JPH05236268A - Method and device for deciding color masking equation - Google Patents

Abstract

PURPOSE:To obtain the color masking equation with practically sufficient accuracy by predicting a color difference of reproduced colors in a uniform color space, selecting an explanation variable so as to obtain the color difference less than an object value and substituting the variable into a multiple regression model equation. CONSTITUTION:A three-primary color main density arithmetic operation means 53 obtains approximated three primary color main density values c', m', y' calculated from a multiple regression equation based on reproduced color density values Dr, Dg, Db actually measured from a sample by an actual measurement means 50. Then a reproduction color prediction means 54 predicts the density of the reproduced color based on the three primary color main density values c, m, y given actually, the result is converted into three stimulus values and converted into coordinates on uniform color space, and a color difference arithmetic operation means 57 obtains a color difference. Then, a color difference comparison means 58 compares the color difference with an object color difference and one of explanation variables in an explanation variable storage means 52 is selected so that the color difference is less than the object color difference and the variable is substituted into a multiple regression model equation. The equation with high accuracy is obtained by deciding the model equation as a conversion equation to obtain the main density of the three primary colors.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to density values (Dr, D) desired to be reproduced in multicolor printing and color printers.
g, Db), a method and apparatus for determining a color masking formula for determining the main densities of the three primary colors for reproducing the color.

[0002]

2. Description of the Related Art Conventionally, a density value (Dr,
Dg, Db) is given, the relationship with the main densities (c, m, y) representing the amounts of the three primary colors for reproducing this color, that is, cyan, magenta, and yellow, is the block type without sub-absorption. Considering the ideal ink of, c = Dr (1) m = Dg (2) y = Db (3) However, there is no ideal block-type ink that has no side absorption.

Considering an existing ink with side absorption, the density measured through the red filter of cyan ink is Drc (main density of cyan ink) and the density measured through the green filter of cyan ink is Dgc (second density of cyan ink). Absorption density) Density measured through cyan ink blue filter Dbc (cyan ink secondary absorption density) Magenta ink red absorption measured density Drm (magenta ink secondary absorption density) Magenta ink green filter measured The measured density is Dgm (main density of magenta ink), the density measured through the blue filter of magenta ink is Dbm (the secondary absorption density of magenta ink), and the density measured through the red filter of yellow ink is Dry (the secondary absorption of yellow ink). Density) Yellow ink When the density measured through the green filter is Dgy (sub-absorption density of yellow ink) and the density measured through the blue filter of yellow ink is Dby (main density of yellow ink), the main density c of cyan ink and the main density of magenta ink The relationship between the reproduction color densities (Dr, Dg, Db) reproduced with the ink having the density m and the main density y of the yellow ink is:

[0004]

[Equation 1] And solving the above determinant for the main concentrations c, m, and y

[Equation 2] Can be expressed as However, ai, j (i = 0 to 2, j = 0 to 2)
Is a coefficient.

Once the density values (Dr, Dg, Db) desired to be reproduced are determined, the main density (c, m, y) representing the amount of each ink can be obtained by the equation (5). Equation (5) is called linear masking. However, it is known that the additive rule and the proportional rule do not hold in printing such as color reproduction on a reflection support, a color printer, and the like, and there is a problem in practical use.

In order to correct the error due to the additive law failure and the proportional law failure, Dr, Dg, D are added to the equations (5).
It is known that a higher order term obtained by combining b is added. For example, the formula for obtaining the main density c of cyan ink is as follows: c = a _1,0 + a _1,1 Dr + a _1,2 Dg + a _1,3 Db + a _1,4 Dr ² + a _1,5 Dg ² + a _{1,6 ^{db 2 + a 1,7 DrDg + a}} 1,8 DrDb + a 1,9 DgDb + a 1,10 Dr 3 + a 1,11 Dg 3 + a 1,12 db 3 + a 1,13 Dr 2 Dg + a 1,14 Dr 2 db + a 1,15 ^{_{Dg 2 Dr + a 1,16 Dg 2}} Db + a 1,17 Db 2 Dr + a 1,18 Db 2 Dg + a 1,19 DrDgDb However, ai, j (j = 0 ~1 9) is a coefficient.

The main density m of magenta ink and the main density y of yellow ink can be similarly expressed. Each coefficient ai, j
Can be determined by printing a large number of color patches whose main densities are known in advance, measuring the reproduced color density values, and using the least squares method from their relationship.

The terms Dr, Dg, Db, D used in the above equation
The accuracy is apparently improved as r ² , Dg ² , Db ² ... Are increased as a function of reproduced color density.
However, there is a problem that the calculation load increases. In addition, these high-order terms are the reproduction color density values Dr and D.
It is created from g and Db, and there is a possibility that a term having a high mutual correlation and a small contribution to the equation is included. It is known that the accuracy of the equation decreases when these terms with small contributions exist. In addition, in practice, the calculation is also performed for the terms that do not contribute to the equation, which leads to an increase in calculation amount and a decrease in calculation efficiency.

As a solution to these problems, a method of performing regression tests, which is a method of multivariate analysis, evaluating the magnitude of the influence of each term on the formula and selecting the one having a certain or more influence is considered. Be done. However, there is a problem in that it is very difficult to set the threshold value because the threshold value set for that purpose is not directly connected to the effect on the appearance of the actual color.

[0010]

SUMMARY OF THE INVENTION The present invention has been made in order to solve the above-mentioned problems of the prior art, and has three objectives.
Three primary colors that give the reproduced color densities (Dr, Dg, Db) by obtaining the main densities (c, m, y) of the primary colors with sufficient accuracy for practical use, and minimizing the number of terms used in the masking equation. When obtaining the main concentration (c, m, y) of
An object of the present invention is to provide a method and apparatus for determining a color masking formula that has sufficient accuracy in practical use and has a small calculation load.

[0011]

In order to achieve the above object, the first color masking method determining method according to the present invention is applied when density values (Dr, Dg, Db) are given as reproduced colors. In a method for determining a color masking formula for obtaining the main densities (c, m, y) of the three primary colors for reproducing the color in color printing or the like, (1)
Density values (Dr, D) of each color such as color patch printed matter obtained from various combinations in which the main densities of the three primary colors are known in advance.
g, Db) is measured by a densitometer, and (2) a multiple regression model equation is set with the main densities (c, m, y) of the three primary colors as the objective variables, and (3) for that multiple regression model equation. A plurality of explanatory variable candidate groups are set based on the density values (Dr, Dg, Db) representing the reproduced color, and (4) one explanatory variable is selected from the above explanatory variable candidate group, and the above basic By adding to the multiple regression model formula, the coefficient for the explanatory variable of the multiple regression model formula is obtained while changing the multiple regression model formula,
(5) The main densities (c ′, m ′, y ′) of the predicted three primary colors for reproducing the actually measured density value are obtained by using the above multiple regression model formula for which the coefficient is obtained, and (6) Predict the density values of the colors reproduced from the predicted main densities (c ', m', y ') and the actually given main densities (c, m, y) of the three primary colors, and (7) predict them. The measured concentration value is the tristimulus value (CIE
1931XYZ), and further predicts the color difference in the uniform color space, and (8) multiple regression is performed by sequentially selecting the explanatory variables from the above explanatory variable candidate group so that the average of the color differences is equal to or less than the target color difference. (9) The multiple regression model formula thus created is incorporated into the model formula, and the reproduced color density values (Dr, Dg, D
It is characterized in that it is determined as a color masking formula for obtaining the main densities (c, m, y) of the three primary colors from b).

The first color masking type determining apparatus according to the present invention reproduces a color when a density value (Dr, Dg, Db) is given as a color to be reproduced, as shown in FIG. A color masking formula determining device for determining a color masking formula for obtaining the main densities (c, m, y) of the three primary colors for (1)
(m, y) means 50 for actually measuring density values (Dr, Dg, Db) of reproduced colors corresponding to print samples in which various combinations of m, y) are combined.
Means 60 for storing data from the above, and (2) multiple regression model storage means 51 for readably storing a basic multiple regression model equation in which main densities of the three primary colors are used as objective variables.
And (3) an explanatory variable storage means 52 for readably storing a plurality of explanatory variable candidate groups for the multiple regression model equation set based on the reproduced color density, and (4) an explanatory variable candidate. Select one explanatory variable from the group, change the multiple regression model formula, perform multiple regression analysis from the measured main concentration and concentration value, find the coefficient of the multiple regression model formula, and use the multiple regression model formula A three-primary-color main-density calculating means 53 for obtaining an approximate value (c ', m', y ') of the three-primary-color main densities with respect to the actually measured density value of each sample, and (5) the actually given three-color primary density. Reproduction color predicting means 54 for predicting the density value of the reproduced color from (c, m, y) and the approximate values (c ', m', y ') of the main densities of the three primary colors, and (6 )
Means 55 for converting the predicted concentration value into a tristimulus value
(7) coordinate conversion means 56 for converting the tristimulus values into uniform color space coordinates, (8) color difference calculation means 57 for calculating a color difference in the uniform color space, and (9) color difference calculation means. Color difference comparing means 58 for comparing the color difference with the target color difference
And (10) when the color difference comparing unit determines that the color difference obtained by the color difference calculating unit is less than or equal to the target color difference, the multiple regression model formula stored in the multiple regression model storage unit at that time is reproduced. The density value (D
When r, Dg, Db) is given, it is characterized by having means 59 for determining as a conversion formula for obtaining the main densities of the three primary colors for reproducing the color.

In the second color masking method determining method according to the present invention, the density value (Dr, D
g, Db), given color printing,
Main density of the three primary colors (c, m, y) to reproduce the color
In the method for determining the color masking formula for obtaining, (1) the color patch printed matter obtained from various combinations in which the main densities of the three primary colors are known in advance is measured with a densitometer, and (2) the three primary colors Set the basic multiple regression model formula with the main concentration (c, m, y) as the objective variable,
(3) A plurality of explanatory variable candidates for the multiple regression model formula are set based on the density values (Dr, Dg, Db) representing the reproduced color, and (4) the basic multiple regression model formula and the above. A multiple regression model formula is set by using both of all explanatory variable candidate groups, and (5) one explanatory variable is selected from each of the above explanatory variable candidate groups and removed from the multiple regression model formula. While changing the multiple regression model formula by, obtain the coefficient for the explanatory variable of the multiple regression model formula, (6)
The main densities (c ', m', y ') of the predicted three primary colors for reproducing the actually measured density values are obtained by using the multiple regression model formula, and (7) the main densities of the predicted three primary colors, The density values of the colors to be reproduced are predicted from the actually given main densities (c, m, y) of the three primary colors, and (8) those density values are converted into tristimulus values, and further on a uniform color space. Predict the color difference at (9)
In order to prevent the average of the color differences from exceeding the target color difference, an explanatory variable is selected in order from the above-mentioned explanatory variable candidate group and removed from the multiple regression model formula, and the reproduced color density value (Dr,
It is characterized in that a color masking formula for determining the main densities (c, m, y) of the three primary colors is determined from Dg, Db).

Further, the second color masking type determining apparatus according to the present invention reproduces a color when a density value (Dr, Dg, Db) is given as a color to be reproduced, as shown in FIG. A color masking formula determining device for determining a color masking formula for determining the main densities (c, m, y) of the three primary colors for (1)
m, y) means 15 for actually measuring density values (Dr, Dg, Db) of reproduced colors corresponding to print samples in which various combinations of m, y) are combined.
0, and (2) means 170 for storing the data,
(3) Basic multiple regression model storage means 151 for readably storing basic multiple regression model formulas in which the main densities of the three primary colors are objective variables, and (4) Explanatory variable candidate group for multiple regression model formulas. The explanatory variable storage unit 152 readablely stores a plurality of explanatory variable candidate groups set based on the reproduced color density, and (5) both the basic multiple regression model formula and the explanatory variable candidate group. A multiple regression model formula storage unit 153 that readablely stores the multiple regression model formula set by using, and (6) one explanatory variable is selected from the above explanatory variable candidate group, and is selected from the multiple regression model formula. Delete and change the multiple regression model formula, perform multiple regression analysis from the measured main concentration and concentration value to obtain the coefficient of the multiple regression model formula, and use the multiple regression model formula for the measured concentration value of each sample. Approximation of the main concentration of the three primary colors (c ',
m ', y') to obtain three primary color main density calculating means 154,
(7) Main density of the three primary colors actually given (c, m, y)
And the approximate values (c ', m', y ') of the main densities of the three primary colors obtained as described above, a reproduction color prediction unit 155 that predicts a color to be reproduced, and (8) the predicted density value To a tristimulus value, and (9) coordinate conversion means 157 that transforms the tristimulus value into uniform color space coordinates.
(10) Color difference calculation means 158 for obtaining the color difference in the uniform color space, (11) Color difference comparison means 159 for comparing the color difference obtained by the color difference calculation means with the target color difference, (1)
2) When it is determined by the color difference comparing means that the color difference obtained by the color difference calculating means is equal to or larger than the target color difference,
At that time, the multiple regression model formula previously stored in the multiple regression model formula storage means is used as the color to be reproduced, and the density value (D
r, Dg, Db), a means 160 for determining as a conversion equation for obtaining the main densities of the three primary colors for reproducing the color.

[0015]

In the present invention, the uniform color space considering the visual characteristics for the appearance of human color is used for the evaluation of the color masking method. Therefore, it is possible to perform evaluation according to the actual appearance of human color, and it is possible to provide a color masking formula with sufficient accuracy for practical use. Further, as the explanatory variables used in the multiple regression model formula, only the explanatory variables necessary for the prediction accuracy are selected from the candidate group of explanatory variables. Therefore, useless explanatory variables are not incorporated in the model formula, the formula is simplified, and an efficient color masking formula is obtained.

[0016]

1 shows an embodiment of a color masking type determining apparatus according to the present invention. In the figure, a CPU (central processing unit) is provided via an input interface 1.
A densitometer 3 is connected to 2.

The densitometer 3 reads the color patch 5 in which the main densities c, m, and y of the cyan, magenta, and yellow primary colors are known in advance, and the combinations of the primary densities (c, m, y) of the primary colors are obtained. Density values (D
The measured information composed of r, Dg, Db) is output to the CPU 2. The CPU 2 stores the input measured information in the memory 6
Memorize inside. The CPU 2 executes the multiple regression model formula determination process described later to determine the color masking formula. The result is output interface 7 if necessary.
Is output to the display device 8 via.

Hereinafter, the process of determining the multiple regression model formula executed by the CPU 2, that is, when density values (Dr, Dg, Db) are given as the colors to be reproduced, the main three primary colors for reproducing the colors are given. First of the multiple regression model formula determination process for obtaining the combination of concentrations (c, m, y)
The method will be described. The first method is a case where the conceptual process shown in FIG. 2 is specifically implemented.

First, in FIG. 1, a large number of color patches whose main densities c, m and y of cyan, magenta and yellow are known in advance are prepared by printing. For example, 11 stages of each color, a total of 1331 colors, or an appropriate sample uniformly distributed in the uniform color space is printed and prepared. Then, the prepared color patch is read by a densitometer, and a combination of the main densities c, m, and y of the three primary colors and the reproduced density values Dr, Dg, Db are read.
The data group of is stored in the memory 6.

Further, a variable group which is a candidate group of explanatory variables for the multiple regression model formula is stored in the memory 6. In the present embodiment, the reproduction color density value (D
r, Dg, Db) squared term, cubic term, and cross term, ie, Dr ² , Dg ² , Db ² , Dr ³ , Dg
³ , Db ³ , DrDg, DrDb, DgDb, Dr ² D
g, Dr ² Db, Dg ² Dr, Dg ² Db, Db ² D
16 variables of r, Db ² Dg and DrDgDb are assumed.

An allowable color difference of reproduced color, for example, color difference 1 is set and stored in the memory 6 at a predetermined address.

Further, as a basic multiple regression model formula, c = a _1,0 + a _1,1 Dr + a _1,2 Dg + a _1,3 Db (6) m = a _2,0 + a _2,1 Dr + a _2,2 Dg + a _2,3 Db (7) y = a _3,0 + a _3,1 Dr + a _3,2 Dg + a _3,3 Db (8) is set and stored in a predetermined storage location of the memory 6.

3 to 5 show the flow of control executed by the CPU 2.

The CPU 2 first reads the basic multiple regression model equations (6) to (8) (step 100), and uses the data D1 obtained from the color patch to sum the squared error of the main densities of the primary colors. Multiple regression analysis is performed to minimize (step 101). By this multiple regression analysis, regression coefficients a _{i , j} (i = 1, 2, 3; j = 0 to 3) are obtained (step 102). This coefficient is used as the multiple regression model formula (6)
Substituted in (8) and actually sampled data group D1
The main densities (c ', m', y ') of the predicted three primary colors with respect to the three density values of Dr, Dg, and Db are calculated (step 10).
3). Then, the predicted main density (c ′,
m ', y') and the main concentration actually given (c, m,
y) Predict the reproduction color density (step 1)
04). Then, this reproduced color density value is set to the tristimulus value (CIE
1931XYZ) (step 105), and the tristimulus values are converted into coordinates on the uniform color space (step 10).
6) The color difference is obtained (step 109). Alternatively, the reproduced color density value corresponding to the actually given main density is read from the measured data D1, the density value is converted into tristimulus values (step 107), and further converted into coordinates on the uniform color space (step). 108), and may be used as it is for the evaluation of the color difference (step 109). As a uniform color space, CIE
There are LAB, CIE LUV, etc., but any one may be used.

Reproduction prediction values Dr ', Dg', Db 'and measured values Dr, Dg, for all sample data.
The color difference from Db is obtained, and their average value, that is, the average color difference dE is obtained (step 109). It should be noted that not only the average color difference but other statistics such as the maximum color difference may be used. If the multiple regression model formula that is being calculated is the basic model formula (“Y” in step 110), the basic model formula and the average color difference
dE is stored in the memory (step 114), the average color difference dE is compared with the target color difference already stored in the memory, and if smaller (“N” in step 116), this basic multiple regression model formula is optimized. It is determined to be a model formula (step 117).

If the average color difference dE is larger than the target color difference in step 116 ("Y"), the process proceeds to step 118, and the multiple regression model equation that is being calculated is the full model equation, that is, all the explanatory variable candidates are taken in. Checks if it is a multiple regression model expression of the type. Since I am thinking about the basic model formulas (6) to (8) and not the full model formula, I proceed to step 120 and increase the explanatory variables by one variable in the whole model formula with respect to the basic model formula. Forgive that. The variable to be increased at this time is 1 from the explanatory variable group D2.
One (step 121). Assuming that Dr ² is an explanatory variable increasing, the newly created multiple regression model formula (step 123) is c = a _1,0 + a _1,1 Dr + a _1,2 Dg + a _1,3 Db + a _1,4 Dr ² m = a _2,0 + a _2,1 Dr + a _2,2 Dg + a _2,3 Db y = a _3,0 + a _3,1 Dr + a _3,2 Dg + a _3,3 Db.

After that, the procedure returns to step 101, and the regression coefficients a _{i , j} with respect to the model formula are obtained in the same manner as above (step 102), the color difference between the reproduction predicted density value and the measured density value is calculated, and the average value is calculated. The color difference dE is obtained (step 109).

In the present flow, since the multiple regression model formulas to be calculated are not the basic model formulas (6) to 8),
In step 110, the result is “N”, and the flow is step 1
Head to 11. In step 111, if the average color difference dE calculated as described above is smaller than the average color difference obtained previously (“Y”), the minimum average color difference obtained up to now and the model formula at that time are stored in a predetermined manner. Store in place (step 112).

When the above evaluation is completed, step 113
Then, the process proceeds to step 123 via, and the following new multiple regression model formula is set.

C = a _1,0 + a _1,1 Dr + a _1,2 Dg + a _1,3 Db m = a _2,0 + a _2,1 Dr + a _2,2 Dg + a _2,3 Db + a _2,4 Dr ² y = a _{3 , 0} + a _3,1 Dr + a _3,2 Dg + a _3,3 Db Then, the model formula is evaluated by the same procedure.

When the evaluation is completed, the model formula is changed as follows: c = a _1,0 + a _1,1 Dr + a _1,2 Dg + a _1,3 Db m = a _2,0 + a _2,1 Dr + a _{2 , 2} Dg + a _2,3 Dby = a _3,0 + a _3,1 Dr + a _3,2 Dg + a _3,3 Db + a _3,4 Dr ² Then, the model formula is evaluated by the same procedure.

Similarly, for each of the variables in the explanatory variable candidate group D2, a model formula containing one variable is tried, and the average color difference is evaluated. As a result, the model formula that minimizes the average color difference when the explanatory variable is increased by 1 and the average color difference dE are obtained (step 112).
Now, assuming that the multiple regression model formula at that time is c = a _1,0 + a _1,1 Dr + a _1,2 Dg + a _1,3 Db m = a _2,0 + a _2,1 Dr + a _2,2 Dg + a _2,3 Db When _{y = a 3,0 + a 3,1 Dr} + a 3,2 Dg + a 3,3 Db + a 3,4 Dg 2, which is determined as a new multiple regression model equation (step 124).

After that, in step 116, the average color difference dE obtained as described above is compared with the target color difference, and if smaller ("N" in step 116), this multiple regression model formula is determined as the optimum model formula. Then, the flow ends (step 117).

If the average color difference dE is larger than the target color difference ("Y") in step 116, the process proceeds to step 120,
Further, it is possible to increase the explanatory variable by one variable in the whole model formula. That is, the model formula in which one explanatory variable is added to the new basic multiple regression model formula is evaluated. At this time, one variable to be increased is selected from the explanatory variable candidate group D2, but if the explanatory variable is already included in the model formula in the previous stage, calculation is not performed (“122” in step 122). Y "). For example, as a newly added explanatory variable, Dg ²
In consideration of, the expressions of c and m are evaluated by adding the explanatory variables, but the expression of y does not perform the calculation because Dg ² is already included.

Hereinafter, the model variables are evaluated by sequentially increasing the explanatory variables by one until the target color difference becomes smaller than the target color difference. If the target color difference is not obtained even after all the explanatory variables are used up (“Y” in step 113, “Y” in step 115, and “Y” in step 116), it is determined to be “Y” in step 118 and the trial is performed. The model expression giving the minimum color difference among the above models and its average color difference dE are set as the optimum model expression (step 117).

As described above, it is possible to obtain the color masking formula which gives the reproduced color at the target reproduced color difference or less and has the smallest calculation load.

The first technique for determining the color masking formula has been described above. From this onwards, the first
A second method different from the above method will be described. This second
The method of is a case where the conceptual process shown in FIG. 6 is specifically implemented.

The second method is shown as a flow chart in FIGS. 7 to 9. The CPU 2 (FIG. 1) first reads the basic multiple regression model formulas (6) to (8) (step 200), then reads all the explanatory variable candidate groups (step 201), and uses them to execute the next Multiple regression model formulas (9) to (11) are set (step 202).

C = a _1,0 + a _1,1 Dr + a _1,2 Dg + a _1,3 Db + a _1,4 Dr ² + a _1,5 Dg ² + a _1,6 Db ² + a _1,7 DrDg + a _1,8 DrDb + a _{1 ^{, 9 DgDb + a 1,10 Dr 3}} + a 1,11 Dg 3 + a 1,12 Db 3 + a 1,13 Dr 2 Dg + a 1,14 Dr 2 Db + a 1,15 Dg 2 Dr + a 1,16 Dg 2 Db + a 1, ^{_{17 Db 2 Dr + a 1,18 Db}} 2 Dg + a 1,19 DrDgDb (9) m = a 2,0 + a 2,1 Dr + a 2,2 Dg + a 2,3 Db + a 2,4 Dr 2 + a 2,5 Dg 2 + a ^{_{2,6 Db 2 + a 2,7 DrDg +}} a 2,8 DrDb + a 2,9 DgDb + a 2,10 Dr 3 + a 2,11 Dg 3 + a 2,12 Db 3 + a 2,13 Dr 2 Dg + a 2,14 Dr 2 Db + a ^{_{2,15 Dg 2 Dr + a 2,16 Dg}} 2 Db + a 2,17 Db 2 Dr + a 2,18 Db 2 Dg + a 2,19 DrDgDb (10) y = a 3,0 + a 3,1 Dr + a 3,2 Dg _{+ A 3,3 Db + a 3,4 Dr} 2 + a 3,5 Dg 2 + a 3,6 Db 2 + a 3,7 DrDg + a 3,8 DrDb + a 3,9 DgDb + a 3,10 Dr 3 + a 3,11 Dg 3 + a 3 ^{_{, 12 Db 3 + a 3,13 Dr}} 2 Dg + a 3,14 Dr 2 Db + a 3,15 Dg 2 Dr + a 3,16 Dg 2 Db + a 3,17 Db 2 Dr + a 3,18 Db 2 Dg + a 3,19 DrDgDb (11 However, ai, j (i = 1,2,3, j = 0 to 19) is a coefficient.

Then, using the data D1 obtained from the color patch, a multiple regression analysis for minimizing the sum of squares of the errors of the main densities of the primary colors is performed (step 203). The regression coefficient ai, j (i = 1,2,3, j = 0 to 19) is obtained by this multiple regression analysis (step 204). Substituting these coefficients into the multiple regression model equations (9) to (11), the main densities (c ′, m ′, y) of the predicted three primary colors with respect to the density values of Dr, Dg, Db of the actually sampled data group D1 are obtained. ') Is obtained (step 205). Then, the predicted main density (c ', m', y ') of each color and the reproduced color density generated by the actually given main density (c, m, y) are predicted (step 206). Then, this reproduced color density value is converted into a tristimulus value (CIE1931XYZ) (step 20).
7) The tristimulus values are converted into coordinates on the uniform color space (step 208), and the color difference is obtained (step 211).

Alternatively, the reproduced color density value corresponding to the actually given main density is read from the measured data D1, and the density value is converted into tristimulus values (step 209) and converted into coordinates on the uniform color space. (Step 210), it may be used for the evaluation of the color difference as it is (Step 211).

As uniform color spaces, CIELAB, CI
Although there is ELUV or the like, either one may be used.

Next, the reproduction predicted values Dr ', Dg', Db 'and the measured values Dr, Dg, D for all the sample data.
The color difference from b is obtained, and their average value, that is, the average color difference dE is obtained (step 211). Note that other statistics such as the maximum color difference may be used instead of the average color difference. If the multiple regression model expression currently being calculated is a full model expression including all explanatory variable candidates (“Y” in step 212), the full model expression and the average color difference dE are stored in the memory (step 2
16) The average color difference dE is compared with the target color difference already stored in the memory, and if it is larger (“Y” in step 218), this multiple regression model formula is determined as the optimum model formula (step 219). ..

If the average color difference dE is smaller than the target color difference ("N") in step 218, the process proceeds to step 226.
The current multiple regression model formula is determined as a new model formula and the formula and the average color difference are stored (step 227). Then, the routine proceeds to step 220, where it is checked whether or not the multiple regression model formula that is being calculated is a basic model formula. Since I am thinking about the full model equations (9) to (11) and not the basic model equation, I proceed to step 222 and delete one explanatory variable from the whole model equation for the full model equation. Forgive that. At this time, one variable to be deleted is selected from the explanatory variable candidate group D2 (step 22).
3). Assuming that Dr ² is an explanatory variable to be deleted, the newly created multiple regression model equation (step 225) is c = a _1,0 + a _1,1 Dr + a _1,2 Dg + a _1,3 Db + a _{1, 5} Dg ² + a _1,6 Db ² + a _1,7 DrDg + a _1,8 DrDb + a _1,9 DgDb + a _1,10 Dr ³ + a _1,11 Dg ³ + a _1,12 Db ³ + a _1,13 Dr ² Dg + a _{1,14 ^{Dr 2 Db + a 1,15 Dg 2}} Dr + a 1,16 Dg 2 Db + a 1,17 Db 2 Dr + a 1,18 Db 2 Dg + a 1,19 DrDgDb m = a 2,0 + a 2,1 Dr + a 2,2 Dg + a 2 ^{_{, 3 Db + a 2,4 Dr 2}} + a 2,5 Dg 2 + a 2,6 Db 2 + a 2,7 DrDg + a 2,8 DrDb + a 2,9 DgDb + a 2,10 Dr 3 + a 2,11 Dg 3 + a 2,12 _{^{db 3 + a 2,13 Dr 2 Dg}} + a 2,14 Dr 2 db + a 2,15 Dg 2 Dr + a 2,16 Dg 2 db + a 2,17 db 2 Dr + a 2,18 db 2 Dg _{a 2,19 DrDgDb y = a 3,0 +} a 3,1 Dr + a 3,2 Dg + a 3,3 Db + a 3,4 Dr 2 + a 3,5 Dg 2 + a 3,6 Db 2 + a 3,7 DrDg + a 3,8 _{DrDb + a 3,9 DgDb + a 3,10} Dr 3 + a 3,11 Dg 3 + a 3,12 Db 3 + a 3,13 Dr 2 Dg + a 3,14 Dr 2 Db + a 3,15 Dg 2 Dr + a 3,16 Dg 2 Db + a the _{^{3,17 Db 2 Dr + a 3,18 Db}} 2 Dg + a 3,19 DrDgDb.

After that, the procedure returns to step 203, and the regression coefficient ai, j for the model formula is calculated in the same manner as above (step 204), the color difference between the reproduced predicted density value and the measured density value is calculated, and the average color difference is further calculated. Find dE (Step 2
11).

In this flow, the multiple regression model formulas to be calculated are not the full model formulas (9) to (11), so that the result at step 212 is "N" and the flow goes to step 213. In step 213, it is determined whether the average color difference dE calculated as described above is the value first obtained when the explanatory variable is decreased by one. What is being considered now is the average color difference first obtained by reducing the explanatory variable by one, so it is determined as "Y" here, and the average color difference and the model formula at that time are stored in a predetermined storage location (step 214). If it is not the first time, it is compared with the minimum average color difference dE obtained so far with the same number of explanatory variables (step 230), and if smaller, the model formula and color difference are stored with "Y" (step 214).

When the above evaluation is completed, step 215
In step 225, the following new multiple regression model formula is set. c = a _1,0 + a _1,1 Dr + a _1,2 Dg + a _1,3 Db + a _1,4 Dr ² + a _1,5 Dg ² + a _1,6 Db ² + a _1,7 DrDg + a _1,8 DrDb + a _1,9 DgDb ^{_{+ a 1,10 Dr 3 + a 1,11}} Dg 3 + a 1,12 Db 3 + a 1,13 Dr 2 Dg + a 1,14 Dr 2 Db + a 1,15 Dg 2 Dr + a 1,16 Dg 2 Db + a 1,17 Db 2 ^{_{Dr + a 1,18 Db 2 Dg +}} a 1,19 DrDgDb m = a 2,0 + a 2,1 Dr + a 2,2 Dg + a 2,3 Db + a 2,5 Dg 2 + a 2,6 Db 2 + a 2,7 DrDg + a 2 _{, 8 DrDb + a 2,9 DgDb +} a 2,10 Dr 3 + a 2,11 Dg 3 + a 2,12 Db 3 + a 2,13 Dr 2 Dg + a 2,14 Dr 2 Db + a 2,15 Dg 2 Dr + a 2,16 Dg 2 ^{_{db + a 2,17 db 2 Dr +}} a 2,18 db 2 Dg + a 2,19 DrDgDb y = a 3,0 + a 3,1 Dr + a 3,2 Dg + a 3,3 db + a 3,4 Dr 2 + a 3,5 Dg 2 + ^{_{a 3,6 Db 2 + a 3,7 DrDg}} + a 3,8 DrDb + a 3,9 DgDb + a 3,10 Dr 3 + a 3,11 Dg 3 + a 3,12 Db 3 + a 3,13 Dr 2 Dg + a 3,14 Dr 2 Db ^{_{+ a 3,15 Dg 2 Dr + a}} 3,16 Dg 2 Db + a 3,17 Db 2 Dr + a 3,18 Db 2 Dg + a 3,19 DrDgDb Then, the evaluation of the model equation to the same procedure is performed.

When the evaluation is completed, the model formula is changed as follows. c = a _1,0 + a _1,1 Dr + a _1,2 Dg + a _1,3 Db + a _1,4 Dr ² + a _1,5 Dg ² + a _1,6 Db ² + a _1,7 DrDg + a _1,8 DrDb + a _1,9 DgDb ^{_{+ a 1,10 Dr 3 + a 1,11}} Dg 3 + a 1,12 Db 3 + a 1,13 Dr 2 Dg + a 1,14 Dr 2 Db + a 1,15 Dg 2 Dr + a 1,16 Dg 2 Db + a 1,17 Db 2 ^{_{Dr + a 1,18 Db 2 Dg +}} a 1,19 DrDgDb m = a 2,0 + a 2,1 Dr + a 2,2 Dg + a 2,3 Db + a 2,4 Dr 2 + a 2,5 Dg 2 + a 2,6 Db 2 + a _{2,7 DrDg + a 2,8 DrDb + a} 2,9 DgDb + a 2,10 Dr 3 + a 2,11 Dg 3 + a 2,12 Db 3 + a 2,13 Dr 2 Dg + a 2,14 Dr 2 Db + a 2,15 Dg 2 Dr + a ^{_{2,16 Dg 2 Db + a 2,17 Db}} 2 Dr + a 2,18 Db 2 Dg + a 2,19 DrDgDb y = a 3,0 + a 3,1 Dr + a 3,2 Dg + a 3,3 Db + a 3,5 Dg 2 + ^{_{a 3,6 Db 2 + a 3,7 DrDg}} + a 3,8 DrDb + a 3,9 DgDb + a 3,10 Dr 3 + a 3,11 Dg 3 + a 3,12 Db 3 + a 3,13 Dr 2 Dg + a 3,14 Dr 2 Db ^{_{+ a 3,15 Dg 2 Dr + a}} 3,16 Dg 2 Db + a 3,17 Db 2 Dr + a 3,18 Db 2 Dg + a 3,19 DrDgDb Then, the evaluation of the model equation to the same procedure is performed.

Similarly, the model formulas in which the variables are removed one by one for all the variables in the explanatory variable candidate group D2 are tried, and the average color difference is evaluated. As a result, a model formula that minimizes the average color difference when one explanatory variable is deleted and the average color difference dE are obtained (step 21).
4). Suppose, the multiple regression model equation of _{time, c = a 1,0 + a 1,1} Dr + a 1,2 Dg + a 1,3 Db + a 1,4 Dr 2 + a 1,5 Dg 2 + a 1,6 Db 2 + a _{1,7 DrDg + a 1,8 DrDb + a} 1,9 DgDb + a 1,10 Dr 3 + a 1,11 Dg 3 + a 1,12 Db 3 + a 1,13 Dr 2 Dg + a 1,14 Dr 2 Db + a 1,15 Dg 2 Dr + a ^{_{1,16 Dg 2 Db + a 1,17 Db}} 2 Dr + a 1,18 Db 2 Dg + a 1,19 DrDgDb m = a 2,0 + a 2,1 Dr + a 2,2 Dg + a 2,3 Db + a 2,4 Dr 2 + a ^{_{2,5 Dg 2 + a 2,6 Db 2}} + a 2,7 DrDg + a 2,8 DrDb + a 2,9 DgDb + a 2,10 Dr 3 + a 2,11 Dg 3 + a 2,12 Db 3 + a 2,13 Dr 2 Dg + a 2 ^{_{, 14 Dr 2 Db + a 2,15}} Dg 2 Dr + a 2,16 Dg 2 Db + a 2,17 Db 2 Dr + a 2,18 Db 2 Dg + a 2,19 DrDgDb y = a 3,0 + a 3,1 Dr + _{3,2 Dg + a 3,3 Db + a} 3,4 Dr 2 + a 3,6 Db 2 + a 3,7 DrDg + a 3,8 DrDb + a 3,9 DgDb + a 3,10 Dr 3 + a 3,11 Dg 3 + a 3,12 Db ³ + a _{3, 13} and ^{_{Dr 2 Dg + a 3,14 Dr 2}} Db + a 3,15 Dg 2 Dr + a 3,16 Dg 2 Db + a 3,17 Db 2 Dr + a 3,18 Db 2 Dg + a 3,19 DrDgDb.

Then, in step 218, the average color difference dE obtained as described above is compared with the target color difference, and if larger ("Y" in step 218), it is determined previously, that is, stored in step 227. The determined multiple regression model formula is determined as the optimum model formula and the flow is ended (step 219).

If the average color difference dE is smaller than the target color difference ("N") in step 218, this is determined as a new multiple regression model equation (step 226) and stored (step 227).

After that, the routine proceeds to step 222, and one explanatory variable is allowed to be deleted in the whole model formula. That is, the model formula in which one explanatory variable is removed from the new multiple regression model formula is evaluated. At this time, one variable to be deleted is selected from the explanatory variable candidate group D2, but if the explanatory variable is not already included in the model formula in the previous stage, calculation is not performed (step 224). "Y"). For example, as an explanatory variable to be newly removed, Dg
^When considering ² , the expressions of c and m are evaluated with the explanatory variables deleted, but in the expression of y, Dg ²
Since is not included, calculation is not performed.

Hereinafter, the model variables are evaluated by deleting the explanatory variables one by one until the color difference becomes larger than the target color difference. Even if all explanatory variables are removed, if the difference is less than the target color difference (“Y” in step 215, “Y” in step 217,
Then, “N” in step 218 is determined to be “Y” in step 220, and the basic model formula is set as the optimum model formula (step 219).

As described above, it is possible to obtain the color masking formula which gives the reproduced color at the target reproduced color difference or less and has the smallest calculation load.

The present invention has been described above with reference to the preferred embodiments, but the present invention is not limited to the embodiments and various modifications can be made without departing from the spirit of the present invention.

[0056]

According to the present invention, the uniform color space is used for the evaluation of the color masking method in consideration of the visual characteristics for the appearance of human color. Therefore, it is possible to perform evaluation according to the actual appearance of human color, and it is possible to provide a color masking formula with sufficient accuracy for practical use.

As the explanatory variables used in the multiple regression model equation, only the explanatory variables required for the prediction accuracy are selected from the candidate group of explanatory variables. Therefore, useless explanatory variables are not incorporated in the model formula, the formula is simplified, and an efficient color masking formula is obtained.

[0058]

[Brief description of drawings]

FIG. 1 is an electrical block diagram showing an embodiment of a color masking type determination device according to the present invention.

FIG. 2 is a functional block diagram of a first embodiment of a color masking type determination device according to the present invention.

3 is a flowchart showing a part of a control flow corresponding to the block diagram of FIG. 2 executed by the central processing unit (CPU) shown in FIG.

FIG. 4 is a flowchart following the flowchart shown in FIG.

FIG. 5 is a flowchart following the flowchart shown in FIG.

FIG. 6 is a functional block diagram of a second embodiment of a color masking type determination device according to the present invention.

7 is a flowchart showing a part of a control flow corresponding to the block diagram of FIG.

FIG. 8 is a flowchart following the flowchart shown in FIG. 7.

9 is a flowchart following the flowchart shown in FIG.

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Toru Mitsuhashi 1-5-1 Taito, Taito-ku, Tokyo, Toppan Printing Co., Ltd. (72) Yuichi Kobayashi 1-5-1 Taito, Taito-ku, Tokyo Toppan Imprint Co., Ltd.

Claims (4)

[Claims] 1. A density value (Dr, D) as a color to be reproduced.
g, Db) is given, in the method for determining the color masking formula for obtaining the main densities (c, m, y) of the three primary colors for reproducing the color, the main densities (c, m, density values (Dr, D) of reproduced colors corresponding to samples obtained by combining various m, y)
g, Db) is measured, a basic multiple regression model formula in which the main densities of the three primary colors are used as objective variables is set, and a plurality of candidate explanatory variables created based on the reproduced density values are set. Select one explanatory variable from the candidate group of explanatory variables, change the multiple regression model formula, perform multiple regression analysis from the main concentration and the actually measured concentration value, obtain the coefficient of the multiple regression model formula, and calculate its weight. 3 for the density value of the reproduced color actually measured for each sample by the regression model formula
The approximate values (c ', m', y ') of the main densities of the primary colors are obtained, and the color difference of the reproduced colors is calculated from the approximate values and the main densities (c, m, y) of the three primary colors. Predict in space and select the explanatory variable from the above explanatory variable candidate group and incorporate it into the multiple regression model formula so that the color difference is less than or equal to the target color difference. A color masking formula determining method, characterized in that, when a density value is given as a color to be reproduced, it is determined as a conversion formula for obtaining the main densities of the three primary colors for reproducing the color. 2. A density value (Dr, D) as a color to be reproduced.
g, Db), a color masking formula determining device for determining a color masking formula for obtaining the main densities (c, m, y) of the three primary colors for reproducing the color. Means for storing the density values (Dr, Dg, Db) of the reproduced color corresponding to the main densities (c, m, y) of the reproduced color, and the basic multiple regression model equation in which the main densities of the three primary colors are used as objective variables. A multiple regression model storage unit that stores the read variable, an explanatory variable storage unit that stores a plurality of explanatory variable candidate groups for the multiple regression model formula set based on the reproduction color density in a readable manner, and the explanatory variables. One explanatory variable is selected from the candidate group of, the multiple regression model formula is changed, multiple regression analysis is performed from the main concentration and the concentration value, the coefficient of the multiple regression model formula is obtained, and the multiple regression model formula is used. For each concentration value A three-primary-color main-density calculating means for obtaining an approximate value (c ′, m ′, y ′) of the three-primary-color main densities, the three-primary-color main-density (c, m, y), and the three-primary-color main-density A reproduction color predicting means for predicting a density value of a reproduced color from the approximate value (c ', m', y '); a means for converting the predicted density value into a tristimulus value; Coordinate conversion means for converting the stimulus value into the uniform color space coordinates, color difference calculation means for obtaining the color difference in the uniform color space, color difference comparison means for comparing the color difference obtained by the color difference calculation means with the target color difference, and color difference calculation The multiple regression model formula stored in the multiple regression model storage means when the color difference obtained by the means is equal to or less than the target color difference is determined by the color difference comparing means,
When a density value (Dr, Dg, Db) is given as a color to be reproduced, there is provided means for determining as a conversion formula for obtaining main densities of the three primary colors for reproducing the color. Masking type decision device. 3. A density value (Dr, D) as a color to be reproduced.
g, Db) is given, in the method for determining the color masking formula for obtaining the main densities (c, m, y) of the three primary colors for reproducing the color, the main densities (c, m, density values (Dr, D) of reproduced colors corresponding to samples obtained by combining various m, y)
g, Db), and set the basic multiple regression model formula that uses the main densities of the three primary colors as objective variables, and set a plurality of explanatory variable candidates created based on the reproduced density values. , A multiple regression model equation is set by using all of the above basic multiple regression model equation and the above explanatory variable candidate group, and one explanatory variable is selected from the candidate group of explanatory variables. The selected explanatory variable is deleted, the multiple regression model formula is changed, multiple regression analysis is performed from the measured main concentration and concentration value, and the coefficient of the multiple regression model formula is obtained. Approximate values (c ', m', y ') of the main densities of the three primary colors with respect to the measured density values of the reproduced colors are obtained, and from the approximate values and the main densities (c, m, y) of the three primary colors, Predict the color difference of the reproduced color in the uniform color space, and So that it does not exceed the target color difference, select an explanatory variable from the above explanatory variable candidate group and remove it from the multiple regression model equation.The multiple regression model equation with the explanatory variable removed is used as the color value to be reproduced. Is determined as a conversion formula for obtaining the main densities of the three primary colors for reproducing that color. 4. A density value (Dr, D) as a color to be reproduced.
g, Db), a color masking formula determining device for determining a color masking formula for obtaining the main densities (c, m, y) of the three primary colors for reproducing the color. Means for storing the density values (Dr, Dg, Db) of the reproduced color corresponding to the main densities (c, m, y) of the reproduced color, and the basic multiple regression model equation in which the main densities of the three primary colors are used as objective variables. A basic multiple regression model storage means for readable storage; an explanatory variable storage means for readable storage of a plurality of explanatory variable candidate groups for the multiple regression model formula set based on the reproduced color density; Multiple regression model storage means for readably storing the multiple regression model equation set using both the multiple regression model equation and the above explanatory variable candidate group, and one explanatory variable is selected from the above explanatory variable candidate group. do it The explanatory variable of is deleted from the multiple regression model formula, multiple regression analysis is performed from the measured main density and density value, the coefficient of the multiple regression model formula is obtained, and the main density of the three primary colors for each density value is calculated by the multiple regression model formula. Of three primary color main densities to obtain an approximate value (c ', m', y ') of the above, main density of the three primary colors (c, m, y), and an approximate value of the main densities of the three primary colors (c' , M ', y'), a reproduction color prediction means for predicting the density value of the reproduced color, a means for converting the predicted density value into a tristimulus value, and a uniform color for the tristimulus value. Coordinate conversion means for converting into space coordinates, color difference calculation means for obtaining a color difference on the uniform color space, color difference comparison means for comparing the color difference obtained by the color difference calculation means with a target color difference, and color difference calculation means. The color difference comparison means determines that the color difference is greater than or equal to the target color difference. At this time, the multiple regression model equation stored in the multiple regression model storage means before that time is used as the reproduced color and the density value (Dr, D
g, Db), and means for determining the main densities of the three primary colors for reproducing the color, as a conversion equation, and a color masking type determining apparatus.