JPH08178752A - Computer color mapping method - Google Patents

Abstract

PURPOSE: To predict the mixing ratio of a mixture having desired color with high accuracy. CONSTITUTION: Three stimulus values X0, Y0 and Z0 are actually measured for a standard color sample of a coloring agent having a known mixing ratio Ci (S2). On the other hand, three stimulus values XT, YT and ZT of an objective mixture of computer color matching, i.e., a gray level limit sample, are set for the measurement of standard color sample while taking account of the manufacturing error (S30). Three stimulus values XM, YM and ZM are then calculated from a known mixing ratio Ci of the standard color sample (S4) and errors ▵X, ▵Y and ▵Z are calculated from the measurements (S5). Subsequently, the three stimulus values XT, YT and ZT of gray level limit sample are corrected using the calculation errors (S6) and three corrected stimulus values XC, YC and ZC are employed as target values in the execution of computer color matching thus predicting the mixing ratio of the gray level limit sample (S7).

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for predicting a blending ratio of a colorant by computer color matching.

[0002]

2. Description of the Related Art So-called computer color matching is used to predict the color of a mixture in which a colorant such as a pigment or dye is mixed with an object to be colored. In computer color matching, the absorption coefficient K of the object to be colored and the colorant is
Using i (λ) and scattering coefficient Si (λ), Duncan (Du
ncan) formula (Formula 1) and Kubelka-Munk
The spectral reflectance R (λ) of an arbitrary mixture can be obtained based on the equation (Equation 2) based on Munk's color mixing theory.

[0003]

[Equation 1]

[0004]

[Equation 2]

Where KM and SM are the absorption coefficient and scattering coefficient of the mixture, Ki and Si are the absorption coefficient and scattering coefficient of the i-th component, and Ci is the mixing ratio of the i-th component. However, in the mathematical formulas in this specification, “(λ)” indicating that it depends on the wavelength λ is omitted. The components of the mixture are the material to be colored and the colorant.

If the spectral reflectance R (λ) of the mixture is known, the tristimulus values X, Y, Z of the mixture can be calculated, so that the color of the mixture can be predicted. Conversely, it is also possible to predict the blending ratio for obtaining a mixture having a target color by computer color matching.

By the way, various colors are set in industrial ceramics such as sanitary ceramics according to various tastes of users. The color of the pottery is determined by the blending ratio of the pigment mixed in the glaze, and thus the glaze corresponds to the mixture in computer color matching. When setting the color of the pottery, the designer first decides the color by coloring the paper or selecting a sample having a desired color from the pre-baked samples. Then, the spectral reflectance of that color is measured with a spectrophotometer, and the blending ratio of the colorant such as a pigment or dye is predicted from the actual measured value of the spectral reflectance using computer matching.

[0008] By the way, even if the same proportion of glaze is used, the actual colors of the manufactured pottery do not become the same, and the colors usually vary. FIG. 1 is an xy showing the variation in color between the designed color and the actual manufactured pottery.
It is a chromaticity diagram. In FIG. 1, the color indicated by the double circle is the designed desired color (standard color) L0, and the small white circle is the distribution of the color of the pottery actually manufactured. It is necessary to recognize a pottery having a color greatly different from the standard color L0 as a defective product. Therefore, as the limit of the shade of the non-defective product, the shade limit color L1 having a color indicated by a black circle in FIG.
L2 is set. Since the chromaticity coordinate value of the standard color L0 is determined by the designer, the chromaticity coordinate value of the standard color L0 is taken into consideration in consideration of manufacturing error and the like, and the two shade limit colors L1, L
Determine a chromaticity coordinate value of 2.

In the actual manufacture of pottery, the standard color L0
The pottery having the above is prepared as a standard color sample, and the two pottery having the shade limit colors L1 and L2 are prepared as the shade limit sample. Then, in the inspection step, the colors of the standard color sample and the light and shade limit sample are compared with the color of the manufactured pottery, and only the pottery in the color range of the light and shade limit sample is regarded as a good product.

[0010]

By the way, since the prediction by the computer color matching involves a considerable error, it takes a lot of time and effort to prepare the standard color sample and the light and shade limit sample from the predicted blending ratio. It is normal. For example, when creating a standard color sample, a large number of samples are fired using a glaze prepared in a compounding ratio predicted by computer color matching, and if there is a sample with a desired standard color, select it. Adopted as a standard color sample. However, if there is no sample having a standard color, the blending ratio is changed according to intuition and experience, a large number of samples are baked again, and this operation is repeated until a sample having a standard color is obtained. Such an operation is also performed on the light / dark limit samples having the light / dark limit colors L1 and L2.

As described above, in the conventional computer color matching, it has been difficult to accurately predict the blending ratio for producing a mixture having a desired color.

The present invention has been made to solve the above problems in the prior art, and an object thereof is to provide a computer color matching capable of accurately predicting the blending ratio of a mixture having a desired color. And

[0013]

In order to solve the above-mentioned problems, a method according to claim 1 is a method for predicting a blending ratio of a colorant of a target mixture having a desired color by computer color matching. And
(A) obtaining an actually measured value of coordinates of a predetermined color system for a near-color sample having a known colorant blending ratio and a color close to the desired color; and (b) known blending of the near-color sample. Obtaining a calculated value of coordinates of the color system representing the color of the adjacent color sample from the ratio, and obtaining a calculation error from the measured value and the calculated value; (c) the color for the color of the target mixture. Setting a target value of coordinates of the system, and (d) correcting the target value using the calculation error,
Predicting the blending ratio of the colorant in the target mixture by executing computer color matching using the corrected target value.

The target value of the coordinate of the coordinate system of the target mixture is corrected by the calculation error of the coordinate value of the color system of the adjacent color sample, and the corrected target value is used for computer color matching. The computer color matching can be executed under the condition that the calculation error of the coordinate value of is reduced.

In the computer color matching method according to a second aspect of the present invention, in the step (a), for a plurality of samples, a database containing a blending ratio of the colorant and an actual measurement value of the coordinates of the color system is used. Retrieving the adjacent color sample by selecting the sample that has the smallest color difference from the target mixture.

By searching the database for the sample having the smallest color difference as the adjacent color sample, the prediction error of the computer color matching can be reduced for the target mixture having an arbitrary color.

[0017]

FIG. 2 is a flow chart showing the overall procedure of processing in the embodiment. The mixture targeted in this example is a glaze for covering the surface of the ceramic body. That is, a base glaze (basic glaze) containing no pigment is an object to be colored, and a glaze obtained by adding a pigment to this base glaze is a mixture to be subjected to computer color matching.

In step S1, a standard color sample is first created. Therefore, the mixing ratio of the colorant of the standard color sample is known. In step S2, the spectral reflectance R'of the created standard color sample is measured with a spectrophotometer, and the spectral reflectance R'is measured.
Then, tristimulus values X0, Y0, and Z0 are calculated according to the following mathematical expression 3.

[0019]

(Equation 3)

Here, S (λ) is the spectral distribution of standard light, x
(Λ), y (λ), z (λ) (with a bar in the formula) are color matching functions.

In step S3, based on the measured values X0, Y0, Z0 of the tristimulus values of the standard color obtained in step S2, the designer considers the manufacturing error and the two shade limit colors shown in FIG. Set tristimulus values for L1 and L2. Note that, for convenience of description, a case will be described below in which a mixing ratio for realizing the first light and shade limit color L1 is predicted. With respect to the second lightness / darkness limit color L2 as well, the mixing ratio can be accurately predicted by the same process.

In step S4, from the mixing ratio Ci of each colorant of the standard color sample prepared in step S1 (i represents the colorant number), the scattering coefficient Si, and the absorption coefficient Ki,
Calculate the calculated tristimulus values XM, YM, and ZM of the standard color sample by the following procedure.

First, when the above-mentioned formula 2 is modified, the spectral reflectance R (λ) of the mixture is given by the following formula 4.

[0024]

[Equation 4]

The ratio of the absorption coefficient to the scattering coefficient of the mixture (K /
S) M is the absorption coefficient Ki (λ) and scattering coefficient S of each colorant.
It can be calculated from i (λ) and the mixing ratio Ci according to the above-described mathematical expression 1. Therefore, the spectral reflectance R (λ) of the mixture can be obtained from the ratio (K / S) M according to the equation (4). Since this spectral reflectance R (λ) is the spectral reflectance in the ideal state (when the thickness of the object to be colored is infinite), the spectral reflectance R ′ (λ) that can be measured with a spectrophotometer is given by Calculate according to Sanderson's formula).

[0026]

(Equation 5)

Here, the coefficients k1 and k2 are values that depend on the optical properties of the object to be colored (base glaze). Coefficient k1,
The value of k2 can be determined from the refractive index n of the object to be colored according to the following formula 6.

[0028]

(Equation 6)

The refractive index n of the base glaze is, for example, about 1.4.

When the spectral reflectance R '(λ) is obtained by the equation 5, the tristimulus values XM, YM, ZM of the mixture can be calculated according to the equation similar to the equation 3 described above.

By the way, the absorption coefficient Ki and the scattering coefficient Si of each colorant include an error, and since the equations 1, 4 to 6 are empirical equations rather than theoretical equations, the tristimulus values obtained in step S4 The calculated values XM, YM and ZM have an error. This calculation error is the actual measurement value X obtained in step S2.
It is the difference from 0, Y0 and Z0. By the way, the prediction of the mixing ratio by computer color matching can
6 to determine tristimulus values of the mixture according to 6. Therefore, when predicting the blending ratio of the shade limit sample by computer color matching, the prediction accuracy can be improved by considering the calculation error of the tristimulus value in the standard color sample.

In step S5 of FIG. 2, the measured values X0, Y0, Z0 of the tristimulus values of the standard color obtained in step S2.
Then, the differences ΔX, ΔY, ΔZ from the calculated values XM, YM, ZM obtained in step S4 are obtained according to the following formula 7.

[0033]

(Equation 7)

In step S6, the tristimulus values in computer color matching are corrected by correcting the tristimulus values XT, YT, ZT of the shade limit sample set in step S3 by the above differences ΔX, ΔY, ΔZ. Target value XC
, YC, ZC are calculated. That is, the target values XC, YC, ZC of the tristimulus values for the light and shade limit sample are given by the following formula 8.

[0035]

(Equation 8)

In step S7, the blending ratio of the shade limit sample is predicted by computer color matching.
In this computer color matching, the blending ratio is calculated so that the target values XC, YC and ZC given by the mathematical formula 8 can be obtained.

FIG. 3 is a flow chart showing the detailed procedure of computer color matching in step S7. The procedure shown in FIG. 3 applies computer color matching using the Newton-Raphson method.

In step S11, the change of the tristimulus value when the mixing ratio Ci of each colorant (pigment) is slightly changed is calculated by the following procedure. First, from the blending ratio Ci of the standard color sample used in step S2 of FIG. 2, only the blending ratio of one colorant is changed by .DELTA.Ci to calculate the tristimulus values XM ', YM', ZM of the mixture. Ask for. This is the equation 1
6 is performed in the same procedure as step S2.
Then, the difference ΔXCi, ΔYCi, Δ from the calculated values XM, YM, ZM of the standard color tristimulus values obtained in step S2.
ZCi is calculated according to the following equation 9.

[0039]

[Equation 9]

Using Equation 9, the blending ratio Ci of each colorant is
The rate of change of the tristimulus values when only a slight change is given is given by the following mathematical formula 10.

[0041]

[Equation 10]

Since the shade limit color indicates a manufacturing error of the standard color, the tristimulus values of both are close to each other.
Therefore, using the rate of change of Equation 10, the target value XC of the tristimulus value of the gray scale limit sample obtained in step S6 of FIG.
The relationship between YC and ZC and the calculated tristimulus values XM, YM and ZM of the standard color sample obtained in step S4 can be expressed by the following formula 11.

[0043]

[Equation 11]

In the equation 11, it is assumed that there are four kinds of colorants. The amount of change in the blending ratio of each colorant △
A constant value is substituted for the total value ΔPCV of Ci. For example, when the sum ΣCi of the mixing ratios Ci of the four kinds of colorants is kept constant, ΔPCV is 0.

Equation 11 shows four unknowns ΔCi (i = 1
.. to 4), it is possible to obtain the value of each unknown .DELTA.Ci by solving this (step S12). In step S13, step S
Using the value .DELTA.Ci obtained in step 12, the compounding ratio CiT of each colorant of the density limit sample is calculated according to the following mathematical expression 12.

[0046]

(Equation 12)

In step S14, the calculated values X1, Y1, Z1 of the tristimulus values are obtained from the mixing ratio CiT obtained in step S13 according to the above-mentioned formulas 1-6. Step S
In 15, the tristimulus values X1, Y1, Z1 thus obtained are
And the target value XC of the tristimulus values obtained in step S6 of FIG.
, YC, ZC, it is determined whether or not the color difference ΔE is less than or equal to a predetermined allowable error δ. It should be noted that the color difference ΔE is given by the following Expression 13 using the Lab color system.

[0048]

(Equation 13)

The color difference ΔE may be defined by using the following expression 14 instead of the expression 13.

[0050]

[Equation 14]

When the color difference ΔE is smaller than the allowable error δ in step S15, the value of the mixing ratio CiT obtained in step S13 is adopted as the predicted value, and the computer color matching is completed. On the other hand, if the color difference ΔE is greater than or equal to the allowable error δ, then in step S16 the calculated values X1, Y1, Z1 of the tristimulus values obtained in step S14.
Is substituted into XM, YM, ZM, and steps S12-S
The process of 15 is repeated. Thus, steps S12 to S1
By repeating step 6, it is possible to obtain the mixing ratio CiT such that the value of the color difference ΔE becomes smaller than the allowable error δ.

FIG. 4 is a table showing the tristimulus values of the standard color sample and the tristimulus values of the shade limit sample used in the embodiment of the present invention. Samples T1, T2 and T3 are standard color samples having different colors. FIG. 4 shows the tristimulus values X0, Y0, Z0 actually measured in step S2 and the tristimulus values XM, YM, ZM calculated in step S4 for each standard color sample. Further, the set values XT, YT, ZT of the tristimulus values of the light and shade limit sample set in step S3 are also shown. The target values XC, YC, and ZC of the tristimulus values of the light and shade limit sample in the computer color matching are calculated by using the above-mentioned equation 7
And 8 are calculated.

FIG. 5 shows the prediction result of the tristimulus values of the light and shade limit sample in the example, the prediction result of the comparative example, and the actual mixing ratio. The compounding ratio of the comparative example is a predicted value obtained when the set values XT, YT, ZT of the tristimulus values of the light and shade limit sample are directly used as the target values for computer color matching. The mixing ratios in the examples are predicted values obtained by using the target values XC, YC, ZC corrected by the calculation error of the standard color sample. In this example, in order to verify the prediction accuracy, a density limit sample was actually manufactured using the mixing ratio shown on the right end of FIG. 5, and the actual measurement values of the tristimulus values were set as shown in FIG. The values are used as XT, YT and ZT.

As can be seen from FIG. 5, the embodiment was able to predict the blending ratio with higher accuracy than the comparative example. Further, although the three pigments of the samples T1 to T3 have considerably different components of the four pigments, it can be understood that the prediction accuracy of the example is higher than that of the comparative example in all the cases.

As described above, in the above-mentioned embodiment, the calculation error of the tristimulus value is obtained for the standard color sample having the tristimulus value close to the shade limit sample, and this is used to calculate the target value of the tristimulus value of the shade limit sample. Is being corrected. As a result, it is possible to improve the prediction accuracy when predicting the blending ratio of the density limit sample.

The present invention is not limited to the above-described embodiments, but can be carried out in various modes without departing from the scope of the invention, and the following modifications can be made.

(1) In the above embodiment, the standard color sample is used as a sample (proximity color sample) having a tristimulus value close to the shade limit sample, and the shade limit is calculated by using the tristimulus value calculation error for the standard color sample. The target value of the tristimulus value of the sample was corrected. However, it is also possible to select a proximity color sample other than the standard color sample and use the calculation error for the proximity color sample. For example, a database that collects samples having various colors may be used to select a sample having a color close to the light and shade limit sample as the adjacent color sample. This database contains the compounding ratio Ci of each colorant and the measured value of tristimulus value (or reflectance R
It is preferable that at least (λ) is included. In the case of searching for a close color sample using a database, the color difference ΔE given by the formula similar to the above-mentioned Formula 13 or Formula 14 is closest to the target mixture (shade limit sample). It is preferable to use a color sample.

By using such a database, not only when predicting the mixing ratio of the light and shade limit sample by computer color matching, but also when predicting the mixing ratio of the target mixture having an arbitrary tristimulus value, There is an advantage that the prediction accuracy can be improved.

(2) Although the XYZ color system is used in the above embodiment, any color system other than the XYZ color system can be used as the color system. For example, it is possible to use the L * a * b * color system or the like.

[0060]

As described above, according to the first aspect of the present invention.
According to the invention described in (1), since the computer color matching is performed after correcting the target value of the coordinate of the color system by the calculation error, the blending ratio of the mixture having a desired color can be accurately predicted.

Further, in the invention described in claim 2, since the sample having the smallest color difference is searched as the adjacent color sample from the database, the prediction error of the computer color matching is calculated with respect to the target mixture having an arbitrary color. It can be reduced.

[Brief description of drawings]

FIG. 1 is an xy chromaticity diagram showing a variation in color between a designed color (standard color) and an actually manufactured pottery.

FIG. 2 is a flowchart showing the overall procedure of processing according to the embodiment.

FIG. 3 is a flowchart showing a detailed procedure of computer color matching in step S7.

FIG. 4 is a table showing the tristimulus values of the standard color sample and the tristimulus values of the density limit sample used in the examples of the present invention.

FIG. 5 is a table showing prediction results of tristimulus values of the light and shade limit sample according to the example, a comparative example, and an actual mixing ratio.

[Explanation of symbols]

 Ci ... Mixing ratio of colorant Ki ... Absorption coefficient of colorant Si ... Scattering coefficient of colorant X0, Y0, Z0 ... Measured value of tristimulus value of standard color sample XM, YM, ZM ... Tristimulus value of standard color sample Calculated values of ΔX, △ Y, ΔZ ... Calculation error of tristimulus value of standard color sample XT, YT, ZT ... Set value of tristimulus value of shade limit sample XC, YC, ZC ... Tristimulus of shade limit sample Target value

Claims (2)

[Claims] 1. A method of predicting a blending ratio of a colorant of a target mixture having a desired color by computer color matching, comprising: (a) having a known blending ratio of the colorant and having a color close to the desired color. A step of obtaining an actual measurement value of a coordinate of a predetermined color system for the close color sample; and (b) a calculated value of the coordinate of the color system representing the color of the close color sample from a known blending ratio of the close color sample. And a step of obtaining a calculation error from the measured value and the calculated value,
(C) setting a target value of the coordinates of the color system with respect to the color of the target mixture; and (d) correcting the target value using the calculation error, and using the corrected target value to generate a computer color. Predicting the blending ratio of the colorant in the target mixture by executing matching, the computer color matching method. 2. The computer color matching method according to claim 1, wherein the step (a) includes a database including a blending ratio of a colorant and an actual measurement value of coordinates of the color system for a plurality of samples. From the step of searching for the adjacent color sample by selecting a sample having a minimum color difference from the target mixture.