JP7081576B2 - Method for estimating pigment concentration in skin tissue - Google Patents
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Description
本発明は、皮膚組織における色素濃度の推定方法に関する。 The present invention relates to a method for estimating a pigment concentration in a skin tissue.
皮膚が光伝搬状態の異なる９層の組織で形成されているという層状モデルを用い、モンテカルロ法を用いて皮膚組織内の色素濃度を推定する方法が提案されている（特許文献１）。この方法では、層状モデルの層ごとに５種の光学パラメータ（散乱係数、吸収係数、非等方性パラメータ、屈折率、層の厚み）を設定し、光伝搬解析を行い、分光反射率曲線をシミュレーションする。この場合、吸収係数＝吸光係数・色素濃度であることにより色素濃度を変化させて吸収係数を変化させ、その他の光学パラメータも順次変化させる。そして、シミュレーションした分光反射率曲線を実測の分光反射率曲線に対してフィッティングし、そのときの光学パラメータを用いて層状モデルの各層のメラニン及びヘモグロビンの色素濃度を求める。 A method of estimating the pigment concentration in the skin tissue by using the Monte Carlo method using a layered model in which the skin is formed of nine layers of tissues having different light propagation states has been proposed (Patent Document 1). In this method, five types of optical parameters (scattering coefficient, absorption coefficient, anisotropic parameter, refractive index, layer thickness) are set for each layer of the layered model, light propagation analysis is performed, and a spectral reflectance curve is obtained. Simulate. In this case, since the absorption coefficient = the absorption coefficient / dye concentration, the dye concentration is changed to change the absorption coefficient, and other optical parameters are also sequentially changed. Then, the simulated spectral reflectance curve is fitted to the actually measured spectral reflectance curve, and the pigment concentrations of melanin and hemoglobin in each layer of the layered model are obtained using the optical parameters at that time.
特許文献１に記載の方法によれば、層状モデルの各層の色素濃度を求めるために、シミュレーションによる分光反射率曲線と実測の分光反射率曲線とのフィッティングを、層状モデルの各層で５種の光学パラメータを順次調整していくという多段階で行う必要があり、煩雑である。
According to the method described in
また、特許文献１に記載の方法を、被験者の分光反射率を測定した肌画像に適用すると、陰影の影響による推定誤差が生じやすいという問題もあった。
Further, when the method described in
これに対し、皮膚組織を形成する、深さが異なる層ごとの色素濃度を簡便な方法で、より精確に推定できるようにすることを課題とする。 On the other hand, it is an object to make it possible to more accurately estimate the pigment concentration for each layer having different depths forming the skin tissue by a simple method.
本発明者は、皮膚の吸光度スペクトルが、皮膚組織の層状モデルの色素含有層の吸収係数の多項式で表されるとした吸光度関数Ｚ(λ)を設定し、この吸光度関数Ｚ(λ)と、皮膚組織の層状モデルに対して光伝搬のシミュレーションをすることにより得た分光反射率Ｒs(λ)とをフィッティングさせることにより吸光度関数Ｚ(λ)の係数を得ておくと、被験者の皮膚の分光反射率Ｒm(λ)を測定することにより吸光度関数Ｚ(λ)を用いて皮膚組織の各層に含まれる色素濃度を推定することができ、５種の光学パラメータを順次変化させてフィッティングすることが不要となって推定方法が簡便化され、推定精度を向上させることも可能となることを想到し、本発明を完成させた。 The present inventor has set an absorbance function Z (λ) in which the absorbance spectrum of the skin is represented by a polyploid of the absorption coefficient of the dye-containing layer of the layered model of the skin tissue. When the coefficient of the absorbance function Z (λ) is obtained by fitting the spectral reflectance Rs (λ) obtained by simulating light propagation to the layered model of the skin tissue, the spectroscopy of the subject's skin is obtained. By measuring the reflectance Rm (λ), the dye concentration contained in each layer of the skin tissue can be estimated using the absorbance function Z (λ), and five types of optical parameters can be sequentially changed for fitting. The present invention was completed with the idea that it would be unnecessary, the estimation method would be simplified, and the estimation accuracy could be improved.
即ち、本発明は、皮膚組織を形成する所定の深さの層における色素濃度の推定方法であって、
皮膚組織の層状モデルに対して光伝搬のシミュレーションを行うことにより皮膚組織の分光反射率Ｒs(λ)を算出し、
一方、皮膚組織の吸光度を、皮膚組織の層状モデルの色素含有層内の色素による吸収係数の多項式で表した吸光度関数Ｚ(λ)を設定し、
吸光度関数Ｚ(λ)を分光反射率Ｒs(λ)に、吸光度スペクトル又は反射率スペクトルとしてフィッティングすることにより吸光度関数Ｚ(λ)の各項の係数を定め、
被験者の皮膚の分光反射率Ｒm(λ)を測定し、
分光反射率Ｒm(λ)と係数を定めた吸光度関数Ｚ(λ)とを、吸光度スペクトル又は反射率スペクトルとして比較することで、層状モデルの所定の色素含有層に対応した深さの層の色素濃度を推定する方法を提供する。
That is, the present invention is a method for estimating a pigment concentration in a layer having a predetermined depth forming a skin tissue.
The spectral reflectance Rs (λ) of the skin tissue was calculated by simulating light propagation for the layered model of the skin tissue.
On the other hand, an absorbance function Z (λ) was set, in which the absorbance of the skin tissue was expressed by a polynomial of the absorption coefficient by the dye in the dye-containing layer of the layered model of the skin tissue.
By fitting the absorbance function Z (λ) to the spectral reflectance Rs (λ) as an absorbance spectrum or a reflectance spectrum, the coefficients of each term of the absorbance function Z (λ) are determined.
The spectral reflectance Rm (λ) of the subject's skin was measured and
By comparing the spectral reflectance Rm (λ) with the absorbance function Z (λ) that defines the coefficient as an absorbance spectrum or a reflectance spectrum, the dye of the layer having a depth corresponding to the predetermined dye-containing layer of the layered model. A method for estimating the concentration is provided.
本発明によれば、吸光度関数Ｚ(λ)を使用するので、特許文献１に記載のように光学パラメータを順次変化させることなく、皮膚組織の層状モデルの色素含有層に対応する被験者の皮膚の深さでの色素の種類と濃度を簡便に推定することができる。したがって、皮膚の所定の深さにおけるオキシヘモグロビン濃度とデオキシヘモグロビン濃度を簡便に推定することができ、これによりヘモグロビンの酸素飽和度がわかり、皮膚における酸素の消費状態や血行状態などを推定することも可能となる。
According to the present invention, since the absorbance function Z (λ) is used, the skin of the subject corresponding to the dye-containing layer of the layered model of the skin tissue without sequentially changing the optical parameters as described in
また、本発明によれば、分光反射率を撮影した被験者の皮膚画像から、皮膚組織の層状モデルの色素含有層に対応する皮膚の深さの色素濃度画像を形成することもできる。色素濃度画像を形成できることで、皮膚を表面から観察したときの見え方と、皮膚中の色素濃度との関係がわかるようになる。また、化粧料を適用した皮膚について、本発明の方法で、例えばメラニン、オキシヘモグロビン、デオキシヘモグロビンの各濃度の経時的変化を調べることにより、化粧料の有効性の評価を行うことが可能となる。 Further, according to the present invention, it is also possible to form a pigment density image of the skin depth corresponding to the pigment-containing layer of the layered model of the skin tissue from the skin image of the subject whose spectral reflectance is photographed. By being able to form a pigment concentration image, it becomes possible to understand the relationship between the appearance of the skin when observed from the surface and the pigment concentration in the skin. In addition, it is possible to evaluate the effectiveness of cosmetics on the skin to which cosmetics have been applied by using the method of the present invention, for example, by examining changes in the concentrations of melanin, oxyhemoglobin, and deoxyhemoglobin over time. ..
さらに、本発明によれば、吸光度関数Ｚ（λ）と分光反射率Ｒs（λ）をフィッテフィングする際に相対吸収スペクトルを使用し、色素濃度に依存しない定数項を相殺することで、色素濃度画像から散乱等の影響を排除することができる。 Further, according to the present invention, the relative absorption spectrum is used when fitting the absorbance function Z (λ) and the spectral reflectance Rs (λ), and the constant term independent of the dye concentration is canceled out to cancel the dye concentration. It is possible to eliminate the influence of scattering and the like from the image.
以下、図面を参照しつつ本発明を詳細に説明する。
（色素濃度の推定方法の概要）
図１は、本発明の一態様の色素濃度の推定方法のフローの説明図である。この方法では、概略、皮膚組織に所定の層数で層状モデルを設定し（STEP 1-1）、皮膚の吸光度スペクトルが、層状モデルにおける複数の色素含有層（即ち、層状モデルを構成する層であって色素が含有されている層）の吸収係数の多項式で表されるとして吸光度関数Ｚ（λ）を設定する(STEP 1-2)。そして、その多項式の係数を求めるために、まず、皮膚組織に対して種々の色素濃度で光伝搬のシミュレーションを行うことにより皮膚組織の分光反射率Ｒs（λ）を算出する(STEP 1-3)。次に、分光反射率Ｒs（λ）を吸光度Ａs（λ）に変換し、その吸光度Ａs（λ）に吸光度関数Ｚ（λ）をフィッティングさせることにより吸光度関数Ｚ（λ）の多項式の係数を求める(STEP 1-4)。
一方、被験者の皮膚の分光反射率Ｒm（λ）を測定する（STEP 2-1）。そして、分光反射率Ｒm（λ）を吸光度Ａm（λ）に変換し、その吸光度Ａm（λ）と、係数を定めた吸光度関数Ｚ（λ）とを比較することで、吸光度関数Ｚ（λ）から所定の色素含有層の色素濃度を求める（STEP 2-2）。こうして求めた色素濃度を、層状モデルの所定の色素含有層に対応する深さの、被験者の皮膚組織の色素濃度と推定する。
Hereinafter, the present invention will be described in detail with reference to the drawings.
(Overview of dye concentration estimation method)
FIG. 1 is an explanatory diagram of a flow of a method for estimating a dye concentration according to an aspect of the present invention. In this method, a layered model is roughly set on the skin tissue with a predetermined number of layers (STEP 1-1), and the absorbance spectrum of the skin is a plurality of dye-containing layers in the layered model (that is, layers constituting the layered model). The absorbance function Z (λ) is set as being represented by a polynomial of the absorption coefficient of the layer containing the dye (STEP 1-2). Then, in order to obtain the coefficient of the polynomial, first, the spectral reflectance Rs (λ) of the skin tissue is calculated by simulating the light propagation with various dye concentrations for the skin tissue (STEP 1-3). .. Next, the spectral reflectance Rs (λ) is converted into the absorbance As (λ), and the absorbance function Z (λ) is fitted to the absorbance As (λ) to obtain the coefficient of the polynomial of the absorbance function Z (λ). (STEP 1-4).
On the other hand, the spectral reflectance Rm (λ) of the subject's skin is measured (STEP 2-1). Then, the spectral reflectance Rm (λ) is converted into the absorbance Am (λ), and the absorbance Am (λ) is compared with the absorbance function Z (λ) for which the coefficient is determined, whereby the absorbance function Z (λ) is obtained. The dye concentration of the predetermined dye-containing layer is obtained from (STEP 2-2). The pigment concentration thus obtained is estimated to be the pigment concentration of the skin tissue of the subject at a depth corresponding to a predetermined pigment-containing layer of the layered model.
（STEP 1-1）皮膚組織の層状モデル
図２に示すように、皮膚組織は複雑な層構造になっていることが知られており、同図に示すように皮膚組織を第１層の上皮角質層、第２層の表皮層、第３層の真皮乳頭層、第４層の乳頭下血管網、第５層の真皮血管層、第６層の皮下血管網、第７層の皮下組織の７層に区分した７層モデル、これを更に細分化した９層モデル、あるいは反対に皮膚組織を表皮、真皮、皮下組織の３層に区分した３層モデルなどが皮膚組織の解析の目的などに応じて使用されている。たとえば、７層モデルでは、第２層の表皮層にはメラニン、カロチン等の色素、第４層の乳頭下血管網と第６層の皮下血管網には血液由来のオキシヘモグロビン、デオキシヘモグロビン、ビリルビン、カロチン等の色素、第７層には皮下脂肪組織に沈着したカロチン等の色素が存在し得る。そこで、本発明の一態様としてはこれらの色素の皮膚の深さ方向の存在位置を正確に特定すると共に、光伝搬のシミュレーションをできる限り簡単にする点から７層モデルを採用し、皮膚組織における典型的な色素分布の例として、第２層の表皮層のメラニンと、第４層の乳頭下血管網及び第６層の皮下血管網のオキシヘモグロビンとデオキシヘモグロビンを考える。
(STEP 1-1) Layered model of skin tissue As shown in Fig. 2, it is known that the skin tissue has a complicated layered structure, and as shown in the figure, the skin tissue is the epithelium of the first layer. The horny layer, the 2nd layer of the epidermal layer, the 3rd layer of the dermal papilla layer, the 4th layer of the subpapillary vascular network, the 5th layer of the dermal vascular layer, the 6th layer of the subcutaneous vascular network, and the 7th layer of the subcutaneous tissue. A 7-layer model divided into 7 layers, a 9-layer model that is further subdivided, or a 3-layer model in which the skin tissue is divided into 3 layers of epidermis, dermis, and subcutaneous tissue is used for the purpose of skin tissue analysis. Used accordingly. For example, in the 7-layer model, pigments such as melanin and carotene are in the epidermal layer of the 2nd layer, and blood-derived oxyhemoglobin, deoxyhemoglobin, and bilirubin are in the subpapillary vascular network of the 4th layer and the subcutaneous vascular network of the 6th layer. , A pigment such as carotene, and a pigment such as carotin deposited in the subcutaneous adipose tissue may be present in the seventh layer. Therefore, as one aspect of the present invention, a 7-layer model is adopted from the viewpoint of accurately specifying the existence position of these pigments in the depth direction of the skin and simplifying the simulation of light propagation as much as possible, in the skin tissue. As an example of a typical pigment distribution, consider melanin in the epidermal layer of the second layer and oxyhemoglobin and deoxyhemoglobin in the subpapillary vascular network of the fourth layer and the subcutaneous vascular network of the sixth layer.
これに対し、例えば、３層モデルを設定してメラニンとオキシヘモグロビンとデオキシヘモグロビンの濃度を推定しようとすると、３層モデルにおいてオキシヘモグロビンとデオキシヘモグロビンが存在する第２層の層厚は厚くなることから、７層モデルのときのオキシヘモグロビンとデオキシヘモグロビンの濃度よりも低く推定される。 On the other hand, for example, when a three-layer model is set to estimate the concentrations of melanin, oxyhemoglobin, and deoxyhemoglobin, the layer thickness of the second layer in which oxyhemoglobin and deoxyhemoglobin are present in the three-layer model becomes thick. Therefore, it is estimated to be lower than the concentrations of oxyhemoglobin and deoxyhemoglobin in the 7-layer model.
また、本発明で濃度を推定する皮膚組織の色素は、メラニン、オキシヘモグロビン、デオキシヘモグロビンに限定されず、ビリルビン、カロチン、最終糖化生成物(advanced glycation end-products；ＡＧＥｓ)等も対象とすることができる。 The pigment of the skin tissue whose concentration is estimated in the present invention is not limited to melanin, oxyhemoglobin, and deoxyhemoglobin, but also includes bilirubin, carotene, advanced glycation end-products (AGEs), and the like. Can be done.
(STEP 1-2)吸光度関数Ｚ（λ）
吸光度関数Ｚ（λ）は、皮膚組織の層状モデルの色素含有層ごとに色素の種類と濃度を推定するために本発明者が設定した関数であって、皮膚の吸光度スペクトルが、色素含有層内の色素による吸収係数の多項式で表されるとしたものである。この多項式は色素含有層ごとの吸収係数の多項式としてもよく、各色素含有層に含まれる色素ごとの吸収係数の多項式としてもよい。例えば、第２層の表皮層にメラニンが存在し、第４層の乳頭下血管網と第６層の皮下血管網にオキシヘモグロビンとデオキシヘモグロビンが存在するとして色素含有層ごとの吸収係数の３次の多項式を考える場合、吸光度関数Ｚ(λ)は次式（１）で表される。
(STEP 1-2) Absorbance function Z (λ)
The absorbance function Z (λ) is a function set by the present inventor to estimate the type and concentration of the dye for each dye-containing layer of the layered model of the skin tissue, and the absorbance spectrum of the skin is within the dye-containing layer. It is assumed that it is represented by a polynomial of the absorption coefficient by the dye of. This polynomial may be a polynomial of the absorption coefficient for each dye-containing layer, or may be a polynomial for the absorption coefficient for each dye contained in each dye-containing layer. For example, melanin is present in the epidermal layer of the second layer, and oxyhemoglobin and deoxyhemoglobin are present in the subpapillary vascular network of the fourth layer and the subcutaneous vascular network of the sixth layer. When considering the polynomial of, the extinction function Z (λ) is expressed by the following equation (1).
Ｚ(λ)＝ｃ1(λ)・Ｍｅl3＋ｃ2(λ)・Ｍｅl2・Ｄｅｒ4(λ)＋ｃ3(λ)・Ｍｅl2・Ｄｅｒ6(λ)＋ｃ4(λ)・Ｄｅｒ4(λ)3＋ｃ5(λ)・Ｄｅｒ4(λ)2・Ｍｅl＋ｃ6(λ)・Ｄｅｒ4(λ)2・Ｄｅｒ6(λ)＋ｃ7(λ)・Ｄｅｒ6(λ)3＋ｃ8(λ)・Ｄｅｒ6(λ)2・Ｍｅl＋ｃ9(λ)・Ｄｅｒ6(λ)2・Ｄｅｒ4(λ)＋ｃ10(λ)・Ｍｅl・Ｄｅｒ4(λ)・Ｄｅｒ6(λ)＋ｃ11(λ)・Ｍｅl2＋ｃ12(λ)・Ｍｅl・Ｄｅｒ4(λ)＋ｃ13(λ)・Ｍｅl・Ｄｅｒ6(λ)＋ｃ14(λ)・Ｍｅl・Ｄｅｒ4(λ)2＋ｃ15(λ)・Ｄｅｒ4(λ)・Ｄｅｒ6(λ)＋ｃ16(λ)・Ｄｅｒ6(λ)2＋ｃ17(λ)・Ｍｅl＋ｃ18(λ)・Ｄｅｒ4(λ)＋ｃ19(λ)・Ｄｅｒ6(λ)＋ｃ20(λ)
式（１）
Z (λ) = c 1 (λ) ・ Mel 3 + c 2 (λ) ・ Mel 2・ Der 4 (λ) ＋ c 3 (λ) ・ Mel 2・ Der 6 (λ) ＋ c 4 (λ) ・ Der 4 (λ) 3 ＋ c 5 (λ) ・ Der4 (λ) 2・ Mel ＋ c 6 (λ) ・ Der4 (λ) 2・ Der6 (λ) ＋ c 7 (λ) ・ Der6 (λ) 3 ＋ c 8 (λ) ・ Der6 (λ) 2・ Mel ＋ c 9 (λ) ・ Der6 (λ) 2・ Der4 (λ) ＋ c 10 (λ) ・ Mell ・ Der4 (λ) ・ Der6 (λ) ＋ c 11 (λ) ・ Mell 2 ＋ c 12 (λ) ・ Mel ・Der4 (λ) ＋ c 13 (λ) ・ Mel ・ Der6 (λ) ＋ c 14 (λ) ・ Mell ・ Der4 (λ) 2 ＋ c 15 (λ) ・ Der4 (λ) ・ Der6 (λ) ＋ c 16 (λ) ・Der6 (λ) 2 + c 17 (λ), Mel + c 18 (λ), Der4 (λ) + c 19 (λ), Der6 (λ) + c 20 (λ)
Equation (1)
式中、ｃ1、・・・ｃ20は係数である。
また、Ｍｅlはメラニンによる第２層の吸収係数、Ｄｅｒ4(λ)はオキシヘモグロビンとデオキシヘモグロビンによる第４層の吸収係数、Ｄｅｒ6(λ)はオキシヘモグロビンとデオキシヘモグロビンによる第６層の吸収係数で、それぞれ次式で表される。
Ｍｅl＝μaM・[Ｍｅｌ]
Ｄｅｒ4(λ)＝μaOhb・[Ｏｈｂ4]＋μaHb・[Ｈｂ4]
Ｄｅｒ6(λ)＝μaOhb・[Ｏｈｂ6]＋μaHb・[Ｈｂ6]
式中、μaMはメラニンの吸光係数
μaOhbはオキシヘモグロビンの吸光係数
μaHbはデオキシヘモグロビンの吸光係数
[Ｍｅｌ]はメラニンの濃度（ｇ／Ｌ）
[Ｏｈｂ4]は第４層におけるオキシヘモグロビン濃度（ｇ／Ｌ）
[Ｈｂ4]は第４層におけるデオキシヘモグロビン濃度（ｇ／Ｌ）
[Ｏｈｂ6]は第６層におけるオキシヘモグロビン濃度（ｇ／Ｌ）
[Ｈｂ6]は第６層におけるデオキシヘモグロビン濃度（ｇ／Ｌ）
μaM、μaOhb、μaHbは既知の数値を使用する。
また、吸光度関数Ｚ（λ）を分光反射率Ｒs（λ）とフィッティングさせるにあたり、[Ｍｅｌ]、[Ｏｈｂ4]、[Ｈｂ4]、[Ｏｈｂ6]、[Ｈｂ6]には設定値を使用する。
In the equation, c 1 , ... c 20 are coefficients.
Mel is the absorption coefficient of the second layer by melanin, Del4 (λ) is the absorption coefficient of the fourth layer by oxyhemoglobin and deoxyhemoglobin, and Del6 (λ) is the absorption coefficient of the sixth layer by oxyhemoglobin and deoxyhemoglobin. Each is expressed by the following equation.
Mel = μa M・ [Mel]
Der4 (λ) = μa Ohb・ [Ohb4] ＋ μa Hb・ [Hb4]
Der6 (λ) = μa Ohb・ [Ohb6] ＋ μa Hb・ [Hb6]
In the formula, μa M is the extinction coefficient of melanin, μa Ohb is the extinction coefficient of oxyhemoglobin, and μa Hb is the extinction coefficient of deoxyhemoglobin.
[Mel] is the concentration of melanin (g / L)
[Ohb4] is the oxyhemoglobin concentration (g / L) in the fourth layer.
[Hb4] is the deoxyhemoglobin concentration (g / L) in the fourth layer.
[Ohb6] is the oxyhemoglobin concentration (g / L) in the sixth layer.
[Hb6] is the deoxyhemoglobin concentration (g / L) in the 6th layer.
For μa M , μa Ohb , and μa Hb , use known values.
Further, in fitting the absorbance function Z (λ) to the spectral reflectance Rs (λ), set values are used for [Mel], [Ohb4], [Hb4], [Ohb6], and [Hb6].
なお、吸光度関数Ｚ（λ）を色素含有層ごとの吸光係数の多項式とする場合に、２次の多項式とすると色素濃度の推定精度が劣り、３次の多項式と４次の多項式では推定精度に差異がないことから、吸光度関数Ｚ（λ）は３次の多項式が好ましい。 When the absorbance function Z (λ) is a polynomial of the absorbance coefficient for each dye-containing layer, the estimation accuracy of the dye concentration is inferior if it is a second-order polynomial, and the estimation accuracy is higher for a third-order polynomial and a fourth-order polynomial. Since there is no difference, the absorbance function Z (λ) is preferably a third-order polynomial.
(STEP 1-3)分光反射率Ｒs（λ）
皮膚組織の分光反射率Ｒs（λ）は、種々の色素濃度で光伝搬のシミュレーションを行うことにより算出する。光伝搬のシミュレーションの手法としては、モンテカルロ法、クベルカムンク法、光伝搬の解析的手法（輸送方程式の解析解や拡散近似の解析解）等を使用することができる。
(STEP 1-3) Spectral reflectance Rs (λ)
The spectral reflectance Rs (λ) of the skin tissue is calculated by simulating light propagation at various dye concentrations. As a method for simulating light propagation, a Monte Carlo method, a Kubelkamunck method, an analytical method for light propagation (an analytical solution of a transport equation or an analytical solution of a diffusion approximation) or the like can be used.
後述する実施例では、このシミュレーションをモンテカルロ法により行い、７層モデルの第２層の表皮層のメラニン濃度を、該第２層の表皮層の体積に対するメラニンの体積の割合として８～１６％の範囲で５段階に変化させ、第４層の乳頭下血管網の血液濃度（酸素飽和度は０．７で固定）を、該第４層の乳頭下血管網の体積に対するオキシヘモグロビンとデオキシヘモグロビンの合計の体積の割合として１０～３０％の範囲で９段階に変化させ、第６層の皮下血管網のヘモグロビン（酸素飽和度は０．７で固定）を該第６層の皮下血管網の体積に対するオキシヘモグロビンとデオキシヘモグロビンの合計の体積の割合として１～１５％の範囲で１５段階に変化させ、合計６７５通りの色素濃度でシミュレーションした。なお、メラニン等の色素濃度を変化させる幅囲は、皮膚濃度を推定する被験者の肌色の人種による差異を考慮して変えることができえる。 In the examples described later, this simulation is performed by the Monte Carlo method, and the melanin concentration in the epidermal layer of the second layer of the 7-layer model is 8 to 16% as the ratio of the volume of melanin to the volume of the epidermal layer of the second layer. The blood concentration of the subpapillary vascular network of the 4th layer (oxygen saturation is fixed at 0.7) is changed in 5 steps in a range, and the blood concentration of oxyhemoglobin and deoxyhemoglobin with respect to the volume of the subpapillary vascular network of the 4th layer is changed. The hemoglobin of the subcutaneous vascular network of the 6th layer (oxygen saturation is fixed at 0.7) is changed in 9 steps in the range of 10 to 30% as the ratio of the total volume, and the volume of the subcutaneous vascular network of the 6th layer. The ratio of the total volume of oxyhemoglobin and deoxyhemoglobin to 15 was changed in 15 steps in the range of 1 to 15%, and simulation was performed with a total of 675 dye concentrations. It should be noted that the range for changing the pigment concentration such as melanin can be changed in consideration of the difference in the skin color of the subject who estimates the skin concentration depending on the race.
分光反射率Ｒs（λ）をシミュレーションするにあたり、７層モデルの各層の厚みなどの設定値は表１の通りとし、波長は４００～９００ｎｍの範囲で１０ｎｍ毎に変化させた。その結果、図３に示す６７５通りの分光反射率Ｒs（λ）のスペクトルを得た。 In simulating the spectral reflectance Rs (λ), the set values such as the thickness of each layer of the 7-layer model are as shown in Table 1, and the wavelength is changed in the range of 400 to 900 nm in increments of 10 nm. As a result, the spectra of the spectral reflectance Rs (λ) shown in FIG. 3 were obtained in 675 ways.
このように７層モデルを考える場合に、光学パラメータのうち屈折率、散乱係数、非等方性パラメータをそれぞれ第１層～第７層で共通の一定値とし、第１層～第７層の層厚を固定し、変化させる光学パラメータの数を減らすことにより、吸光度関数Ｚ(λ)と分光反射率Ｒ(λ）のフィッティングが容易となる。 When considering a 7-layer model in this way, the refractive index, scattering coefficient, and isotropic parameters of the optical parameters are set to constant values common to the 1st to 7th layers, respectively, and the 1st to 7th layers have different values. By fixing the layer thickness and reducing the number of optical parameters to be changed, the fitting of the absorbance function Z (λ) and the spectral reflectance R (λ) becomes easy.
(STEP 1-4)吸光度関数Ｚ(λ)と分光反射率Ｒ(λ）のフィッティング
一般に拡散反射スペクトルＡ(λ)は透過スペクトルＲ(λ)と等価であるとされ、拡散反射スペクトルと吸光度スペクトルは次式により変換できる。
Ａ(λ)＝－ｌｏｇＲ(λ)
そこで、図３に示した分光反射率Ｒs（λ）のスペクトルから図４に示した吸光度スペクトルＡs（λ）を得ることができる。
(STEP 1-4) Fitting of absorbance function Z (λ) and spectral reflectance R (λ) Generally, the diffuse reflection spectrum A (λ) is considered to be equivalent to the transmission spectrum R (λ), and the diffuse reflection spectrum and the absorbance spectrum are considered to be equivalent. Can be converted by the following equation.
A (λ) =-logR (λ)
Therefore, the absorbance spectrum As (λ) shown in FIG. 4 can be obtained from the spectrum of the spectral reflectance Rs (λ) shown in FIG.
したがって、吸光度関数Ｚ(λ)を分光反射率Ｒs(λ）とフィッティングさせる場合、分光反射率Ｒs(λ)を吸光度スペクトルＡs(λ)に変換し、吸光度関数Ｚ(λ)と吸光度スペクトルＡs(λ)とをフィッティングさせることができ、また、吸光度関数Ｚ(λ)を反射率スペクトルＲs’(λ)に変換し、反射率スペクトルＲs’(λ)と分光反射率Ｒs(λ）とをフィッティングさせることもできる。ただし、フィッティングを線形関係で議論し、推定精度を上げる点から、分光反射率Ｒs(λ)を吸光度スペクトルＡs(λ)に変換し、吸光度関数Ｚ(λ)と吸光度スペクトルＡs(λ)とをフィッティングさせることが好ましい。 Therefore, when the absorbance function Z (λ) is fitted to the spectral reflectance Rs (λ), the spectral reflectance Rs (λ) is converted into the absorbance spectrum As (λ), and the absorbance function Z (λ) and the absorbance spectrum As (λ) are converted. λ) can be fitted, and the absorbance function Z (λ) is converted into the reflectance spectrum Rs'(λ), and the reflectance spectrum Rs'(λ) and the spectral reflectance Rs (λ) are fitted. You can also let it. However, from the viewpoint of discussing the fitting in a linear relationship and improving the estimation accuracy, the spectral reflectance Rs (λ) is converted into the absorbance spectrum As (λ), and the absorbance function Z (λ) and the absorbance spectrum As (λ) are obtained. It is preferable to have them fitted.
吸光度関数Ｚ(λ)と分光反射率Ｒs(λ）とのフィッティングでは、吸光度関数Ｚ(λ)と、分光反射率Ｒs(λ）から変換した吸光度スペクトルＡs(λ)との次式の誤差関数ＲＳＳが最小となるように吸光度関数Ｚ(λ)の係数を定める。 In the fitting of the absorbance function Z (λ) and the spectral reflectance Rs (λ), the error function of the following equation between the absorbance function Z (λ) and the absorbance spectrum As (λ) converted from the spectral reflectance Rs (λ). The coefficient of the absorbance function Z (λ) is determined so that the RSS is minimized.
あるいは、吸光度関数Ｚ(λ)を反射率の関数に変換したｅｘｐ｛－Ｚ(λ)｝を用いた次式の誤差関数ＲＳＳRが最小となるように関数ＺR(λ)の係数を定める。 Alternatively, the coefficient of the function Z R (λ) is determined so that the error function RSS R of the following equation using exp {-Z (λ)} obtained by converting the absorbance function Z (λ) into a function of reflectance is minimized. ..
吸光度関数Ｚ(λ)と分光反射率Ｒ(λ）のフィッティングの手法としては、上述のＲＳＳの他、ＭＡＥ（Mean Absolute Error、平均絶対誤差）、ＲＭＳＰＥ（Root Mean Square Percentage Error、平均平方二乗誤差率）が最小になるようにしてもよい。 As a method of fitting the absorbance function Z (λ) and the spectral reflectance R (λ), in addition to the above-mentioned RSS, MAE (Mean Absolute Error, mean absolute error), RMSPE (Root Mean Square Percentage Error, mean square error) The rate) may be minimized.
なお、上述の例では分光反射率Ｒs(λ）を波長４００～９００ｎｍの範囲で１０ｎｍ毎に算出し、吸光度関数Ｚ(λ)とフィッティングしたが、フィッティングに使用する波長の好ましいバンド数は、濃度を推定する色素の種類の数や吸光度関数の次数に応じて変えることができる。例えば、濃度を推定する色素の種類を７層モデルの第２層のメラニン、第４層の総ヘモグロビン、及び第６層の総ヘモグロビンの３種とする場合には、散乱の影響を鑑みて４バンド以上とすることが好ましく、６バンド以上とすることがより好ましい。 In the above example, the spectral reflectance Rs (λ) was calculated every 10 nm in the wavelength range of 400 to 900 nm and fitted with the absorbance function Z (λ), but the preferred number of bands of the wavelength used for fitting is the concentration. It can be changed according to the number of types of dyes to be estimated and the order of the absorbance function. For example, when the types of dyes for which the concentration is estimated are 3 types of melanin in the 2nd layer of the 7-layer model, total hemoglobin in the 4th layer, and total hemoglobin in the 6th layer, 4 in consideration of the influence of scattering. It is preferably band or more, and more preferably 6 bands or more.
（STEP 2-1）被験者の皮膚の分光反射率Ｒm（λ）の測定
被験者の皮膚の分光反射率Ｒm（λ）の測定は、分光カメラを用いて行うことができる。分光カメラの波長分解能は１～１０ｎｍ、空間分解能は０．０１～０．５ｍｍ／画素が好ましい。また、照明光は可視から近赤外（９５０ｎｍ程度まで）を含む光源が好ましく、例えば、人工太陽灯を使用することができる。
(STEP 2-1) Measurement of the spectral reflectance Rm (λ) of the subject's skin The spectral reflectance Rm (λ) of the subject's skin can be measured using a spectroscopic camera. The wavelength resolution of the spectroscopic camera is preferably 1 to 10 nm, and the spatial resolution is preferably 0.01 to 0.5 mm / pixel. Further, the illumination light is preferably a light source including visible to near infrared rays (up to about 950 nm), and for example, an artificial sunlamp can be used.
皮膚測定部位は特に制限はなく、顔、腕等とすることができ、好ましくは影が映りにくい平坦な部分がよい。 The skin measurement site is not particularly limited and may be a face, an arm, or the like, and a flat portion where shadows are less likely to be reflected is preferable.
（STEP 2-2）被験者の皮膚の色素濃度の推定
(STEP 1-4)で係数を求めた吸光度関数Ｚ(λ)と、（STEP 2-1）で求めた被験者の分光反射率Ｒm（λ）を変換して得られる吸光度スペクトルＡm(λ)とを比較することにより、あるいは、吸光度関数Ｚ(λ)を変換して得られる反射率の関数と被験者の分光反射率Ｒm（λ）とを比較することにより、吸光度関数Ｚ(λ)が吸光度スペクトルＡm(λ)と等価となるときの吸光度関数Ｚ(λ)中の色素含有層の濃度を求める。この場合も、推定精度を向上させる点及び計算が簡易になる点から吸光度関数Ｚ(λ)と吸光度スペクトルＡm(λ)を比較することが好ましい。また、好ましくは４バンド以上、より好ましくは６バンド以上で比較することが好ましい。
(STEP 2-2) Estimating the skin pigment concentration of the subject
The absorbance function Z (λ) obtained by obtaining the coefficient in (STEP 1-4) and the absorbance spectrum Am (λ) obtained by converting the spectral reflectance Rm (λ) of the subject obtained in (STEP 2-1). Or by comparing the reflectance function obtained by converting the absorbance function Z (λ) with the spectral reflectance Rm (λ) of the subject, the absorbance function Z (λ) is the absorbance spectrum. The concentration of the dye-containing layer in the absorbance function Z (λ) when it is equivalent to Am (λ) is obtained. Also in this case, it is preferable to compare the absorbance function Z (λ) and the absorbance spectrum Am (λ) from the viewpoint of improving the estimation accuracy and simplifying the calculation. Further, it is preferable to compare with 4 bands or more, more preferably 6 bands or more.
こうして得られた色素濃度は、層状モデルにおける所定の色素含有層の色素濃度に対応するから、所定の色素含有層に対応する深さの被験者の皮膚組織の色素濃度が得られることになる。 Since the dye concentration thus obtained corresponds to the dye concentration of the predetermined dye-containing layer in the layered model, the dye concentration of the skin tissue of the subject having a depth corresponding to the predetermined dye-containing layer can be obtained.
よって、本発明によれば被験者の皮膚の所定の深さにおける色素濃度を精度よく推定することが可能となる。また、この色素濃度は、分光カメラを用いて得る被験者の皮膚画像の画素ごとに得られるので、本発明によれば、皮膚組織の層状モデルの色素含有層に対応する皮膚の深さでの色素濃度画像を形成することも可能となる。 Therefore, according to the present invention, it is possible to accurately estimate the pigment concentration at a predetermined depth of the skin of the subject. Further, since this pigment concentration is obtained for each pixel of the skin image of the subject obtained by using a spectroscopic camera, according to the present invention, the pigment at the skin depth corresponding to the pigment-containing layer of the layered model of the skin tissue. It is also possible to form a density image.
（色素濃度に依存しない散乱等の影響の除去）
皮膚組織に対して種々の色素濃度で光伝搬のシミュレーションを行うことにより算出した分光反射率Ｒs（λ）を変換して得られる吸光度スペクトルＡs（λ）には図４に示したようにスペクトルの形状にばらつきの幅が存在する。これに対し、本発明者はこれらのスペクトルを、スペクトル相互の相対スペクトルとするとばらつきの幅が収束すると予想し、次式（２ａ）で表される平均スペクトルを基準スペクトルとし、
(Removal of effects such as scattering that do not depend on dye concentration)
As shown in FIG. 4, the absorbance spectrum As (λ) obtained by converting the spectral reflectance Rs (λ) calculated by simulating light propagation at various dye concentrations on the skin tissue is the spectrum as shown in FIG. There is a range of variations in shape. On the other hand, the present inventor predicts that the range of variation will converge if these spectra are relative spectra to each other, and the average spectrum represented by the following equation (2a) is used as the reference spectrum.
吸光度スペクトルＡs（λ）を基準スペクトルＡs_avで規格化すること、即ち、
相対吸光度＝Ａs（λ）－Ａs_av
を求めることにより図５に示した相対吸収スペクトルを得た。
Normalizing the absorbance spectrum As (λ) with the reference spectrum As_ av , that is,
Relative absorbance = As (λ) -As_ av
The relative absorption spectrum shown in FIG. 5 was obtained.
式（２ａ）で表される基準スペクトルＡs_avは波長に依存せず、角質層内の散乱等が影響していると考えられる。 The reference spectrum As_ av represented by the equation (2a) does not depend on the wavelength, and it is considered that the scattering in the stratum corneum has an influence.
なお、分光反射率Ｒs（λ）に対する同様の基準スペクトルは次式（２ｂ）で得ることができる。 A similar reference spectrum for the spectral reflectance Rs (λ) can be obtained by the following equation (2b).
図５に示した相対吸光度（Ａs(λ)－Ａs_av）にフィッティングさせる吸光度関数Ｚ（λ）としては、前述の式（１）の係数ｃ1～ｃ20を求めた吸光度関数とは別個に、規格化した分光反射率Ｒs'(λ）を用いて係数をフィッティングにより求めた相対吸光度関数Ｚ’（λ）を得ておく。 The absorbance function Z (λ) to be fitted to the relative absorbance (As (λ) −As_av ) shown in FIG. 5 is different from the absorbance function obtained from the coefficients c 1 to c 20 in the above equation (1). , The relative absorbance function Z'(λ) obtained by fitting the coefficient using the standardized spectral reflectance Rs'(λ) is obtained.
また、相対吸光度関数Ｚ'（λ）と、被験者の皮膚の分光反射率Ｒm（λ）を変換した吸光度スペクトルＡm（λ）とを比較して被験者の色素濃度を求める場合、被験者の吸光度スペクトルＡm（λ）の平均スペクトルＡm_avを求め、被験者の吸光度スペクトルＡm（λ）から平均スペクトルＡm_avを差し引いた
相対吸光度＝Ａm（λ）－Ａm_av
と相対吸光度関数Ｚ'(λ)とを比較すればよい。
このように相対吸光度を用いることにより、色素濃度の推定精度を更に向上させることができる。
Further, when the dye concentration of the subject is obtained by comparing the relative absorbance function Z'(λ) with the absorbance spectrum Am (λ) obtained by converting the spectral reflectance Rm (λ) of the subject's skin, the absorbance spectrum Am of the subject is obtained. The average spectrum Am_ av of (λ) is obtained, and the relative absorbance = Am (λ) -Am_ av obtained by subtracting the average spectrum Am_ av from the absorbance spectrum Am (λ) of the subject.
And the relative absorbance function Z'(λ) may be compared.
By using the relative absorbance in this way, the accuracy of estimating the dye concentration can be further improved.
以下、実施例に基づいて本発明を具体的に説明する。
（１）吸光度関数Ｚ（λ）の取得
表１に示したパラメータで波長を４００～９００ｎｍの範囲で１０ｎｍ毎に変化させてシミュレーションすることにより得た分光反射率Ｒs(λ）を吸光度スペクトルＡs(λ)に変換し、その吸光度スペクトルＡs(λ)に式（１）の吸光度関数Ｚ（λ）をフィッティングさせることにより吸光度関数Ｚ（λ）の係数ｃ1、・・・ｃ20を定め、係数ｃ1、・・・ｃ20が定まった吸光度関数Ｚ（λ）を得た。
Hereinafter, the present invention will be specifically described based on Examples.
(1) Acquisition of Absorbance Function Z (λ) The absorbance spectrum As (λ) obtained by simulating by changing the wavelength in the range of 400 to 900 nm every 10 nm with the parameters shown in Table 1. By converting to λ) and fitting the absorbance function Z (λ) of the equation (1) to the absorbance spectrum As (λ), the coefficients c 1 and ... c 20 of the absorbance function Z (λ) are determined, and the coefficients are determined. An absorbance function Z (λ) in which c 1 , ... c 20 was determined was obtained.
（２）皮膚の分光反射率Ｒm（λ）の測定
分光反射率Ｒm（λ）を測定する皮膚の測定部位を前腕の背側とし、手及び前腕を温浴又は炭酸浴中に浸漬し、その後放置した。図６に示すタイミングで分光反射率Ｒm（λ）を６回測定した。
(2) Measurement of the spectral reflectance Rm (λ) of the skin The measurement site of the skin for measuring the spectral reflectance Rm (λ) is the back side of the forearm, and the hands and forearms are immersed in a warm bath or a carbonated bath and then left to stand. did. The spectral reflectance Rm (λ) was measured 6 times at the timing shown in FIG.
この場合、室温は２３℃、温浴と炭酸浴の浴温はそれぞれ４０～４２℃とし、炭酸浴には入浴剤（バブ（登録商標）、花王株式会社）で炭酸を発生させた。 In this case, the room temperature was 23 ° C., the bath temperature of the hot bath and the carbonated bath was 40 to 42 ° C., respectively, and carbonic acid was generated in the carbonated bath with a bath agent (Bab (registered trademark), Kao Corporation).
分光反射率Ｒm（λ）の測定は、暗室において人工太陽灯（ＳＯＬＡＸ（登録商標） ＸＣ－５００、セリック株式会社）で偏光板を通して測定部位を照明し、前面に偏光板を備えた分光カメラ（ＩｍＳｐｅｃｔｏｒ（登録商標）、ＪＦＥ テクノリサーチ株式会社）（波長分解能２．８ｍｍ、空間分解能０．１ｍｍ）で、表面反射光が受光されないように測定部位を撮影することにより行い、３０×３０画素の領域の反射率を波長４００～９００ｎｍの範囲で測定し、式（１）の吸光度関数Ｚ（λ）を用いて、温浴後及び炭酸浴後のそれぞれの第２層のメラニン濃度、第４層の血液濃度及び第６層の血液濃度を計測した。ここで、血液濃度としては、オキシヘモグロビンとデオキシヘモグロビンの合計の総ヘモグロビンの濃度を計測した。温浴後の第４層の血液濃度の計測画像を図７に示し、炭酸浴後の第４層の血液濃度の計測画像を図８に示す。図７及び図８において、血液濃度の単位（％）は、第４層の体積に対する総ヘモグロビンが占める体積の割合（体積％）である。
また、温浴後の第２層のメラニン濃度、第４層の血液濃度及び第６層の血液濃度の経時変化を図９に示し、炭酸浴後の第２層のメラニン濃度、第４層の血液濃度及び第６層の血液濃度の経時変化を図１０に示す。図９及び図１０において縦軸は体積分率である。
The spectral reflectance Rm (λ) is measured by illuminating the measurement site through a polarizing plate with an artificial solar lamp (SOLAX (registered trademark) XC-500, Celic Co., Ltd.) in a dark room, and a spectroscopic camera equipped with a polarizing plate on the front surface. ImSpectro (registered trademark), JFE Techno Research Co., Ltd. (wavelength resolution 2.8 mm, spatial resolution 0.1 mm) is used to photograph the measurement site so that surface reflected light is not received, and the area is 30 x 30 pixels. The reflectance was measured in the wavelength range of 400 to 900 nm, and the melanin concentration of the second layer and the blood concentration of the fourth layer after the hot bath and the carbonic acid bath were used using the absorbance function Z (λ) of the formula (1). And the blood concentration of the 6th layer was measured. Here, as the blood concentration, the total hemoglobin concentration of the total of oxyhemoglobin and deoxyhemoglobin was measured. The measurement image of the blood concentration of the fourth layer after the hot bath is shown in FIG. 7, and the measurement image of the blood concentration of the fourth layer after the carbonated bath is shown in FIG. In FIGS. 7 and 8, the unit (%) of blood concentration is the ratio (% by volume) of the volume occupied by the total hemoglobin to the volume of the fourth layer.
In addition, FIG. 9 shows changes over time in the melanin concentration of the second layer, the blood concentration of the fourth layer, and the blood concentration of the sixth layer after the warm bath, and the melanin concentration of the second layer and the blood concentration of the fourth layer after the carbonated bath are shown in FIG. And the time course of the blood concentration of the sixth layer are shown in FIG. In FIGS. 9 and 10, the vertical axis is the volume fraction.
図７から、第４層の血液濃度は温浴で急激に上昇し、１０分後には温浴前に戻っていることがわかる。これに対し、図８から、第４層の血液濃度は、炭酸浴で急激に上昇するが、その後の血液濃度の低下は温浴の場合よりも緩やかであり、血液濃度の上昇効果が持続することがわかる。 From FIG. 7, it can be seen that the blood concentration of the fourth layer rises sharply in the hot bath and returns to that before the hot bath after 10 minutes. On the other hand, from FIG. 8, the blood concentration of the fourth layer rises sharply in the carbonated bath, but the subsequent decrease in blood concentration is slower than in the case of the warm bath, and the effect of increasing the blood concentration is sustained. I understand.
また、図９及び図１０から、メラニン濃度は、温浴によっても炭酸浴によっても変化が見られず、第４層の血液濃度は、炭酸浴が温浴に比べて上昇率が高く、上昇した血液濃度の持続時間も長いこと、第６層の血液濃度は、温浴では上昇しないが、炭酸浴では上昇することがわかる。 Further, from FIGS. 9 and 10, the melanin concentration did not change between the hot bath and the carbonated bath, and the blood concentration in the fourth layer was higher in the carbonated bath than in the hot bath, and the increased blood concentration. It can be seen that the blood concentration of the sixth layer does not increase in the warm bath, but increases in the carbonated bath.
Claims (5)
皮膚組織の層状モデルに対して色素濃度を変えて光伝搬のシミュレーションを行うことにより色素濃度が異なる複数の分光反射率Ｒs(λ)を算出し、
色素濃度が異なる複数の分光反射率Ｒs(λ)から、分光反射率の平均スペクトルＲｓ_ av 又は吸光度の平均スペクトルＡs_ av を求め、一方、皮膚組織の吸光度を、皮膚組織の層状モデルの色素含有層内の色素による吸収係数の多項式で表した吸光度関数Ｚ(λ)を設定し、
吸光度関数Ｚ(λ)を、吸光度の相対スペクトル又は反射率の相対スペクトルとフィッティングすることにより、吸光度関数Ｚ(λ)の各項の係数を定めた相対吸光度関数Ｚ’（λ）を得、ここで吸光度の相対スペクトルは吸光度スペクトルから吸光度の平均スペクトルＡs_ av を差し引いたものであり、反射率の相対スペクトルは分光反射率Ｒs(λ)から分光反射率の平均スペクトルＲｓ_ av を差し引いたものであり、
被験者の皮膚の分光反射率Ｒm(λ)を測定し、
分光反射率Ｒm(λ)と相対吸光度関数Ｚ’(λ)とを、吸光度スペクトル又は反射率スペクトルとして比較することで、層状モデルの所定の色素含有層に対応した深さの層の色素濃度を推定する方法。 A method for estimating the pigment concentration in a layer having a predetermined depth forming skin tissue.
By simulating light propagation with different dye concentrations for a layered model of skin tissue, multiple spectral reflectances Rs (λ) with different dye concentrations were calculated.
From a plurality of spectral reflectances Rs (λ) having different dye concentrations, the average spectral reflectance Rs_av or the average absorbance As_av is obtained, while the absorbance of the skin tissue is determined by the dye-containing layer of the layered model of the skin tissue. Set the absorbance function Z (λ) expressed by the polynomial of the absorption coefficient by the dye in the
By fitting the absorbance function Z (λ) to the relative spectrum of absorbance or the relative spectrum of reflectance, a relative absorbance function Z'(λ) that defines the coefficients of each term of the absorbance function Z (λ) is obtained. Here, the relative spectrum of absorbance is the absorbance spectrum minus the average spectrum of absorbance As_ av , and the relative spectrum of reflectance is the spectral reflectance Rs (λ) minus the average spectrum Rs_ av of the spectral reflectance. can be,
The spectral reflectance Rm (λ) of the subject's skin was measured and
By comparing the spectral reflectance Rm (λ) and the relative absorbance function Z ' (λ) as an absorbance spectrum or a reflectance spectrum, the dye concentration of the layer having a depth corresponding to a predetermined dye-containing layer of the layered model can be obtained. How to estimate.
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