Color processing apparatus and color processing method

Abstract

The present invention provides a color processing apparatus and a color processing method that can perform spectral color reproduction with sufficient accuracy while suppressing the amount of computation required. [Solution] The color processing apparatus 1 has a control unit, and the distribution of each of the multiple inks that reproduce the sample color is calculated by the control unit. The control unit separates the target spectral transmittance TT, which is the spectral transmittance of the sample, into a fundamental component, which is the component whose tristimulus value matches the original reflectance, and a metameric black component, which is the component whose tristimulus value is zero. The control unit also performs a convergence calculation to minimize the difference between the target spectral transmittance TT and the reproduced spectral transmittance, which is the spectral transmittance related to each distribution, by updating the estimated spectral transmittance of the metameric black while fixing the fundamental component. The convergence calculation is performed by a sequential quadratic planning process SS with the target XYZ value TC, which is the tristimulus value of the target color obtained by calculating the target spectral transmittance, as a constraint condition.

Description

[Technical Field]

[0001] The present invention relates to a color processing apparatus and a color processing method. [Background technology]

[0002] Spectroscopic color reproduction is known, as disclosed in Japanese Patent Publication No. 2005-508125 (Patent Document 1) and the paper by Iino et al. (Non-Patent Document 1). In the spectral color reproduction described in Patent Document 1, the color of the target image obtained from the target color device and the color of the copy image produced by the output printer of that target image are processed to match spectrally. In the spectral color reproduction described in Non-Patent Document 1, spectral color reproduction is performed using the parameric decomposition method. In spectral color reproduction, at least one of the spectral transmittance and spectral reflectance related to a given target color, i.e., spectral transmittance, is measured, and the goal is to ensure that the spectral transmittance of the color reproduced by the ink, etc., perfectly matches that of the target color. When the spectral transmittances perfectly match, it is called perfect color matching. When perfect color matching is achieved, perfect color reproduction is achieved under any light source. Another known method of color reproduction is colorimetric color reproduction. In colorimetric color reproduction, a standard observer with a specific viewing angle under a specific light source is assumed, and the tristimulus values ​​for the standard observer are calculated to ensure that the tristimulus values ​​of the target color match those of the color to be reproduced. In colorimetric color reproduction, color matching is ensured under the light source related to the standard observer, but color matching under other light sources is not guaranteed. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Special Publication No. 2005-508125 [Non-Patent Document 1] Koichi Iino, et al., "Spectroscopic Color Reproduction Using Parameric Decomposition Method," Journal of the Japan Society of Printing Science and Technology, Japan Society of Printing Science and Technology, 2012, Vol. 49, No. 6, pp. 424-434. [Overview of the project] [Problems that the invention aims to solve]

[0004] The spectral color reproduction described above is effective in that it can achieve equal color under various light sources compared to colorimetric color reproduction. However, in spectral color reproduction, perfect matching of spectral transmittance, etc., is difficult due to the limitations of the colors that inks can represent and the manifestation of at least one of the nonlinearities of the color mixing model. This makes the calculations for spectral color reproduction complex and increases the amount of computation required.

[0005] The main objective of the present invention is to provide a color processing apparatus and a color processing method that can perform spectral color reproduction with sufficient accuracy while suppressing the amount of computation required. [Means for solving the problem]

[0006] This specification discloses a color processing apparatus. The color processing apparatus has a control unit, and the distribution of each of a plurality of dyes that reproduce the color of a sample may be calculated by the control unit. The control unit may use the fact that at least one of the target spectral transmittance, which is the spectral transmittance of the sample, and the target spectral reflectance, which is the spectral reflectance of the sample, can be separated into a fundamental component, which is a component whose tristimulus value matches at least one of the original transmittance and reflectance, and a metameric black component, which is a component whose tristimulus value is zero. The control unit may perform a convergence calculation to minimize the error between at least one of the target spectral transmittance and target spectral reflectance and the reproduced spectral transmittance, which is the spectral transmittance related to each distribution, and the reproduced spectral reflectance, which is the spectral reflectance related to each distribution, by updating the metameric black of at least one of the estimated spectral transmittance and spectral reflectance while fixing the fundamental component. The convergence calculation may be performed by a nonlinear optimization method that uses the parameters of the target color obtained by calculating at least one of the target spectral transmittance and target spectral reflectance as constraints. Furthermore, this specification discloses a color processing method. This color processing method may be executed by a computer having a control unit, and each distribution of a plurality of dyes for reproducing the color of a sample may be calculated by the control unit. The color processing method may include a convergence calculation step that uses the fact that at least one of the target spectral transmittance, which is the spectral transmittance of the sample, and the target spectral reflectance, which is the spectral reflectance of the sample, can be separated into a fundamental, whose tristimulus values match the original reflectance, and a metameric black, whose tristimulus values are zero. The color processing method may include a convergence calculation step that performs a convergence calculation to minimize the error between at least one of the target spectral transmittance and the target spectral reflectance and the reproduced spectral transmittance, which is the spectral transmittance related to each distribution, and the reproduced spectral reflectance, which is the spectral reflectance related to each distribution, by updating at least one of the estimated spectral transmittance and spectral reflectance while fixing the fundamental. The convergence calculation may be performed by a non-linear optimization method that uses, as a constraint condition, the parameters of the target color obtained by calculating at least one of the target spectral transmittance and the target spectral reflectance.

Advantages of the Invention

[0007] The main advantage of the present invention is to provide a color processing apparatus and a color processing method that can perform spectral color reproduction with sufficient accuracy while suppressing the amount of calculation.

Brief Description of the Drawings

[0008] [Figure 1] It is a block diagram of a color processing apparatus and related devices according to the present invention. [Figure 2] It is a flowchart related to the process executed in the color processing apparatus of FIG. 1. [Figure 3] It is a graph showing the relationship between the concentration of each of red, yellow, and blue and the natural logarithm of Trep, -log(Trep), for light with a wavelength of 480 nm in Example 1-1. [Figure 4]This graph shows the relationship between the color concentrations of red, yellow, and blue light at a wavelength of 600 nm and the natural logarithm of Trep, which is -log(Trep), in Example 1-1. [Figure 5] This graph shows the spectral transmittance of the sample and the spectral transmittance of the spectral color reproduction in Example 1-1. [Figure 6] This graph shows the spectral transmittance of the sample and the spectral transmittance of the spectral color reproduction in Example 1-2. [Figure 7] This graph shows the relationship between the color intensities of red, yellow, and blue and the natural logarithm of Trep, -log(Trep), for light with a wavelength of 480 nm in Example 2-1. [Figure 8] This graph shows the relationship between the color concentrations of red, yellow, and blue light at a wavelength of 600 nm and the natural logarithm of Trep, which is -log(Trep), in Example 2-1. [Figure 9] This graph shows the spectral transmittance of the sample and the spectral transmittance of the spectral color reproduction in Example 2-1. [Figure 10] This graph shows the spectral transmittance of the sample and the spectral transmittance of the spectral color reproduction in Example 2-2. [Modes for carrying out the invention]

[0009] Examples of embodiments of the present invention are described below. The present invention is not limited to the following embodiments.

[0010] The color processing device 1 according to this embodiment includes a computer and, as shown in Figure 1, comprises a display unit 2, an input unit 4, a storage unit 6, a communication unit 7, and a control unit 8.

[0011] The display unit 2 displays various types of information and is, for example, a liquid crystal display or an organic electroluminescent display. The input unit 4 accepts input of various types of information, and is, for example, at least one of a keyboard and a pointing device. Furthermore, the display unit 2 and the input unit 4 may be integrated, such as a touch panel.

[0012] The storage unit 6 stores various types of information and is, for example, at least one of a hard disk, memory, and disk drive. The communication unit 7 communicates various types of information with external devices, and in this case, it communicates with devices connected to a local area network (LAN). The control unit 8 controls various parts of the color processing device 1, such as the central processing unit (CPU). The control unit 8 sequentially reads the color processing program stored in the memory unit 6 and performs color reproduction processing according to the program.

[0013] The color processing method is carried out by the processing performed in the color processing apparatus 1. In this processing, spectral color reproduction is performed by optimization with colorimetric constraints, and the parameric decomposition method is used. Below, the color of a translucent and colored sample is reproduced when dyeing a translucent substrate using C=(C1,C2,C3,···,C n The process for determining the ink distribution for each of the n colors is explained. Each ink belongs to the pigment, which is the substance that gives color to an object. In spectral color reproduction, the sample color is reproduced by a combination of multiple pigments. Furthermore, the applications of the present invention are not limited to dyeing such substrates, but can include a variety of other applications, such as printing electronic images, i.e., determining the ink distribution in a printer to reproduce the colors of an electronic image in printed material, or displaying electronic images, i.e., determining the brightness distribution in each pixel to reproduce the colors of an electronic image on a display. Printer inks and display pixels belong to the category of pigments. Moreover, pigments are not limited to the three colors of red, yellow, and blue; some or all of these may be changed to other colors, or other colors may be added to make four or more colors, or there may be just two colors.

[0014] In the parameric decomposition method, at least one of the spectral transmittance and spectral reflectance, i.e., spectral transmittance, is separated into fundamental stimuli and metameric black (separation step). Fundamental stimuli are the spectral transmittance components whose tristimulus value matches the original reflectance. Metameric black are the spectral transmittance components whose tristimulus value is 0. For the sake of explanation, the case where spectral transmittance is used will be mainly described below. When spectral reflectance is used instead of spectral transmittance, or when spectral transmittance and spectral reflectance are used in combination, the processing is carried out in the same manner as when spectral transmittance is used. In this spectral color reproduction, the estimated metameric black is minimized using a nonlinear optimization method, with the constraint that the fundamentals obtained from the measured values ​​are fixed, as shown in equation (1-1) below. Equation (1-1) is stored in the memory unit 6 as part of the color processing program (while the color processing program is accessible). Similarly, other equations from equation (1-2) onward, described later, are also stored in the memory unit 6.

[0015]

number

[0016] Here, T target This is the measured spectral transmittance of the target color, X target , Y target , and Z target is, T target This also includes the tristimulus values ​​of the target color, calculated from the information of the specified light source and the color matching function of a standard observer.

[0017] Also, T rep This is shown by the following equation (1-2).

[0018]

number

[0019] That is, T repis the coefficient vector a obtained from the spectral transmittance T0 of the base material and the spectral transmittance of the single-color ink k (k = 1, 2, 3, ···, n) is used, and it is the reproduced spectral transmittance that is the spectral transmittance reproduced from the ink concentration parameter RYB value. X, Y, and Z are the tristimulus values calculated from f in Equation (1-1). The concentration of the ink can also be regarded as the distribution of the ink. n is the number of ink types and can be any natural number of 2 or more. Also, k is the number corresponding to the type of pigment

[0020] Furthermore, ε is a constant parameter (for example, 0.01) representing an error or a margin

[0021] T target , T0 are both functions of wavelength. Also, a k are both functions of wavelength. C k is the distribution of each ink, and here it takes values that are stepwise, discrete, and relative (for example, natural numbers from 0 to 512 respectively)

[0022] Also, when the natural logarithm is taken on both sides of Equation (1-2), it becomes the following Equation (1-3)

[0023]

Equation

[0024] In order to suppress the error more than the above Equation (1-2), as shown in the following Equations (1-4) and (1-5), the function of the transmittance calculation may be non-linearized. Here, f k (C k ) is the function of each ink for fitting Also, as shown in the following Equations (1-4) and (1-6), if the functions g(C) of a plurality of inks for fitting and the error constant E are further taken into account for Equation (1-5), the error is further suppressed

[0025]

Equation

[0026]

number

[0027]

number

[0028] Furthermore, when the natural logarithm is taken on both sides of equations (1-4) and (1-6), we obtain the following equation (1-7).

[0029]

number

[0030] Nonlinear optimization methods are techniques used for nonlinear problems, obtaining the optimal solution by repeatedly solving subproblems to find the best solution that satisfies the objective function and constraints.

[0031] By using a nonlinear optimization method (convergence calculation step) employing parameric decomposition, the coloring of each ink in a calculated distribution is applied to a predetermined substrate relative to the sample, thereby obtaining a colored substrate, i.e., a product, with spectrally reproduced color.

[0032] The following explanation will describe the case where successive quadratic programming is used as the nonlinear optimization method, where n is n=3, k is k=(1,2,3), and the ink distributions for R (red), Y (yellow), and B (blue) are determined. Note that the nonlinear optimization method is not limited to successive quadratic programming. Figure 2 is a flowchart showing the processes performed in the color processing apparatus 1 in this case. The following describes the process of determining the R (red), Y (yellow), and B (blue) ink distributions to reproduce the color of a translucent, colored sample when dyeing a translucent substrate.

[0033] In this case, the general equation (1-1) becomes the more specific equation (2-1).

[0034]

number

[0035] Here, X target , Y target , and Z target is, T target This also includes the tristimulus values ​​of the target color, i.e., the target XYZ values ​​TC, calculated from the information of the specified light source and the color matching function of a standard observer. Also, T in equation (1-2) rep Since log-linear interpolation LI is performed, it is expressed by the following equation (2-2).

[0036]

number

[0037] T rep This is a coefficient vector (a) obtained from the spectral transmittance T0 of the substrate and the spectral transmittance of the single color of the ink. R ,a Y ,a B The reproduced spectral transmittance is the spectral transmittance reproduced from the ink concentration parameter RYB value using ), where X, Y, and Z are tristimulus values ​​calculated from f in equation (2-1). T target T0 is a function of wavelength in both cases. Also, a R a Y a B R, Y, and B are the coefficients for red, yellow, and blue, respectively, and are functions of wavelength.

[0038] Furthermore, when the natural logarithm is taken on both sides of equation (2-2), we obtain the following equation (2-3).

[0039]

number

[0040] In order to suppress errors beyond those shown in equation (2-2) relating to the log-linear interpolation LI above, the function for calculating transmittance should be made nonlinear, as shown in the following equations (2-4) and (2-5), which correspond to equations (1-4) and (1-5) in order. Here, f1(R) is a function of R for fitting, f2(Y) is a function of Y for fitting, and f3(B) is a function of B for fitting. Furthermore, as shown in equations (2-4) and (2-6) which correspond to equations (1-4) and (1-6) above, if a fitting function g(R,Y,B) and an error constant E are added to equation (2-5), the error can be suppressed even further.

[0041]

number

[0042]

number

[0043]

number

[0044] Furthermore, when the natural logarithm is taken on both sides of equations (2-4) and (2-6), we obtain the following equation (2-7).

[0045]

number

[0046] Sequential Least Squares Programming (SLSQP) is a widely used method for nonlinear problems, obtaining the optimal solution by repeatedly solving subproblems to find the best solution that satisfies the objective function and constraints. Figure 2 shows the known information KI, information processing IP, and output OP related to the sequential quadratic programming method.

[0047] The known information KI includes the target spectral transmittance TT, the substrate spectral transmittance BT, and the monochromatic spectral transmittance ST of RYB as a monochromatic spectral transmittance. The known information KI is stored in the storage unit 6. The target spectral transmittance TT is the spectral transmittance of the sample, indicates the sample color, and has an aspect as an input. The target spectral transmittance TT can be input from the input unit 4. The substrate spectral transmittance BT is a parameter file determined by the selected substrate. Since the substrate spectral transmittance BT is uniquely determined by the substrate selection, it has aspects of an internal parameter. The substrate selection can be input via input unit 4. The RYB monochromatic spectral transmittance ST is the spectral transmittance of each ink color. Since the RYB monochromatic spectral transmittance ST is uniquely determined by the type of ink and substrate used, it has aspects of an internal parameter. The selection of each ink can be input via input unit 4. Furthermore, at least one of the substrate spectral transmittance BT and the RYB monochromatic spectral transmittance ST may be input directly from the input unit 4.

[0048] The output OP is obtained as a result of information processing IP using known information KI. The output OP is the R, Y, and B values, i.e., the RYB value ID, which represents a spectral color reproduction that takes into account the substrate relative to the sample.

[0049] In the information processing IP, various processes for performing sequential quadratic programming SS related to the constrained least squares method are carried out by the control unit 8. Through sequential quadratic programming SS, part or all of the output OP is calculated to converge from part or all of the known information KI. The sequential quadratic programming process SS requires initial values, constraints, and an objective function for the search for the optimal solution. The sequential quadratic programming process SS outputs the RYB value ID. The least squares method in sequential quadratic programming (SS) is a technique for minimizing the error between the target spectral transmittance and the reproducible spectral transmittance. However, the least squares method is not the only method for minimizing errors.

[0050] Regarding the initial values ​​as parameters, the control unit 8 uses the provisional RYB value TP obtained by multiple regression analysis HR of spectral color reproduction results without constraints as the initial value. The provisional RYB value TP represents the provisional distribution of each ink, i.e., the provisional pigment distribution. The control unit 8 uses the substrate-excluded target spectral transmittance WT and the RYB wavelength slope data EP in the multiple regression analysis HR. The substrate-excluded target spectral transmittance WT is calculated from the logarithmic difference LD between the target spectral transmittance TT and the substrate spectral transmittance BT. The RYB wavelength slope data EP is obtained by performing logarithmic linear interpolation LI on the RYB monochromatic spectral transmittance ST.

[0051] Regarding the constraint conditions, the control unit 8 assumes the color matching function of a standard observer in a 10° field of view under an AAA light source when calculating tristimulus values. Therefore, it calculates the target XYZ value TC from the result of the XYZ value calculation XC under a 10° field of view AAA light source and uses this as the constraint condition. Furthermore, the constraints are not limited to target XYZ values, which are tristimulus values, but can be any values ​​that can be derived from spectral transmittance or the like through a linear transformation, as long as they are parameters of the target color.

[0052] Regarding the objective function, the control unit 8 obtains the objective function from the target spectral transmittance TT. In the case of equation (2-2), the coefficient vector (a R ,a Y ,a B ) is determined for each wavelength by linear regression from the spectral transmittance of 4 types (12 types in total) dyed in a single color by a specific distribution of red, yellow, and blue. R ,a Y ,a B This is taken into account as an initial value in the sequential secondary programming process SS, as a provisional pigment distribution, which is a hypothetical distribution of each pigment. In the cases of equations (2-4) and (2-5), the functions f1(R), f2(Y), and f3(B) are determined, for example, from the respective spectral transmittances in the same manner as in the case of equation (2-2) by nonlinear regression including log-nonlinear interpolation and multiple regression analysis. The functions f1(R), f2(Y), and f3(B) are taken into account as initial values ​​in the sequential quadratic programming process SS as a hypothetical dye distribution function, which is a function relating to the hypothetical distribution of each dye. In the cases of equations (2-4) and (2-6), the functions f1(R), f2(Y), f3(B), g(R,Y,B), and the predetermined error constant E are determined, for example, from the spectral transmittances in the same way as in the case of equation (2-2) by nonlinear regression including log-nonlinear interpolation and multiple regression analysis. The functions f1(R), f2(Y), f3(B), and g(R,Y,B) are taken into account as initial values ​​in the sequential quadratic programming process SS as a hypothetical dye distribution function, which is a function relating to the hypothetical distribution of each dye.

[0053] By performing a sequential quadratic programming process SS (convergence calculation step) using the parameric decomposition method, information processing IP related to the convergence calculation is performed on the known information KI, and once output OP is obtained, the calculated distribution, i.e., the coloring of each ink at the RYB value ID, is applied to the sample onto a predetermined substrate, thereby obtaining a colored substrate, i.e., a product, with spectrally reproduced color. [Examples]

[0054] Next, Examples 1 and 2 of the present invention will be described. Example 1 includes Example 1-1 relating to the reproduction of existing colors and Example 1-2 relating to the reproduction of non-existent colors. Example 2 includes Example 2-1 relating to the reproduction of existing colors and Example 2-2 relating to the reproduction of non-existent colors. Here, "existing color" refers to a color measured in a product created using a specific RYB value with a designated device. "Non-existent color" refers to a color that cannot be reproduced by the designated device related to a specific RYB value, but is the optimal color for a given transmittance shape based on a hypothetical RYB value. Furthermore, the present invention is not limited to the following examples. Depending on how the present invention is interpreted, some examples may be comparative examples that do not belong to the present invention.

[0055] [Example 1-1] Example 1-1 attempts to reproduce existing colors using equations (2-2) and (2-3) related to logarithmic linear interpolation LI. Figure 3 shows the concentrations of red, yellow, and blue light and T for light with a wavelength of 480 nm. rep log(T) is the natural logarithm of log(T) rep This graph shows the relationship between the concentrations of red, yellow, and blue light and T for light with a wavelength of 600 nm. Figure 4 shows the relationship between the concentrations of red, yellow, and blue light and T rep log(T) is the natural logarithm of log(T) rep This graph shows the relationship with ). In Figures 3 and 4, the solid line relates to blue, the dashed line relates to red, and the dotted line relates to yellow. Also, in Figures 3 and 4, the horizontal axis is concentration (relative value, unitless), and the vertical axis is log(T). rep This is the logarithmic transmittance.

[0056] In Example 1-1, a spectral color reproduction of the transmittance distribution of a sample was achieved using an ink having RYB wavelength slope data EP after logarithmic linear interpolation LI for the RYB monochromatic spectral transmittance ST, as shown in Figures 3 and 4, and a predetermined substrate. Figure 5 is a graph showing the spectral transmittance of the sample and the spectral transmittance of the spectral color reproduction in this case. As shown in Figure 5, the spectral transmittance of the sample and the spectral transmittance of the spectrally reproduced color almost completely overlap across the entire visible spectrum. Therefore, the sample color is spectrally reproduced in the range of existing colors. Here, the visible range is the wavelength range from 400 nm to 800 nm. The visible range can be varied. For example, the lower limit (nm) of the visible range could be any of 380, 390, 410, 420, 430, 440, or 450. Similarly, the upper limit (nm) of the visible range could be any of 700, 720, 740, 750, 760, 770, 780, 790, 810, or 820.

[0057] [Examples 1-2] Examples 1-2 attempt to reproduce non-existent colors using equations (2-2) and (2-3) related to logarithmic linear interpolation LI. For the red, yellow, and blue inks, those shown in Figures 3 and 4, etc., are used, as in Example 1-1. In Example 1-2, unlike Example 1-1, if the condition that the tristimulus values ​​X, Y, and Z match is met in the sequential secondary planning process SS, spectral color reproduction related to spectral transmittance that differs in some respects from the spectral transmittance of the sample is permitted. Therefore, in Example 1-2, for example as shown in Figure 6, although the spectral transmittance differs from that of the sample in some parts of the visible range, such as between 550 nm and 670 nm, color reproduction is achieved because the tristimulus values ​​X, Y, and Z match, thus reproducing colors that do not exist.

[0058] [Summary of Example 1] The color processing apparatus 1 of Example 1 has a control unit 8, and the distribution of each of the multiple inks that reproduce the sample color is calculated by the control unit 8. The control unit 8 utilizes the fact that the target spectral transmittance TT, which is the spectral transmittance of the sample, can be separated into a fundamental component, which is the component whose tristimulus value matches the original reflectance, and a metameric black component, which is the component whose tristimulus value is zero. Furthermore, while fixing the fundamental component, the control unit 8 updates the estimated spectral transmittance of the metameric black component, and performs a convergence calculation to minimize the error between the target spectral transmittance TT and the reproduced spectral transmittance, which is the spectral transmittance related to each distribution, using the least squares method as an example of an error minimization method. The convergence calculation is performed by a sequential quadratic programming process SS as an example of a nonlinear optimization method, with the target XYZ value TC, which is the tristimulus value of the target color as an example of a parameter of the target color obtained by calculating the target spectral transmittance TT, as a constraint condition. Therefore, the color processing apparatus 1 of Example 1 can perform spectral color reproduction with sufficient accuracy while suppressing the amount of computation.

[0059] Furthermore, in Embodiment 1, the control unit 8 uses as an initial value a provisional RYB value TP, which is a provisional distribution of each ink calculated based on the coefficient vector obtained by log-linear interpolation LI from the RYB monochromatic spectral transmittance ST, which is the spectral transmittance of each ink, i.e., the RYB wavelength slope data EP. Therefore, in the color processing apparatus 1 of Example 1, the amount of computation is further reduced, and spectral color reproduction can be performed with even greater accuracy.

[0060] [Example 2-1] Example 2-1 attempts to reproduce existing colors using equations (2-4), (2-6), and (2-7) related to logarithmic nonlinear interpolation. Figure 7 shows the concentrations of red, yellow, and blue light and T for light with a wavelength of 480 nm. rep log(T) is the natural logarithm of log(T) rep This graph shows the relationship between the intensity of red, yellow, and blue light and T for light with a wavelength of 600 nm. Figure 8 shows the relationship between the intensity of each color (red, yellow, and blue) and T rep log(T) is the natural logarithm of log(T) rep This graph shows the relationship with ). In Figures 7 and 8, the solid line relates to blue, the dashed line relates to red, and the dotted line relates to yellow. Also, in Figures 7 and 8, the horizontal axis is concentration (relative value, unitless), and the vertical axis is log(T). rep This is the logarithmic transmittance.

[0061] In Example 2-1, the spectral color reproduction of a sample transmittance distribution was performed using an ink having RYB wavelength slope data EP after logarithmically nonlinear interpolation of the RYB monochromatic spectral transmittance ST, as shown in Figures 7 and 8, and a predetermined substrate. Logarithmic nonlinear interpolation was performed instead of logarithmic linear interpolation LI in Figure 2. Here, the control unit 8 divided the density of each color into multiple intervals delimited by endpoints where the slope in the graph changes, and treated f1(R), f2(Y), and f3(B) as nonlinear functions with slopes in each respective interval. The control unit 8 may also perform nonlinear interpolation by fitting f1(R), f2(Y), f3(B), and g(R,Y,B) to a quadratic function, a cubic function, or a function of order four or higher, in addition to setting multiple intervals. Setting multiple intervals and fitting to a quadratic function or the like may be used in combination. Figure 9 is a graph showing the spectral transmittance of the sample and the spectral transmittance of the spectral color reproduction in this case. As shown in Figure 9, the spectral transmittance of the sample and the spectral transmittance of the spectrally reproduced color almost completely overlap across the entire visible spectrum. Therefore, the sample color is spectrally reproduced in the range of existing colors. Furthermore, the agreement rate between the spectral transmittance of the sample in Figure 9 related to Example 2-1 and the spectral transmittance of the spectral color reproduction is higher than the agreement rate between the spectral transmittance of the sample in Figure 5 related to Example 1-1 and the spectral transmittance of the spectral color reproduction. Therefore, Example 2-1, which relates to log-nonlinear interpolation, achieves even better spectral color reproduction than Example 1-1, which relates to log-linear interpolation LI.

[0062] [Example 2-2] Example 2-2 attempts to reproduce non-existent colors using equations (2-4), (2-6), and (2-7) related to logarithmic nonlinear interpolation. For the red, yellow, and blue inks, those shown in Figures 7 and 8, etc., are used, as in Example 2-1. In Example 2-2, unlike Example 2-1, if the condition that the tristimulus values ​​X, Y, and Z match is met in the sequential secondary planning process SS, spectral color reproduction related to spectral transmittance that differs in some respects from the spectral transmittance of the sample is permitted. Therefore, in Example 2-2, for example as shown in Figure 10, although the spectral transmittance differs from that of the sample in some parts of the visible range, such as between 550 nm and 670 nm, color reproduction is achieved because the tristimulus values ​​X, Y, and Z match, thus reproducing colors that do not exist. Furthermore, the agreement rate between the spectral transmittance of the sample in Figure 10 related to Example 2-2 and the spectral transmittance of the spectral color reproduction is higher than the agreement rate between the spectral transmittance of the sample in Figure 6 related to Example 1-2 and the spectral transmittance of the spectral color reproduction. Therefore, Example 2-2, which relates to log-nonlinear interpolation, achieves even better spectral color reproduction than Example 1-2, which relates to log-linear interpolation LI.

[0063] [Summary of Example 2] The color processing apparatus 1 of Example 2 has a control unit 8, and the distribution of each of the multiple inks that reproduce the sample color is calculated by the control unit 8. The control unit 8 utilizes the fact that the target spectral transmittance TT, which is the spectral transmittance of the sample, can be separated into a fundamental component, which is the component whose tristimulus value matches the original reflectance, and a metameric black component, which is the component whose tristimulus value is zero. Furthermore, while fixing the fundamental component, the control unit 8 updates the estimated spectral transmittance of the metameric black component, and performs a convergence calculation to minimize the error between the target spectral transmittance TT and the reproduced spectral transmittance, which is the spectral transmittance related to each distribution, using the least squares method as an example of an error minimization method. The convergence calculation is performed by a sequential quadratic programming process SS as an example of a nonlinear optimization method, with the target XYZ value TC, which is the tristimulus value of the target color as an example of a parameter of the target color obtained by calculating the target spectral transmittance TT, as a constraint condition. Therefore, the color processing apparatus 1 of Example 2 can perform spectral color reproduction with sufficient accuracy while suppressing the amount of computation.

[0064] In Example 2, the control unit 8 uses as an initial value a hypothetical dye distribution function, which is a function relating to the distribution of each ink, calculated based on functions f1(R), f2(Y), f3(B), and g(R,Y,B) obtained by logarithmic nonlinear interpolation from the RYB monochromatic spectral transmittance ST, which is the spectral transmittance for each ink, in the sequential secondary planning process SS. Therefore, although the computational load of the color processing apparatus 1 in Example 2 is slightly increased compared to Example 1, spectral color reproduction can be performed with higher accuracy than in Example 1. [Explanation of Symbols]

[0065] 1. Color Processing Equipment 8. Control Unit EP··RYB wavelength slope data (coefficient vector) LI ·· Logarithmic linear interpolation SS...Sequential Secondary Schedule Processing ST··RYB Monochromatic Spectral Transmittance (Monochromatic Spectral Transmittance) TC ··Target XYZ values TT··Target spectral transmittance

Claims

1. A color processing apparatus having a control unit, wherein the distribution of each of a plurality of pigments that reproduce a sample color is calculated by the control unit, The control unit, Using the fact that at least one of the spectral transmittance of the sample, which is the target spectral transmittance, and the spectral reflectance of the sample, which is the target spectral reflectance, can be separated into a fundamental component whose tristimulus value matches at least one of the original transmittance and reflectance, and a metameric black component whose tristimulus value is zero, While fixing the fundamentals, a convergence calculation is performed to minimize the error between at least one of the target spectral transmittance and target spectral reflectance and the reproduced spectral transmittance, which is the spectral transmittance related to each of the distributions, and the reproduced spectral reflectance, which is the spectral reflectance related to each of the distributions, by updating the metameric black of the estimated spectral transmittance and spectral reflectance. The convergence calculation is performed using a nonlinear optimization method that uses the target color parameter obtained by calculating at least one of the target spectral transmittance and the target spectral reflectance as a constraint. A color treatment apparatus characterized by the following:

2. The control unit, In the convergence calculation, the parameter is a hypothetical color distribution, which is a hypothetical distribution of each color calculated based on coefficient vectors obtained by log-linear interpolation from the spectral transmittance of each monochromatic color, which is the spectral transmittance of each color. The color processing apparatus according to claim 1.

3. The control unit, In the convergence calculation, the parameter is a hypothetical dye distribution function, which is a function relating to the hypothetical distribution of each dye, calculated based on a function obtained by logarithmic nonlinear interpolation from the monochromatic spectral transmittances, which are the spectral transmittances for each dye. The color processing apparatus according to claim 1.

4. The minimization of the error in the aforementioned convergence calculation is performed by the least squares method. The color processing apparatus according to claim 1.

5. The parameters of the target color are the target XYZ values, which are the tristimulus values ​​of the target color. The color processing apparatus according to claim 1.

6. The aforementioned nonlinear optimization method is a successive quadratic programming method. The color processing apparatus according to claim 1.

7. A color processing method performed by a computer having a control unit, wherein the distribution of each of a plurality of pigments that reproduce a sample color is calculated by the control unit, Using the fact that at least one of the spectral transmittance of the sample, which is the target spectral transmittance, and the spectral reflectance of the sample, which is the target spectral reflectance, can be separated into a fundamental component whose tristimulus value matches the original reflectance, and a metameric black component whose tristimulus value is zero, A convergence calculation step is performed to minimize the error between at least one of the target spectral transmittance and target spectral reflectance and the reproduced spectral transmittance, which is the spectral transmittance related to each distribution, and the reproduced spectral reflectance, which is the spectral reflectance related to each distribution, by updating the metameric black of at least one of the estimated spectral transmittance and spectral reflectance while fixing the fundamentals. It is equipped with, The convergence calculation is performed using a nonlinear optimization method that uses the target color parameter obtained by calculating at least one of the target spectral transmittance and the target spectral reflectance as a constraint. A color processing method characterized by the above.

8. In the convergence calculation step, the parameter is a hypothetical color distribution, which is a hypothetical distribution of each color calculated based on a coefficient vector obtained by log-linear interpolation from the monochromatic spectral transmittance, which is the spectral transmittance for each color. The color treatment method according to feature 7.

9. In the convergence calculation step, the parameter is a hypothetical dye distribution function, which is a function relating to the hypothetical distribution of each dye, calculated based on a function obtained by logarithmic nonlinear interpolation from the monochromatic spectral transmittances, which are the spectral transmittances for each dye. The color treatment method according to feature 7.

10. The minimization of the error in the aforementioned convergence calculation is performed by the least squares method. The color treatment method according to feature 7.

11. The parameters of the target color are the target XYZ values, which are the tristimulus values ​​of the target color. The color treatment method according to feature 7.

12. The aforementioned nonlinear optimization method is a successive quadratic programming method. The color treatment method according to feature 7.

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