Spectral characteristic prediction method and spectral characteristic prediction program

Abstract

To allow accurate prediction of spectral characteristics of a prediction target gradation value for a prediction target color when an intermediate gradation value with known spectral characteristics is present in the prediction target color by using information on the known spectral characteristics.SOLUTION: A spectral characteristic prediction method includes: determining a first relational expression representing the characteristics of sample colors (S110); and for each of the sample colors, determining a prediction value of the spectral characteristics of a gradation value with acquired characteristics for a prediction target color by using the first relational expression (S120). The method includes: determining a difference value between the predicted value and a measured value (S130); and selecting a sample color in which the smallest difference value is obtained as a reference color (S140). The method includes: determining a second relational expression representing the characteristics of the reference color (S150); and determining a prediction value of the spectral characteristics of a prediction target gradation value for the prediction target color by using the second relational expression (S160).SELECTED DRAWING: Figure 4

Description

[Technical field]

[0001] The present invention relates to a method for predicting the spectral characteristics (eg, spectral reflectance) that will be obtained by applying an ink to a substrate. [Background technology]

[0002] In recent years, digital printing devices have become more and more popular in the printing industry. However, in the field of labels and packaging, printing (offset printing, gravure printing, flexography, etc.) is still often performed using printing devices that use printing plates (hereinafter referred to as "conventional printing devices" or simply "printing devices"). However, there is an increasing demand for shorter delivery times for design and content production, and when using conventional printing devices, the problem is that when there is a change in design, etc., the cost of remaking printing plates and reverting the process is high. In this regard, digital printing devices do not use printing plates, so there is no need to replace or remake printing plates. In other words, by adopting digital printing devices, it is possible to print small lots at low cost, and it is also possible to meet the demand for shorter delivery times for design and content production at low cost.

[0003] In the field of labels and packaging, there is a tendency to use spot colors frequently to improve color expression. For this reason, in order to print on a digital printing device using print data generated for printing on a conventional printing device, it is necessary to predict the color obtained by overprinting spot color inks and reproduce the predicted color on the digital printing device. In the following, the predicted value that specifies the color obtained by overprinting multiple color inks (specifically, reflectance or tristimulus values ​​X, Y, and Z in the CIE1931XYZ color space) is referred to as the "overprint predicted value."

[0004] Non-Patent Document 1, which will be described later, discloses a relatively simple method (hereinafter referred to as the "Deshpande et al. method") for predicting the color (overprint predicted value) obtained by overprinting multiple ink colors, including spot colors. In the Deshpande et al. method, the overprint predicted value is expressed as in the following formulas (1) to (3) using tristimulus values ​​X, Y, and Z (see FIG. 19). X=j x ×(X b X f )+k x (1) Y=j y ×(Y b ×Y f )+k y (2) Z=j z ×(Z b xZ f )+k z (3) where X b ,Y b , and Z b are the tristimulus values ​​of the background color, and X f ,Y f , and Z f are the tristimulus values ​​of the foreground color, and j x ,j y , and j z is a scaling factor, and k x ,k y , and k z is a constant. In the following, j x ,j y ,j z ,k x ,k y , and k z These are collectively called the "overprint coefficients."

[0005] By the way, there are additive and subtractive color reproduction methods for color reproduction, and in printing, subtractive color reproduction is used. In this regard, if ideal subtractive color reproduction is used, for example, the stimulus value X of a color obtained by overprinting is "X b X f" (The same applies to the stimulus values ​​Y and Z). However, to obtain a more accurate value, correction is required that takes into account errors caused by the use of opaque ink, the reflection of light on the surface, and other factors. Therefore, in the method proposed by Deshpande et al., correction is performed using a linear equation, as shown in equations (1) to (3) above.

[0006] In the method of Deshpande et al., for example, a color chart as shown in FIG. 20 is used. This color chart is called a "CxF chart." In the example shown in FIG. 20, the CxF chart is composed of 22 patches. The 11 patches in the upper row are patches obtained by printing a target spot color ink on a base material such as paper with a dot percentage in increments of 10%. The 11 patches in the lower row are patches obtained by printing a target spot color ink on black (solid black) with a dot percentage in increments of 10%. In this way, the CxF chart includes multiple patches corresponding to multiple levels of ink density. The overprint predicted value is calculated using values ​​(colorimetric values) obtained by measuring the color of the patches of such a CxF chart.

[0007] Below, with reference to the flowchart shown in FIG. 21, the method of Deshpande et al. will be described in detail, taking as an example the calculation of an overprint prediction value when the background color is a spot color with a dot percentage of 40% (for convenience, referred to as "spot color 1") and the foreground color is another spot color with a dot percentage of 60% (for convenience, referred to as "spot color 2").

[0008] First, a CxF chart is printed using spot color 1 ink, and then a CxF chart is printed using spot color 2 ink (step S900).

[0009] Next, the overprint coefficient j of the above formulas (1) to (3) for spot color 2 is calculated using a CxF chart printed using the ink of spot color 2 (for convenience, referred to as the "spot color 2 chart"). x ,j y ,j z ,k x ,ky , and k z is calculated (step S910). For example, when the above formula (1) is taken into consideration, X b X f The practical maximum and minimum values ​​for Y are the values ​​obtained by applying the ink of special color 2 on a base material and on a black (solid black), respectively. b ×Y f and Z b xZ f Therefore, in order to calculate the overprint coefficient, in the coordinate system expressing the above formulas (1) to (3) (see FIG. 22: however, FIG. 22 shows only the coordinate system expressing the above formula (1)), the coordinates expressing the stimulus values ​​in a state in which the ink of spot color 2 with a dot percentage of 60% is applied on black are set as the first calibration point P91, and the coordinates expressing the stimulus values ​​in a state in which the ink of spot color 2 with a dot percentage of 60% is applied on the base material are set as the second calibration point P92.

[0010] For example, when focusing on X among the tristimulus values, for the first calibration point P91, the following values ​​are substituted into the above formula (1): b The value obtained by measuring the patch PA92 of the special color 2 chart (the stimulus value when the special color 2 ink with a dot percentage of 60% is applied to the substrate) is X f and the value obtained by measuring the patch PA91 of the spot color 2 chart (stimulus value of the state where the ink of spot color 2 with a dot percentage of 60% is applied on black) is substituted for X (see FIG. 20). For the second calibration point P92, the following values ​​are substituted into the above formula (1): The value obtained by measuring the patch PA94 of the spot color 2 chart (stimulus value of the substrate) is substituted for X. b The value obtained by measuring the patch PA92 of the special color 2 chart (the stimulus value when the special color 2 ink with a dot percentage of 60% is applied to the substrate) is X f and is substituted for X (see Figure 20).

[0011] The overprint coefficient j is calculated by solving the simultaneous equations of the equation for the first calibration point P91 and the equation for the second calibration point P92. x ,k x That is, the equation representing the straight line indicated by the symbol L91 in FIG. 22 is obtained. y ,j z ,k y , and k z is also calculated in the same manner.

[0012] In the CxF chart shown in Figure 20, patches are arranged in 10% increments, and an overprint coefficient corresponding to the dot percentage between two horizontally adjacent patches can be calculated based on the colorimetric values ​​obtained by linear interpolation.

[0013] Next, a CxF chart printed using the ink of the special color 1 (for convenience, referred to as the "special color 1 chart") is used to calculate the final overprint prediction value by subtracting X from the above formulas (1) to (3). b ,Y b , and Z b Specifically, the color of the patch PA95 (see FIG. 20) of the spot color 1 chart is measured, and the value of X b ,Y b , and Z b The value of is obtained.

[0014] Next, using the special color 2 chart, X in the above formulas (1) to (3) is used to calculate the final overprint prediction value. f ,Y f , and Z f Specifically, the value of X (the tristimulus value of the foreground color) is obtained by measuring the color of the patch PA92 (see FIG. 20) of the spot color 2 chart (step S930). f ,Y f , and Z f The value of is obtained.

[0015] Finally, the tristimulus values ​​X, Y, and Z are calculated as overprint predicted values ​​by substituting the values ​​obtained in steps S910 to S930 into the above formulas (1) to (3) (step S940). b " and "X obtained in step S930 f " is equivalent to calculating the value of X on the vertical axis when it is multiplied by ".

[0016] In the above process, the patches PA91, PA92, and PA93 of the special color 2 chart are measured, and the X, X f , and X b However, if a highly accurate overprint prediction value is not required, for simplicity, the first calibration point P91 can be considered to be located at the origin of the graph in FIG. 22. In this case, color measurement of the patches PA91 and PA93 of the special color 2 chart is unnecessary (X and X of the second calibration point P92). f (It is still necessary to measure the color of patch PA92 in order to obtain the value of (a)). In this case, it is possible to calculate the tristimulus values ​​X, Y, and Z as overprint predicted values ​​without printing the lower patch group including patches PA91 and PA93 of the CxF chart shown in Fig. 20. For the sake of convenience, this specification will refer to a CxF chart that has the upper patch group shown in Fig. 20 and does not have the lower patch group.

[0017] As described above, according to the method of Deshpande et al., color prediction is performed using a CxF chart such as that shown in FIG. 20. However, even when printing using spot colors is performed, such a CxF chart is usually not printed in advance. For this reason, it becomes necessary to print the same number of CxF charts as the number of spot colors and measure the color of each patch. This causes an increase in cost and man-hours.

[0018] Therefore, the applicant of the present application filed an application for an invention of a color prediction method for predicting the color of a patch to be included in a CxF chart (see JP 2020-159821 A). The outline of the color prediction process described in JP 2020-159821 A is as follows. First, a color close to the prediction target color is selected as a similar color from among multiple sample colors for which the spectral reflectances of multiple patches have been obtained. Next, for the similar color, a relational equation is obtained that expresses the relationship between the spectral reflectance of a solid patch (a patch with the maximum ink density) and the spectral reflectance of the color prediction target patch. Finally, the spectral reflectance of the solid patch for the prediction target color is applied to the relational equation to obtain a predicted value of the spectral reflectance of the color prediction target patch for the prediction target color. [Prior art documents] [Patent documents]

[0019] [Patent Document 1] JP 2020-159821 A [Non-patent literature]

[0020] [Non-Patent Document 1] K. Deshpande, P. Green, "Recommendations for predicting spot colour overprints", [online], [Retrieved June 7, 2018], Internet<URL: http: / / www.color.org / ICC_white_paper_43_Draft2kd.doc> Summary of the Invention [Problem to be solved by the invention]

[0021] According to the invention disclosed in JP 2020-159821 A, if the spectral reflectance of a solid patch for the prediction target color is obtained, the spectral reflectance of a halftone patch can be predicted. Therefore, it is possible to obtain a predicted value of the spectral reflectance of a halftone patch assuming that a CxF chart is printed without printing a CxF chart. However, in reality, the spectral reflectance of a halftone patch may be obtained by using color balls or the like. That is, for some halftone patches, colorimetric values ​​may be obtained without printing a CxF chart. At this time, for halftone patches for which colorimetric values ​​are obtained, there is an error between the actual measured value (colorimetric value) and the predicted value. For this reason, for example, when colorimetric values ​​corresponding to a patch with a halftone dot percentage of 50% are obtained, as shown in FIG. 23, a large inconsistency may occur between the color based on the actual measured value and the color based on the predicted value. In this regard, if a halftone patch with a known colorimetric value exists, it is considered that the prediction accuracy can be improved by using the information on the colorimetric value.

[0022] In addition, the method of Deshpande et al. is based on the premise that colorimetric values ​​corresponding to dot percentages in 10% increments are obtained, but in recent years, various operations have been carried out for the objects to be measured. For example, when only three colorimetric values ​​corresponding to three patches with dot percentages of 100%, 50%, and 0% are obtained for a certain color, the spectral reflectance of an arbitrary patch for another color may be predicted based on the information of the three colorimetric values ​​for the certain color. Therefore, it is preferable to be able to predict the spectral reflectance of an arbitrary gradation value for the color to be predicted.

[0023] In view of the above circumstances, an object of the present invention is to enable highly accurate prediction of the spectral characteristics of a target gradation value for a target color by utilizing information on the known spectral characteristics when intermediate gradation values ​​for which the spectral characteristics, such as the spectral reflectance, of the target color are known. [Means for solving the problem]

[0024] A first aspect of the present invention is a method for predicting spectral characteristics obtained by applying an ink to a substrate, the method comprising the steps of: The spectral characteristics of the maximum gradation value, the spectral characteristics of the minimum gradation value, and N pieces (N is an integer equal to or greater than 1) a prediction target color setting step of setting the color of the ink for which the spectral characteristics of the intermediate gradation value of The intermediate gradation value for which the spectral characteristics have been obtained for the prediction target color is defined as a characteristic-acquired gradation value, A color other than the prediction target color, the spectral characteristic of the maximum gradation value, the spectral characteristic of the minimum gradation value, and (N+1) or more a first relational expression calculation step of calculating a first relational expression that expresses a relationship between the spectral characteristic of the maximum gradation value and the spectral characteristic of the characteristic-acquired gradation value for each of a plurality of sample colors that are a plurality of ink colors for which spectral characteristics of intermediate gradation values ​​of a first prediction step of calculating a predicted value of the spectral characteristics of the characteristic-acquired gradation value for the prediction target color by applying the spectral characteristics of the maximum gradation value for the prediction target color to a corresponding first relational expression for each of the plurality of sample colors; a difference value calculation step of calculating a difference value between the predicted value calculated in the first prediction step and an actual measurement value of the spectral characteristics of the characteristic-acquired gradation value for the prediction target color for each of the plurality of sample colors; a reference color selection step of selecting, as a reference color, the sample color that has the smallest difference value in the difference value calculation step from among the plurality of sample colors; a second relational expression calculation step of determining a second relational expression that expresses a relationship between the spectral characteristics of the reference gradation value and the spectral characteristics of the processing target gradation value for the reference color, using the maximum gradation value or the characteristic-acquired gradation value as a reference gradation value and the gradation value for which spectral characteristics have been obtained for the reference color or the characteristic-acquired gradation value as a processing target gradation value; a second prediction step of obtaining a predicted value of the spectral characteristics of the prediction target gradation value for the prediction target color using the second relational expression; The present invention is characterized by comprising:

[0025] The second invention is the first invention, The number of the characteristic-acquired gradation values ​​is 1, In the second relational expression calculation step, With respect to the processing target gradation value between the maximum gradation value and the characteristic-acquired gradation value, an equation expressing a relationship between the spectral characteristic of the maximum gradation value and the spectral characteristic of the processing target gradation value is obtained as the second relational equation, with the spectral characteristic of the maximum gradation value being a first reference and the spectral characteristic of the characteristic-acquired gradation value being a second reference; The present invention is characterized in that, for the processing target gradation value between the characteristic-acquired gradation value and the minimum gradation value, an equation expressing the relationship between the spectral characteristics of the characteristic-acquired gradation value and the spectral characteristics of the processing target gradation value is obtained as the second relational equation, with the spectral characteristics of the characteristic-acquired gradation value being a first reference and the spectral characteristics of the minimum gradation value being a second reference.

[0026] The third invention is the first invention, The spectral characteristics of the color to be predicted are obtained. N pieces the intermediate gradation value includes a first gradation value and a second gradation value smaller than the first gradation value, In the second relational expression calculation step, a second relational expression is obtained that expresses a relationship between the spectral characteristics of the maximum gradation value and the spectral characteristics of the processing target gradation value between the maximum gradation value and the first gradation value, the spectral characteristics of the maximum gradation value being a first reference and the spectral characteristics of the first gradation value being a second reference; With respect to the processing target gradation value between the first gradation value and the second gradation value, an equation expressing a relationship between the spectral characteristics of the first gradation value and the spectral characteristics of the processing target gradation value is obtained as the second relational equation, with the spectral characteristics of the first gradation value being a first reference and the spectral characteristics of the second gradation value being a second reference; The present invention is characterized in that, for the processing target gradation value between the second gradation value and the minimum gradation value, the second relational equation is an equation expressing the relationship between the spectral characteristics of the second gradation value and the spectral characteristics of the processing target gradation value, with the spectral characteristics of the second gradation value being a first reference and the spectral characteristics of the minimum gradation value being a second reference.

[0027] The fourth invention relates to the first invention, The spectral characteristics of the color to be predicted are obtained. N pieces the intermediate gradation values ​​include m gradation values ​​from the first gradation value to the mth gradation value, where m is an integer equal to or greater than 3; where k is an integer between 1 and (m-1), and the kth gradation value is greater than the (k+1)th gradation value; In the second relational expression calculation step, a second relational expression is obtained that expresses a relationship between the spectral characteristics of the maximum gradation value and the spectral characteristics of the processing target gradation value between the maximum gradation value and the first gradation value, the spectral characteristics of the maximum gradation value being a first reference and the spectral characteristics of the first gradation value being a second reference; With respect to the processing target gradation value between the k gradation value and the (k+1) gradation value, an equation expressing a relationship between the spectral characteristics of the k gradation value and the spectral characteristics of the processing target gradation value is obtained as the second relational equation, with the spectral characteristics of the k gradation value being a first reference and the spectral characteristics of the (k+1) gradation value being a second reference; The present invention is characterized in that, for the processing target gradation value between the m gradation value and the minimum gradation value, an equation expressing the relationship between the spectral characteristics of the m gradation value and the spectral characteristics of the processing target gradation value is obtained as the second relational equation, with the spectral characteristics of the m gradation value being a first reference and the spectral characteristics of the minimum gradation value being a second reference.

[0028] The fifth invention is any one of the second to fourth inventions, In the second relational expression calculation step, data on the spectral characteristics is normalized so that a value of the second reference spectral characteristic becomes 1.

[0029] The sixth invention is any one of the first to fifth inventions, In the second relational expression calculation step, an expression expressing a relationship between the spectral characteristics of the maximum gradation value and the spectral characteristics of the processing target gradation value for the reference color is obtained as the second relational expression; The second prediction step is characterized in that a predicted value of the spectral characteristics of the prediction target gradation value for the prediction target color is obtained by applying the spectral characteristics of the maximum gradation value for the prediction target color to the second relational expression.

[0030] The seventh aspect of the present invention is any one of the first to fifth aspects of the present invention, The number of the prediction target gradation values ​​is 2 or more, The second prediction step includes: a second relational expression utilization step of determining a predicted value of the spectral characteristics of a gradation value, of which spectral characteristics have been obtained for the reference color, among the two or more prediction target gradation values ​​by applying the spectral characteristics of the reference gradation value for the prediction target color to a corresponding second relational expression; an interpolation step of determining a predicted value of the spectral characteristics of a gradation value, of which the spectral characteristics have not been obtained for the reference color, among the two or more prediction target gradation values ​​by performing spline interpolation based on the predicted value determined in the second relational expression utilization step; The present invention is characterized by comprising:

[0031] The eighth aspect of the present invention is any one of the first to fifth aspects of the present invention, a union creation step of creating a union of gradation values ​​for which spectral characteristics have been obtained for the reference color and gradation values ​​for which spectral characteristics have been obtained for the prediction target color, In the second relational expression calculation step, the gradation value included in the union is set as the processing target gradation value; The number of the prediction target gradation values ​​is 2 or more, The second prediction step includes: a second relational expression utilization step of determining a predicted value of the spectral characteristics of the gradation values ​​included in the union of the two or more prediction target gradation values ​​by applying the spectral characteristics of the reference gradation values ​​for the prediction target color to a corresponding second relational expression; an interpolation step of determining a predicted value of the spectral characteristics of the gradation values ​​not included in the union of the two or more prediction target gradation values ​​by performing spline interpolation based on the predicted value determined in the second relational expression utilization step; The present invention is characterized by comprising:

[0032] A ninth aspect of the present invention relates to the eighth aspect of the present invention, The method is characterized in that it includes a third prediction step between the union creation step and the second relational expression calculation step, which determines a predicted value of the spectral characteristics of the gradation value to be processed for the reference color, which is the spectral characteristic of the gradation value for which no spectral characteristic has been obtained for the reference color, by performing spline interpolation based on the known spectral characteristics of the reference color.

[0033] A tenth aspect of the present invention is any one of the first to ninth aspects of the present invention, The difference value calculated in the difference value calculation step is a square error between the predicted value calculated in the first prediction step and an actual measurement value of the spectral characteristics of the characteristic-acquired gradation value for the prediction target color.

[0034] The eleventh aspect of the present invention is any one of the first to ninth aspects of the present invention, The difference value calculated in the difference value calculation step is a color difference based on the predicted value calculated in the first prediction step and an actual measurement value of the spectral characteristics of the characteristic-acquired gradation value for the prediction target color.

[0035] A twelfth aspect of the present invention is any one of the first to eleventh aspects of the present invention, The spectral characteristic is any one of a spectral reflectance, a spectral absorptance, and a spectral absorption coefficient.

[0036] A thirteenth aspect of the present invention is a spectral characteristic prediction program for predicting a spectral characteristic obtained by applying an ink to a base material, the program comprising: On the computer, The spectral characteristics of the maximum gradation value, the spectral characteristics of the minimum gradation value, and N pieces (N is an integer equal to or greater than 1) a prediction target color setting step of setting the color of the ink for which the spectral characteristics of the intermediate gradation value of The intermediate gradation value for which the spectral characteristics have been obtained for the prediction target color is defined as a characteristic-acquired gradation value, A color other than the prediction target color,the spectral characteristic of the maximum gradation value, the spectral characteristic of the minimum gradation value, and (N+1) or more a first relational expression calculation step of calculating a first relational expression that expresses a relationship between the spectral characteristic of the maximum gradation value and the spectral characteristic of the characteristic-acquired gradation value for each of a plurality of sample colors that are a plurality of ink colors for which spectral characteristics of intermediate gradation values ​​of a first prediction step of calculating a predicted value of the spectral characteristics of the characteristic-acquired gradation value for the prediction target color by applying the spectral characteristics of the maximum gradation value for the prediction target color to a corresponding first relational expression for each of the plurality of sample colors; a difference value calculation step of calculating a difference value between the predicted value calculated in the first prediction step and an actual measurement value of the spectral characteristics of the characteristic-acquired gradation value for the prediction target color for each of the plurality of sample colors; a reference color selection step of selecting, as a reference color, the sample color that has the smallest difference value in the difference value calculation step from among the plurality of sample colors; a second relational expression calculation step of determining a second relational expression that expresses a relationship between the spectral characteristics of the reference gradation value and the spectral characteristics of the processing target gradation value for the reference color, using the maximum gradation value or the characteristic-acquired gradation value as a reference gradation value and the gradation value for which spectral characteristics have been obtained for the reference color or the characteristic-acquired gradation value as a processing target gradation value; a second prediction step of obtaining a predicted value of the spectral characteristics of the prediction target gradation value for the prediction target color using the second relational expression; Execute the command. Effect of the Invention

[0037] According to the first aspect of the present invention, a first relational expression is obtained for each sample color, which expresses the relationship between the spectral characteristics of the maximum gradation value and the spectral characteristics of the characteristic-acquired gradation value (intermediate gradation value for which the spectral characteristics are acquired for the prediction target color), and a predicted value of the spectral characteristics of the characteristic-acquired gradation value for the prediction target color is obtained using the first relational expression for each sample color. Then, a difference value between the predicted value and the actual value is obtained, and the sample color for which the smallest difference value is obtained is selected as a reference color. A second relational expression is obtained for the characteristics of the reference color, and a predicted value of the spectral characteristics of the prediction target gradation value for the prediction target color is obtained using the second relational expression. As described above, the spectral characteristics of the prediction target color are predicted using the color that can most accurately predict the known spectral characteristics of the prediction target color as the reference color, so that a highly accurate predicted value can be obtained. As described above, when intermediate gradation values ​​whose spectral characteristics are known exist for the prediction target color, it is possible to highly accurately predict the spectral characteristics of the prediction target gradation value for the prediction target color by using information on the known spectral characteristics.

[0038] According to the second aspect of the present invention, the second relational expression for predicting the spectral characteristics of any prediction target gradation value is created using the characteristic acquired gradation value as a reference (first reference or second reference). Therefore, the predicted value of the spectral characteristics of the characteristic acquired gradation value for the prediction target color is equal to the actual measured value. This improves the prediction accuracy of the spectral characteristics for gradation values ​​between the maximum gradation value and the characteristic acquired gradation value and for gradation values ​​between the characteristic acquired gradation value and the minimum gradation value. As a result, it becomes possible to predict the spectral characteristics of each gradation value from the minimum gradation value to the maximum gradation value so as to obtain a smooth density change, and the occurrence of tone jumps is suppressed.

[0039] According to the third aspect of the invention, the second relational expression for predicting the spectral characteristics of any prediction target gradation value is created using the characteristic acquired gradation value as a reference (first reference or second reference). Therefore, the predicted value of the spectral characteristics of the characteristic acquired gradation value for the prediction target color is equal to the actual measured value. This improves the prediction accuracy of the spectral characteristics for gradation values ​​between the maximum gradation value and the maximum characteristic acquired gradation value, gradation values ​​between two characteristic acquired gradation values, and gradation values ​​between the minimum characteristic acquired gradation value and the minimum gradation value. As a result, it is possible to predict the spectral characteristics of each gradation value from the minimum gradation value to the maximum gradation value so as to obtain a smooth density change, and the occurrence of tone jumps is suppressed.

[0040] According to the fourth aspect of the invention, the same effects as those of the third aspect of the invention can be obtained.

[0041] According to the fifth aspect of the present invention, the second relational expression can be suitably determined regardless of the values ​​of the spectral characteristics that are used as the first criterion and the second criterion.

[0042] According to the sixth aspect of the invention, the same effects as those of the first aspect of the invention can be obtained.

[0043] According to the seventh aspect of the present invention, predicted values ​​of the spectral characteristics can be found with relatively high accuracy even for those tone values ​​among the prediction target tone values ​​for which no spectral characteristics have been obtained for the reference color.

[0044] According to the eighth aspect of the present invention, it is possible to prevent the actual process of predicting the spectral characteristics from becoming complicated.

[0045] According to the ninth aspect of the present invention, a predicted value of the spectral characteristics can be obtained with relatively high accuracy even for gradation values ​​for which spectral characteristics have not been obtained for the reference color among the processing target gradation values ​​(gradation values ​​constituting the union of gradation values ​​for which spectral characteristics have been obtained for the reference color and gradation values ​​for which spectral characteristics have been obtained for the prediction target color).

[0046] According to the tenth aspect of the present invention, the reference color is suitably selected from a plurality of sample colors, thereby improving the prediction accuracy of the spectral characteristics.

[0047] According to the eleventh aspect of the present invention, the same effects as those of the tenth aspect of the present invention can be obtained.

[0048] According to the twelfth aspect of the present invention, the same effects as those of the first aspect of the present invention can be obtained.

[0049] According to the thirteenth aspect of the present invention, the same effects as those of the first aspect of the present invention can be obtained. [Brief description of the drawings]

[0050] [Figure 1] FIG. 1 is a diagram for explaining the terms used in this specification regarding the CxF chart. [Diagram 2] 1 is an overall configuration diagram of a printing system according to a first embodiment of the present invention. [Diagram 3] FIG. 2 is a hardware configuration diagram of a print data generating device in the first embodiment. [Figure 4] 13 is a flowchart showing a procedure of a spectral reflectance prediction process in the first embodiment. [Diagram 5] FIG. 11 is a diagram for explaining normalization when calculating a first relational expression in the first embodiment. [Figure 6] FIG. 2 is a diagram for explaining combination data in the first embodiment. [Figure 7] FIG. 11 is a diagram for explaining calculation of a first relational expression in the first embodiment. [Figure 8] FIG. 2 is a diagram showing an example of one plot in the first embodiment. [Figure 9] FIG. 4 is a diagram for explaining how to obtain a square error in the first embodiment. [Figure 10] 13 is a flowchart showing the procedure of step S160 in the first embodiment in the case where the prediction target gradation values ​​include gradation values ​​other than those for which spectral reflectances have been obtained for the reference colors. [Figure 11]11A and 11B are diagrams for explaining the occurrence of a tone jump in the vicinity of a characteristic-acquired gradation value. [Figure 12] 13A and 13B are diagrams for explaining the occurrence of an error between a predicted value and an actually measured value regarding the spectral reflectance of a characteristic-acquired tone value. [Figure 13] FIG. 11 is a diagram for explaining calculation of a second relational expression in the second embodiment of the present invention. [Figure 14] FIG. 11 is a diagram for explaining an effect of the second embodiment. [Figure 15] FIG. 11 is a diagram for explaining an effect of the second embodiment. [Figure 16] FIG. 13 is a diagram for explaining a union in the third embodiment of the present invention. [Figure 17] 13 is a flowchart showing a procedure of a spectral reflectance prediction process in the third embodiment. [Figure 18] FIG. 13 is a diagram for explaining a case in which the spectral reflectances of all gradation values ​​included in a union are obtained for a reference color in the third embodiment. [Figure 19] FIG. 1 is a diagram for explaining the method of Deshpande et al., as a conventional example. [Figure 20] FIG. 1 is a diagram showing a schematic example of a CxF chart according to a conventional example. [Figure 21] 1 is a flowchart for explaining the method of Deshpande et al., regarding a conventional example. [Figure 22] FIG. 1 is a diagram for explaining the method of Deshpande et al., as a conventional example. [Diagram 23] 11A and 11B are diagrams for explaining a significant inconsistency that occurs between a color based on an actual measurement value and a color based on a predicted value in a conventional example. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0051] <0. Introduction> Before describing the embodiments, the terms used in this specification and basic matters related to the present invention will be described with reference to FIG. 1. Regarding the CxF chart shown in FIG. 1, the upper patch (patch in the row marked with reference number 71) is a patch obtained by printing the target ink on a substrate, and the lower patch (patch in the row marked with reference number 72) is a patch obtained by printing the target ink on black. A patch that represents the color of the substrate itself (patch marked with reference number PA1 in FIG. 1) is called a "paper white patch," and a patch in a state where the target ink is solidly applied on the substrate (patch marked with reference number PA2 in FIG. 1) is called a "solid patch." However, in the following embodiments, processing is performed not by focusing on the patch, but by focusing on the gradation value. Also, in the following embodiments, a prediction is made of the spectral reflectance obtained by printing the target ink on the substrate.

[0052] As described above, in the following embodiments, processing is performed with attention to the gradation value. In this regard, it is assumed that the maximum gradation value is 1 and the minimum gradation value is 0. The state in which the substrate is applied with ink at the maximum ink density corresponds to the maximum gradation value, and the state in which the substrate is not applied with ink corresponds to the minimum gradation value. In other words, the maximum gradation value corresponds to the solid patch PA2, and the minimum gradation value corresponds to the paper white patch PA1. When the gradation value and the halftone percentage are associated with each other, for example, a gradation value of 1 corresponds to a halftone percentage of 100%, a gradation value of 0.5 corresponds to a halftone percentage of 50%, and a gradation value of 0 corresponds to a halftone percentage of 0%.

[0053] In order to predict a color obtained by overprinting a plurality of inks including a special color, colorimetric values ​​of a color to be referenced in prediction (hereinafter referred to as "reference color") are required. More specifically, for the reference color, information on the spectral reflectance of the maximum gradation value (colorimetric value), information on the spectral reflectance of the minimum gradation value (colorimetric value), and information on the spectral reflectance of at least one intermediate gradation value (colorimetric value) are required. In addition, in each of the following embodiments, information on the spectral reflectance of the maximum gradation value (colorimetric value), information on the spectral reflectance of the minimum gradation value (colorimetric value), and information on the spectral reflectance of at least one intermediate gradation value (colorimetric value) are required for the color to be predicted. Incidentally, the spectral reflectance of the maximum gradation value and the minimum gradation value can be obtained relatively easily. In the following, a case where the spectral reflectance is obtained in 10 nm increments in the wavelength range of 380 nm to 730 nm (i.e., a case where one color is specified by 36 spectral reflectances) is assumed. However, this is not limited to this, and each of the embodiments (including modified examples) described below can also be applied to cases where a spectral reflectance is obtained by dividing a wavelength range including 400 nm to 700 nm by a unit wavelength range of an appropriate size.

[0054] The spectral reflectance of the maximum gradation value (spectral reflectance of solid patch PA2) can be obtained, for example, by measuring the color of a color ball or a portion of the corresponding color contained in a printed matter. The spectral reflectance of the maximum gradation value can also be substituted with the spectral reflectance obtained by measuring a color sample of the corresponding color. This is because the color sample represents the target color when the corresponding color is applied solidly.

[0055] The spectral reflectance of the minimum gradation value (spectral reflectance of the paper white patch PA1) is obtained by performing color measurement on an unprinted portion of the substrate. Also, if the same paper is used as the substrate when printing, the spectral reflectance of the minimum gradation value is constant regardless of the ink color. Therefore, even if processing is performed with inks of multiple colors, as long as the same paper is used, the measurement of the spectral reflectance of the minimum gradation value needs to be performed only once.

[0056] For intermediate gradation values, accurate spectral reflectance cannot be obtained unless color measurement is performed using a CxF chart or the like actually printed on a substrate. However, as mentioned above, the spectral reflectance of some intermediate gradation values ​​can be obtained using color balls, etc.

[0057] Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings.

[0058] <1. First embodiment> <1.1 Overall configuration of the printing system> 2 is an overall configuration diagram of a printing system according to a first embodiment of the present invention. This printing system is composed of a print data generating device 100 that performs various processes on input data such as a PDF file to generate print data, a plate making device 200 that creates printing plates based on the print data, a printing device 300 that performs printing using the printing plates created by the plate making device 200, a digital printing device 350 such as an inkjet printer or copier that performs printing based on the print data, which is digital data, without using printing plates, and a colorimeter (e.g., a spectrophotometer) 400 that measures colors. The print data generating device 100, the plate making device 200, the digital printing device 350, and the colorimeter 400 are connected to each other so that they can communicate with each other via a communication line CL.

[0059] In this embodiment, a spectral reflectance prediction process is performed in the print data generating device 100 to predict the spectral reflectance obtained by applying an ink of a prediction target color (typically, a spot color ink) to a base material. In the spectral reflectance prediction process, at least one gradation value is designated as a prediction target gradation value, and a predicted value of the spectral reflectance of the prediction target gradation value for the prediction target color is obtained.

[0060] Furthermore, the print data generating device 100 performs an overprint prediction process to predict a color obtained by overprinting a plurality of color inks (typically, a color of a portion where a plurality of spot color inks are overprinted or a portion where a spot color ink and a process color ink are overprinted). In the overprint prediction process, the result of the spectral reflectance prediction process (predicted value of the spectral reflectance) is used as necessary. Furthermore, the print data generating device 100 also performs a process to convert the data obtained by the overprint prediction process into print data in a format that can be printed out by the digital printing device 350. Note that the specific method of the overprint prediction process may be the above-mentioned method by Deshpande et al., or another method may be used.

[0061] <1.2 Configuration of the print data generating device> 3 is a hardware configuration diagram of the print data generating device 100 in this embodiment. The print data generating device 100 is realized by a personal computer, and has a CPU 11, a ROM 12, a RAM 13, an auxiliary storage device 14, an input operation unit 15 such as a keyboard, a display unit 16, an optical disk drive 17, and a network interface unit 18. The manuscript data sent via the communication line CL is input into the print data generating device 100 via the network interface unit 18. The print data generated by the print data generating device 100 is sent to the digital printing device 350 via the communication line CL through the network interface unit 18.

[0062] A spectral reflectance prediction program 141 for executing the spectral reflectance prediction process is stored in the auxiliary storage device 14. The spectral reflectance prediction program 141 is provided by being stored in a computer-readable recording medium (non-transient recording medium) such as a CD-ROM or a DVD-ROM. That is, a user purchases, for example, an optical disk (CD-ROM, DVD-ROM, etc.) 170 as a recording medium for the spectral reflectance prediction program 141, loads it into the optical disk drive 17, reads out the spectral reflectance prediction program 141 from the optical disk 170, and installs it in the auxiliary storage device 14. Alternatively, the spectral reflectance prediction program 141 sent via the communication line CL may be received by the network interface unit 18 and installed in the auxiliary storage device 14.

[0063] <1.3 Spectral reflectance prediction method (spectral characteristic prediction method)> The following describes a spectral reflectance prediction process that realizes the spectral reflectance prediction method (spectral characteristic prediction method) according to this embodiment. Note that the spectral reflectance prediction process is performed by the print data generating device 100 executing the spectral reflectance prediction program 141.

[0064] FIG. 4 is a flowchart showing the procedure of the spectral reflectance prediction process in this embodiment. Note that before the spectral reflectance prediction process is executed, it is necessary to obtain the spectral reflectance of the maximum gradation value, the spectral reflectance of the minimum gradation value, and the spectral reflectance of at least one intermediate gradation value for an appropriate number of ink colors (hereinafter referred to as "sample colors"). However, here, it is assumed that the spectral reflectance of all gradation values ​​in 0.1 increments from the minimum gradation value (gradation value 0) to the maximum gradation value (gradation value 1) for each of the multiple sample colors is obtained. To achieve this, for example, it is sufficient to print a CxF chart (which may be a simplified CxF chart) as shown in FIG. 1 for each sample color and measure the color of the chart. For example, 32 spot colors are used as the sample colors. Note that the sample colors may include process colors. The flow shown in FIG. 4 will be described below.

[0065] First, the prediction target color is set (step S100). In this embodiment, the color of the ink for which the spectral reflectance of the maximum gradation value, the spectral reflectance of the minimum gradation value, and the spectral reflectance of at least one intermediate gradation value are obtained is set as the prediction target color. In this regard, for example, the processing of step S100 may be realized by the user inputting information on the prediction target color on a predetermined screen, or the processing of step S100 may be realized by the spectral reflectance prediction program 141 reading a data file including information on the prediction target color. In the following, the intermediate gradation value for which the spectral reflectance is obtained for the prediction target color is referred to as the "characteristics-acquired gradation value". For example, if the spectral reflectance of the gradation value 0.3 and the spectral reflectance of the gradation value 0.5 are obtained for the prediction target color, 0.3 and 0.5 are the characteristics-acquired gradation values.

[0066] Next, for each of the above-mentioned multiple sample colors, a relational equation (hereinafter referred to as a "first relational equation") that expresses the relationship between the spectral reflectance of the maximum gradation value and the spectral reflectance of the characteristic-acquired gradation value is found (step S110). In this step S110, for each sample color, a number of first relational equations equal to the number of characteristic-acquired gradation values ​​are found. In the above example, when 0.3 and 0.5 are characteristic-acquired gradation values, two first relational equations are found for each sample color.

[0067] The method of obtaining the first relational expression will be described in detail. As described above, for the sample colors, colorimetric values ​​(spectral reflectances) of all gradation values ​​in increments of 0.1 from the minimum gradation value (gradation value 0) to the maximum gradation value (gradation value 1) are obtained. That is, data corresponding to a curve (curve representing spectral reflectance) as shown in part A of FIG. 5 is obtained for all 11 gradation values ​​in increments of 0.1 from 0 to 1 (in FIG. 5, the horizontal axis is wavelength (unit: nm) and the vertical axis is reflectance). Note that part A of FIG. 5 shows only curves corresponding to four of the 11 gradation values ​​(similar to part B of FIG. 5). The curve marked with reference numeral 51 is the curve for the minimum gradation value, and the curve marked with reference numeral 52 is the curve for the maximum gradation value. Such data is normalized so that the spectral reflectance of the minimum gradation value is set to 1. As a result, data is obtained that corresponds to a curve (a curve representing the spectral reflectance) as shown in part B of FIG. 5 (however, the minimum gradation value that was the standard for normalization is a straight line).

[0068] Here, one intermediate gradation value (hereinafter referred to as "target gradation value") that is a gradation value whose characteristics have been acquired among the nine intermediate gradation values ​​is focused on. With respect to the graph shown in part B of FIG. 5, it is assumed that the curves for the maximum gradation value and the target gradation value in the vicinity of a wavelength of 480 nm are as shown in FIG. 6. In this case, the reflectance of the maximum gradation value is 0.15, and the reflectance of the target gradation value is 0.52. In this embodiment, such data combining the reflectance of the maximum gradation value and the reflectance of the target gradation value is treated as "combined data". As described above, the spectral reflectance data is composed of 36 reflectances, so that 36 pieces of combined data of the reflectance of the maximum gradation value (reflectance after normalization) and the reflectance of the target gradation value (reflectance after normalization) are obtained. Each combined data is represented as one plot on a graph (hereinafter referred to as "relationship graph" for convenience) with the reflectance of the maximum gradation value on the horizontal axis and the reflectance of the target gradation value on the vertical axis, as shown in FIG. 7. For example, the combination data based on the data shown in Fig. 6 is represented on the relationship graph as a plot indicated by reference numeral 53 in Fig. 8. Thus, in this embodiment, 36 plots are represented on the relationship graph. Calculation of the first relational expression corresponds to finding a curve (for example, the curve indicated by reference numeral 54 in Fig. 7) that passes through positions as close as possible to the positions of these 36 plots.

[0069] In the example shown in part B of FIG. 5, the reflectance is at its minimum value near a wavelength of 560 nm, and the same reflectance appears at wavelengths greater than 560 nm and smaller than 560 nm. Therefore, for example, if the wavelengths are plotted on the relationship graph in order from the highest to the lowest, the locus will turn around. However, as can be seen from FIG. 7, the relationship between the reflectance of the maximum gradation value and the reflectance of the target gradation value does not change before and after the turnaround. From the above, if the sample color and the prediction target color are close to each other, it is considered that the reflectance of the target gradation value for the prediction target color can be accurately obtained from the reflectance of the maximum gradation value for the prediction target color by utilizing the "relationship between the reflectance of the maximum gradation value and the reflectance of the target gradation value" for the sample color.

[0070] In view of the above, in step S110 of Fig. 4, a first relational expression (an approximation expression for obtaining an approximation of the spectral reflectance of the target tone value from the spectral reflectance of the maximum tone value) expressing the relationship between the spectral reflectance of the maximum tone value and the spectral reflectance of the target tone value is obtained based on the 36 combination data as described above. The first relational expression is obtained by a known method. For example, the first relational expression can be obtained by solving the simultaneous equations obtained from the 36 combination data by Gaussian elimination or Gauss-Jordan algorithm.

[0071] In this embodiment, a quintic equation is adopted as the first relational expression (approximation expression). As an example, a quintic equation such as the following equation (4) is obtained by the process of step S110 in Fig. 4. In addition, in the following equation (4), y is the reflectance of the target gradation value (gradation value whose characteristics have been acquired), and x is the reflectance of the maximum gradation value.

number

[0072] However, there may be cases where the characteristic-acquired gradation value is not included in the gradation values ​​for which the spectral reflectance is obtained for the sample color. In the above example, the spectral reflectance of all gradation values ​​from 0 to 1 in increments of 0.1 is obtained for the sample color, but the characteristic-acquired gradation value may be 0.25. In such a case, in this embodiment, a quintic equation corresponding to a gradation value of 0.2 and a quintic equation corresponding to a gradation value of 0.3 are obtained, and then the coefficients of the quintic equation corresponding to a gradation value of 0.25 are obtained by interpolation. Then, the quintic equation having the coefficients obtained by the interpolation is adopted as the first relational equation.

[0073] After step S110 is completed, the predicted value of the spectral reflectance of the characteristic-acquired tone value for the prediction target color is obtained by applying the spectral reflectance of the maximum tone value for the prediction target color to the first relational expression for each of the multiple sample colors (step S120). If 32 colors are prepared as sample colors, 32 predicted values ​​are obtained for one characteristic-acquired tone value in step S120.

[0074] Then, for each of the multiple sample colors, a difference between the predicted value obtained in step S120 and the actual measurement value of the spectral reflectance of the characteristic-acquired gradation value for the prediction target color is obtained (step S130). In this embodiment, the squared error between the predicted value obtained in step S120 and the actual measurement value of the spectral reflectance of the characteristic-acquired gradation value for the prediction target color is obtained as the difference. The method of obtaining the squared error will be described below.

[0075] Here, a variable Ci (i is an integer equal to or greater than 1) is used to distinguish between multiple sample colors, and the predicted values ​​of spectral reflectance obtained for sample color Ci (predicted values ​​of 36 reflectances) are represented as Vp(i)(1) to Vp(i)(36) (see FIG. 9). Also, the actual measured values ​​of spectral reflectance (actual measured values ​​of 36 reflectances) of the characteristic-acquired gradation values ​​for the prediction target color are represented as Vr(1) to Vr(36). Then, the squared error E(1) between the predicted value obtained for the first sample color C1 and the actual measured value for the prediction target color can be calculated using the following equation (5):

number

[0076] Similarly, the square error E(i) between the predicted value obtained for the i-th sample color Ci and the actual measured value for the color to be predicted is calculated by the following equation (6). However, a weighting coefficient may be added for each wavelength.

number

[0077] Meanwhile, when the number of characteristic-acquired gradation values ​​is 1 (for example, when the gradation value 0.5 is the only characteristic-acquired gradation value), the squared error E(i) calculated by the above equation (6) can be directly adopted as the difference value for the i-th sample color Ci.

[0078] On the other hand, if the number of characteristic-acquired gradation values ​​is two or more, the squared error is found for each characteristic-acquired gradation value using the above formula (6), and the average value of these squared errors is used as the difference value, for example. For example, if the number of characteristic-acquired gradation values ​​is three, three squared errors are found, and the average value of the three squared errors is used as the difference value. Note that instead of a simple average value of the squared errors, a weighted average value of the squared errors may be used as the difference value.

[0079] After step S130 is completed, the sample color for which the smallest difference value (squared error) is obtained in step S130 is selected as the reference color (step S140). That is, in this embodiment, the sample color for which the spectral reflectance of the characteristic-acquired gradation value for the prediction target color can be predicted most accurately using the first relational expression is selected as the reference color.

[0080] Next, a relational equation (hereinafter referred to as the "second relational equation") expressing the relationship between the spectral reflectance of the maximum gradation value and the spectral reflectance of the prediction target gradation value for the reference color is found (step S150). Note that here, it is assumed that 11 gradation values ​​in increments of 0.1 from gradation value 0 to gradation value 1 are the prediction target gradation values. The specific method for finding the second relational equation is the same as the method for finding the first relational equation. The second relational equation is found for each prediction target gradation value, so here 11 second relational equations are found.

[0081] Finally, the second relational expression is used to find a predicted value of the spectral reflectance of the prediction target tone value for the prediction target color (step S160). Specifically, the spectral reflectance of the maximum tone value for the prediction target color is applied to the second relational expression found in step S150 to find a predicted value of the spectral reflectance of the prediction target tone value for the prediction target color. Here, since the number of prediction target tone values ​​is 11, the spectral reflectance of the maximum tone value for the prediction target color is applied to 11 second relational expressions. As a result, a predicted value of the spectral reflectance of each of the 11 prediction target tone values ​​for the prediction target color is found.

[0082] The process of obtaining the predicted value of the spectral reflectance (the process of step S160) will be described in more detail. At the start of the process of step S160, a quintic equation such as the above formula (4) is obtained as the second relational expression for each prediction target gradation value for the reference color. As described above, the data of the spectral reflectance is composed of 36 reflectances. Therefore, in step S160, 36 reflectances that are the data of the spectral reflectance of the maximum gradation value for the prediction target color are substituted one by one into the corresponding second relational expression (a relational expression that represents the relationship between the spectral reflectance of the maximum gradation value and the spectral reflectance of the corresponding prediction target gradation value) for each prediction target gradation value, thereby obtaining 36 reflectances that are the data of the spectral reflectance of the corresponding prediction target gradation value for the prediction target color. In this embodiment, when calculating the second relational expression, normalization is performed so that the spectral reflectance of the minimum gradation value is 1. Therefore, the 36 reflectances obtained from the second relational expression are inversely normalized (processing that returns data in a normalized state to data in an unnormalized state) based on the actual spectral reflectance of the minimum gradation value.

[0083] In the above example, the gradation value for which the spectral reflectance is obtained for the reference color and the prediction target gradation value match. However, a case is also assumed where the prediction target gradation value includes a gradation value other than the gradation value for which the spectral reflectance is obtained for the reference color. For the gradation value other than the gradation value for which the spectral reflectance is obtained for the reference color, the spectral reflectance cannot be directly obtained from the second relational expression. Therefore, the spectral reflectance of such a gradation value is obtained by performing spline interpolation (for example, cubic spline interpolation) based on the data of the spectral reflectance obtained directly from the second relational expression. In such a case, the above step S160 is composed of steps S162 and S164 as shown in FIG. 10. In step S162, a predicted value of the spectral reflectance of the gradation value for which the spectral reflectance is obtained for the reference color among the multiple gradation values ​​as the prediction target gradation value is obtained by applying the spectral reflectance of the maximum gradation value for the prediction target color to the corresponding second relational expression. Then, in step S164, predicted values ​​of the spectral reflectance of the gradation values ​​for which the spectral reflectance has not been obtained for the reference color among the multiple gradation values ​​as the prediction target gradation value are obtained by performing spline interpolation based on the predicted values ​​obtained in step S162. Note that linear interpolation can be used instead of spline interpolation, but spline interpolation provides a more accurate prediction value than linear interpolation.

[0084] In this manner, the predicted value of the spectral reflectance of the prediction target tone value for the prediction target color is obtained, and the spectral reflectance prediction process is completed.

[0085] In this embodiment, step S100 realizes a prediction target color setting step, step S110 realizes a first relational expression calculation step, step S120 realizes a first prediction step, step S130 realizes a difference value calculation step, step S140 realizes a reference color selection step, step S150 realizes a second relational expression calculation step, and step S160 realizes a second prediction step. Also, step S162 realizes a second relational expression utilization step, and step S164 realizes an interpolation step.

[0086] <1.4 Effects> According to this embodiment, a first relational expression is obtained for each sample color, which expresses the relationship between the spectral reflectance of the maximum gradation value and the spectral reflectance of the characteristic-acquired gradation value (intermediate gradation value for which the spectral reflectance is obtained for the prediction target color), and a predicted value of the spectral reflectance of the characteristic-acquired gradation value for the prediction target color is obtained using the first relational expression for each sample color. Then, the difference between the predicted value and the actual value is obtained, and the sample color for which the smallest difference value is obtained is selected as the reference color. A second relational expression is obtained for the reference color, which expresses the relationship between the spectral reflectance of the maximum gradation value and the spectral reflectance of the prediction target gradation value, and the spectral reflectance (predicted value) of the prediction target gradation value for the prediction target color is obtained by applying the spectral reflectance of the maximum gradation value for the prediction target color to the second relational expression. As described above, the spectral reflectance of the prediction target color is predicted using the color that can most accurately predict the known spectral reflectance of the prediction target color as the reference color, so that a highly accurate predicted value can be obtained. As described above, according to this embodiment, when there are intermediate gradation values ​​for which the spectral reflectance is known for the color to be predicted, it is possible to predict with high accuracy the spectral reflectance of the gradation value to be predicted for the color to be predicted by utilizing information on the known spectral reflectance.

[0087] <1.5 Modification> The following describes modified examples of the first embodiment. The following first to fifth modified examples can also be applied to the second and third embodiments described later.

[0088] <1.5.1 First modified example> In the first embodiment, the selection of the reference color from among the multiple sample colors (step S140 in FIG. 4) is performed based on the square error between the predicted value and the actual measured value. However, the present invention is not limited to this, and the reference color can also be selected based on the color difference. This will be described below.

[0089] In this modified example, in step S130 in Fig. 4, a color difference is calculated based on the predicted value calculated in step S120 and the actual measured value of the spectral reflectance of the characteristic-acquired gradation value for the prediction target color. Then, in step S140 in Fig. 4, the sample color with the smallest color difference is selected as the reference color.

[0090] The color difference based on a certain predicted value and an actual measured value can be calculated, for example, as follows. First, tristimulus values ​​X, Y, and Z are calculated for each of the predicted value and the actual measured value by a predetermined calculation formula. Next, CIELAB values ​​(L * Value, a * value, and b * value). Next, L * Value, a * value, and b * For each value, the difference between the predicted value and the actual measured value is calculated. The square root of the sum of the squares of the three differences obtained is the color difference (positive value).

[0091] <1.5.2 Second modified example> In the first embodiment, a quintic expression was adopted as the relational expressions (first relational expression and second relational expression). However, the degree of the relational expressions is not limited to 5. An n-th degree expression, where n is an integer of 2 or more, may be adopted as the relational expressions.

[0092] In this regard, a relational equation of a different order may be adopted for each color. For example, for colors with a narrow numerical range of the spectral reflectance of the maximum gradation value, if the order of the relational equation is high, overfitting may occur and the approximation accuracy may deteriorate. Therefore, for such colors, the deterioration of the approximation accuracy caused by overfitting can be suppressed by lowering the order of the relational equation.

[0093] <1.5.3 Third modified example> Furthermore, expressions expressed using power functions may be adopted as the relational expressions (first relational expression and second relational expression). In this case, for example, the values ​​of variables A and B in the following expression (7) are found based on the above-mentioned combination data (data represented as a plot on the relational graph). Then, an expression reflecting the values ​​of variables A and B is used as the relational expression. When the first relational expression is expressed by the following expression (7), y is the reflectance of the characteristic-acquired gradation value, and x is the reflectance of the maximum gradation value. When the third relational expression is expressed by the following expression (7), y is the reflectance of the prediction target gradation value, and x is the reflectance of the maximum gradation value.

number

[0094] <1.5.4 Fourth modified example> In the first embodiment, a process for predicting the spectral reflectance is performed as the spectral characteristic. However, the present invention is not limited to this, and a process for predicting a spectral characteristic other than the spectral reflectance may be performed. Examples of the spectral characteristic other than the spectral reflectance include the spectral absorptance (a value obtained by subtracting the spectral reflectance from 1) and the spectral absorption coefficient α obtained from the following equation (8). The reflectance at paper white (minimum gradation value) at a certain wavelength is R 0 If the reflectance of the corresponding tone value is R and the thickness of the ink is x, then when multiple reflections are not taken into consideration, the spectral absorption coefficient α is expressed by the following equation (8). α=-(1 / (2x))·ln(R / R 0 ) ···(8)

[0095] <1.5.5 Fifth modified example> In the first embodiment, an equation expressing the relationship between the spectral reflectance of the maximum gradation value and the spectral reflectance of the characteristic-acquired gradation value is adopted as the first relational expression. However, the relationship expressed by the first relational expression is not limited to this. For example, an equation expressing the relationship between the spectral absorptance of the maximum gradation value and the spectral absorptance of the characteristic-acquired gradation value, an equation expressing the relationship between the spectral reflectance of the maximum gradation value and the spectral absorptance of the characteristic-acquired gradation value, or the like, may be adopted as the first relational expression. Similarly, an equation expressing the relationship between the spectral absorptance of the maximum gradation value for the reference color and the spectral absorptance of the prediction target gradation value, or an equation expressing the relationship between the spectral reflectance of the maximum gradation value for the reference color and the spectral absorptance of the prediction target gradation value, or the like, may be adopted as the second relational expression.

[0096] <2. Second embodiment> <2.1 Advance Consideration> In the first embodiment, the sample color that can most accurately predict the spectral reflectance of the characteristic acquired gradation value of the prediction target color using the first relational expression based on the characteristics of the sample colors is selected as the reference color, and the spectral reflectance of the prediction target gradation value of the prediction target color is predicted using the second relational expression based on the characteristics of the reference color. With this configuration, some error occurs between the predicted value and the actual measurement value for the characteristic acquired gradation value. For example, when 11 gradation values ​​in 0.1 increments from gradation value 0 to gradation value 1 are the prediction target gradation values, and only gradation value 0.5 is the characteristic acquired gradation value, the spectral reflectance of the 11 gradation values ​​(prediction target gradation values) is predicted using the second relational expression based on the characteristics of the reference color. At this time, some error occurs between the predicted value and the actual measurement value for the gradation value 0.5. Here, if the actual measurement value is adopted for the gradation value 0.5 to make the error for the gradation value 0.5 0, a tone jump occurs near the gradation value 0.5 as can be seen from FIG. 11.

[0097] In the above example, if the spectral reflectances of the 11 gradation values ​​for the reference color are known, the spectral reflectances of the 11 gradation values ​​(prediction target gradation values) for the prediction target color are predicted using 11 second relational expressions represented by lines (curved or straight) with the code G(z) (z is a value from 0 to 1 in increments of 0.1) in FIG. 12. It is assumed that normalization has been performed with the spectral reflectance of the minimum gradation value set to 1. In the example shown in FIG. 12, the spectral reflectance of the maximum gradation value and the spectral reflectance of the minimum gradation value are the references. Therefore, when the spectral reflectance of the prediction target color is predicted using the second relational expression based on the characteristics of the reference color, the error between the predicted value and the actual measurement value for the maximum gradation value and the minimum gradation value is 0. However, since the characteristics of the reference color do not completely match the characteristics of the prediction target color, an error occurs between the predicted value and the actual measurement value for the spectral reflectance of the characteristic acquired gradation value. Therefore, in this embodiment, as described later, the spectral reflectance of the characteristic acquired gradation value is included as a reference when creating the second relational expression.

[0098] <2.2 Configuration and Spectral Reflectance Prediction Method (Spectral Characteristics Prediction Method)> The overall configuration of the printing system and the configuration of the print data generating device are similar to those in the first embodiment (see FIGS. 2 and 3), and therefore description thereof will be omitted.

[0099] The procedure of the spectral reflectance prediction process that realizes the spectral reflectance prediction method (spectral characteristic prediction method) according to this embodiment is generally similar to that of the first embodiment (see FIG. 4). However, the detailed method of calculating the second relational expression in step S150 in FIG. 4 is different from that of the first embodiment. This will be described below.

[0100] In this embodiment, in step S150, the second relational expression is calculated by including the spectral reflectance of the characteristic-acquired gradation value as a criterion. For example, if 11 gradation values ​​in increments of 0.1 from the minimum gradation value (gradation value 0) to the maximum gradation value (gradation value 1) are the prediction target gradation values, the spectral reflectances of these 11 gradation values ​​have been obtained for the reference color, and only the gradation value 0.5 is the characteristic-acquired gradation value, the criterion for creating the second relational expression corresponding to the prediction target gradation values ​​with gradation values ​​of 0.5 or more is different from the criterion for creating the second relational expression corresponding to the prediction target gradation values ​​with gradation values ​​of 0.5 or less. Specifically, the second relational expression corresponding to the prediction target gradation value of 0 or more and 0.5 or less is created with the spectral reflectance of gradation value 0.5 as the first reference and the spectral reflectance of gradation value 0 as the second reference (see part A of FIG. 13), and the second relational expression corresponding to the prediction target gradation value of 0.5 or more and 1 or less is created with the spectral reflectance of gradation value 1 as the first reference and the spectral reflectance of gradation value 0.5 as the second reference (see part B of FIG. 13). Note that as the second relational expression for predicting the spectral reflectance of gradation value 0.5 for the prediction target color, the second relational expression created with the spectral reflectance of gradation value 0.5 as the first reference and the spectral reflectance of gradation value 0 as the second reference may be adopted, or the second relational expression created with the spectral reflectance of gradation value 1 as the first reference and the spectral reflectance of gradation value 0.5 as the second reference may be adopted. In addition, since the gradation value 0.5 is a gradation value whose characteristics have been acquired, the actual measured value may be applied as is to the spectral reflectance of the gradation value 0.5 of the prediction target color without using the second relational expression. The actual measured values ​​may also be applied as is to the spectral reflectance of the maximum gradation value (gradation value 1) and the minimum gradation value (gradation value 0) of the prediction target color without using the second relational expression.

[0101] In the above example, the second relational expression is obtained in step S150 as follows. However, in the following, the target gradation value for which the spectral reflectance is obtained by the second relational expression is referred to as the "processing target gradation value." The processing target gradation value is the gradation value for which the spectral reflectance is obtained for the reference color or the characteristic-acquired gradation value. For example, an equation expressing the relationship between the spectral reflectance of gradation value 1 and the spectral reflectance of gradation value 0.7, with the spectral reflectance of gradation value 1 as the first reference and the spectral reflectance of gradation value 0.5 as the second reference, is obtained as the second relational expression for obtaining the spectral reflectance of gradation value 0.7 for the prediction target color. Also, for example, an equation expressing the relationship between the spectral reflectance of gradation value 0.5 and the spectral reflectance of gradation value 0.2, with the spectral reflectance of gradation value 0.5 as the first reference and the spectral reflectance of gradation value 0 as the second reference, is obtained as the second relational expression for obtaining the spectral reflectance of gradation value 0.2 for the prediction target color.

[0102] As described above, when the number of characteristic-acquired gradation values ​​is 1, in step S150, for the gradation values ​​to be processed between the maximum gradation value and the characteristic-acquired gradation value, a second relational equation is found that expresses the relationship between the spectral reflectance of the maximum gradation value and the spectral reflectance of the gradation value to be processed, with the spectral reflectance of the maximum gradation value being the first reference and the spectral reflectance of the characteristic-acquired gradation value being the second reference, and for the gradation values ​​to be processed between the characteristic-acquired gradation value and the minimum gradation value, a second relational equation is found that expresses the relationship between the spectral reflectance of the characteristic-acquired gradation value and the spectral reflectance of the gradation value to be processed, with the spectral reflectance of the characteristic-acquired gradation value being the first reference and the spectral reflectance of the minimum gradation value being the second reference.

[0103] In the above example, only the gradation value 0.5 was a characteristic-acquired gradation value. In other words, the number of characteristic-acquired gradation values ​​was 1. When the number of characteristic-acquired gradation values ​​is 2 or more, the second relational expression can be found as follows:

[0104] First, a case where the number of characteristic-acquired gradation values ​​is two will be described. Here, attention is focused on the case where "11 gradation values ​​in increments of 0.1 from the minimum gradation value (gradation value 0) to the maximum gradation value (gradation value 1) are the gradation values ​​to be predicted, the spectral reflectances of these 11 gradation values ​​have been obtained for the reference color, and gradation values ​​0.3 and 0.5 are the characteristic-acquired gradation values." For this case, the second relational expression is obtained in step S150 as follows. For example, an expression expressing the relationship between the spectral reflectance of gradation value 1 and the spectral reflectance of gradation value 0.7, with the spectral reflectance of gradation value 1 as the first reference and the spectral reflectance of gradation value 0.5 as the second reference, is obtained as the second relational expression for calculating the spectral reflectance of gradation value 0.7 for the prediction target color. Also, for example, an equation expressing the relationship between the spectral reflectance of gradation value 0.5 and the spectral reflectance of gradation value 0.4, with the spectral reflectance of gradation value 0.5 as a first reference and the spectral reflectance of gradation value 0.3 as a second reference, is obtained as a second relational equation for obtaining the spectral reflectance of gradation value 0.4 for the prediction target color. Also, for example, an equation expressing the relationship between the spectral reflectance of gradation value 0.3 and the spectral reflectance of gradation value 0.1, with the spectral reflectance of gradation value 0.3 as a first reference and the spectral reflectance of gradation value 0 as a second reference, is obtained as a second relational equation for obtaining the spectral reflectance of gradation value 0.1 for the prediction target color.

[0105] As described above, when the first gradation value (0.5 in the above case) and the second gradation value (0.3 in the above case) smaller than the first gradation value are characteristic-acquired gradation values, in step S150, for the processing target gradation values ​​between the maximum gradation value and the first gradation value, the spectral reflectance of the maximum gradation value is set as a first reference and the spectral reflectance of the first gradation value is set as a second reference, and an equation expressing the relationship between the spectral reflectance of the maximum gradation value and the spectral reflectance of the processing target gradation value is obtained as a second relational equation. With respect to the gradation value to be processed, an equation expressing the relationship between the spectral reflectance of the first gradation value and the spectral reflectance of the gradation value to be processed is obtained as a second relational equation, with the spectral reflectance of the first gradation value being a first reference and the spectral reflectance of the second gradation value being a second reference, and with respect to the gradation value to be processed between the second gradation value and the minimum gradation value, an equation expressing the relationship between the spectral reflectance of the second gradation value and the spectral reflectance of the gradation value to be processed is obtained as a second relational equation, with the spectral reflectance of the second gradation value being a first reference and the spectral reflectance of the minimum gradation value being a second reference.

[0106] Next, a case where the number of characteristic acquired gradation values ​​is three or more will be described. Here, attention is paid to the case where "11 gradation values ​​in increments of 0.1 from the minimum gradation value (gradation value 0) to the maximum gradation value (gradation value 1) are the prediction target gradation values, the spectral reflectances of these 11 gradation values ​​have been obtained for the reference color, and gradation values ​​0.3, 0.5, and 0.7 are characteristic acquired gradation values." For this case, the second relational expression is obtained in step S150 as follows. For example, an expression expressing the relationship between the spectral reflectance of gradation value 1 and the spectral reflectance of gradation value 0.9, with the spectral reflectance of gradation value 1 as the first reference and the spectral reflectance of gradation value 0.7 as the second reference, is obtained as the second relational expression for obtaining the spectral reflectance of gradation value 0.9 for the prediction target color. Also, for example, an equation expressing the relationship between the spectral reflectance of gradation value 0.7 and the spectral reflectance of gradation value 0.6, with the spectral reflectance of gradation value 0.7 as the first reference and the spectral reflectance of gradation value 0.5 as the second reference, is obtained as the second relational equation for obtaining the spectral reflectance of gradation value 0.6 for the prediction target color. Also, for example, an equation expressing the relationship between the spectral reflectance of gradation value 0.5 and the spectral reflectance of gradation value 0.4, with the spectral reflectance of gradation value 0.5 as the first reference and the spectral reflectance of gradation value 0.3 as the second reference, is obtained as the second relational equation for obtaining the spectral reflectance of gradation value 0.4 for the prediction target color. Also, for example, an equation expressing the relationship between the spectral reflectance of a gradation value of 0.3 and the spectral reflectance of a gradation value of 0.1, with the spectral reflectance of a gradation value of 0.3 as a first reference and the spectral reflectance of a gradation value of 0 as a second reference, is obtained as a second relational equation for calculating the spectral reflectance of a gradation value of 0.1 for the color to be predicted.

[0107] As described above, when m gradation values ​​from the first gradation value to the m-th gradation value, where m is an integer of 3 or more, are characteristic-acquired gradation values, and k is an integer of 1 or more and (m-1) or less, and the k-th gradation value is greater than the (k+1)-th gradation value, in step S150, for processing target gradation values ​​between the maximum gradation value and the first gradation value, the spectral reflectance of the maximum gradation value is set as a first reference and the spectral reflectance of the first gradation value is set as a second reference, and an equation expressing the relationship between the spectral reflectance of the maximum gradation value and the spectral reflectance of the processing target gradation value is found as a second relational equation, With respect to processing target gradation values ​​between the (k+1) gradation value, an equation expressing the relationship between the spectral reflectance of the k-th gradation value and the spectral reflectance of the (k+1)-th gradation value is obtained as a second relational equation, with the spectral reflectance of the k-th gradation value as a first reference and the spectral reflectance of the (k+1)-th gradation value as a second reference, and with respect to processing target gradation values ​​between the m-th gradation value and the minimum gradation value, an equation expressing the relationship between the spectral reflectance of the m-th gradation value and the spectral reflectance of the minimum gradation value is obtained as a second relational equation, with the spectral reflectance of the m-th gradation value as a first reference and the spectral reflectance of the minimum gradation value as a second reference.

[0108] Here, in this embodiment, attention is paid to the case where the prediction target gradation values ​​include gradation values ​​other than the gradation values ​​for which the spectral reflectance is obtained for the reference color. In this case, for example, if the gradation value 0.5 is the only characteristic acquired gradation value, the predicted value of the spectral reflectance of the gradation value for which the spectral reflectance is obtained for the reference color among the prediction target gradation values ​​between the maximum gradation value and the characteristic acquired gradation value is obtained by applying the spectral reflectance of the maximum gradation value for the prediction target color to the corresponding second relational expression, and the predicted value of the spectral reflectance of the gradation value for which the spectral reflectance is obtained for the reference color among the prediction target gradation values ​​between the characteristic acquired gradation value and the minimum gradation value is obtained by applying the spectral reflectance of the characteristic acquired gradation value for the prediction target color to the corresponding second relational expression. In other words, the predicted value of the spectral reflectance of the gradation value for which the spectral reflectance is obtained for the reference color among two or more prediction target gradation values ​​is obtained by applying the spectral reflectance of the reference gradation value for the prediction target color to the corresponding second relational expression, with the maximum gradation value or the characteristic acquired gradation value being the reference gradation value. Thus, in this embodiment, in step S162 of Fig. 10, the predicted value of the spectral reflectance is calculated by applying the spectral reflectance of the maximum gradation value or the characteristic acquired gradation value for the prediction target color to the second relational expression. Then, in step S164 of Fig. 10, the predicted value of the spectral reflectance of the gradation value for which the spectral reflectance has not been obtained for the reference color among the prediction target gradation values ​​is obtained by performing spline interpolation (e.g., cubic spline interpolation) based on the predicted value obtained in step S162. At this time, the predicted value of the spectral reflectance of the prediction target gradation value between the maximum gradation value and the characteristic acquired gradation value is obtained by performing spline interpolation based on predicted values ​​for three or more gradation values ​​including the gradation value between the maximum gradation value and the characteristic acquired gradation value and the gradation value between the characteristic acquired gradation value and the minimum gradation value, rather than spline interpolation based on predicted values ​​only for three or more gradation values ​​between the maximum gradation value and the characteristic acquired gradation value. The same is true for the predicted value of the spectral reflectance of the prediction target gradation value between the characteristic acquired gradation value and the minimum gradation value. Although linear interpolation can be used instead of spline interpolation, the predicted value can be obtained with greater accuracy by spline interpolation than by linear interpolation.

[0109] <2.3 Effects> According to this embodiment, the second relational expression for predicting the spectral reflectance of any prediction target gradation value is created using the characteristic acquired gradation value as a reference (first reference or second reference). Therefore, the predicted value of the spectral reflectance of the characteristic acquired gradation value for the prediction target color is equal to the actual measured value. This improves the prediction accuracy of the spectral reflectance for the gradation value between the maximum gradation value and the maximum characteristic acquired gradation value, the gradation value between two characteristic acquired gradation values, and the gradation value between the minimum characteristic acquired gradation value and the minimum gradation value. As a result, it is possible to predict the spectral reflectance of each gradation value from the minimum gradation value to the maximum gradation value so as to obtain a smooth density change as shown in FIG. 14, and the occurrence of tone jumps is suppressed. In this way, it is possible to predict the spectral reflectance of the prediction target gradation value for the prediction target color with higher accuracy than the first embodiment.

[0110] Fig. 15 shows the results of a prediction test of 25 colors when the gradation value 0.5 is the only gradation value with acquired characteristics. It can be seen from Fig. 15 that the method of the first embodiment significantly improves the overall prediction accuracy compared to the conventional method. It can also be seen from Fig. 15 that the method of the second embodiment significantly improves the prediction accuracy of the spectral reflectance of gradation values ​​near the gradation values ​​with acquired characteristics compared to the method of the first embodiment.

[0111] <3. Third embodiment> <3.1 Overview> In this embodiment, in the spectral reflectance prediction process, after the reference color is selected, the union of the gradation values ​​for which the spectral reflectance is obtained for the reference color and the gradation values ​​for which the spectral reflectance is obtained for the prediction target color is obtained. For example, if the gradation values ​​for which the spectral reflectance is obtained for the reference color are 0, 0.2, 0.5, 0.8, and 1, and the gradation values ​​for which the spectral reflectance is obtained for the prediction target color are 0, 0.3, 0.5, and 1, the union is 0, 0.2, 0.3, 0.5, 0.8, and 1 (see FIG. 16). For the prediction target gradation values ​​included in the union, the predicted value of the spectral reflectance is obtained by the second relational expression, and for the prediction target gradation values ​​not included in the union, the predicted value of the spectral reflectance is obtained by spline interpolation (for example, cubic spline interpolation).

[0112] In this embodiment, it is assumed that the second relational expression is calculated in the same manner as in the second embodiment. However, the second relational expression may be calculated in the same manner as in the first embodiment.

[0113] <3.2 Configuration and Spectral Reflectance Prediction Method (Spectral Characteristic Prediction Method)> The overall configuration of the printing system and the configuration of the print data generating device are similar to those in the first embodiment (see FIGS. 2 and 3), and therefore description thereof will be omitted.

[0114] 17 is a flowchart showing the procedure of the spectral reflectance prediction process in this embodiment. The processes in steps S200 to S240 are similar to the processes in steps S100 to S140 in the first embodiment (see FIG. 4).

[0115] After step S240 is completed, the above-mentioned union is created (step S250). Then, for the reference color, a predicted value of the unknown spectral reflectance among the spectral reflectances of the gradation values ​​included in the union is obtained (step S260). The predicted value of the unknown spectral reflectance is obtained, for example, by performing spline interpolation based on the known spectral reflectance of the reference color. In the example shown in FIG. 16, the gradation value 0.3 is included in the union, but the spectral reflectance of the gradation value 0.3 is not obtained for the reference color. Therefore, in step S260, the spectral reflectance of the gradation value 0.3 for the reference color is obtained, for example, by performing spline interpolation based on the spectral reflectance of at least three gradation values ​​(at least three of gradation values ​​0, 0.2, 0.5, 0.8, and 1) for the reference color. For example, if the spectral reflectances of 11 gradation values ​​in increments of 0.1 from 0 to 1 have been obtained for the reference color, and the spectral reflectances of the prediction target color are obtained for gradation values ​​of 0, 0.5, and 1, then the spectral reflectances of all the gradation values ​​included in the union have been obtained for the reference color, as can be seen from Fig. 18. In such a case, there is no spectral reflectance to be calculated in step S260.

[0116] Next, the maximum gradation value or the characteristic-acquired gradation value is used as the reference gradation value, and a second relational expression expressing the relationship between the spectral reflectance of the reference gradation value and the above-mentioned spectral reflectance of the processing target gradation value for the reference color is obtained in the same manner as in the second embodiment (step S270). In this embodiment, the gradation value included in the union is the processing target gradation value. In the example shown in FIG. 16, the second relational expression corresponding to each of the gradation values ​​0, 0.2, 0.3, 0.5, 0.8, and 1 is obtained by this step S270. In this regard, for example, the second relational expression corresponding to the gradation value 0.2 expresses the relationship between the spectral reflectance of the gradation value 0.3 and the spectral reflectance of the gradation value 0.2, with the spectral reflectance of the gradation value 0.3 as the first reference and the spectral reflectance of the gradation value 0 as the second reference. Furthermore, for example, the second relational expression corresponding to a gradation value of 0.8 represents the relationship between the spectral reflectance of a gradation value of 1 and the spectral reflectance of a gradation value of 0.8, with the spectral reflectance of a gradation value of 1 being the first reference and the spectral reflectance of a gradation value of 0.5 being the second reference.

[0117] After the second relational expression is obtained, the predicted value of the spectral reflectance of the gradation values ​​included in the union of the multiple gradation values ​​as the prediction target gradation value is obtained by applying the spectral reflectance of the reference gradation value (maximum gradation value or characteristic acquired gradation value) for the prediction target color to the corresponding second relational expression (step S280). If 11 gradation values ​​in increments of 0.1 from gradation value 0 to gradation value 1 are the prediction target gradation values, in the example shown in Fig. 16, predicted values ​​of the spectral reflectance of the prediction target color for gradation values ​​0, 0.2, 0.3, 0.5, 0.8, and 1 are obtained by this step S280. In this regard, the predicted value of the spectral reflectance of the gradation value 0.2, for example, is obtained by applying the spectral reflectance of the gradation value 0.3 for the prediction target color to the corresponding second relational expression. For example, the predicted value of the spectral reflectance for a gradation value of 0.8 is found by applying the spectral reflectance for the gradation value of 1 for the color to be predicted to the corresponding second relational expression. Note that for the spectral reflectances of gradation values ​​0, 0.3, 0.5, and 1, the actual measured values ​​may be applied as they are without using the second relational expression.

[0118] Finally, the predicted values ​​of the spectral reflectance of the gradation values ​​not included in the union among the multiple gradation values ​​as the prediction target gradation value are obtained by performing spline interpolation based on the predicted values ​​obtained in step S280 (step S290). If 11 gradation values ​​in increments of 0.1 from gradation value 0 to gradation value 1 are the prediction target gradation values, in the example shown in FIG. 16, predicted values ​​of the spectral reflectance of the prediction target color for gradation values ​​0.1, 0.4, 0.6, 0.7, and 0.9 are obtained by this step S280. At this time, spline interpolation is performed using the predicted values ​​of the spectral reflectance of at least three gradation values ​​of gradation values ​​0, 0.2, 0.3, 0.5, 0.8, and 1 (the predicted values ​​obtained in step S280). Note that linear interpolation can be used instead of spline interpolation, but spline interpolation provides a more accurate prediction value than linear interpolation. However, if all of the multiple gradation values ​​serving as the prediction target gradation value are included in the union, at the end of step S280, the spectral reflectances of all of the prediction target gradation values ​​for the prediction target color have been obtained, and therefore no spectral reflectance is obtained in step S290.

[0119] In this manner, the predicted value of the spectral reflectance of the prediction target tone value for the prediction target color is obtained, and the spectral reflectance prediction process is completed.

[0120] In this embodiment, step S200 realizes a prediction target color setting step, step S210 realizes a first relational expression calculation step, step S220 realizes a first prediction step, step S230 realizes a difference value calculation step, step S240 realizes a reference color selection step, step S250 realizes a union creation step, step S260 realizes a third prediction step, step S270 realizes a second relational expression calculation step, and steps S280 and S290 realize a second prediction step. Also, step S280 realizes a second relational expression utilization step, and step S290 realizes an interpolation step.

[0121] <3.3 Effects> According to this embodiment, the same effects as those of the first and second embodiments can be obtained. In addition, by using the union, the processing of the spectral reflectance prediction program 141 can be prevented from becoming complicated.

[0122] <4.Other> The present invention is not limited to the above-described embodiments (including the modified examples), and various modifications can be made without departing from the spirit of the present invention. For example, in the above-described embodiments, the spectral reflectance obtained by printing the target ink on a substrate is predicted, but the method of the above-described embodiments can also be used to predict the spectral reflectance obtained by printing the target ink on a black substrate. Furthermore, the above-described embodiments and the modified examples can be appropriately combined and implemented so as not to cause any contradiction. [Explanation of symbols]

[0123] 100...print data generating device 141...Spectral reflectance prediction program 200…Plate making equipment 300...Printing device 350…Digital printing equipment 400...colorimeter

Claims

1. A method for predicting a spectral characteristic obtained by applying an ink to a substrate, comprising the steps of: a prediction target color setting step of setting the color of ink for which the spectral characteristics of the maximum gradation value, the spectral characteristics of the minimum gradation value, and N (N is an integer equal to or greater than 1) intermediate gradation value spectral characteristics have been obtained as a prediction target color; a first relational equation calculation step of determining, as a characteristic-acquired gradation value, a middle gradation value for which spectral characteristics have been obtained for the prediction target color, for each of a plurality of sample colors that are colors of a plurality of inks other than the prediction target color and for which the spectral characteristics of the maximum gradation value, the spectral characteristics of the minimum gradation value, and the spectral characteristics of (N+1) or more middle gradation values ​​have been obtained, to express a relationship between the spectral characteristics of the maximum gradation value and the spectral characteristics of the characteristic-acquired gradation value; a first prediction step of calculating a predicted value of the spectral characteristics of the characteristic-acquired gradation value for the prediction target color by applying the spectral characteristics of the maximum gradation value for the prediction target color to a corresponding first relational expression for each of the plurality of sample colors; a difference value calculation step of calculating a difference value between the predicted value calculated in the first prediction step and an actual measurement value of the spectral characteristics of the characteristic-acquired gradation value of the prediction target color for each of the plurality of sample colors; a reference color selection step of selecting, as a reference color, the sample color that has the smallest difference value in the difference value calculation step from among the plurality of sample colors; a second relational expression calculation step of determining a second relational expression that expresses a relationship between the spectral characteristics of the reference gradation value and the spectral characteristics of the processing target gradation value for the reference color, using the maximum gradation value or the characteristic-acquired gradation value as a reference gradation value and the gradation value for which spectral characteristics have been obtained for the reference color or the characteristic-acquired gradation value as a processing target gradation value; a second prediction step of obtaining a predicted value of the spectral characteristics of the prediction target gradation value for the prediction target color using the second relational expression; A method for predicting spectral characteristics, comprising:

2. The number of the characteristic-acquired gradation values ​​is 1, In the second relational expression calculation step, With respect to the processing target gradation value between the maximum gradation value and the characteristic-acquired gradation value, an equation expressing a relationship between the spectral characteristic of the maximum gradation value and the spectral characteristic of the processing target gradation value is obtained as the second relational equation, with the spectral characteristic of the maximum gradation value being a first reference and the spectral characteristic of the characteristic-acquired gradation value being a second reference; 2. The method for predicting spectral characteristics according to claim 1, wherein, for the processing target gradation value between the characteristic-acquired gradation value and the minimum gradation value, an equation expressing a relationship between the spectral characteristics of the characteristic-acquired gradation value and the spectral characteristics of the processing target gradation value is obtained as the second relational equation, with the spectral characteristics of the characteristic-acquired gradation value being a first reference and the spectral characteristics of the minimum gradation value being a second reference.

3. the N intermediate gradation values ​​for which spectral characteristics have been obtained for the prediction target color include a first gradation value and a second gradation value smaller than the first gradation value, In the second relational expression calculation step, a second relational expression is obtained that expresses a relationship between the spectral characteristics of the maximum gradation value and the spectral characteristics of the processing target gradation value between the maximum gradation value and the first gradation value, the spectral characteristics of the maximum gradation value being a first reference and the spectral characteristics of the first gradation value being a second reference; With respect to the processing target gradation value between the first gradation value and the second gradation value, an equation expressing a relationship between the spectral characteristics of the first gradation value and the spectral characteristics of the processing target gradation value is obtained as the second relational equation, with the spectral characteristics of the first gradation value being a first reference and the spectral characteristics of the second gradation value being a second reference; 2. The method for predicting spectral characteristics according to claim 1, wherein, for the processing target gradation value between the second gradation value and the minimum gradation value, an equation expressing a relationship between the spectral characteristics of the second gradation value and the spectral characteristics of the processing target gradation value is obtained as the second relational equation, with the spectral characteristics of the second gradation value being a first reference and the spectral characteristics of the minimum gradation value being a second reference.

4. the N intermediate gradation values ​​for which spectral characteristics have been obtained for the prediction target color include m gradation values ​​from a first gradation value to an m-th gradation value, where m is an integer equal to or greater than 3; where k is an integer between 1 and (m-1), the kth gradation value is greater than the (k+1)th gradation value; In the second relational expression calculation step, a second relational expression is obtained that expresses a relationship between the spectral characteristics of the maximum gradation value and the spectral characteristics of the processing target gradation value between the maximum gradation value and the first gradation value, the spectral characteristics of the maximum gradation value being a first reference and the spectral characteristics of the first gradation value being a second reference; With respect to the processing target gradation value between the k gradation value and the (k+1) gradation value, an equation expressing a relationship between the spectral characteristic of the k gradation value and the spectral characteristic of the processing target gradation value is obtained as the second relational equation, with the spectral characteristic of the k gradation value being a first reference and the spectral characteristic of the (k+1) gradation value being a second reference; 2. The method for predicting spectral characteristics according to claim 1, wherein, for the processing target gradation value between the m gradation value and the minimum gradation value, an equation expressing a relationship between the spectral characteristics of the m gradation value and the spectral characteristics of the processing target gradation value is obtained as the second relational equation, with the spectral characteristics of the m gradation value being a first reference and the spectral characteristics of the minimum gradation value being a second reference.

5. 5. The method for predicting spectral characteristics according to claim 2, wherein in the second relational expression calculation step, data on the spectral characteristics is normalized so that a value of the second reference spectral characteristic becomes 1.

6. In the second relational expression calculation step, an expression expressing a relationship between the spectral characteristics of the maximum gradation value and the spectral characteristics of the processing target gradation value for the reference color is obtained as the second relational expression; 6. The method for predicting spectral characteristics according to claim 1, wherein in the second prediction step, a predicted value of the spectral characteristics of the prediction target gradation value for the prediction target color is obtained by applying the spectral characteristics of the maximum gradation value for the prediction target color to the second relational expression.

7. the number of the prediction target gradation values ​​is two or more, The second prediction step includes: a second relational expression utilization step of determining a predicted value of the spectral characteristics of a gradation value, of which spectral characteristics have been obtained for the reference color, among the two or more prediction target gradation values ​​by applying the spectral characteristics of the reference gradation value for the prediction target color to a corresponding second relational expression; an interpolation step of determining a predicted value of the spectral characteristics of a gradation value, of which the spectral characteristics have not been obtained for the reference color, among the two or more prediction target gradation values ​​by performing spline interpolation based on the predicted value determined in the second relational expression utilization step; The method for predicting a spectral characteristic according to claim 1 , further comprising:

8. a union creation step of creating a union of gradation values ​​for which spectral characteristics have been obtained for the reference color and gradation values ​​for which spectral characteristics have been obtained for the prediction target color, In the second relational expression calculation step, the gradation value included in the union is set as the processing target gradation value; the number of the prediction target gradation values ​​is two or more, The second prediction step includes: a second relational expression utilization step of determining a predicted value of the spectral characteristics of the gradation values ​​included in the union of the two or more prediction target gradation values ​​by applying the spectral characteristics of the reference gradation values ​​for the prediction target color to a corresponding second relational expression; an interpolation step of determining a predicted value of the spectral characteristics of the gradation values ​​not included in the union of the two or more prediction target gradation values ​​by performing spline interpolation based on the predicted value determined in the second relational expression utilization step; The method for predicting a spectral characteristic according to claim 1 , further comprising:

9. 9. The method for predicting spectral characteristics according to claim 8, further comprising, between said union creation step and said second relational expression calculation step, a third prediction step of determining a predicted value of the spectral characteristics of a gradation value for which the spectral characteristics are not obtained for said reference color, said gradation value being the spectral characteristics of the processing target gradation value for said reference color, by performing spline interpolation based on known spectral characteristics for said reference color.

10. 10. The method for predicting spectral characteristics according to claim 1, wherein the difference value calculated in the difference value calculation step is a square error between the predicted value calculated in the first prediction step and an actual measurement value of the spectral characteristics of the characteristic-acquired tone value for the prediction target color.

11. 10. The method for predicting spectral characteristics according to claim 1, wherein the difference value calculated in the difference value calculation step is a color difference based on the predicted value calculated in the first prediction step and an actual measurement value of the spectral characteristics of the characteristic-acquired tone value for the prediction target color.

12. The method for predicting a spectral characteristic according to claim 1 , wherein the spectral characteristic is any one of a spectral reflectance, a spectral absorptance, and a spectral absorption coefficient.

13. A spectral characteristic prediction program for predicting a spectral characteristic obtained by applying an ink to a substrate, On the computer, a prediction target color setting step of setting the color of ink for which the spectral characteristics of the maximum gradation value, the spectral characteristics of the minimum gradation value, and N (N is an integer equal to or greater than 1) intermediate gradation value spectral characteristics have been obtained as a prediction target color; a first relational equation calculation step of determining, as a characteristic-acquired gradation value, a middle gradation value for which spectral characteristics have been obtained for the prediction target color, for each of a plurality of sample colors that are colors of a plurality of inks other than the prediction target color and for which the spectral characteristics of the maximum gradation value, the spectral characteristics of the minimum gradation value, and the spectral characteristics of (N+1) or more middle gradation values ​​have been obtained, to express a relationship between the spectral characteristics of the maximum gradation value and the spectral characteristics of the characteristic-acquired gradation value; a first prediction step of calculating a predicted value of the spectral characteristics of the characteristic-acquired gradation value for the prediction target color by applying the spectral characteristics of the maximum gradation value for the prediction target color to a corresponding first relational expression for each of the plurality of sample colors; a difference value calculation step of calculating a difference value between the predicted value calculated in the first prediction step and an actual measurement value of the spectral characteristics of the characteristic-acquired gradation value of the prediction target color for each of the plurality of sample colors; a reference color selection step of selecting, as a reference color, the sample color that has the smallest difference value in the difference value calculation step from among the plurality of sample colors; a second relational expression calculation step of determining a second relational expression that expresses a relationship between the spectral characteristics of the reference gradation value and the spectral characteristics of the processing target gradation value for the reference color, using the maximum gradation value or the characteristic-acquired gradation value as a reference gradation value and the gradation value for which spectral characteristics have been obtained for the reference color or the characteristic-acquired gradation value as a processing target gradation value; a second prediction step of obtaining a predicted value of the spectral characteristics of the prediction target gradation value for the prediction target color using the second relational expression; A spectral characteristic prediction program for executing the above.

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