WO2014204007A1

WO2014204007A1 - Method for evaluating cosmetic effects of cosmetic product on skin

Info

Publication number: WO2014204007A1
Application number: PCT/JP2014/066493
Authority: WO
Inventors: Hirono TOTSUKA; Eunsook Kim; Dominique BATISSE; Christophe Hadjur; Takayuki Sota; Takashi Nagaoka
Original assignee: LOreal SA
Current assignee: LOreal SA
Priority date: 2013-06-19
Filing date: 2014-06-17
Publication date: 2014-12-24
Anticipated expiration: 2015-12-19
Also published as: JP2016529470A; JP6437466B2; CN105324068A; CN105324068B

Abstract

The present invention relates to a method for evaluating the cosmetic effects of a cosmetic product on the skin by determining multi-dimensional vectors from the diffuse reflection spectrum at the surfaces of the reference and the object skin before and after the application, and comparing any indices of relative spectral lengths of the object skin, spectral angles and an entropy after the application of the cosmetic product to the indices before the application of the cosmetic product. The method according to the present invention can evaluate the cosmetic effects of a cosmetic product on the skin with high precision and accuracy, and provide new indices directly linked to customer perception.

Description

DESCRIPTION

METHOD FOR EVALUATING COSMETIC EFFECTS OF COSMETIC PRODUCT ON SKIN TECHNICAL FIELD

The present invention relates to a method for evaluating the cosmetic effects of a cosmetic product on the skin. BACKGROUND ART

Recently, some methods for measuring the cosmetic effects of a cosmetic product have been developed. For examples, JP-A-2007-307084 discloses a method for evaluating the whitening effect by measuring an increase in whiteness of skin color due to a skin color change caused by promoted blood circulation. The whitening effect is determined by the increase rate of the average hemoglobin content in this method.

JP-A-2008-245666 discloses a method for evaluating skin pigmentation comprising a step of obtaining a color image of a color chart for adjusting a white balance by using a camera. This method is based on RGB information which provides a color image and conventional color parameters which do not teach homogeneity of skin color and pigmentary spots.

However, consumer perception is very complex and thus multi instrumental parameters are often used to understand what consumers feel and think. Also, the results obtained by current technologies are not precise enough to understand consumers' needs.

The conventional methods for evaluating the cosmetic effects of a cosmetic product are based primarily on color information by a spectrum or average spectrum of an area. However, discrepancies may be found with customer perception in the cosmetic application by methods based on color analysis.

On the other hand, a hyperspectral imaging method coupled with spectral angle map fractal analysis has been developed for a method and an apparatus for a non-invasive measurement of human skin melanin. For example, JP-A-2010-51589 discloses a non-invasive method for measuring the amount of melanin in human skin. JP-A-2010- 125288 discloses a method for creating images for melanoma diagnosis by using spectral analysis in a non-invasive manner. JP-A-2010-252904 discloses a method for deriving an index for discriminating melanoma using a spectra analysis. The hyperspectral imaging method has numerous advantages. For example, the method is non-invasive, non-contact and enables swift measurement. In addition, information on the molecular level can be obtained by the method.

The hyperspectral imaging method has been mainly focused on the biomedical field for the purpose of pre-diagnostics application of superficial cancer and images of lentigo malignant melanoma. However, the hyperspectral imaging method has not been investigated in the cosmetic field so far.

DISCLOSURE OF INVENTION

An objective of the present invention is to provide a new method for evaluating the cosmetic effects of a cosmetic product on the skin with high precision and accuracy. Another objective is to provide new indices directly linked to customer perception.

The above objectives of the present invention can be achieved by a method for evaluating the cosmetic effects of a cosmetic product on the skin, comprising steps of:

(i) measuring diffuse reflection spectrum at the surfaces of a reference and an object skin before an application to acquire positional information at the surfaces of the reference and the object skin, and pixel data including the diffuse reflection spectrum at the pixel,

(ii) applying the cosmetic product to the surface of the object skin,

(iii) measuring diffuse reflection spectrum at the surfaces of the object skin after the application to acquire positional information at the surfaces of the object skin, and pixel data including the diffuse reflection spectrum at the pixel,

(iv) determining multi-dimensional vectors from the diffuse reflection spectrum at the surfaces of the reference and the object skin before and after the application,

(v) evaluating the cosmetic effects of the cosmetic product by comparing any indices of relative spectral lengths of the object skin, spectral angles and an entropy after the application of the cosmetic product to the indices before the appli cation of the cosmetic product,

wherein

the average spectral lengths of the object skin relative to the spectral length of the reference before and after the application are determined from the multi-dimensional vectors of the object skin before and after the application using the reference vector,

the spectral angles are determined from the multi-dimensional vectors of the reference and the object skin before and after the application using the reference vector, and

the entropy is determined from the spectral angles, the positional information and the pixel data.

The multi-dimensional vectors of the reference and the object skin before and after the appl ication in the step (iv) may be determined by vectors whose components are the diffuse reflectances at wavelength bands at the pixel.

The relative spectral lengths of the object skin before and after the application ( £ _sb and £ _sa ) in step (v) can be determined by the followin equations:

L sa

£ sa (2) wherein

Lr is the average length of the multi-dimensional vectors of the reference,

L_s is the average length of the multi-dimensional vectors of the object skin before the application, and

L_sa is the average length of the multi-dimensional vectors of the object skin after the application, wherein

\2 I 2

(5)

N j=l

wherein

a, ^J is the diffuse reflectance component at the i-th wavelength band of the j-th pixel of the reference,

b, ^J is the diffuse reflectance component at the i-th wavelength band of j-th pixel of the object skin before the application,

c,^J is the diffuse reflectance component at the i-th wavelength band of j-th pixel of the object skin after the application,

n is the total number of wavelength bands, and

N is the total number of pixels. The spectral angles before the application (6b^J) and those after the application (9_a ^J) at the j-th pixel in step (v) can be determined by the following equations:

wherein

L_r ^J is the length of the multi-dimensional vector at the j-th pixel of the reference,

L_sb^J is the length of the multi-dimensional vector at the j-th pixel of the object skin before the application,

L_sa ^J is the length of the multi-dimensional vector at the j-th pixel of the object skin after the application,

Gb^J is the spectral angle at the j-th pixel of the object skin before the application, 0_a ^J is the spectral angle at the j-th pixel of the object skin after the application,

a™ is the diffuse reflectance component at the i-th wavelength band of m-th pixel of the reference, bi is the diffuse reflectance component at the i-th wavelength band of the j-th pixel of the object skin before the application,

c,^J is the diffuse reflectance component at the i-th wavelength band of the j-th pixel of the object skin after the application,

n is the total number of wavelength bands, and

N is the total number of pixels. The entropy before and after the application in step (v) can be determined by the following equations: epy_b = -∑fi(e_blk)iog₂ A(e_b,k) (8)

k=0

wherein

epyb is the entropy before the application,

epy_a is the entropy after the application,

n(e_bfk ) = (n(e_bjk)- ti(e_bjk.₁ ))/ N ( 10)

wherein

n(9_{b k} ) is the number of pixels with the corresponding spectral angles less than 0_{b k} , η(θ_{3 k} ) is the number of pixels with the corresponding spectral angles less than 9_{a k} , and

N is the total number of pixels

wherein

Θ \ ct.max °a,min / ■ Λ 1 T V

a,k = ^ > k = 0,l,A- -, , K is the total number of segments between θ_{α mjn} = min^ ) and ^.max = max(<¾ ) with a = b, a .

A wavelength of the diffuse reflection spectrum may be in the range of 450 to 750 nm. The reference may be the skin of inner arms.

The object skin may be the skin of a face. The cosmetic product may be for a topical application.

The cosmetic product for the topical application can be a skin care product, a makeup product for the skin, or a sun protection product.

The skin care product can be selected from the group consisting of a cleanser, a lotion, a cream, a gel, a facial mask, a skin Tightener, a skin whitener, and a serum. The skin care product can be for skin lightening, skin whitening, skin bleaching or self-tanning.

The method according to the present invention can be non-invasive.

The method according to the present invention can be for evaluating a lightening or whitening effect, for evaluating a protective effect against ultraviolet radiation and for evaluating a makeup effect.

BRIEF DESCRIPTION OF DRAWINGS Figure 1 shows a schematic diagram of an example of an apparatus used in the present invention.

Figure 2 shows a block diagram of a spectrometer which is mounted on the apparatus shown in Figure 1.

BEST MODE FOR CARRYING OUT THE INVENTION

After diligent research, the inventors have discovered that it is possible to provide a method for evaluating the cosmetic effects of a cosmetic product on the skin with high precision and accuracy, and to provide new indices directly linked to customer perception. The method according to the present invention can provide accurate analytical results by considering the spectral angles and spectral lengths in correlation with skin color tone so that accurate information on the homogeneity of skin color and the effect of whitening cosmetic products can be obtained. The method can achieve an increase in data quality so that consumer perception can be understood precisely due to the parameters from the spectral angles and spectral lengths.

In addition, the method according to the present invention has advantageous effects as follows: the device used for the method according to the present invention provides a fast data acquisition time, lower data-fluctuation during the time course, and a lower failure-frequency. The software for the method according to the present invention provides an operator-friendly interface, easy navigation for positioning, an automated calibration, and a malfunction indicator.

Hereinafter, the method for evaluating the cosmetic effects of a cosmetic product on the skin according to the present invention will be explained in more detail. [Method for Evaluating Cosmetic Effects]

The method for evaluating the cosmetic effects of a cosmetic product on the skin according to the present invention comprises the steps of:

(ii) applying the cosmetic product to the surface of the object skin,

(v) evaluating the cosmetic effects of the cosmetic product by comparing any indices of relative spectral lengths of the object skin, spectral angles and an entropy after the application of the cosmetic product to the indices before the application of the cosmetic product,

wherein

In the steps (i) and (iii), diffuse reflection spectrum at the surfaces of a reference and an object skin before and after the application are measured to acquire positional information at the surfaces of the reference and the object skin, and pixel data including the diffuse reflection spectrum at the pixel. The diffuse reflection spectrum obtained in the steps (i) and (iii) are related to the wavelength in the two-dimensional plane.

In order to utilize the information at the molecular level, the wavelength of the diffuse reflection spectrum is preferably in the range of 450 to 750 nm, more preferably in the range of 500 to 750 nm which is a visible - near infrared spectrum. The visible - near infrared spectrum includes the information of components at the molecular level that constitutes the object.

In the measurement of the diffuse reflection spectrum, al l predetermined spatial regions may be scanned. Therefore, there is a possibility that unnecessary pixel data will also be acquired.

Consequently, preferably, after acquiring the pixel data, the pixel data having a predetermined reflectivity at a given wavelength should be excluded by filtering.

The reference used in the method according to the present invention is preferably the skin of inner arms. In the step (iv), multi-dimensional vectors from the diffuse reflection spectrum at the surfaces of the reference and the object skin before and after the application are determined. The multidimensional vectors of the reference and the object skin before and after the application can be determined by vectors whose components are the diffuse reflectances at wavelength bands at the pixel.

In the step (v), the cosmetic effects of the cosmetic product are evaluated by comparing any indices of relative spectral lengths of the object skin, spectral angles and an entropy after the application of the cosmetic product to the indices before the application of the cosmetic product.

The relative spectral lengths and the spectral angles are calculated by Spectral Angle Mapper (SAM) described in F. A. Kruse et al., "The spectral image processing system (SIPS) - interactive visualization and analysis of imaging spectrometer data", (1993) Remote Sensing of Environment, 44, pp. 145-163.

The relative spectral lengths of the object skin before and after the application ( £ _sb and I _sa ) in step (v) can be determined from the multi-dimensional vectors. These lengths indicate the change in net light absorption caused by change in melanin content in the skin. The relative spectral lengths can be determined by the following equations: ^ = ^ > (1)

^a ^ - (2) wherein

L_r is the average length of the multi-dimensional vectors of the reference,

L_sb is the average length of the multi-dimensional vectors of the object skin before the application, and

wherein

a,^J is the diffuse reflectance component at the i-th wavelength band of the j-th pixel of the reference, b, ^J is the diffuse reflectance component at the i-th wavelength band of j-th pixel of the object skin before the application,

c, ^J is the diffuse reflectance component at the i-th wavelength band of j-th pixel of the object skin after the application,

n is the total number of wavelength bands, and

N is the total number of pixels.

The longer the relative spectral lengths are, the more reflectances are acquired from the skin.

The spectral angles before the application (6 ^J) and after the application (0_a ^J) at the j-th pixel in step (v) can be determined from inner products of the multi-dimensional vectors. These spectral angles indicate the qualitative change in spectrum characteristics between the reference and the object skin at a molecular level, such as differences in the ratio of constituents in the skin due to a change in balance between melanin and hemoglobin amounts. These spectral angles can be determined by the following equations:

wherein

9 ^J is the spectral angle at the j-th pixel of the object skin before the application,

9_a ^J is the spectral angle at the j-th pixel of the object skin after the application,

a™ is the diffuse reflectance component at the i-th wavelength band of m-th pixel of the reference, b, ^J is the diffuse reflectance component at the i-th wavelength band of the j-th pixel of the object skin before the application,

c, ^J is the diffuse reflectance component at the i-th wavelength band of the j-th pixel of the object skin after the application,

n is the total number of wavelength bands, and

N is the total number of pixels.

The smaller the spectral angles are, the closer to the reference the object skin is.

The entropy is one of the indices reflecting molecular information at the surface of the object skin. This entropy indicates the width of spectral angle distribution associated with homogeneity of the skin. The entropy before and after the application in step (v) can be determined by the following equations: epy_b = -∑A(e_b,k )log₂ n(e_{b k} ) (8)

k=0 epy_a = -X n(e_a,k)log₂ n(6_{a k} ) (9) wherein

epy_b is the entropy before the application,

epy_a is the entropy after the application,

^_a,k)= We_a,k) - n(e_a,k_, ))/ N (11) wherein

n(6_{b k} ) is the number of pixels with the corresponding spectral angles less than 9_{b k} , η(θ_{3 k} ) is the number of pixels with the corresponding spectral angles less than 9_{a k} , and

N is the total number of pixels

wherein

Q_{a k} = ^a'msx k = 0,1,2,· -, K ,

K

K is the total number of segments between θ_{α min} = min^ ) and ^_,m,„ = max(<¾ ) with a = b, a. The smaller the entropy is, the more homogeneous the color of the skin is.

By setting a threshold value for spectral angles and the percentage in the spectral angle distribution, spots of no interest can be excluded from analysis. The spectral angles of the object skin should be smaller than the threshold value, so that if there are spots having a higher threshold value with a certain percentage, they will be excluded from the target spots.

The method according to the present invention can be used for the application of skin color analysis and color analysis of cosmetic products by determining (1) the differences before and after an application, and (2) the differences immediately after the application and after any numbers of hours of the application of the cosmetic products.

The method according to the present invention is a beneficial evaluation tool that provides accurate analytical results by considering spectral angles and spectral lengths in correlation with the object skin color tone. The method can achieve an increase in data quality for precise understanding of consumers' perception using the parameters from the spectral angles and spectral lengths.

[Cosmetic Product]

In step (ii) of the method according to the present invention, a cosmetic product is applied to the surface of the object skin. The object skin is preferably the skin of a face.

The cosmetic product used in the present invention is preferably for a topical application. The cosmetic product for the topical application may be a skin care product, a makeup product for the skin, or a sun protection product. The skin care product is not limited specifically, and can be selected from the group consisting of a cleanser, a lotion, a cream, a gel, a facial mask, and a serum. The skin care product can be for skin lightening, skin whitening, skin bleaching or self-tanning.

The skin lightener and the skin whitener are compositions for applying to the surface of the body of a human being for the purpose of lightening or whitening, and are preferably cosmetics or agents for topical application on the skin. Cosmetics or agents for topical application on the skin means a product to be applied onto the skin, and may correspond to a dermatological drug or quasi drug. The terms "lightening" and "whitening" mean all effects of inhibiting the production and/or deposition of melanin, and include inhibiting of the production of melanin, and reducing the produced melanin.

In the case of the skin lightener or the skin whitener being a cosmetic water, the cosmetic water is preferably transparent or preferably has a uniform outer appearance. Here, the expression "transparent" means a transilluminating property without any deviation caused due to refraction or reflection. Transparency of a composition such as a cosmetic water can be measured by means of a turbidimeter. For example, a portable turbidimeter model 2100 P (trade name) manufactured by Hach Company can be employed in order to measure the transparency limit of a composition. When a composition has a measured turbidity value ranging from 0 to 250 NTU, the composition can be considered as being transparent.

The skin lightener or the skin whitener is employed in a cosmetic treatment process comprising the step of applying the skin lightener or the skin whitener onto the skin. The process is, in particular, suitable for removing brownish pigmentation blemishes, for example, caused by external factors, and/or blemishes caused by, for example, internal factors such as aging and the like, and/or is suitable for lightening the brown skin.

The cosmetic product used in the present invention may be in the form of a suspension, a dispersion; an oil-in-water, water-in-oil or multiple emulsion; a gel or a mousse; an oily or emulsified gel; a dispersion of vesicles, especially lipid vesicles; a two-phase or multi-phase lotion; a spray; a loose, compact or cast powder; an anhydrous paste. The cosmetic product may have the appearance of a lotion, a cream, a pomade, a soft paste, an ointment, a mousse, a cast or molded solid, or a compacted solid. The cosmetic product may also be in the form of a composition for protecting or caring for the skin of the face, the neck, the hands or the body.

The cosmetic product used in the present invention can comprise components typically employed in cosmetics, such as acids, bases, salts, pigments, antioxidants, UV absorbing agents, blood circulation accelerators, metal chelators, sebum controllers, powders, astringents, skin softeners, humectants, surfactants, oils, organic solvents, silicones, silicone derivatives, natural extracts derived from animals or vegetables, waxes, and the like.

[Apparatus]

The apparatus used in the present invention will be described with reference to Figures 1 and 2. In Figure 1, 1 is the subject S. 2 is a white light source, and spectrometer 4 with a slit 3 is integrated with the CCD camera 5. Spectrometer 4 is an imaging spectrometer equipped with a transmission grating. The light reflected from the one line of the measurement object passes through the slit 3, is imaged on a light receiving surface of the CCD camera 5 serving as the detector, and is dispersed by the spectrometer. That is, the X-axis of the light receiving surface of the CCD camera 5 corresponds to the position of one line of the measurement object, and the Y-axis direction is the spectrum of the light dispersed. The detailed structure of spectrometer 4 is shown in Figure 2. Slit 3 is composed of a lens 3b to condense light and the slit body 3a. In addition, spectrometer 4 is composed of a prism 4b of the transmissive grating system which is between two lens 4a and 4c. Using an EM (Electron Multiplying) CCD camera, CCD camera 5 enhances the sensitivity to even weak light. Since the optical part of the apparatus is configured as stated above, the diffuse reflection spectrum data of one line of the object S can be obtained from one frame of the CCD camera. This data is input to the data processing device 6. Then, to get to the next frame of the CCD camera, the optical part of the apparatus is moved at a short distance and the diffuse reflection spectrum data of the next line is sent to the data processing device 6. By repeating this operation, it is possible to obtain diffuse reflectance spectral data of a two-dimensional plane. In fact, by the mechanism which moves in the direction perpendicular to the one line of the measurement object surface corresponding to the X-axis such as control unit 6b, the optical part is moved substantially continuously, and the data is acquired synchronously by the CCD camera 5. Although not shown, the apparatus used in the present invention is provided with a pair of polarizing plates. The light from the white light source 2 is linearly polarized by the polarizing plate, and only the perpendicular linearly polarized light component from the white light source 2 is incident on the spectrometer 4. Thus, the influence of irregular reflection occurring at the surface of the object S is suppressed. In addition, the direction of the polarizing plate can be set freely.

Although not shown, the apparatus used in the present invention has an Automatic focus (AF) function which can always focus on the center of the measuring point. Accordingly, the effects of shadows caused by large irregularities in the frequency space relatively on the surface of the object S can be suppressed.

The apparatus used in the present invention can store the diffuse reflection spectrum in the wavelength band that is determined by the characteristics of the spectrometer 4 in a

two-dimensional image in each pixel. The basic length scale of the two-dimensional image is determined by the measurement screen vertical dimension determined by an optical slit length of the slit 3 and the optical system magnification of the spectrometer 4, the measurement lateral screen dimension determined by the optical slit width of the slit 3 and the drive software setting of the control means 7, the one pixel dimension of the CCD cam era 5, and the one pixel dimension determined by the optical slit width of the slit 3 and the optical system magnification of spectrometer 4. Information on the position and diffuse reflection spectrum can be acquired in a short time by line scanning perpendicular to the longitudinal direction of the optical slit.

Analysis of the diffuse reflection spectrum of the target object obtained makes it possible to draw a two-dimensional spectral image. Therefore, it is possible to highlight the area where there is a qualitative or quantitative difference optically in the diffuse reflection spectrum with the apparatus. It is also possible to reconfigure the pseudo-color image by calculating and drawing the three primary colors element value from the diffuse reflectance spectrum.

[Cosmetic Application]

The method according to the present invention can be used for various applications. For example, the method can be used for evaluating a lightening or whitening effect of a cosmetic product such as a skin lightener and a skin whitener on the skin. The method according to the present invention can also be used for evaluating a protective effect against ultraviolet radiation of a sun protection product on the skin.

The method according to the present invention can also be used for evaluating a makeup effect of a makeup product for the skin.

EXAMPLES

The present invention will be described in a more detailed manner by way of examples.

However, they should not be construed as limiting the scope of the present invention.

[Apparatus]

A hyperspectral imaging device MSI-03, Mitaka Kohki Co., Ltd., Tokyo, Japan) was used for this study. The details of this apparatus are as follows: Spectral resolution: 1.51 nm,

Spectral range: 450.23-749.95 nm,

Measurement area: 16.09 mm x 21.52 mm,

Spatial resolution: 32.7 μηι,

Measurement time: about 10 s,

Power of light source: 150 W,

Total number of wavelength bands (n): 199

Total number of pixels (N): 323736

Total number of segments (K): 80

[Reference and Object for Evaluation]

An inner arm of one person is used as a reference for the measurements. A diffuse reflection spectrum at the surface of the inner arm is measured to acquire positional information at the surface of the inner arm, and pixel data including the diffuse reflection spectrum at the pixel.

30 models who had solar lentigos on both sides of their faces were selected by a dermatologist.

[Protocol for Evaluation]

Two products (One is a whitening product with active and the other is a placebo, i.e. a product without active) were applied to the left and right side of the faces of the models for 8 weeks. The models washed their faces with standard cleansing procedures every morning and evening. The application side was randomly selected for each model. During the test period, the models were prohibited to use any other serum. The rest of the skincare and makeup items they used normally were kept in their beauty routine.

The diffuse reflection spectrums at the surfaces of the skins of the faces were measured before the test (TO) and after 8 weeks (T8). Relative spectral lengths, spectral angles and entropies after the application of the whitening product were determined from the diffuse reflection spectrum at the surfaces of the reference and the skin of the faces before and after the application.

[Results] Average spectral lengths, average spectral angles and entropy were determined from the multi-dimensional vectors, and these indices for the whitening product and the placebo are shown in Tables 1 and 2. The values shown are averages for 30 models.

Table 1 Cosmetic product without active (Placebo) at TO and T8

Averaged spectral length 1.0 ± 0.1 1.0 ± 0.1

Table 2 Cosmetic product with active at TO and T8

TO T8

Entropy 3.1 ± 0.6 3.0 ± 0.5

Averaged spectral angle 3.8 ± 1.6 3.5 ± 1.5

Averaged spectral length 1.0 ± 0.1 1.0 ± 0.1

The differences in average spectral lengths, average spectral angles and entropy between TO and T8 calculated from the values in Tables 1 and 2 are shown in Table 3.

Table 3 Difference between Placebo and Whitening Product, T8 - TO

Comparing the results of the placebo and those of the whitening product, entropy and average spectral angle are decreased significantly. These results show that the target skin of the face is whitened by the whitening product.

Claims

A method for evaluating the cosmetic effects of a cosmetic product on the skin, comprising steps of:

(ii) applying the cosmetic product to the surface of the object skin,

(iv) determining multi-dimensional vectors from the diffuse reflection spectrum at the surfaces of the reference and the object ski n before and after the application,

(v) evaluating the cosmetic effects of the cosmetic product by comparing any

indices of relative spectral lengths of the object skin, spectral angles and an entropy after the application of the cosmetic product to the indices before the application of the cosmetic product,

wherein

the average spectral lengths of the object skin relative to the spectral length of the reference before and after the application are determined from the multi-dimensional vectors of the object skin before and after the application using the reference vector, the spectral angles are determined from the multi-dimensional vectors of the reference and the object skin before and after the application using the reference vector, and the entropy is determined from the spectral angles, the positional information and the pixel data.

The method according to Claim 1, characterized in that the multi-dimensional vectors of the reference and the object skin before and after the application in the step (iv) are determined by vectors whose components are the diffuse reflectances at wavelength bands at the pixel.

The method according to Claim 1 or 2, characterized in that the relative spectral lengths of the object skin before and after the application ( i _sb and t _sa ) in step (v) are determined by the followin equations:

*- = Τ^· (2) wherein

L_r is the average length of the multi-dimensional vectors of the reference, L_sb is the average length of the multi-dimensional vectors of the object skin before the application, and

Lsa is the average length of the multi-dimensional vectors of the object skin after the application,

wherein

wherein

n is the total number of wavelength bands, and

N is the total number of pixels.

The method according to any one of Claims 1 to 3, characterized in that the spectral angles before the application (Gy¹) and after the application (0_a ^J) at the j-th pixel in step are determined by the following equations:

wherein

Lr^J is the length of the multi-dimensional vector at the j-th pixel of the reference, L_sb^J is the length of the multi-dimensional vector at the j-th pixel of the object skin before the application,

0b^J is the spectral angle at the j-th pixel of the object skin before the application, 0_a ^J is the spectral angle at the j-th pixel of the object skin after the application, a, ^m is the diffuse reflectance component at the i-th wavelength band of m-th pixel of the reference,

b, ^J is the diffuse reflectance component at the i-th wavelength band of the j-th pixel of the object skin before the application,

n is the total number of wavelength bands, and

N is the total number of pixels.

The method according to any one of Claims 1 to 4, characterized in that the entropy before and after the application in step (v) is determined by the following equations: epy_b = -∑n(e_{b k} )log₂ n(e_{b k}) (8)

k=0 epy. = -∑n(e.._k )iog₂ fi(e_a,k) (9)

k=l

wherein

epy_b is the entropy before the application,

epy_a is the entropy after the application,

A(e_b,k ) = (ti(e_b,k )- n(e_b,k_₁))/ N (io) ti(e._,k ) = (n(e_Bik ) - n(e_eik__I))/ N (11)

wherein

n(9_{b k} ) is the number of pixels with the corresponding spectral angles less than G_b k » ^η(θ_{3 k} ) is the number of pixels with the corresponding spectral angles less than 6_{a k} , and

N is the total number of pixels

wherein

Q —A

a,k = > ^k = 0,1, ,· · ·, K ,

K is the total number of segments between θ_{α min} = min^ ) and =^1M fe ) ^{with a = b}> ^a-

The method according to any one of Claims 1 to 5, characterized in that a wavelength of the diffuse reflection spectrum is in the range of 450 to 750 nm.

7. The method according to any one of Claims 1 to 6, characterized in that the reference is the skin of inner arms.

8. The method according to any one of Claims 1 to 7, characterized in that the object skin is the skin of a face.

9. The method according to any one of Claims 1 to 8, characterized in that the cosmetic product is for a topical application.

10. The method according to Claim 9, characterized in that the cosmetic product for the topical application is a skin care product, a makeup product for the skin, or a sun protection product.

11. The method according to Claim 10, characterized in that the skin care product is selected from the group consisting of a cleanser, a lotion, a cream, a gel, a facial mask, and a serum.

12. The method according to any one of Claims 1 to 11, characterized in that the method is non-invasive.

13. The method according to any one of Claims 1 to 12, characterized in that the method is for evaluating a lightening or whitening effect.

14. The method according to any one of Claims 1 to 12, characterized in that the method is for evaluating a protective effect against ultraviolet radiation.

15. The method according to any one of Claims 1 to 12, characterized in that the method is for evaluating a makeup effect.