CN108280044B - Newcastle equation correction method based on halftone field - Google Patents
Newcastle equation correction method based on halftone field Download PDFInfo
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Abstract
The invention discloses a method for correcting a neugebauer equation based on a halftone field tristimulus value, which specifically comprises the following steps: obtaining basic color element tristimulus values, dot area rates and field tristimulus value related parameters by using the test sample sheet; constructing a Neugebauer equation set, matching different dot area rates by reversely solving the equation set, and establishing a halftone on-site tristimulus value parameter corresponding to the dot area rate; and carrying out variable analysis on the halftone field tristimulus value result, establishing a functional relation by taking the area rates of different tone dots as independent variables and taking the halftone field tristimulus value as dependent variables to obtain a correction model, and realizing correction of the Neugebauer equation through the correction model. The method is simple in calculation process and high in calculation accuracy, and finally improves equation precision.
Description
Technical Field
The invention belongs to the technical field of printed matter color separation, and particularly relates to a neugebauer equation correction method based on halftone field.
Background
With the rapid development of printing technology, the market of high-grade printed matters is continuously developed to meet the requirements of people, the reproduction precision of the printed matters gradually becomes the focus of attention of people, and accordingly, the significance and the value of the printing color separation technology are reflected. The Neugebauer equation plays an important role in printing reproduction as an important method in a printing color separation algorithm.
The neugebauer equation is a print color formulation equation established based on a print dot model and the grassmann color mixing law. The equation is shown in equation (1):
the above equation establishes the relationship between the original color and the color separation CMY dot area ratio, where XYZ is the tristimulus value of the original color, f is the color element area ratio, and c, m, and y are the dot area ratios of the cyan-magenta-yellow three-color plate, respectively.
In the era of digital plate making and digital printing, the neugebauer equation has more important practical value and becomes one of the most basic formulas for calculating the color of a printed matter. In color management software, neugebauer's equation is an important means to build a color profile for an output device. The neugebauer equation not only explains the color generation mechanism of the printed matter from the aspect of coloriology, but also gives a method for calculating the color value of the printed matter from the aspect of mathematics, and therefore, the neugebauer equation plays an important role in color printing and copying. The neugebauer equation has the advantages of clear principle and capability of solving by measuring a small amount of ink color samples.
However, in practical applications, it is found that a dot value directly calculated by the neugebauer equation has a large deviation from a dot value obtained by actual printing, and printing according to the directly calculated value causes a large color error of a printed product. Therefore, there have been many studies on correcting neugebauer's equation, and many correction methods have been proposed. However, some correction methods proposed so far cause low equation stability and comprehensive accuracy, such as linear regression neugebauer equation provided in "error analysis of 3 color separation algorithms based on partitioned neugebauer equation" causes low equation accuracy and stability, some cause complex calculation and difficult determination of correction coefficients, and for example, n index correction methods proposed in "theoretical analysis of neugebauer equation index correction method" and "theoretical value and limitation research of neugebauer equation" cause difficult determination of correction coefficients or poor generality. These correction methods still have difficulty in easily and rapidly correcting the neugebauer equation with higher accuracy.
Disclosure of Invention
The invention aims to provide a halftone-based neugebauer equation correction method, which optimizes a neugebauer equation, improves the precision of the neugebauer equation, and solves the problems of complexity in correction, low precision and the like of the existing neugebauer equation.
The technical scheme adopted by the invention is that a halftone field-based Neugebauer equation correction method is implemented according to the following steps:
step 1, test sample sheet design and output:
according to the standardized requirements of printing colors, the design and output of test samples are completed, and sample training test positions are selected from the test samples to obtain the relevant parameters of basic color element tristimulus values, dot area rates and field tristimulus values;
step 2, constructing a halftone field tristimulus value of a Neugebauer equation:
constructing a Neugebauer equation set, matching different dot area rates by reversely solving the equation set, and establishing a halftone on-site tristimulus value parameter corresponding to the dot area rate;
step 3, correcting the Neugebauer equation:
and (3) carrying out variable analysis on the result of the halftone field tristimulus values in the step (2), establishing a functional relation by taking the area rates of different tone dots as independent variables and the halftone field tristimulus values as dependent variables to obtain a correction model, and realizing the correction of the Neugebauer equation through the correction model.
The neugebauer equation correction method can be used for correcting the neugebauer equation of the three primary colors of the green product yellow and can also be used for correcting the neugebauer equation of the three superimposed colors of the red, the green and the blue.
When correcting the green and yellow tricolor neugebauer equation, the green and yellow tricolor half-tone field tristimulus value parameters corresponding to the area rate of the dots are established in the step 2, and a functional relation is established by taking the area rates of the dots with different gradations as independent variables and the field tristimulus values of the green and yellow tricolor half-tone as dependent variables in the step 3, so that the correction of the green and yellow tricolor neugebauer equation is completed.
The system of the three primary color neugebauer equations is shown in formula (2):
where XYZ is the tristimulus value of primary color standard sample, [ X ]w，Yw，Zw]Indicates the tri-stimulus value of white solid of paper, [ X ]i，Yi，Zi]Representing the ground-area tristimulus value of a certain primary color. f. ofiRepresenting the base color dot area ratio.
The three-primary-color halftone solid tristimulus value parameter relationship is shown as formula (3):
when the RGB triplet neugebauer equation is corrected, the RGB triplet halftone real-time tristimulus value parameters corresponding to the dot area rates are established in the step 2, and a functional relation is established by taking the dot area rates with different gradations as independent variables and the RGB triplet halftone real-time tristimulus values as dependent variables in the step 3, so that the RGB triplet neugebauer equation is corrected.
The system of equations of RGB triplet neugebauer is shown in formula (4):
in the formula [ Xi，Yi，Zi]，[Xj，Yj，Zj]Halftone solid tristimulus value, [ X ], representing two primary colors to be superimposedij，Yij，Zij]A field tristimulus value representing a red green blue superimposed color,firepresenting the area ratio of the primary color dots, fijThe cross-color dot area ratio is expressed.
The solid tristimulus value parameter relation of the red, green and blue superimposed color halftone is shown as a formula (5):
the present invention is also characterized in that,
in step 1, the specific method for obtaining the basic color element tristimulus values by selecting the sample training test positions in the test sample sheet comprises the following steps: in the range of the dot area rate of 5% -100%, selecting a sample training test position by taking the dot area rate difference of 5% -15% as a step length, and acquiring related parameters of a basic color element tristimulus value, the dot area rate and a field tristimulus value by using a spectrodensitometer.
In step 3, the analysis among variables is specifically as follows: and (3) performing variable analysis on the halftone on-site tristimulus value result by adopting curve fitting in a function approximation method and utilizing the least square principle.
The method has the advantages that on the basis of research and experiment on a printing process, the correction method based on the halftone field tristimulus values is provided, the calculation process is simplified, high calculation accuracy is obtained, the practical value is high, great guiding significance is achieved for actual production, unknown colors can be accurately predicted, and a small color target is realized to replace a large color target in printing color separation.
Drawings
FIG. 1 is a schematic flow chart of a specific process for correcting the Neugebauer equation of the present invention;
FIG. 2 is a schematic diagram of the halftone solid area at different dot area ratios in the present invention;
FIG. 3 is a standard test coupon for the design output of the present invention;
FIG. 4 is a sample training test position selected for use in the test swatch in accordance with the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
The neugebauer equation correction method based on the halftone field tristimulus values can be used for correcting the green product yellow tricolor neugebauer equation and can also be used for correcting the red green blue triplet neugebauer equation, and is shown in figure 1.
The correction of the equation of the three primary colors of the Huangpinqing is specifically implemented according to the following steps:
step 1, testing design and output of a sample:
and (4) printing out qualified standard documents according to the requirements of G7 printing color standardization. The method comprises the steps of obtaining a test sample sheet through design output, selecting a sample training test position in the test sample sheet by taking a dot area rate difference value of 5% -15% as a step length in the range of 5% -100%, and measuring and obtaining relevant parameters of each basic color element tristimulus value, a dot area rate and a field tristimulus value of the sample training test position by using an X-RITE 528 spectrodensitometer under the conditions of a D50 light source, a 2-degree field of view, a D50 light source, a 10-degree field of view, a D65 light source, a 2-degree field of view, a D65 light source and a 10-degree field of view.
Step 2, constructing a halftone field tristimulus value of a Huangpinqing tricolor Newcastle equation:
firstly, constructing a three-primary color Neugebauer equation system, wherein the primary color Neugebauer equation system is shown as a formula (2). In the neugebauer equation set, the solid tristimulus value is the corresponding tristimulus value when the dot area is 100%. However, in actual calculation, the solid areas corresponding to different tones are not the same as the 100% large solid area, and therefore the solid tristimulus values of different tones are not the solid tristimulus values at a halftone dot area of 100%. For example, the solid area corresponding to the halftone dot at 50% is smaller than the solid area corresponding to the halftone dot at 100%, and therefore the solid area corresponding to the halftone dot at 50% is the solid area corresponding to the solid area, and the tristimulus value at this time is also the solid tristimulus value of the halftone dot of the area, that is, the solid tristimulus value of halftone dot, as shown in fig. 2.
Then, combining the tristimulus values XYZ sample set and the dot area rate sample set to obtain the solid tristimulus values of the base color halftone, and obtaining the parameter relationship of the solid tristimulus values of the base color halftone, as shown in formula (3).
Step 3, correcting the equation of the three primary colors of the Huangpinqing:
the method comprises the steps of adopting curve fitting in a function approximation method, utilizing a least square principle to carry out variable analysis on a basic color halftone field tristimulus value result, specifically adopting a polyfit (x, y, n) function in MATLAB software, taking different gradation dot area rates as independent variables, taking a halftone field tristimulus value as a dependent variable, and establishing a functional relation between the dot area and the halftone field tristimulus value, namely completing the correction of a yellowness green tristimulus neugebauer equation.
The correction of the red, green and blue triplet color neugebauer equation is specifically implemented according to the following steps:
step 1, testing design and output of a sample:
and (4) printing out qualified standard documents according to the requirements of G7 printing color standardization. The method comprises the steps of obtaining a test sample sheet through design output, selecting a sample training test position in the test sample sheet by taking a dot area rate difference value of 5% -15% as a step length in the range of 5% -100%, and measuring and obtaining three-stimulus values of all basic color elements, dot area rates and field three-stimulus value related parameters of the sample training test position by using an X-RITE 528 spectrodensitometer under the conditions of a D50 light source, a 2-degree field of view, a D50 light source, a 10-degree field of view, a D65 light source, a 2-degree field of view and a D65 light source and a 10-degree field of view respectively.
Step 2, constructing a halftone field tristimulus value of a RGB triplet neugebauer equation:
first, a three-fold color neugebauer equation set is constructed, as shown in equation (4). And (3) reversely solving through a triplet color neugebauer equation set, matching different dot area rates, and combining the triplet color tristimulus value XYZ sample set and the dot area rate sample set to obtain the triplet color halftone field tristimulus values so as to obtain the triplet color halftone field tristimulus value parameter relation, as shown in a formula (5).
Step 3, correcting the red, green and blue triplet color neugebauer equation:
and (3) similarly, fitting the half-tone field tristimulus value result in the step (2) by using MATLAB, establishing a functional relation by using the area rates of different tone dots as independent variables and the field tristimulus values of the superimposed color half-tone as dependent variables to obtain a correction model, and finishing the correction of the RGB triplet neugebauer equation through the correction model.
And evaluating the established correction model in two dimensions of horizontal and vertical to illustrate the effectiveness of the correction method.
Longitudinal evaluation: the method is mainly used for verifying the technical feasibility of the correction method, namely verifying whether the correction method is feasible or not through the color difference result.
Transverse evaluation: after the correction method is verified to be feasible through longitudinal evaluation, whether the precision of the Neugebauer equation correction model established by the method is improved compared with that of the existing Neugebauer equation model or not is evaluated through a transverse evaluation method through a chromatic aberration result.
The evaluation is carried out from two dimensions of the transverse direction and the longitudinal direction, and the calculation is carried out by using a CIE1976L a b color difference formula, wherein the color difference formula is shown as a formula (4):
examples
Taking a product single color and a red superimposed color as an example, a correction process of a neugebauer equation based on a halftone solid tristimulus value is specifically described.
(1) According to the standard document required to be printed according to the G7 print color standardization, as shown in fig. 3, in the range of the dot area ratio of 5% to 100%, the sample training test position is selected from the test samples by using the dot area ratio difference as the step length shown in table 1, and the sample training test position is shown in fig. 4. And measuring basic color element tristimulus values XYZ, dot area rate and solid tristimulus values of the standard file at different dot areas by using an X-RITE 528 spectral densitometer under the conditions of a D50 light source and a 2-degree field of view.
(2) And (5) solving a product color neugebauer equation set in a reverse way, and matching the half-tone field tristimulus values corresponding to different dot areas. The solid tristimulus values of the halftone were obtained by combining the sample set of the tristimulus values XYZ of the magenta color with the sample set of the dot area ratio, and the results are shown in table 1:
TABLE 1 real-world tristimulus values for magenta-based halftone
The halftone solid tristimulus values of the primary color M at different sampling points are listed in table 1, and the results in the table show that the halftone solid tristimulus values change with the change of different tones, and when the dot area gradually approaches 100%, the halftone solid tristimulus values also approach 100% and finally are consistent.
(3) Describing discrete points of the halftone solid tristimulus values obtained in the step (2) by using a function approximation method, and then performing curve fitting. And (3) taking the area rates of the halftone dots with different tones as independent variables and taking the solid tristimulus values of the halftone as dependent variables, carrying out analysis among the variables, and finally establishing a relationship. And programming the function by using MATLAB software, calling a polyfit (x, y, n) function programming algorithm, and constructing the function. The constructed M-primary halftone solid tristimulus value algorithm is as follows:
in the above results, X, Y, Z represent solid tristimulus values of M primary color halftone, and X, Y, Z represent dot area ratios.
(4) Reversely solving and matching the half-tone field tristimulus value groups corresponding to different tones by utilizing a red double-tone neugebauer equation set, combining a red double-tone tristimulus value XYZ sample set and a dot area rate sample set, unlocking the half-tone field tristimulus value groups to obtain corresponding half-tone field tristimulus values, wherein the results of the red double-tone field tristimulus values are shown in a table 2:
TABLE 2 Red-fold-color halftone solid tristimulus values
Table 2 lists the halftone solid tristimulus values of the superimposed color R at different sampling points, and it can be seen from the table that the tristimulus values result in agreement with the monochrome results, the halftone solid tristimulus values change with the change of different gradations, and when the halftone dot area gradually approaches 100%, the halftone solid tristimulus values also approach 100% solid tristimulus values.
(5) The same method as (3) is used for function approximation, the dot area rate is used as an independent variable, the R-fold halftone solid area is used as a dependent variable, and an MATLAB programming algorithm is used for constructing the R-fold halftone solid area tristimulus value algorithm as follows:
in the above formula, X, Y, and Z represent solid tristimulus values of the red halftone, and X, Y, and Z represent dot area ratios.
(6) Verification of product-based color correction model
a. Longitudinal evaluation
Calculating the on-site tristimulus value of halftone by using a primary color correction model, substituting the result into the Neugebauer equation to calculate the tristimulus value result of the sample, and comparing the result with the measured tristimulus value to obtain the color difference delta E1The results are shown in table 3:
TABLE 3 evaluation of color difference distribution in primary color longitudinal direction
b. Transverse evaluation
Substituting 100% of the on-site tristimulus values into an uncorrected neugebauer equation to obtain a sample tristimulus value X1Y1Z1And X is1Y1Z1Determination of the colour difference Δ E from the tristimulus values measured2。
Calculating Delta E1And Delta E2The difference between the two is averaged, and the change of the difference between the two is analyzed, the result is shown in table 4:
TABLE 4 evaluation of color difference distribution in transverse direction of primary color
Tables 3 and 4 show the color difference distributions evaluated in the different dimensions of the M single color in the longitudinal and transverse directions.
From the results, it can be seen that the color difference is significantly reduced when running the calculation with the halftone solid model, wherein the color difference can be reduced by 1.8NBS at maximum, and the average color difference is 1.6 NBS. And along with the change of the area ratio of the dots, when the sampling point is gradually close to 100%, the chromatic aberration is close to 0, which shows that the accuracy of the equation is effectively improved by constructing the M-primary color correction model.
(7) Red overlay correction model verification
a. Longitudinal evaluation
The method comprises the steps of utilizing the color superposition correction model to calculate the on-site tristimulus value of the halftone, substituting the result into the Neugebauer equation to obtain the result of the tristimulus value of the sample, comparing the result with the measured tristimulus value to obtain the color difference delta E3The results are shown in table 5:
TABLE 5 longitudinal evaluation of color difference distribution for red overlay
b. Transverse evaluation
Substituting 100% of the on-site tristimulus values into an uncorrected neugebauer equation to obtain a sample tristimulus value X2Y2Z2And X is2Y2Z2Determination of the colour difference Δ E from the tristimulus values measured4。
Calculating Delta E3And Delta E4The difference between the two is averaged, and the change of the difference between the two is analyzedThe results are shown in Table 6:
TABLE 6 lateral evaluation of color difference distribution for red overlay
Tables 5 and 6 show the color difference distributions evaluated in the different dimensions of the longitudinal and transverse directions of the R-fold.
From the results, it can be seen that the color difference is significantly reduced when running the calculation with the halftone solid model, wherein the color difference can be reduced by 2.2NBS at maximum, and the average color difference is 1.0 NBS. And along with the change of the area rate of the dots, when the sampling point is gradually close to 100%, the chromatic aberration is close to 0, which shows that the accuracy of the equation is effectively improved by constructing the R superimposed color correction model.
The correction of the neugebauer equation based on the half-tone field tristimulus value is completed through the steps, and meanwhile, the feasibility and the effectiveness of the correction method are verified.
Claims (5)
1. A neugebauer equation correction method based on halftone solid area is characterized by comprising the following steps:
step 1, test sample sheet design and output:
according to the standardized requirements of printing colors, the design and output of a test sample are completed, and the test sample is used for selecting a sample training position to obtain the relevant parameters of basic color element tristimulus values, dot area ratios and field tristimulus values;
step 2, constructing a halftone field tristimulus value of a Neugebauer equation:
constructing a Neugebauer equation set, matching different dot area rates by reversely solving the equation set, and establishing a halftone on-site tristimulus value parameter corresponding to the dot area rate;
step 3, correcting the Neugebauer equation:
and (3) carrying out variable analysis on the result of the halftone field tristimulus values in the step (2), establishing a functional relation by taking the area rates of different tone dots as independent variables and the halftone field tristimulus values as dependent variables to obtain a correction model, and realizing the correction of the Neugebauer equation through the correction model.
2. The neugebauer equation correction method based on halftone field according to claim 1, wherein when the correction method is used for correcting a three-primary-color neugebauer equation, the three-primary-color halftone field tristimulus value parameters corresponding to the dot area rate are established in step 2, the functional relationship established in step 3 is established by taking the dot area rates of different tones as independent variables and the three-primary-color halftone field tristimulus values as dependent variables;
the system of equations for the three primary colors neugebauer is:
the parameters of the solid tristimulus values of the three-primary-color halftone are as follows:
3. the neugebauer equation correction method based on halftone solid area according to claim 1, wherein when the correction method is used for correcting a tri-fold color neugebauer equation, the tri-fold color halftone solid tristimulus value parameters corresponding to the dot area rate are established in step 2, and the functional relationship established in step 3 is established by taking the dot area rates of different gradations as independent variables and the tri-fold color halftone solid tristimulus values as dependent variables;
the equation set for the three fold color neugebauer is:
the three-color half-tone solid tristimulus value parameter relationship is as follows:
4. the neugebauer equation correction method based on halftone solid area according to claim 1, wherein the specific method for obtaining the basic color element tristimulus value by selecting the sample training position with the test sample in step 1 is as follows: in the range of the dot area rate of 5% -100%, selecting a sample training test position by taking the dot area rate difference of 5% -15% as a step length, and acquiring related parameters of a basic color element tristimulus value, the dot area rate and a field tristimulus value by using a spectrodensitometer.
5. The neugebauer equation correction method based on halftone solid areas, according to claim 1, wherein the inter-variable analysis in step 3 is specifically: and (3) performing variable analysis on the halftone on-site tristimulus value result by adopting curve fitting in a function approximation method and utilizing the least square principle.
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