JPH0894442A - Computerrized color matching method - Google Patents

Abstract

PURPOSE: To obtain a computerized color matching method in which an estimation error can be reduced without correcting the absorption and the scattering coefficient of every component by a method wherein a neural network in made to learn the relationship between the coordinate value of colorimetric systems regarding a plurality of samples and the estimation error. CONSTITUTION: A plurality of coloring agents are mixed, and a plurality of samples whose mixing rate is different from each other are prepared. The spectral reflectance of the samples is measured, and the actually measured value of the coordinate value of colorimetric systems expressing respective colors of the plurality of samples is found on the basis of the measured value of the spectral reflectance. A neural network in made to learn the relationship between the coordinate value of the colorimetric systems and an estimation error. By using the neural network which has been learnt, an estimation is performed by a computerized color matching operation. The neural network comprises a three-layer hierarchical structure which is constituted of an input layer 10, an intermediate layer 20 and an output layer 30. The input layer 10 is constituted of neurons N11 to N13 , the intermediate layer 20 is constituted of neurons N21 to N25 , and the output layer 30 is constituted of neurons N31 to N33 .

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of predicting a blending ratio of a colorant or a color of a mixture 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.

In general, there is an error in the prediction by computer color matching, and it is necessary to devise a method for reducing the prediction error. Conventionally, in order to reduce the prediction error, the absorption coefficient Ki and the reflection coefficient Si of each colorant are corrected so as to be close to accurate values.

[0008]

However, in order to bring the absorption coefficient Ki and the reflection coefficient Si of each component close to accurate values, a large number of mixture samples containing each colorant alone in the object to be colored are prepared. Then, the spectral reflectance must be measured, which requires a huge amount of work. Further, when a natural pigment is used as a colorant, the absorption coefficient Ki and the scattering coefficient Si do not always become constant values, so it is difficult to bring the absorption coefficient Ki and the scattering coefficient Si close to accurate values. It was

The present invention has been made to solve the above-mentioned problems in the prior art, and is a computer capable of reducing the prediction error without correcting the absorption coefficient Ki and the scattering coefficient Si of each component. The purpose is to provide a color matching method.

[0010]

In order to solve the above-mentioned problems, the computer color matching described in claim 1 of the present invention comprises: (a) mixing a plurality of coloring agents, and mixing ratios thereof are different from each other. A step of preparing a plurality of samples; and (b) measuring a spectral reflectance of each of the plurality of samples, and using a measured value of the spectral reflectance, a predetermined color system that represents each color of the plurality of samples. And (c) calculating a prediction error of the coordinate value of the color coordinate system for each of the plurality of samples, and (d) the color coordinate system for the plurality of samples. Analyzing the relationship between the coordinate values of the above and the prediction error by a predetermined error correction method, and (e) correcting the target value or prediction value of the computer color matching using the error correction method. One, characterized in that it comprises a step of performing color prediction for prediction or a mixture of the compounding ratio of the colorant in the new mixture by computer color matching, the.

A coordinate value of a predetermined color system and a prediction error for a plurality of samples are analyzed by a predetermined error correction method, and the prediction is performed while correcting the target value or predicted value of computer color matching by the error correction method. Since it is performed, the prediction error can be reduced without correcting the absorption coefficient Ki and the scattering coefficient Si of each component.

In the computer color matching method according to claim 2, the step (d) includes a step of causing a neural network to learn the relationship between the coordinate value of the color system and the prediction error for the plurality of samples. Including, the step (e) includes a step of performing prediction by computer color matching using a learned neural network.

If the prediction error is corrected by using a neural network, the prediction error can be reduced by learning many samples.

In the computer color matching method according to claim 3, the neural network is 3
It has a three-layer hierarchical structure including an input layer composed of one neuron, an intermediate layer composed of a plurality of neurons, and an output layer composed of three neurons.

[0015]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 is a flow chart showing the overall procedure of processing in an 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, learning of a neural network for correcting the prediction result (tristimulus value) of computer color matching is performed. Steps S2-S
In 5, the target value of the computer color matching is corrected by using the learned neural network to obtain the accurate prediction result. In the following, first, step S2
Before describing the contents of S5 to S5, the configuration of the neural network and the detailed procedure of step S1 will be described.

FIG. 2 is an explanatory diagram showing the structure of the neural network. This neural network has a three-layer hierarchical structure including an input layer 10, an intermediate layer 20, and an output layer 30. The input layer 10 is composed of three neurons N11 to N13, the intermediate layer 20 is composed of five neurons N21 to N25, and the output layer 30 is composed of three neurons N31 to N33.

Three neurons N11 to N13 of the input layer 10
Is input with tristimulus values X, Y, and Z, respectively. Neurons Nij of the input layer 10 to neurons N of the intermediate layer 20
The signal transmitted to k has a weight Wi of each input signal.
It is the product of j and k. Here, i is a number indicating the layer of interest, j is a number indicating the order of neurons in the layer of interest, and k is a number indicating the order of neurons in the next layer. For example, the signal transmitted from the first neuron N11 of the input layer 10 to the first neuron N21 of the intermediate layer 20 is W11, 1X, and the signal from the first neuron N11 of the input layer 10 to the second neuron of the intermediate layer 20 is The signals transmitted to the neuron N22 are W11, 2X.

Input uij of each neuron Nij of the intermediate layer 20
And the output Qij are given by the information transfer function f (uij) shown in the following Expression 3.

[0020]

[Equation 3]

Here, Q (i-1) j is the j-th neuron N (i-1) j of the (i-1) -th layer (that is, the input layer 10).
2 is output, and in the example of FIG. 2, Q11 = X, Q12 = Y, Q13
= Z. W (i-1) j, k is a weight applied to a signal transmitted from the j-th neuron N (i-1) j of the (i-1) th hierarchy to the focused neuron Nij. . t
Is a threshold value, and a constant value is assigned. The information transfer function f (uij) of Expression 3 is called a sigmoid function.

For example, when the equation 3 is applied to the input / output relation of the first neuron N21 of the intermediate layer 20, the following equation 4 is obtained.

[0023]

[Equation 4]

The input / output relationship of each neuron of the output layer 30 is also given by the above mathematical expression 3. In the embodiment shown in FIG. 2, outputs Q11 to Q13 of the three neurons N31 to N33 in the output layer 30.
Is the prediction error ΔX, ΔY, ΔZ of the tristimulus value by computer color matching (CCM).

The learning of the neural network is correct by giving many relations between the inputs (X, Y, Z) to the input layer 10 and the outputs (ΔX, ΔY, ΔZ) from the output layer 30. This is a work for determining the value of the weight Wij, k that gives the input / output relationship.

FIG. 3 is a flow chart showing the detailed procedure of step S1 of FIG. In step S11, in computer color matching, a plurality of tristimulus values (X
It, Yit, Zit) is determined, and the blending ratio of a plurality of samples having these plurality of tristimulus values is determined by computer color matching. FIG. 4 is a conceptual diagram showing a color prediction target range PA in computer color matching and a distribution of a plurality of tristimulus values covering the prediction target range PA. In this embodiment, colors are represented by the CIE-XYZ color system, and the color prediction target range PA is given as a three-dimensional range of the XYZ coordinate system. The prediction target range PA indicates the range of colors that the mixture to be predicted can take, and is a range that can be set arbitrarily.

In this embodiment, the prediction target range PA
7 sets of tristimulus values shown by white circles in FIG. In step S11, these 7
The compounding ratios of seven types of samples M1 to M7 having a set of tristimulus values (Xit, Yit, Zit) were predicted by computer color matching.

Here, the color prediction and the compounding ratio prediction by computer color matching will be briefly described.
By transforming Equation 2, the spectral reflectance R (λ) of the mixture is
It is given by the following Equation 5.

[0029]

[Equation 5]

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 Si of each component.
Since it can be calculated from (λ) and the blending ratio Ci according to Formula 1, the spectral reflectance R (λ) of the mixture can be obtained from Formula 5 above. 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
It is calculated according to the following Equation 6 (Sanderson's equation).

[0031]

[Equation 6]

Here, the coefficients k1 and k2 are values that depend on the optical properties of the object to be colored (base glaze). Coefficient k1,
k2 can be determined from the refractive index n of the object to be colored according to the following formula 7.

[0033]

[Equation 7]

The base glaze used in the examples is
The refractive index n is about 1.4.

When the spectral reflectance R '(λ) is obtained by the equation 6, tristimulus values X, Y, Z of the mixture are obtained by the following equation 8.

[0036]

[Equation 8]

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.

When predicting the color of the mixture by computer color matching, as described above, based on the absorption coefficient and the scattering coefficient of each component of the mixture, equations 1, 5 to 8 are used.
The tristimulus values X, Y, Z of the mixture are calculated according to Since the tristimulus value represents the color of the mixture, the color of any mixture can be predicted.

When predicting the blending ratio of a mixture having a desired color, assuming the blending ratio of the mixture, the tristimulus values thereof are calculated by the procedure described above, and successive approximations such as the Newton-Raphson method are performed. By the method, a blending ratio that matches a desired color within a predetermined error is obtained.

In step S12 of FIG. 3, step S1
A plurality of samples having the compounding ratio Ci predicted at 1 are prepared. In this example, seven sets of tristimulus values (X
7 samples M1 to M7 corresponding to it, Yit, Zit)
It was created. In step S13, the spectral reflectance of each sample Mi is measured by a spectrophotometer, and the tristimulus values (Xim, Yim, Zim) thereof are calculated according to the above-mentioned formula 8.

In step S14, for each sample Mi, the measured values (Xim, Yim,
Zim) and the target value (Xit, Yi determined in step S11)
t, Zit), the prediction error ΔMi
(Xim-Xit, Yim-Yit, Zim-Zit) is calculated. FIG. 5 shows seven samples M1 to M obtained in the examples.
It is a conceptual diagram which shows the prediction error of 7. Further, FIG. 6 is an explanatory diagram showing target values (values determined in step S11) of tristimulus values and prediction errors ΔMi (ΔX, ΔY, ΔZ) of each sample.

The predicted value (Xic, Yic, Zic) of the tristimulus value of each sample is obtained from the blending ratio Ci obtained in step S11 by computer color matching.
Measured values (Xim, Yim, Zim) and predicted values (Xic, Yic, Z)
ic) (Xim−Xic, Yim−Yic, Zim−Zic) may be defined as the prediction error ΔMi. When determining the mixture ratio Ci by computer color matching, the target values (Xit, Yit, Zit) of the tristimulus values and the predicted values (Xic, Yic, Z) are used.
ic), the blending ratio Ci is determined so that the difference is less than or equal to a predetermined allowable error. Therefore, the target value (Xit, Yit, Zit) and the predicted value (Xic, Yic, Zic) are substantially equal to each other. Have Therefore, the difference (Xim-Xic, Yim-Y) between the measured value (Xim, Yim, Zim) and the predicted value (Xic, Yic, Zic).
ic, Zim-Zic) is defined as the prediction error ΔMi, the difference (Xim-Xit, Yim-Yit, Zim-) between the measured value (Xim, Yim, Zim) and the target value (Xit, Yit, Zit) is also defined. Even if Zit) is defined as the prediction error ΔMi, it is substantially the same.

In step S15 of FIG. 3, target values (Xit, Yit, Zit) of tristimulus values of each sample Mi shown in FIG.
And the prediction error ΔMi are used to learn the neural network, and the weights Wij, k in the equation 3 are determined. As a learning method of the neural network, for example, an inverse error propagation learning method is used.

FIG. 7 is an explanatory diagram showing the verification results of learning of the neural network in the embodiment. Here, another one included in the prediction target range PA shown in FIGS.
Set a set of tristimulus values as a target value for computer color matching, and carry out an eighth sample M8 having this target value.
It was created. Then, the tristimulus values of this sample M8 were measured. In FIG. 7, "CCM target value" means the eighth
Means the target value used for the computer color matching of Sample M8. The "error (true value)" is the difference between the target value and the measured value of the tristimulus values. "Neuro prediction error" is a prediction error obtained when the CCM target value is input to the learned neural network (FIG. 2). From the result of FIG. 7, it is understood that the learned neural network can accurately predict the error of the tristimulus value.

When the learning of the neural network is completed in this way, steps S2 to S5 of FIG. 1 are executed to predict the mixing ratio of the color sample of which the mixing ratio is unknown. In step S2, the spectral reflectance of the color sample of which the blending ratio is unknown is measured, and its tristimulus values (Xs, Ys, Zs) are obtained. In step S3, the tristimulus values (Xs, Ys, Zs) of the color sample are input to the neural network shown in FIG. 2, and the prediction error Δ (Δ
Xs, ΔYs, ΔZs) is obtained. In step S4, the tristimulus values (Xs, Ys, Zs) are corrected with the prediction error Δ,
Target values (Xs-ΔXs, Ys-ΔYs, Zs) of tristimulus values used for predicting the compounding ratio of computer color matching
-ΔZs) is calculated. In step S5, computer color matching is executed using the target values thus corrected, and the mixing ratio of the color sample is predicted.

FIG. 8 is an explanatory diagram showing the results of an experiment conducted to verify the prediction accuracy of computer color matching in the embodiment. Here, since the purpose is to demonstrate the prediction accuracy, the tristimulus value is actually measured for the color sample whose mixing ratio is known, and the mixing ratio that realizes the measured value (Xs, Ys, Zs) is predicted by computer color matching. did. From the result of FIG. 7, it can be seen that the true value of the mixing ratio and the predicted value by computer color matching are extremely well matched.

By using the learned neural network shown in FIG. 2, it is possible to accurately predict the tristimulus value of a mixture having a known mixing ratio. That is, the tristimulus values are calculated from the compounding ratio Ci of the mixture to be predicted using the above formulas 1 to 5, and the tristimulus values are input to the neural network of FIG. 2 to calculate the prediction error Δ. Then, if the tristimulus value obtained by the equation 8 is corrected by the prediction error Δ, the tristimulus value extremely close to the actual value can be obtained.

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 target value of the tristimulus values in the computer color matching was input to the neural network, but the input of the neural network is the measured values (Xim, Yim) of the tristimulus values of each sample Mi. , Zim) may be used, or the predicted values (Xic, Yic, Zi by computer color matching).
c) may be used. That is, the neural network may be made to learn the relationship between the tristimulus values (the coordinate values of the XYZ color system) of a plurality of samples and the prediction error thereof.

(2) In the above embodiment, the neural network is used to correct the tristimulus values, but it is also possible to use other error correction methods such as regression analysis and neuro-fuzzy techniques.

(3) Although the XYZ color system is used in the above embodiment, the present invention can be applied to the case of using any other color system such as the L * a * b * color system.

(4) Computer color matching for matching the coordinate values of the XYZ color system and the L * a * b * color system is as follows.
It is generally called the metameric match method. On the other hand, there is also a method called an isometric match method for matching the curves of the spectral reflectance R (λ) of the mixture. The present invention can be applied not only to the metameric match method but also to computer color matching by the isometric match method.

(5) In the above embodiment, the computer color matching for the glaze of ceramics was explained, but the present invention is not limited to this, and can be applied to the computer color matching for other types of mixtures. Is possible.

[0054]

As described above, according to the computer color matching method of the present invention, the coordinate value of a predetermined color system and the prediction error of a plurality of samples are analyzed by a predetermined error correction method, Since the prediction is performed by correcting the target value or predicted value of the computer color matching by the error correction method, the prediction error can be reduced without correcting the absorption coefficient Ki and the scattering coefficient Si of each component.

If a prediction error is corrected using a neural network, it is possible to reduce the prediction error by learning many samples.

[Brief description of drawings]

FIG. 1 is a flowchart showing an overall procedure of processing according to an embodiment.

FIG. 2 is an explanatory diagram showing a configuration of a neural network.

FIG. 3 is a flowchart showing a detailed procedure of step S10.

FIG. 4 is a conceptual diagram showing a distribution of tristimulus values of a prediction target range PA and a plurality of samples M1 to M7 by computer color matching.

FIG. 5 is a conceptual diagram showing prediction errors of seven samples M1 to M7 in the example.

FIG. 6 is a target value of tristimulus values of each sample (step S1
1) and prediction error △ Mi (△ X, △ Y, △
Explanatory drawing which shows Z).

FIG. 7 is an explanatory diagram showing a verification result of learning of the neural network in the example.

FIG. 8 is an explanatory diagram showing a verification result of prediction of computer color matching in an example.

[Explanation of symbols]

 10 ... Input layer 20 ... Intermediate layer 30 ... Output layer M1-M7 ... Sample Nij ... Neuron PA ... Prediction target range Qij ... Neuron output uij ... Neuron input Wij, k ... Weights ΔX, ΔY, ΔZ ... Prediction error

Claims (3)

[Claims] 1. A method for predicting a blending ratio of a colorant or a color of a mixture by computer color matching, comprising: (a) mixing a plurality of colorants to prepare a plurality of samples having different blending ratios. And the process of
(B) A step of measuring the spectral reflectances of the plurality of samples, respectively, and obtaining an actual measurement value of coordinate values of a predetermined color system representing each color of the plurality of samples from the measured values of the spectral reflectances. And (c) calculating a prediction error of coordinate values of the color system for each of the plurality of samples, and (d) coordinating coordinate values of the color system and the prediction error of the plurality of samples. Analyzing the relationship by a predetermined error correction method, and (e) predicting the blending ratio of the colorant in the new mixture while correcting the target value or predicted value of computer color matching using the error correction method. And a step of performing color prediction of the mixture by computer color matching. 2. The computer color matching method according to claim 1, wherein in the step (d), a neural network learns a relationship between coordinate values of the color system and the prediction error regarding the plurality of samples. A computer color matching method, wherein the step (e) includes a step of performing prediction by computer color matching using a learned neural network. 3. The computer color matching method according to claim 2, wherein the neural network includes an input layer including three neurons, an intermediate layer including a plurality of neurons.
A computer color matching method having a three-layer hierarchical structure composed of an output layer composed of three neurons.