JP4775572B2 - Pigment identification method - Google Patents

Description

  The present invention relates to a pigment identification method, and more particularly to a pigment identification method for Japanese painting.

In recent years, color identification has been automated by computers, and various methods have been proposed.
However, with regard to pigments including natural pigments, they are judged as different pigments due to subtle variations in the optical properties of the pigments that should be regarded as the same, or conversely, the optical properties between the pigments that are considered as different. Since the difference is small, it may be determined that the same pigment is used, and its identification is difficult.
This situation is particularly remarkable in the case of Japanese painting pigments, and the identification of the pigments ultimately depends largely on the skills of traditional experts.

  As an expression method of optical characteristics commonly used in television and computer graphics, RGB tri-primary color expression, tristimulus value XYZ expression obtained by converting RGB three primary colors, or Lab expression obtained by further converting tristimulus value XYZ expression, In addition, there are LCh (lightness / saturation / hue) representations, etc., which can be converted by converting the Lab representation into cylindrical coordinates, while the RGB three primary color representations are physical measurements, while the last LCh representation is for human color sense. The best match.

Therefore, it is natural to adopt the LCh expression for the classification of the pigment. For example, when 256 gradations are used for each of the three primary colors of RGB, the resolution is almost sufficient, and the above RGB expression is converted to the LCh expression. Since conversion coefficients are also established, they are often used for color area classification, which is a major classification of pigments.
However, since the determination of fine differences in the same color region is delicate as described above, accurate identification of the pigment may be difficult even in LCh expression.

Therefore, attention is paid to the expression based on the spectral reflectance as a physical measurement value instead of the RGB primary color expression.
This is because the spectral reflectance is expressed by a spectral waveform of reflectance in the visible light range of 400 nm to 700 nm, for example, but the difference in pigment classification corresponds well with the spectral waveform of spectral reflectance.

However, although RGB representation data can be easily obtained for the pigment to be identified, spectral reflectance data is generally not easily obtained.
Therefore, although it is necessary to convert the RGB expression data into spectral reflectance data, it is difficult to determine the conversion coefficient, and in particular, it has not been possible to accurately determine the subtle determination of natural pigments such as Japanese painting.

For example, in Patent Document 1, the spectral reflectance is measured (calculated) on the sending side and transmitted on the receiving side in relation to the toning of a specific color, and the tristimulus value XYZ expression is calculated from the receiving side. A technique for reproducing color in a color printer is disclosed.
However, nothing is touched on the method of calculating the XYZ expression from the spectral reflectance, including the method for determining the conversion coefficient for conversion from the spectral reflectance to the XYZ expression.
JP 2001-275001 A

  The object of the present invention, which has been made in order to solve the problems in the identification of pigments as described above, particularly pigments in Japanese painting, is to efficiently identify pigments, particularly pigments in Japanese painting, from their RGB representation data. It is to provide a method.

  Another object of the present invention is to provide a method for determining the parameters of the above-mentioned method so that pigments, particularly Japanese painting pigments, can be accurately identified.

The pigment identification method according to the present invention made to solve the above problems comprises stages 1, 2, and 3, as shown in claim 1, and more specifically,
The stage 1
Step 1 of actually measuring the source RGB data of the target pigment (the pigment to be identified);
Step 2 of performing gamma (γ) correction on the source RGB data to obtain an RGB vector;
Step 3 of linearly transforming the RGB vector to obtain an XYZ vector;
Converting the XYZ vector into a Lab vector; and
Performing a cylindrical coordinate transformation on the Lab vector to obtain an LCh vector; and
A step 6 of determining, by the LCh vector, which color region the target pigment belongs to among a plurality of color regions;
Calculating a high-order RGB vector from the RBG vector,
Stage 2 is
The source RGB data is measured for each of the plurality of reference pigments, and the RGB vector, the XYZ vector, the Lab vector, and the LCh vector are sequentially calculated according to the same procedure as Step 1 to Step 5 in the stage 1, and the LCh vector is used. Determining a color region to which the reference pigment belongs, and storing the RGB vector and the LCh vector in a pigment database divided by the belonging color region;
Measuring a reference reflectance vector for each of the plurality of reference pigments, and storing the reference reflectance vector in a pigment database divided by the color area;
Storing a conversion parameter matrix specific to each color region based on the RGB vectors and the reference spectral reflectance vectors of all the reference pigments belonging to that color region and storing them in the pigment database;
Stage 3 is
Selecting and reading out the conversion parameter matrix defined for the color region to which the target pigment belongs from the pigment database;
Transforming the higher order RGB vector with a transformation parameter matrix to obtain an estimated spectral reflectance vector;
Calculating the difference by sequentially comparing the estimated spectral reflectance vector and a reference spectral reflectance vector of the reference pigment belonging to the corresponding color region;
A reference pigment having a smallest difference between the estimated spectral reflectance vector and a reference spectral reflectance vector of the reference pigment as an identification candidate of a target pigment;
It is characterized by including.

The method for identifying a pigment according to the present invention made to solve the above problems comprises stages 1, 2, and 3, as shown in claim 2, and more specifically,
The stage 1
Step 1 of actually measuring the source RGB data of the target pigment;
Step 2 of performing gamma (γ) correction on the source RGB data to obtain an RGB vector;
Step 3 of linearly transforming the RGB vector to obtain an XYZ vector;
Converting the XYZ vector into a Lab vector; and
Performing a cylindrical coordinate transformation on the Lab vector to obtain an LCh vector; and
Determining, according to the LCh vector, which color region of the plurality of color regions the pigment belongs to, and
Stage 2 is
The source RGB data is measured for each of the plurality of reference pigments, and the RGB vector, the XYZ vector, the Lab vector, and the LCh vector are sequentially calculated according to the same procedure as Step 1 to Step 5 in the stage 1, and the LCh vector is used. Determining a color region to which the reference pigment belongs, and storing the RGB vector and the LCh vector in a pigment database divided by the belonging color region,
Stage 3 is
The Lab vectors of all reference pigments belonging to the color region to which the target pigment belongs determined in Step 6 are read from the pigment database, and sequentially compared with the Lab vectors of the target pigment obtained in Step 4, and the difference is determined. Calculating step 31;
A reference pigment having the smallest difference between the Lab vector of the target pigment and the Lab vector of the reference pigment as a candidate for identification of the target pigment, step 32;
It is characterized by including.

According to a third aspect of the present invention, the method for calculating the XYZ vector from the RGB vector in step 3 of the stage 1 is a linear transformation using a matrix represented by the following equation.

Further, according to the fourth aspect of the present invention, in step 4 of the stage 1, the method of calculating the Lab vector from the XYZ vector is configured such that the tristimulus values of illumination light are xn, yn, and zn, and each component of the XYZ The conversion defined by the following equation is performed on x, y, and z, and a Lab vector whose components are el, a, and b, which are conversion results, is obtained.

Further, as shown in claim 5, the high-order RGB vector in Step 7 of the stage 1 has at least the primary components r, g, and b, 2, where r, g, and b are components of the RGB vector. Secondary components r ² , g ² , b ² , gb, br and rg, tertiary components r ³ , g ³ , b ³ , r ² g, rg ² , g ² b, gb ² , b ² r, br ² , And rgb, quaternary components r ⁴ , g ⁴ , b ⁴ , r ³ g, rg ³ , g ³ b, gb ³ , b ³ r, br ³ , r ² g ² , g ² b ² , b ² r ² , r ² gb, g ² br, and b ² rg as components.

  In addition, as shown in claim 6, in step 23 of the stage 3, the difference between the estimated spectral reflectance vector and the reference spectral reflectance vector of the reference pigment is the difference between the estimated spectral reflectance vector and the reference spectral reflectance. The square of the length of the difference vector of the rate vector is defined as a reflectance error, and the square of the length of the difference vector of the difference vector of the estimated spectral reflectance and the difference vector of the reference spectral reflectance is defined as a reflectance differential error. In this case, it is a weighted average of the reflectance error and the reflectance differential error.

  Also, as shown in claim 7, in step 31 of the stage 3, the difference between the Lab vector of the target pigment and the Lab vector of the reference pigment is the difference between the Lab vector of the target pigment and the Lab vector of the reference pigment. It is the length of a vector.

Further, as shown in claim 8, in step 13 of the stage 2, the conversion parameter matrix H unique to each color region is converted into the RGB vectors of all the reference pigments belonging to the color region and the reference spectral reflectance. To calculate based on a vector:
Expanding the color area to partially overlap with an adjacent color area, 41;
A random value is added to each component of the RGB vector for each of the reference pigments belonging to the enlarged color region to generate a plurality of derived RGB vectors, which are enlarged together with the original reference pigment. Generating a reference pigment 42;
Calculating a higher order RGB vector from each RGB vector of the enlarged reference pigment; and
Define the spectral reflectance vector of each of the enlarged reference pigments to be the same as the spectral reflectance vector of the original reference pigment, and calculate the estimated spectral reflectance vector by the product of the unknown matrix and the higher-order RGB vector Defining 44 and determining the unknown matrix so as to minimize the difference between the spectral reflectance vector and the estimated spectral reflectance vector to be the conversion parameter matrix H;
It is characterized by including.

  In addition, as shown in claim 9, in the step 44, the difference between the spectral reflectance vector and the estimated spectral reflectance vector is the square of the length of the difference vector between the spectral reflectance vector and the estimated spectral reflectance vector. And the conversion parameter matrix is determined by a multiple regression analysis method.

According to the pigment identification method of the first aspect of the present invention, only the RGB expression data of the target pigment that is relatively easily available is used as the original data, and separately sensitive to the difference between the RGB expression data and the pigment and has strong discrimination power. Prepare a reference pigment with spectral dispersion rate data, determine a conversion parameter from RGB representation to spectral reflectance based on the reference pigment belonging to the same color region, and use this to determine the RGB representation of the target pigment The data is converted into an estimated spectral reflectance, and a target pigment is identified by obtaining a reference pigment having a spectral reflectance closest to the estimated spectral reflectance.
Therefore, pigment identification, particularly Japanese painting pigment sensitive to subtle differences, can be accurately and efficiently performed.

According to the pigment identification method of the second aspect of the present invention, the Lab vector is calculated using only the RGB expression data of the target pigment that can be obtained relatively easily as the original data, and separately the RGB expression data and the Lab calculated from the RGB expression data. A reference pigment having a vector is prepared, and a target pigment is identified by obtaining a reference pigment having the closest Lab vector among reference pigments belonging to the same color region.
Therefore, identification of pigments, particularly identification of Japanese pigments sensitive to subtle differences, can be performed relatively simply and efficiently, and is suitable for preliminary identification.

  According to the pigment identification method of claims 3 and 4 of the present invention, the conversion from the RGB vector to the XYZ vector and the conversion from the XYZ vector to the Lab vector are performed by established methods.

  According to the pigment identification method of claim 5 of the present invention, when the spectral reflectance is handled as a nonlinear function of the RGB vector, at least the fourth-order nonlinear dependence is reflected, and the spectral reflectance of the target pigment is estimated. High accuracy.

  According to the pigment identification method of the sixth aspect of the present invention, the difference between the estimated spectral reflectance vector of the target pigment and the spectral reflectance vector of the reference pigment is the sum of squares of the difference in reflectance at each frequency, Since the sum of squares of the difference in rate gradient is further weighted and averaged, it can be accurately evaluated as the difference in shape of the entire spectral reflectance spectrum.

  According to the pigment identification method of the seventh aspect of the present invention, the difference between the Lab vector of the target pigment and the Lab vector of the reference pigment is simply calculated as the sum of squares of the differences between the Lab vector elements L, a, and b. Is done.

According to the pigment identification method according to claim 8 of the present invention, the determination of the conversion parameter unique to each specific color area is all references belonging to the color area expanded so as to partially overlap with the adjacent color area. It is based on the pigment and prevents the reference pigment near the border of the color region from being lost due to measurement errors.
Furthermore, random number values are added to each component of the RGB vector to generate a plurality of derived RGB vectors, and the measurement error of all reference pigments is randomized. The effect of measurement errors on the conversion parameters is mitigated.

  According to the pigment identification method of claim 9 of the present invention, the conversion is performed so that the sum of the squares of the lengths of the difference vectors between the spectral reflectance vector and the estimated spectral reflectance vector over all the enlarged reference pigments is minimized. Since the parameter matrix is determined by the multiple regression analysis method, an optimal conversion parameter matrix is obtained.

  Hereinafter, embodiments and effects according to the present invention will be specifically described with reference to FIGS.

In the following description, all scalar quantities (eg, R, G, B in RGB representation) are represented by lowercase letters (eg, r, g, b), and all vector quantities (eg, RGB vector R). = [R, g, b]) is represented by uppercase letters, and the component is represented by row display as described above, and the column display is represented by ^RT .
The component _{r i} of the i-th vector R (i = 1 to N), the display by the component _{r i} of the vector R and R = _{[r i],} the matrix is case: expressed in (Example transformation parameter matrix M), The display by the component m _ij is M = [m _ij ].
The scalar product of vectors R and R ^T in R * R ^T, a product of the matrix M and vector R ^T represents at M * R ^T, a product sum of the individual components in a product of the scalar product and the matrix-vector The expression is omitted because it is obvious by the definition of scalar product.

FIG. 1 is a flowchart of a pigment identification method according to this embodiment.
The method consists of stages 1, 2, and 3.
In stage 1, LCh vectors and the like are obtained from the source RGB data of the target pigment (the pigment to be identified).
First, in step 1, source RGB data (sr, sg, sb; here, 256 gradations of 0 to 255 are measured) of the target pigment.

Next, in step 2, the following conversion is performed on each component of the source RGB data (sr, sg, sb) using γ = 2.2 as the γ correction value, and the conversion results are respectively expressed as r, g, Let b be an RGB vector whose components are R = [r, g, b].
r = (sr / 255) ^2.2
g = (sg / 255) ^2.2
b = (sb / 255) ^2.2

Next, in step 3, the RGB vector and R are linearly converted by the matrix A defined by the following equation, and the conversion results are x, y, and z, respectively, and XYZ vectors having these as components, X = [x, y, z].
X ^T = A * R ^T

Next, in step 4, the XYZ vector and the components x, y, and z of X are subjected to conversion defined by the following equation, and the conversion results are el (el), a, and b, respectively, and Lab using these as components. Define a vector, L = [el, a, b].
Tristimulus value xn of the illumination light, yn, as zn, using the case of the illumination light _{D 65.}

Next, in step 5, cylindrical coordinates conversion is performed for the Lab vector L, as follows, and the conversion results are set to lightness el (el), saturation ρ, hue angle θ, and LCh vector K having these as components, K = [El, ρ, θ] is defined.
el = el
ρ = {a ² + b ² } ^1/2
θ = arctan (b / a)

Next, in step 6, referring to Table 1 or equivalent FIG. 2, it is determined to which of the 25 color regions Rv to Nww the vector L or the vector K equivalent thereto belongs. .
In the present embodiment, the case where the color areas are the specific 25 types shown in FIG. 2 is shown, but the present invention is not limited to this.
2A is a color area division diagram in the ab plane (ρ-θ plane, that is, the saturation-hue plane), and FIG. 2B is a color according to the L coordinate (brightness). The subdivision of the area is shown.
In general, pigments used in Japanese paintings have many red (R), yellow (Y), green (G), and white (w) hues, particularly yellow (Y), blue-green (T), blue ( B) Since there are few types of hues of purple (P) and black (b), in order to reflect this, the color area divisions in Table 1 and FIG. The parts are roughly divided.

Next, in step 7, high-order factors of the RGB vector are introduced.
This is to reflect the nonlinearity of this conversion when the RGB vector and R of the pigment to be identified are converted and the spectral reflectance vector and M are estimated as described below.
That is, in addition to the primary factor vector R ₁ = R = [r, g, b], in this embodiment,
Quadratic factor vector R ₂ = [r ² , g ² , b ² , gb, br, rg],
Third-order factor vector R ₃ = [r ³ , g ³ , b ³ , r ² g, rg ² , g ² b, gb ² , b ² r, br ² , rgb],
Fourth-order factor vector R ₄ = [r ⁴ , g ⁴ , b ⁴ , r ³ g, rg ³ , g ³ b, gb ³ , b ³ r, br ³ , r ² g ² , g ² b ² , b ² r ² , r ² gb, g ² br, b ² rg],
Higher order RGB vector C = [R ₁ , R ₂ , R ₃ , R ₄ ] = [c _i ]; i = 1 to 34
Define (For example, c ₁ = r,... C ₄ = r ² ,... C ₃₄ = b ² rg)
In this embodiment, a high-order RGB vector composed of first-order to fourth-order factor vectors is used. However, higher-order factor vectors (for example, fifth-order factor vector R ₅ = By adding all or part of [r ⁵ ,..., B ² r ² g], the identification accuracy can be further improved.

On the other hand, in stage 2, a conversion parameter matrix H is obtained for each color region from source RGB data of a plurality of reference pigments.
In the first step 11, RGB vector, the _{R r} was measured for each of a plurality of reference pigments, Lab vector from the vector _{R r,} an _{L r} is calculated in the same manner as described above, the vector _{R r,} the vector _{L r,} In the same manner as above, based on the vector L _r , the data are classified into 25 color regions shown in Table 1 and stored in the pigment database DB.

Next, in step 12, the reference spectral reflectance vector, _Mr, is measured for each of the plurality of reference pigments.
The reference spectral reflectance vector, M _r, includes 31 reference spectral reflectances m _{r i} measured in increments of 10 nm in the visible light range of 400 nm to 700 nm for the reference pigment. That is,
M _r = [ _{m r i} ]; i = 1 to 31
The vector _{Mr is} also stored in the pigment database DB classified by 25 color regions as described above.

Next, in step 13, a conversion parameter matrix H = [h _ij ] specific to each color region is calculated based on the RGB vector, R _r , reference spectral reflectance vector, and M _r of the reference pigment belonging to that color region. Store in the pigment database DB.
The conversion parameter matrix H is for estimating the spectral reflectance vector and M by converting the RGB vector and R of the pigment to be identified in Step 22 below, and the calculation method will be described in Example 3 below. .

In stage 3, from the LCh vector and K of the target pigment obtained in stage 1 and the conversion parameter matrix H for each color region obtained in stage 2, an estimated value M of the spectral reflectance vector is obtained and Identification candidates are obtained with priority.
First, in step 21, the conversion parameter matrix H = [h _ij ] defined for the color region to which the pigment to be identified, determined in step 6, is selected and read from the pigment database DB.

Next, in step 22, the high-order RGB vector and C obtained in step 7 are converted by the conversion parameter matrix H as follows to obtain an estimated value M of the spectral reflectance vector.
M ^T = H * C ^T

Next, in step 23, the estimated spectral reflectance vector M, and a reference spectral reflectance vector M _r of the reference pigment belonging to the relevant color region are sequentially compared.
That is, for example, the reflectance error E1 and the reflectance differential error E2 are obtained by defining them as follows.
E1 = root {(M−M _r ) * (M−M _r ) ^T }
E2 = root {(D−D _r ) * (D−D _r ) ^T }
Where
Estimated spectral reflectance difference vector, D = [d _i ]; i = 2-30
Reference spectral reflectance difference vector, D _r = [dr _i ]; i = 2-30
d _i = {(m _{i + 1} −m _i ) − (m _i −m _i−1 )} / 2
_{dr i = {(mr i +} 1 -mr i) - (mr i -mr i-1)} / 2

Next, in step 24, the reflectance error E1 and the reflectance differential error E2 are comprehensively compared and determined, and the reference pigments are enumerated in order of increasing overall error, and are used as identification candidates for the target pigment. .
More specifically, for example, when the reflectance error E1 is the minimum, second, third, and fourth or less, respectively, α1, α2, α3, and α4 are set, and the reflectance differential error E2 is the minimum, second. The cases of the third, fourth and lower cases are set as β1, β2, β3, and β4, respectively, and the general priorities as shown in Table 2 are given.
However, for the reflectance error E1 and the reflectance differential error E2, for example, an α threshold value and a β threshold value shown in Table 2 are provided, respectively, and if the error exceeds this threshold value, they are excluded from the ranking.

このようにして、複数個の有力な同定候補顔料に対して、総合優先度及び信頼度をつけて与えることができる。
なお、これらの総合優先度及び信頼度決定の仕様は環境設定により変更可能であるのが望ましい。 Further, the reliability as shown in Table 3 is given to the overall priority.

In this way, it is possible to give a plurality of potential identification candidate pigments with overall priority and reliability.
In addition, it is desirable that the specifications for determining the overall priority and the reliability can be changed by the environment setting.

FIG. 3 is a flowchart of the pigment identification method according to the present embodiment, which includes stages 1, 2, and 3 as in the case of the first embodiment (FIG. 1).
Also in the present embodiment, steps 1 to 6 of stage 1 and step 11 of stage 2 are the same as in the case of the first embodiment, and thus description thereof is omitted.

However, in this embodiment, compared Lab vector of the reference pigment interest pigments, L, a L _r directly, higher RGB vector does not use the C and transformation parameter matrix H, Step 7 Stage 1 of Example 1 , And steps 12 and 13 of stage 2 are unnecessary, and the identification work is simplified, which is suitable for preliminary identification (pre-estimation).

In stage 3, first, in step 31, the Lab vector L of the pigment to be identified obtained in step 4, L is the Lab vector of the reference pigment belonging to the color region to which the pigment belongs, determined in step 6. sequentially compared with the L _r.
In step 32, the reference pigment having the smallest difference between the Lab vector of the target pigment and the Lab vector of the reference pigment is set as the target pigment identification candidate.
For example, the color error E3 is obtained by defining it as follows.
E3 = root {(L−L _r ) * (L−L _r ) ^T }
In this case, the third to third reference pigments having the smallest color error E3 are identified as candidate identification pigments of priority 1, 2, and 3, and their reliability is 3, 2, and 1, respectively.
Here, a threshold value (for example, 5.0, 15.0, 20.0, respectively) is provided for each priority (reliability) 1, 2, and 3 for the color error E3, and the color error is the threshold value. If it exceeds, it will be excluded from the ranking.

  The present embodiment relates to a method for calculating and determining a conversion parameter matrix H specific to each color region in step 13 of the first embodiment, and a flowchart thereof is shown in FIG.

First, in step 41, the boundary of the color area is expanded so as to partially overlap with the adjacent color area rather than the definition in Table 1 above.
For example, a reference pigment in which the LCh vector is expanded within ± 5 °, the saturation ρ is ± 5, and the hue θ is expanded ± 10 ° is considered in the color region.
This is to prevent the reference pigment near the boundary from leaking out of consideration due to measurement errors.

Next, in step 42, for each of the reference pigments belonging to the enlarged color region, a random number value of -5 to +5 is added to each of the components (r, g, b) of the RGB vector to obtain 10 pieces. The derived RGB vector is generated. (When the random number addition result is 0 or less or 255 or more, it is fixed to 0 or 255, respectively.)
The spectral reflectance vector M _r of the derived reference pigment is all the same as the vector M _r of the original reference pigment.

  For example, when there are Ne = 30 reference pigments belonging to the enlarged specific color region, 300 (= Ne × 10) derived reference pigments are added and a total of 330 (= Ne × 11) is used as the enlarged reference pigment. Define and consider the following. In any case, the number of enlarged reference pigments must be higher than the higher order RGB vector, the order of C (34 in this embodiment).

  Next, in step 43, for each of the enlarged reference pigments, a high-order RGB vector, C, is calculated from the above (original or derived) RGB vector.

Next, in step 44, the difference (M _r −M) between the spectral reflectance vector M _r and the estimated spectral reflectance vector M = H * C ^T (the product of the unknown conversion parameter matrix H and the higher-order RGB vector C). Determine the unknown matrix H = [h _ij ] so that = (M _r −H * C ^T ) is minimized across all extended reference pigments.

For example, the evaluation of the difference (M _r −M) is evaluated by the sum E4 of all the extended reference pigments (including derived reference pigments) belonging to the color region, which is the square of the length of the (M _r −M) vector. In this case, E4 is defined by the following equation.
E4 = Σ {(M _r −H * C ^T ) * (M _r −H * C ^T ) ^T }
In this case, the determination of the matrix H by minimizing E4 is an estimation by the multiple regression analysis method.

An actual example of estimation by the multiple regression analysis method will be described next.
In this actual example, the color area division is slightly changed from the above Table 1 to be as shown in Table 4.
That is, in accordance with the color area distribution of the reference pigment, the color area where the reference pigment does not exist (for example, Pv) is excluded, and the color area with many distributions is further divided so that the total number of color areas is 26.
The total number of reference pigments is 442 (total in the Nn column), and the number of samples in each color region is 17.0 on average over 3 to 31 as shown in the Nn column in the number of nets. As shown in the Ne column, the number in the case of enlarging to the edge of the adjacent color region ranges from 6 to 52 and is an average of 34.1.

For these reference pigment groups, the matrix H was determined by multiple regression analysis estimation for each color region.
In this case, an average value e of the mean square error for each color region is as shown in the rightmost column of Table 4.
Where e is the following equation using the difference vector (M _r −H * C ^T ) of Ne expanded reference pigments (in this case excluding derived reference pigments) belonging to each expanded color region: Defined by
e = (1 / Ne) Σroot [{(M _r −H * C ^T ) * (M _r −H * C ^T ) ^T } / 31]
Here, “31” is the dimension of the spectral reflectance vector M, that is, the number of spectral reflectance data in increments of 10 nm in this case.
Since the spectral reflectances are all in the scale range of 0.0 to 1.0 by definition, from Table 4, the mean square root error is within 4.9% of the scale even in the worst case (color region G1). I understand that.

Further, the true value of spectral reflectance of a typical pigment (spectral reflectance vector M _r ) is compared with an estimated value (estimated spectral reflectance vector M = H * C ^T ) using H based on the multiple regression analysis estimation. Examples are shown in FIGS.
5A, 5B, 6C, and 6A, 6B, and 6C, respectively, are related to cinnabar, cocoon, pine needle patina, ultramarine blue, dark mouth powder, and powder solution.
The assigned color regions of these pigments are R2, YR3, G2, B2, YR1, and N1, respectively, in the order described above.
From these figures, it can be seen that the estimation errors of the individual spectral reflectances are in most cases within 0.05, that is, within 5% of the scale.
This makes it possible to expect that a certain high identification accuracy can be obtained when identifying the unknown pigment from the source RGB data by the method according to the present invention.

3 is a flowchart of a pigment identification method according to Example 1. FIG. 2 is a color area division diagram according to the first embodiment, where (A) relates to a saturation-hue plane, and (B) relates to lightness. 6 is a flowchart of a pigment identification method according to Example 2. 12 is a flowchart for calculating and determining a conversion parameter matrix H according to the third embodiment. (A), (B), and (C) are comparative examples of the true value and estimated value of the spectral reflectance of a representative pigment according to Example 3, respectively. (A), (B), and (C) are comparative examples of the true value and estimated value of the spectral reflectance of a representative pigment according to Example 3, respectively.

Claims (9)

It consists of stages 1, 2, and 3.
In stage 1,
Measure the source RGB data of the target pigment (the pigment you want to identify), calculate the RGB vector, XYZ vector, Lab vector, and LCh vector in sequence,
The LCh vector determines which color region the target pigment belongs to among a plurality of color regions,
Calculating a higher order RGB vector from the RBG vector;
In stage 2,
For each of the plurality of reference pigments, the source RGB data and the reference reflectance vector are measured, and the RGB vector, the XYZ vector, the Lab vector, and the LCh vector are sequentially calculated.
The color region to which the reference pigment belongs is determined by the LCh vector, and the RGB vector, the LCh vector, and the reference reflectance vector are stored in a pigment database divided by the color region to be assigned,
A conversion parameter matrix unique to each color region is calculated based on the RGB vectors and the reference spectral reflectance vectors of all the reference pigments belonging to the color region.
In stage 3,
The conversion parameter matrix defined for the color region to which the target pigment belongs is selected and read from the pigment database,
The higher order RGB vector is converted by a conversion parameter matrix to obtain an estimated spectral reflectance vector,
Sequentially comparing the estimated spectral reflectance vector and the reference spectral reflectance vector of the reference pigment belonging to the corresponding color region to calculate the difference;
A reference pigment having the smallest difference between the estimated spectral reflectance vector and the reference spectral reflectance vector of the reference pigment is used as an identification candidate of the target pigment.
A pigment identification method characterized by the above. It consists of stages 1, 2, and 3.
In stage 1,
Measure the source RGB data of the target pigment (the pigment you want to identify) and calculate the RGB vector, XYZ vector, Lab vector, and LCh vector in sequence,
The LCh vector determines which color region the target pigment belongs to among a plurality of color regions.
In stage 2,
For each of the plurality of reference pigments, the source RGB data is actually measured, and the RGB vector, the XYZ vector, the Lab vector, and the LCh vector are sequentially calculated.
The color region to which the reference pigment belongs is determined based on the LCh vector, and the RGB vector, the Lab vector, and the LCh vector are stored in a pigment database divided according to the color region.
In stage 3,
The Lab vectors of all reference pigments belonging to the color region to which the target pigment belongs are read from the pigment database and sequentially compared with the Lab vector of the target pigment, and the difference is calculated.
A reference pigment having the smallest difference between the Lab vector of the target pigment and the Lab vector of the reference pigment is used as an identification candidate of the target pigment.
A pigment identification method characterized by the above. 3. The pigment identification method according to claim 1, wherein the method of calculating the XYZ vector from the RGB vector in the stage 1 is a linear transformation using a matrix represented by the following equation.

The method for calculating the Lab vector from the XYZ vector in the stage 1 is that the tristimulus values of illumination light are xn, yn, and zn, and the transformation defined by the following equations for each component x, y, and z of the XYZ The pigment identification method according to claim 1, wherein a Lab vector having components el, a, and b as conversion results is obtained.

The high-order RGB vectors in the stage 1 are at least primary components r, g, and b, secondary components r ² , g ² , b ² , gb, where r, g, and b are components of the RGB vectors. br, and rg, tertiary components r ³ , g ³ , b ³ , r ² g, rg ² , g ² b, gb ² , b ² r, br ² , and rgb, quaternary components r ⁴ , g ⁴ , b ⁴ , r ³ g, rg ³ , g ³ b, gb ³ , b ³ r, br ³ , r ² g ² , g ² b ² , b ² r ² , r ² gb, g ² br, and b ² The pigment identification method according to claim 1, wherein rg is calculated as a component.   In the stage 3, the difference between the estimated spectral reflectance vector and the reference spectral reflectance vector of the reference pigment reflects the square of the length of the difference vector between the estimated spectral reflectance vector and the reference spectral reflectance vector. The reflectance error and the reflectance differential error when the reflectance differential error is the square of the length of the difference vector of the difference vector of the estimated spectral reflectance and the difference vector of the reference spectral reflectance. The pigment identification method according to claim 1, wherein the pigment identification method is a weighted average.   The stage 3 is characterized in that the difference between the Lab vector of the target pigment and the Lab vector of the reference pigment is the length of the difference vector between the Lab vector of the target pigment and the Lab vector of the reference pigment. 3. The pigment identification method according to 2. In the stage 2, a method for calculating a conversion parameter matrix unique to each color region based on the RGB vectors and the reference spectral reflectance vectors of all the reference pigments belonging to the color region,
Expanding the color area to partially overlap with an adjacent color area, 41;
A random value is added to each component of the RGB vector for each of the reference pigments belonging to the enlarged color region to generate a plurality of derived RGB vectors, which are enlarged together with the original reference pigment. Generating a reference pigment 42;
Calculating a higher order RGB vector from each RGB vector of the enlarged reference pigment; and
Define the spectral reflectance vector of each of the enlarged reference pigments to be the same as the spectral reflectance vector of the original reference pigment, and calculate the estimated spectral reflectance vector by the product of the unknown matrix and the higher-order RGB vector Defining 44 and determining the unknown matrix so as to minimize the difference between the spectral reflectance vector and the estimated spectral reflectance vector, and converting the unknown matrix into the conversion parameter matrix;
The pigment identification method according to claim 1, comprising: In step 44, the difference between the spectral reflectance vector and the estimated spectral reflectance vector is the sum of the squares of the lengths of the difference vectors between the spectral reflectance vector and the estimated spectral reflectance vector over all the enlarged reference pigments. The pigment identification method according to claim 8, wherein the conversion parameter matrix is determined by a multiple regression analysis method.

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