for

pigments detection is examined under a microscope

or analyzed based on a series of chemical processes

by taking a small skin sample from the individuals,

and is called biopsy (Zerbino, 1994). As skin ap-

pearance can be affected by many pigments, such

as melanin, hemoglobin, etc., researchers found that

https://orcid.org/0000-0002-8765-9283

https://orcid.org/0000-0002-1842-0404

https://orcid.org/0000-0002-0353-8995

light waves can penetrate the skin, and the outgoing

wave (also called diffuse reﬂectance) which is scat-

tered back, carries the inner information. In the past

two decades, the non-invasive detection of pigments

deposited inside the skin has progressed based on

skin diffuse reﬂectance. Combined with skin mod-

els, light-skin interaction approaches are applied to

analyze skin diffuse reﬂectance monitored by diffuse

reﬂectance spectroscopy (DRS) instruments and ob-

tain the pigments content. These light-skin interac-

tion approaches describe how light transports inside

the tissue, and derive diffuse reﬂectance based on

the optical parameters of skin models, which gener-

ally are formed as a function of volume fractions of

skin pigments. With the development of DRS tech-

niques and hyper-spectral sensors, the acquisition of

diffuse reﬂectance with high resolution (usually 1-20

nm) becomes easier and cost-effective. These tech-

niques have been applied to diagnose skin diseases,

etc. (Mazzoli et al., 2010; Mehr

ubeo

glu et al., 2002;

Salomatina et al., 2006; Wallace et al., 2000).

Light-skin interaction approaches have been stud-

ied and improved over the past four decades, such

as diffuse approximation (DA), kubelka-munk theory,

604

Li, S., Ardabilian, M. and Zine, A.

Quantitative Analysis of Skin using Diffuse Reﬂectance for Non-invasive Pigments Detection.

DOI: 10.5220/0010326806040614

In Proceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2021) - Volume 4: VISAPP, pages

604-614

ISBN: 978-989-758-488-6

and Monte Carlo simulations (MC) (Sharma et al.,

2014; Zonios et al., 2008; Vyas et al., 2013; Ishi-

maru, 1978). Besides, machine learning methods

have also been applied more commonly to map dif-

fuse reﬂectance and skin physiological parameters

(Zhang et al., 2010; Chen et al., 2016). Among these

approaches, MC is mostly used to validate other ap-

proaches as the ﬁrst veriﬁcation because it simulates

the movement of energy packets that obey radiative

transport rules and has a good ﬁtting performance

with the measured data (Jacques, 1996). Fredriksson,

Larsson, and Strmberg presented a 3-layered analy-

sis model based on MC which is able to estimate mi-

cro circulatory parameters (Fredriksson et al., 2012).

Sharma et al. proposed a 2-layered lookup table

based on MC, which is generalized to be used for a

wide variety of probe-geometries with the error of ab-

sorption properties varying from 12 to 25% (Sharma

et al., 2014). Nonetheless, MC accelerated by GPU

(Alerstam et al., 2008) needs around a day to run the

curve-ﬁtting process for only one hyper-spectral dif-

fuse reﬂectance. With this in mind, it is inefﬁcient

when processing amounts of diffuse reﬂectance spec-

tra data and cannot satisfy the demand to extract skin

physiological parameters rapidly. DA is known to

be a second-order differential equation that gives ap-

proximate solutions of the Boltzmann transport equa-

tion on the basis of spherical harmonics. Spott and

Svaasand focused on collimated light sources in tur-

bid media and proposed a hybrid approach by reﬁning

the source terms or increasing the approximation or-

der in DA (Spott and Svaasand, 2000). Nagli et al.

tested the suitability of DA for ﬁtting the diffuse re-

ﬂectance spectra and extracting bio-parameters from

human skin in vivo (Nagli

c et al., 2019). DA as-

sumes that the scattering dominates light-skin inter-

action over the absorption and is much faster than

MC. However, its not appropriate when light source

is near the interface of skin tissue (Furutsu, 1980) or

the tissue is highly anisotropic and lowly scattered

(Zherebtsov et al., 2019). Yudovsky and Pilon de-

veloped a semi-empirical model to relate the diffuse

reﬂectance to the radiative properties and thickness of

2-layered media [18,19]. However, this model is lim-

ited to that the scattering must be strongly forward.

Zonios et al. found that the optical absorption spec-

trum of in vivo melanin exhibits an exponential de-

pendence on wavelength and presented a new method

for studying melanin but is assumes skin is a homo-

geneous semi-inﬁnite medium with one layer (Zonios

et al., 2008). The empirical models usually have many

restrictions, which means the feasibility and the prac-

ticability are not enough for applications. Recently,

with the development of machine learning and deep

learning, support vector regression, artiﬁcial neural

networks, etc. have been applied in this domain fre-

quently. Yudovsky, Nguyen, and Durkin simulated

spatial frequency domain reﬂectance of skin for mul-

tiple wavelength with a forward neural network and

found that the optical properties could be determined

independently with minimal coupling (Yudovsky and

Durkin, 2011; Yudovsky et al., 2012). This model-

ing method is not only precise but also robust (Tsui

et al., 2018) when dealing with the reﬂectance col-

lected by a separated source detectors system, how-

ever, it suffers from some limitations, for example,

ﬁxing the thickness of skin layers. The inverse neural

network is also applied to solve the problem, which

is faster than forward neural network but with large

prediction errors (Wang et al., 2012). There are still

many potentials in applying neural networks to detect

skin physiological parameters.

Two categories have been designed based on the

mapping directions. The forward one is to map skin

physiological parameters to skin diffuse reﬂectance,

and the inverse one is the reverse. We have built a 3-

layered skin model composed of 12 parameters and

generated a skin diffuse reﬂectance database using

MC. This database, which contains 50000 samples to

avoid overﬁtting, was then used for training a forward

mapping neural network (FNN). Afterward, we tested

the performance of FNN compared with MC in three

skin types. In total 30 samples from lightly pigmented

to darkly pigmented were created with the help of MC

and then used for the ﬁrst validation. The measured

skin reﬂectance database was used for the second vali-

dation. Moreover, an inverse mapping neural network

(INN) was also proposed and studied in our research

for speeding up the detection of melanin content. Our

research aims at: 1) applying both FNN and INN in

non-invasively extracting melanin, hemoglobin, etc.

based on DRS; 2) analyzing the effects of skin physi-

ological parameters on reconstructing skin diffuse re-

ﬂectance; 3) testing the suitability of neural networks

when dealing with three different skin types.

2 METHODOLOGY

2.1 Skin Model

For quantitative analysis of skin, we ﬁrst need to build

a skin model. Human skin is a multi-layered biologi-

cal tissue, which generally is divided into three layers:

the epidermis, the dermis, and the subcutis. These

three layers can be detailed with many sub-layers.

To our best knowledge, a maximum 9-layered skin

model has been researched by reﬁning the epidermis

and the dermis which consists of stratum corneum,

Quantitative Analysis of Skin using Diffuse Reﬂectance for Non-invasive Pigments Detection

605

stratum granulosum, stratum basal, papillary dermis,

subpapillary dermis, upper blood net dermis, reticular

dermis, deep blood net dermis, and subcutis (Maeda

et al., 2010). Although a complex structure contains

more information, it increases the computational time

especially using MC. In our research, a 3-layered

model including the epidermis, the dermis, and the

subcutis is taken into account.

Skin appearance is mainly inﬂuenced by the op-

tical properties of each layer. Following this, we

deﬁned each layer with thickness, absorption coef-

ﬁcient, scattering coefﬁcient, refractive index, and

anisotropic factor. The thickness of the epidermis

varies from 0.027 to 0.15 mm (Baranoski and Krish-

naswamy, 2010). Light propagating in this layer is ab-

sorbed mostly by melanin, which is a common natural

biological pigment. There are two types of melanin,

of which the absorption spectra are not identical. Eu-

melanin and pheomelanin exhibit differences in color.

The absorption coefﬁcient of the epidermis can be ex-

plained as a linear wavelength-dependent function as:

a epi

= C

∗ (µ

a pheo

∗ β+ µ

a eu

∗ (1 − β))

w epi

∗ µ

a w

+ (1 − C

− C

w epi

) ∗ µ

a base

(1)

where C

and C

w epi

represent the volume fraction

of melanin and water in the epidermis; β is the ratio

between pheomelanin and eumelanin; µ

a pheo

, µ

a eu

and µ

a w

are the absorption coefﬁcient of pheome-

lanin, eumelanin, and water respectively; the absorp-

tion of skin baseline µ

a base

is an approximation given

by (Jacques, 1996) and it can be considered as the

absorption of collagen ﬁbers inside skin without any

skin pigments.

The dermis is composed of dense, irregular con-

nective tissue, and blood vessels. The thickness of

the dermis is from 0.6 to 3 mm (Baranoski and Kr-

ishnaswamy, 2010). The dominant pigment in this

layer is hemoglobin in the blood. Hemoglobin can

also be divided into two types based on if it is oxy-

genated. The absorption spectra of oxy-hemoglobin

and deoxy-hemoglobin differ clearly in the visible

light range. The absorption coefﬁcient of the dermis

is a weighted combination of the primary hemoglobin

absorption and the minor absorption of skin baseline

and water, given by:

a der

= C

bl der

∗ (µ

a oxy

∗ S + µ

a deoxy

∗ (1 − S))

+ (1 − C

bl der

) ∗ C

w der

∗ µ

a w

+ (1 − C

bl der

) ∗ (1 − C

w der

) ∗ µ

a base

(2)

where C

bl der

and C

w der

are the volume fraction of

blood and water in the dermis; S indicates the oxy-

gen saturation in the blood; µ

a oxy

and µ

a deoxy

stand

for the absorption coefﬁcient of oxy-hemoglobin and

deoxy-hemoglobin respectively considering the con-

centration of hemoglobin in the blood.

Lastly, the subcutis is assumed to be an up to 5

mm thick tissue. The absorption elements in the sub-

cutis include blood, fat, water, and skin baseline. The

absorption coefﬁcient of this layer is similar to the

dermis by adding the extra absorption of fat, given

by:

a sub

= C

bl sub

∗ (µ

a oxy

∗ S + µ

a deoxy

∗ (1 − S))

+ (1 − C

bl sub

) ∗ C

f at

∗ µ

a f at

+ (1 − C

bl sub

) ∗ (1 − C

f at

) ∗ C

w sub

∗ µ

a w

+ (1 − C

bl sub

) ∗ (1 − C

f at

) ∗ (1 − C

w sub

)

∗ µ

a base

(3)

Note that all absorption coefﬁcients of skin pigments

are taken from in vivo experimentation (Jacques and

Prahl, ). And for (2) and (3), we introduced a mathe-

matical method residual volume fraction to avoid that

the sum of volume fractions of all pigments surpasses

1. We assume that µ

is the absorption coefﬁcient of

the i-th pigment with the volume fraction C

in one

layer. Then, the absorption coefﬁcient of this layer

a layer

is generally deﬁned as a linear form:

layer

∑

i=1

+ (1 −

∑

i=1

)µ

a base

s.t.

∑

i=1

< 100%

(4)

where n is the total number of pigments types in this

layer. However, when n is too large, it’s quite normal

that the condition can not be satisﬁed. That’s why we

introduce residual volume fraction. And the modiﬁed

equation is shown as:

a layer

∑

i=1

i−1

∏

j=1

(1 − C

)

∏

i=1

(1 − C

)µ

a base

(5)

Besides the absorption, the scattering events oc-

cur massively inside skin. To deﬁne these events,

Rayleigh scattering and Mie scattering are commonly

used in skin optics. The scattering coefﬁcient is ﬁt

with an equation to match those experimentation re-

sults according to (Jacques, 2013):

= µ

500(nm)

∗ ( f

Ray

∗ (

500(nm)

)

−4

+ (1 − f

Ray

) ∗ (

500(nm)

)

−b

Mie

)

(6)

where µ

500(nm)

is the scattering coefﬁcient measured at

500 nm; f

Ray

indicates the fraction of Rayleigh scat-

tering, and clearly 1 − f

Ray

is that of Mie scattering;

Mie

is called the scattering power which is acquired

by ﬁtting the measured data.

VISAPP 2021 - 16th International Conference on Computer Vision Theory and Applications

606

The refractive index (n

epi

, n

der

, n

sub

) and the

anisotropic factors (g

epi

, g

der

, g

sub

) of each layer are

ﬁxed as 1.44, 1.37, 1.37 and 0.8, 0.86, 0.75 respec-

tively. All parameters in skin model are given in Ta-

ble. I with descriptions and ranges.

2.2 Monte Carlo Simulations

With a well-deﬁned skin model, we then implemented

MC for reconstructing skin diffuse reﬂectance. The

MC was coded in Python v3.6.4, following the man-

ual of MCML (Wang et al., 1995). Fig. 1 shows the

detailed ﬂowchart of MC. To speed up the computa-

tional time, we reduced trigonometry operations by

creating an array for indexing which directly stores

the results. And GPU techniques were then applied

to accelerate MC with almost 1000 times faster (Fang

and Boas, 2009). For each simulation, 1E07 energy

packets (or photons) were emitted perpendicular to

the interface of tissue. Detection window was set

as a circle with a radius 2 cm to ensure the total

diffuse reﬂectance. The optical properties of tissue

were calculated and set based on our 3-layered skin

model. 50000 samples were simulated using MC by

randomly deﬁning 12 skin physiological parameters

and the wavelength in the range from 450 to 700 nm.

It took in total 18.2 hours for generating the skin re-

ﬂectance database with Intel Core i7-7700HQ CPU

and Nvidia GeForce GTX1060 GPU.

2.3 Neural Networks

Two neural networks have been built in our research

with opposite mapping directions using the Deep

Learning Toolbox in MATLAB R2018a. They are

both composed of two hidden layers with 55 neurons

(Tsui et al., 2018), one input layer and one output

layer. For FNN, the inputs are the optical parame-

ters of skin model with nine dimensions (e.g. µ

a epi

a der

, µ

a sub

, µ

s epi

, µ

s der

, µ

s sub

, d

epi

, d

der

, and d

sub

)

and the output is skin diffuse reﬂectance at one spec-

iﬁed wavelength. For INN, the input is skin diffuse

reﬂectance spectrum from 450 to 700 nm and the out-

put are the volume fractions of skin pigments. The

training function was set as the scaled conjugate gra-

dient method. Besides this, normalization and ran-

dom data division were applied to databases. Note

that the database generated by MC was applied for

training FNN, and another database generated with

the help of FNN was then applied for training INN

since MC needs a signiﬁcant amount of time to re-

produce the reﬂectance spectrum, and FNN provides

very similar results to MC and works much faster than

MC.

Figure 1: Flowchart of Monte Carlo simulations: energy

packets are considered as photons with an initial weight 1.

3 EXPERIMENTATION AND

RESULTS

The FNN was trained using the database generated

by MC based on 3-layered skin model. Fig. 2 shows

the performance which is the mean squared error dur-

ing the training process. As illustrated, the error de-

creases dramatically at the start, then it tends to fall

smoothly after 5000 epochs, and eventually, it holds

steady. After FNN training was completed, the dif-

fuse reﬂectance can be reproduced by predeﬁning

skin physiological parameters. Then we tested FNN

on the performance of reconstructing skin diffuse re-

ﬂectance. Taking pigmented degree into account, we

sampled 10 times for lightly, moderately, and darkly

pigmented in turn. The volume fraction of melanin

varies from [1.3% 3%], [11% 16%], and [18% 43%]

respectively (Jacques et al., 1996). 30 samples in to-

tal were created consequently. Starting from the same

randomly assigned 12 parameters of skin model, FNN

and MC reconstructed skin diffuse reﬂectance in the

range from 450 to 700 nm. As can be seen in Fig. 3,

the reconstructed diffuse reﬂectance curve gradually

increases in the range from 450 to 500 nm, and a W

pattern comes out from 500 to 600 nm. This is due

Quantitative Analysis of Skin using Diffuse Reﬂectance for Non-invasive Pigments Detection

607

Table 1: Descriptions, symbols, and ranges of parameters in skin model.

Symbol Description Range

volume fraction of melanin 1.3-43% (Jacques, 1996)

β ratio of pheomelanin to eumelanin 4.9-36% (Parsad et al., 2003)

w epi

volume fraction of water in epidermis 10-20%

epi

thickness of epidermis 0.027-0.15mm (Baranoski and Krishnaswamy, 2010)

bl der

volume fraction of blood in dermis 0.2-7% (Flewelling, 2000)

w der

volume fraction of water in dermis 40-90%

S oxygen saturation 50-95% (Angelopoulou, 2001)

der

thickness of dermis 0.6-3mm (Baranoski and Krishnaswamy, 2010)

bl sub

volume fraction of blood in subcutis 5-20%

w sub

volume fraction of water in subcutis 40-90%

f at

volume fraction of fat 40-70%

sub

thickness of subcutis 1-5mm

0 0.5 1 1.5 2 2.5 3

31391 Epochs

-8

-6

-4

-2

Mean Squared Error (mse)

Best Validation Performance is 6.8471e-08 at epoch 30891

Train

Validation

Test

Best

Figure 2: Performance for FNN trained by the MC

database.

to the unique absorption of oxy-hemoglobin. Here,

for sample no.1, the oxygen saturation in the blood

is 65.1%. Generally, the higher the volume fraction

of blood and oxy-hemoglobin, the more apparent this

W pattern. When melanin dominates the absorption,

the ”W” pattern is no longer apparent. The root mean

squared relative error (RMSRE) was used for evaluat-

ing the ﬁtting performance, given by:

RMSRE =

∑

λ=700nm

λ=450nm

(

−T

)

(7)

where R

and T

are respectively the diffuse re-

ﬂectance produced by our method and the target

reﬂectance; N

is number of wavelengths (bands),

equaling 251 in our research. Then the RMSRE were

calculated for all 30 samples in different groups. The

average values of RMSRE using FNN are 0.0033,

0.0037, and 0.0061 for three groups. It turns out

that FNN can yield skin diffuse reﬂectance extremely

close to the target reﬂectance simulated by MC start-

ing from the same skin physiological parameters.

Figure 3: Reconstructing skin reﬂectance by MC and FNN:

sample no.1.

3.1 Effects Analysis of Skin Parameters

on Reconstructing Reﬂectance

Before detecting pigments information, we would like

to ﬁrst analyze the effects of skin parameters on re-

constructing skin diffuse reﬂectance. One parameter

is analyzed by varying its value while all other pa-

rameters are ﬁxed. All parameters are initialized as

the lower limit in Table. I.

The volume fraction of melanin is set from 1.3 to

43% with 2% increment in turn. Fig. 4(a) shows

the results of reconstructing diffuse reﬂectance with

varying C

. We ﬁnd that in general the reﬂectance

decreases when C

increases. The reﬂectance curve

tends to be more ﬂattened, and typical W pattern be-

comes less evident. The absorption coefﬁcient of

melanin decreases gradually and steadily over 450-

700 nm. Accordingly, the diffuse reﬂectance in-

creases gradually and steadily while C

is too large

and melanin dominates the absorption. Changing β

does not really affects the shape of reﬂectance curve

as shown in Fig. 4(b) since two types of melanin have

similar absorption spectra in the visible light range,

and µ

a pheo

is slightly smaller than µ

a eu

. When β

increases, the proportion of pheomelanin increases,

thus, the total absorption caused by melanin decreases

VISAPP 2021 - 16th International Conference on Computer Vision Theory and Applications

608

a little. Consequently, the diffuse reﬂectance grows.

The difference between µ

a pheo

and µ

a eu

becomes

larger in long wavelength range. This is also reﬂected

in the reconstructed diffuse reﬂectance, where the dif-

ference in long wavelength range is more evident.

The absorption of blood is mainly expressed as

hemoglobin and oxygen saturation. Fig. 4(c), Fig.

4(d), and Fig. 4(e) illustrate the effects of blood in the

dermis and subcutis, and oxygen saturation on recon-

structing skin diffuse reﬂectance. With the volume

fraction of blood increasing both in the dermis and

subcutis, skin reﬂectance decreases. Moreover, the ef-

fects of blood in the dermis are more signiﬁcant than

in the subcutis since only small parts of light can pen-

etrate into the subcutis and the long-wavelength light

has better penetration. Thats why the effects of blood

in the subcutis mainly locate in the range from 600

to 700 nm. On the other hand, the effects of oxygen

saturation are not uniform since oxy-hemoglobin has

a unique W pattern absorption coefﬁcient. When S

increases, the diffuse reﬂectance decreases from 450

to nearly 500 nm, increases from about 550 to 575

nm, and increases signiﬁcantly from 600 to 700 nm.

This can be explained under the comprehensive ab-

sorption of oxy- and deoxy-hemoglobin. From 450 to

500 nm, µ

a oxy

is larger than µ

a deoxy

. The absorption

is enhanced while S grows. From 550 to 575 nm and

above 600 nm, µ

a oxy

is smaller than µ

a deoxy

. Then,

we can see that skin diffuse reﬂectance increases as S

grows.

The thickness of skin layers are also involved and

the effects of the thickness of each layer are not the

same. Skin diffuse reﬂectance decreases while d

epi

grows. However, it increases while d

der

, d

sub

grows.

Note that all parameters are initialized as the lower

limit. This means the absorption of skin is possibly

insufﬁcient and the transmitted light is large. The re-

sults may change in realistic condition. Other pig-

ments (e.g. water and fat) are not listed here in this

study because they are less weighted in skin absorp-

tion given that their absorption coefﬁcients are much

smaller than melanin or hemoglobin.

3.2 INN Training and Acceleration

We have proved FNN reconstructs extremely simi-

lar skin diffuse reﬂectance to MC. Therefore, another

database composed of reﬂectance spectra from 450

to 700 nm and melanin information was built using

FNN for speeding up. 50000 samples were created

within 4.3 hours by randomly predeﬁning skin phys-

iological parameters. Note that this second database

contains the reﬂectance spectra but not the reﬂectance

at one wavelength. It took 57 minutes 38 seconds to

complete the training process for INN. Moreover, we

applied principal components analysis (PCA) for di-

mensionality reduction and speeding up. PCA uses

orthogonal transformation to linearly transform the

observations of a series of possibly related variables,

thereby projecting the values of a series of linear

unrelated variables. These unrelated variables are

called principal components. In our research, we have

50000 observations with 251 variables (from 450 to

700 nm with 1 nm increment), represented by a ma-

trix X (251×50000). Then, a principal components

matrix Y is deﬁned:

= X

= (W DV

)

= V D

(8)

where X = W DV

is the singular value decomposi-

tion; W is the eigenvector matrix of XX

(251×251);

D is a 251×50000 non-negative rectangular diag-

onal matrix; V is the eigenvector matrix of X

(50000×50000). We calculated the inﬂuence of ev-

ery principal component and the ﬁrst seven principal

components accounted for above 99.53%. Then, a

data matrix X is transformed to a matrix 7×50000

with reduced dimensionality. Another INN was

trained based on this low-dimension matrix within 10

minutes 35 seconds.

3.3 Veriﬁcation of Pigments Detection

with Synthetic Data

Although our methods give favorable results in re-

gression, to extract or quantify skin physiological pa-

rameters, the inverse problem is undoubtedly more

important. In other words, our methods need to ﬁt

the diffuse reﬂectance curve precisely without know-

ing those parameters in prior. The ﬂowcharts of two

neural networks are shown in Fig. 5. For FNN,

RMSRE between the target and reconstructed diffuse

reﬂectance was reduced until reaching the limits of

the optimization process by adjusting the inputs iter-

atively. In our research, the interior-point algorithm

was selected to minimize RMSRE. The maximum

number of iterations was assigned to 1000. The initial

physiological parameters were randomly set within

the proper range and 5 start points were arranged.

For INN, we directly obtained the volume fraction

of melanin based on inputting the diffuse reﬂectance

spectrum. To validate our methods, we ﬁrst used 30

samples in three different groups generated by MC as

we mentioned above. We ﬁrst focused on the results

of FNN. For lightly pigmented group, satisfactory es-

timations were obtained for the volume fraction of

Quantitative Analysis of Skin using Diffuse Reﬂectance for Non-invasive Pigments Detection

609

(a) (b)

(e)

Figure 4: Reconstructing skin diffuse reﬂectance using varying (a) C

; (b) β; (c) C

bl der

; (d) C

bl sub

; (e) S.

melanin and blood in the dermis, the oxygen satu-

ration, and the thickness of ﬁrst two layers. Yet not

every parameter can be extracted accurately. The rest

parameters were not estimated with acceptable errors.

Table II shows some estimation results using FNN.

The prediction error for the volume fraction of water

reaches a maximum of nearly 30%. From the perspec-

tive of the absorption coefﬁcients of skin pigments,

water is less weighted and has less impact on the dif-

fuse reﬂectance although its volume fraction is large

enough. By contrast, melanin and hemoglobin dom-

inate the light absorption within the skin, thus, the

prediction errors are favorable. The situation is quite

similar in moderately and darkly pigmented groups.

And we ﬁnd that the estimation of ratio of pheome-

lanin to eumelanin becomes more accurate when the

volume fraction of melanin grows. The average rel-

ative errors of β is reduced to almost 5% for darkly

pigmented group. Moreover, the thickness of ﬁrst two

layers can be also estimated correctly with the aver-

age relative errors 1.11%, 4.80% for d

epi

and d

der

The average relative errors of C

, C

bl der

, and S for

all three groups are 1.36%, 8.69%, and 3.37% respec-

tively. For the volume fraction of blood in the subcutis

and fat, the estimation errors are less than 10%. Dur-

ing this optimization process, the average RMSRE

for 30 samples equals to 0.0078, which means FNN

can accurately ﬁt the synthetic reﬂectance curve with-

out knowing skin physiological parameters in prior.

Besides, it costs an average of 17 seconds to ﬁt the

curve and quantify parameters for one sample. Given

that MC needs roughly 332 seconds to reconstruct a

spectrum while FNN needs only 0.0019 seconds in

our experimentation, using inverse MC probably costs

dozens of hours to ﬁnish the detection task.

To furthermore speed up the detection, INN was

applied to estimate the volume fraction of melanin

from 30 samples. Both INN and INN+PCA were

tested. Table III gives the detection results for

all groups. For lightly pigmented group, the root-

mean-square errors (RMSE) and standard deviations

(STD) of INN and INN+PCA are 0.30%±0.30% and

0.21%±0.42% respectively. The small values of

RMSE and STD imply that two methods are robust

VISAPP 2021 - 16th International Conference on Computer Vision Theory and Applications

610

Figure 5: The ﬂowcharts of FNN and INN.

when estimating the volume fraction of melanin. For

moderately pigmented group, RMSE and STD of INN

and INN+PCA are 0.40%±0.39% and 0.5%±1.34%.

Both two methods have acceptable results and INN

becomes more accurate than INN+PCA. For darkly

pigmented group, RMSE and STD of INN and

INN+PCA are 2.00%±1.93% and 2.33%±5.6%. The

errors become larger but are still acceptable. Given

that the target volume fraction of melanin for lightly

pigmented group is too low, varying from 1.3% to

3%, the relative errors for this group are the largest

among three groups. To sum up, INN and INN+PCA

estimate close results for three groups most of time.

Although INN is more accurate than INN+PCA, it

costs more training time. FNN can estimate precisely

not only melanin information but also the oxygen

saturation and blood information. However, it costs

more time to ﬁnish the estimation task while INN and

INN+PCA cost only about 0.012 seconds.

3.4 Veriﬁcation of Pigments Detection

with Measured Data

Our methods detect several skin physiological pa-

rameters successfully from the synthetic diffuse re-

ﬂectance. The next step is to detect these parame-

ters from the measured data. NIST skin reﬂectance

database was used in this part. The skin diffuse re-

ﬂectance spectra were acquired with a commercially

available spectrophotometer with the help of integrat-

ing sphere and this database contains 100 samples

with spanning the wavelength range from 250 to 2500

nm with an increment 3 nm (Cooksey et al., 2017).

These samples were reshaped using the interpolation

algorithm and only the range from 450 to 700 nm was

saved for further uses. Afterward, the curve-ﬁtting

process was applied and the optimization goal was to

minimize RMSRE for FNN and MC. For INN and

INN+PCA, they directly detected the melanin infor-

mation from the target spectrum. Table IV provides

the detection results for three samples from NIST

database. As we can see, FNN and MC obtained ap-

proximate ﬁtting performance. They both need the

Figure 6: The measured and reconstructed spectra by FNN

from NIST.

curve-ﬁtting process to complete the detection task.

INN and INN+PCA also obtained approximate values

compared to FNN and MC. For spectrum 1, all meth-

ods obtained C

around 2% which belongs to lightly

pigmented group. The estimation results of C

bl der

and S are also extremely close for FNN and MC. FNN

has a better ﬁtting performance than MC with RM-

SRE equals to 2.08%. For the rest two spectra, C

were estimated as about 3% and 10%, which matches

well the spectra as shown in Fig. 6. In the range from

450 to 700 nm, the diffuse reﬂectance of spectrum 2

is evenly higher than spectrum 3. Overall, our meth-

ods have favorable estimation results in detecting pig-

ments information from the measured spectra.

4 DISCUSSION AND

CONCLUSION

Our research gives a quantitative analysis of skin

based on its diffuse reﬂectance. MC is used for gen-

erating the synthetic training database based on a 3-

layered skin model. FNN has been trained to solve

the detection task. The absorption of skin is inﬂu-

enced by the combination of various pigments and the

thickness of layers. The effects of several skin pig-

ments are analyzed separately. We ﬁnd that the unique

”W” pattern absorption of oxy-hemoglobin can be

reﬂected clearly on the diffuse reﬂectance spectrum

when the absorption of other pigments is not over

weighted. The results present that FNN has excel-

lent ﬁtting performance when dealing with synthetic

data. And when it comes to the measured data, the ﬁt-

ting performance is also acceptable. The visible light

range from 450 to 700 nm is taken into account in our

experimentation. As we know, the longer-wavelength

light generally has better penetration capacity. The

thicker the skin layers, the less likely light will pene-

trate. A 3-layered skin model is necessary when deal-

ing with thin skin and long-wavelength light. Besides,

the pigments detection for melanin and blood in the

Quantitative Analysis of Skin using Diffuse Reﬂectance for Non-invasive Pigments Detection

611

Table 2: The ﬁtting results of FNN for one sample in each group.

β C

water epi

water der

water sub

bl der

Sample no.1 Optimized 0.0251 0.0673 0.1496 0.5549 0.6611 0.0623

Target 0.0251 0.1698 0.1712 0.4724 0.8811 0.0672

Sample no.11 Optimized 0.1577 0.0966 0.1497 0.5545 0.7662 0.0061

Target 0.1563 0.0870 0.1337 0.6185 0.7512 0.0064

Sample no.21 Optimized 0.2859 0.3380 0.1507 0.6576 0.7755 0.0096

Target 0.2865 0.3534 0.1607 0.7400 0.8396 0.0102

bl sub

S C

f at

epi

der

sub

Sample no.1 Optimized 0.0676 0.6508 0.5473 0.0107 0.2574 0.2074

Target 0.1455 0.6510 0.4865 0.0108 0.2836 0.2381

Sample no.11 Optimized 0.0769 0.5325 0.4702 0.0122 0.0720 0.3485

Target 0.0560 0.5362 0.4540 0.0124 0.0792 0.2471

Sample no.21 Optimized 0.0566 0.8896 0.5197 0.0116 0.2836 0.1901

Target 0.0871 0.8854 0.4995 0.0117 0.2627 0.2153

Table 3: Melanin[%] detection results of proposed INN methods for three groups.

Samples no.1 no.2 no.3 no.4 no.5 no.6 no.7 no.8 no.9 no.10

Target 2.51 2.02 1.76 1.85 2.26 1.74 1.96 1.88 2.79 1.47

INN 2.30 1.78 2.13 1.88 2.41 1.67 1.66 1.30 3.24 1.32

INN+PCA 2.47 1.86 2.23 1.83 2.30 1.56 2.08 1.52 2.78 1.53

no.11 no.12 no.13 no.14 no.15 no.16 no.17 no.18 no.19 no.20

Target 15.63 12.44 12.18 13.01 13.82 13.48 11.24 14.28 14.45 11.43

INN 15.72 12.59 12.28 12.60 13.77 13.64 12.10 13.89 14.05 11.98

INN+PCA 16.25 12.34 12.29 13.00 13.85 13.41 11.29 14.17 14.42 12.85

no.21 no.22 no.23 no.24 no.25 no.26 no.27 no.28 no.29 no.30

Target 28.65 24.49 30.97 19.79 36.19 39.78 27.24 28.35 22.17 37.46

INN 28.64 24.01 30.73 19.28 36.14 33.88 27.02 30.42 22.02 37.83

INN+PCA 28.03 24.80 30.69 19.73 35.79 34.91 27.50 33.76 22.35 38.20

dermis (hemoglobin together with the oxygen satu-

ration) are very promising. Other skin physiological

parameters like the thickness of each layer are also ac-

ceptable. However, for water content, the estimation

results are not accurate due to its low light absorption

from 450 to 700 nm. This problem may be solved by

expanding the light range to infrared where the ab-

sorption coefﬁcient of water increases a lot. More-

over, we also introduce INN and PCA to speed up the

melanin detection. The accuracy of INN is similar to

FNN. INN needs much less computational time than

FNN because it doesn’t rely on the curve-ﬁtting pro-

cess. This also makes INN less robust and intuitive

than FNN. FNN with the curve-ﬁtting process can re-

construct the diffuse reﬂectance very well compared

with the measured data. As perspectives, we plan to

improve our skin model by adding separately upper

and deep blood plexus. In tissue, blood is not evenly

distributed, but rather conﬁned to vessels (Van Veen

et al., 2002). This fact affects the reﬂectance spectra

and is called the vessel packaging effect. The estima-

tion results of the oxygen saturation and the blood can

be more accurate with accounting for the vessel pack-

aging. Moreover, the selection of wavelength bands is

also an approach to improve detection performance.

For example, we can focus on the ”W” pattern range

when detecting the oxygen saturation because it is a

unique pattern of the absorption coefﬁcient of oxy-

hemoglobin. With the development of DRS instru-

ments, we plan to implement FNN and INN to detect

skin pigments information non-invasively and in real-

time together with the automatic recognition of skin

diseases (Carcagn

ı et al., 2019). This will be much

helpful for the quantitative diagnosis of some skin dis-

eases, such as vitiligo and melanoma.

ACKNOWLEDGEMENTS

We would like to thank China Scholarship Council

(CSC) the grant contract number is 201701810030

which partially supports this research.

VISAPP 2021 - 16th International Conference on Computer Vision Theory and Applications

612

Table 4: The extractiong results of 2L-FANN and 3L-FANN.

Sample Methods C

bl der

S RMSRE

spectrum 1 FNN 1.31% 0.56% 90.23% 2.08%

MC 2.13% 0.54% 90.45% 3.28%

INN 1.84%

INN+PCA 1.72%

spectrum 2 FNN 3.23% 1.02% 94.95% 4.27%

MC 3.69% 1.08% 94.91% 5.69%

INN 2.90%

INN+PCA 2.87%

spectrum 3 FNN 10.09% 2.41% 80.00% 10.76%

MC 9.79% 2.03% 80.02% 8.37%

INN 10.69%

INN+PCA 10.73%

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