JP2008312119A - Method of estimating colorimetric value related to color patch, method of preparing device profile using the same and image processor - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To more precisely estimate a colorimetric value using a small number of color patch. <P>SOLUTION: As a first step, the colorimetric value related to N color patches is approximated by a printing system model and a parameter thereof to store the model parameter. As a second step, the colorimetric value related to M (<N) color patches using the model parameter obtained in the first step as an initial value is approximated by the model and model parameter. The colorimetric value to an arbitrary color patch is estimated through the two steps. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a measurement value estimation method for color patches, a device profile creation method using the method, and an image processing apparatus, and more particularly to estimation of colorimetric values for color matching between various input / output devices. It is.

  Color matching using a profile, which is data representing color conversion characteristics, is performed between a plurality of color input / output devices such as an input device such as a scanner or a digital camera, or an output device such as a monitor or a printer.

  For example, a printer output profile is created by the following method. First, based on RGB values (or CMYK values) which are color signals in a color space depending on the printer, a predetermined number of color patches of those colors are output by the printer, and the color patches are color-measured to depend on the printer. An XYZ value (or Lab value), which is a color signal in the color space not to be obtained, is obtained, and a relationship between the R, G, B value and the X, Y, Z value is obtained. Next, the masking coefficient is determined by an iterative method or the like using the relationship from the RGB value thus obtained to the XYZ value, and the mapping from the RGB value to the XYZ value is obtained, thereby reversing the relationship between them. A relationship from an XYZ value (or Lab value) to an RGB value (or CMYK value), which is a conversion relationship, can be obtained as color correction data.

  In the profile creation process as described above, when obtaining the relationship from the RGB value (or CMYK value) to the XYZ value (or Lab value), the accuracy increases as the number of samples such as patches increases. It is not realistic to print out all the colors as samples. Therefore, in order to obtain the relationship from the RGB value (or CMYK value) to the XYZ value (or Lab value), the following method has been conventionally used.

  (1) A method of obtaining an XYZ value by a Neugebauer equation that measures a basic color such as RGB and uses it as a stimulus value.

  (2) The color patches having the same distance in the color space are measured to obtain the relationship between the RGB values and the XYZ values, and the colorimetric values are estimated by linear interpolation for intermediate colors between these color patches. To find the relationship.

(3) A method that is similar to the method of (2) above, but performs curve interpolation in order to improve the accuracy of the relationship obtained by measuring the color of the patch.
Japanese Unexamined Patent Publication No. 2000-050090 JP-A 63-254888

  The above method (1) is based on C (Cyan), M (Magenta), Y (Yellow), R (Red), G (Green), B (Blue), K (Black), and the print medium color W (White). This is a method of estimating the XYZ values for arbitrary CMY values by the Neugebauer equation using the XYZ values as the stimulus values for the eight points and the area ratios of basic colors such as CMY. This method is equivalent to three-dimensional interpolation with eight basic colors as vertices, but the actual color conversion characteristics are more complicated, and there is a problem that the accuracy is generally inferior.

  The methods (2) and (3) are both methods using patches at equal intervals. As the color patch values, as shown in FIG. 9, coordinate values of lattice points at equal intervals in the RGB space created by the print signal of the printer are selected (in the case of 5 × 5 × 5 in the example in the figure). In this case, generally, if the number of grid points is increased, the accuracy of colorimetric value estimation is improved, but the number of times of colorimetry is increased, so that the time required for measurement becomes longer. The distribution of color patches is uniform in a coordinate system depending on the device such as RGB or CMYK. However, when the measured XYZ values are mapped to a uniform color space such as Lab values, the distribution is usually biased. For this reason, even if the number of grid points is increased, there are portions where the accuracy improvement effect can be obtained and portions where it cannot be obtained, and the efficiency of the estimation process may be reduced.

  In the method (2), when the colorimetric values of points between patches are estimated, the XYZ values (or Lab values) obtained by the colorimetry are stored in a lookup table (hereinafter also simply referred to as “LUT”). A method of estimating XYZ values by linear interpolation such as 8-point interpolation or 4-point interpolation using 8 points or 4 points in the vicinity of RGB values or CMYK values stored in the corresponding grid points It is. In such linear interpolation, since the interpolation result generally lacks smoothness and the error from the actual characteristic is relatively large, when the estimation result by this method is stored in the AtoBOTag etc. of the ICC profile, There is a problem that a lot of noise is included when the print result is previewed on the monitor. In addition, when an input value such as an RGB value indicates the same coordinates as a grid point, the output value becomes the colorimetric value itself, and there is a problem that the colorimetric error during colorimetry is directly reflected in the output.

  In contrast to the above method (2), the method (3) uses a LUT as in the method (2), and interpolates curves using three or more points in the vicinity of RGB or CMYK values. Yes (for example, Japanese Patent Application Laid-Open No. 63-254888), there is a high possibility of obtaining better results than linear interpolation. However, since attention is paid only to points in the vicinity of the input value, there is also a problem that the colorimetric error during colorimetry is relatively large for each point in the vicinity and cannot be alleviated.

  In addition, the methods (2) and (3) have a problem that the accuracy rapidly decreases as the number of patches decreases.

  The present invention has been made to solve the above-described problems, and the object of the present invention is to provide a colorimetric value capable of estimating a colorimetric value with higher accuracy using a small number of patches. Estimation method, device profile creation method and image processing apparatus using the method.

  Therefore, according to the present invention, a conversion value between a sample value that is a color space value depending on the printing device and a colorimetric value of a color patch printed by the printing device based on the sample value is used to determine other values in the printing device. A method for estimating a colorimetric value with respect to a sample value, comprising: preparing a nonlinear model expression representing input / output characteristics of a printing apparatus that takes a color space value as an input and outputs a colorimetric value corresponding to the value; As one step, the conversion relationship between N sample values and the colorimetric values of the color patches based on the N sample values is obtained, and the inverse conversion relationship of the sample values with respect to the colorimetric values is obtained from the conversion relationship. The sample value determined from the inverse transformation relationship with respect to a predetermined colorimetric value is used as the input of the nonlinear model equation to obtain a colorimetric value as the output, and the obtained colorimetric value and the According to the color difference from a constant colorimetric value, the nonlinear model equation is determined by adjusting the coefficient of the nonlinear model equation so that the color difference is smaller than a predetermined value, and the colorimetric value is determined by the determined nonlinear model equation. As a second step, the conversion relationship between M (<N) sample values and the colorimetric values of the color patches based on the M (<N) sample values is obtained, and from the conversion relationship The inverse transformation relationship of the sample value with respect to the colorimetric value is obtained, and the nonlinear model equation is obtained by using the coefficient of the nonlinear model equation determined in the first step for the predetermined colorimetric value from the inverse transformation relationship as an initial value. The non-linear model so that the color difference is smaller than the predetermined value according to the color difference between the calculated color measurement value and the predetermined colorimetric value. Adjust the coefficient of the formula to determine the nonlinear model formula And a step of estimating a colorimetric value by the determined nonlinear model formula.

  Also, a device profile of the printing device is created from the conversion relationship between the sample value that is a color space value depending on the printing device and the colorimetric value of the color patch printed by the printing device based on the sample value. A non-linear model expression representing an input / output characteristic of a printing apparatus that inputs a value of the color space and outputs a colorimetric value corresponding to the value, and receives the colorimetric value as an input A color correction expression that outputs the value of the color space that is input to the expression is prepared, and the conversion of N sample values and color patch colorimetric values based on the N sample values as a first step A relationship is obtained, an inverse transformation relationship of the sample value with respect to the colorimetric value is obtained from the transformation relationship, and a sample value determined from the inverse transformation relationship with respect to a predetermined colorimetric value is input to the nonlinear model equation. To obtain a colorimetric value as the output and adjust the coefficient of the nonlinear model equation so that the color difference is smaller than the predetermined value according to the color difference between the calculated colorimetric value and the predetermined colorimetric value. The nonlinear model equation is determined, a predetermined colorimetric value is input to the correction equation, a color space value obtained by the input is input to the nonlinear model equation, and a colorimetric value is obtained. According to the color difference between the measured color measurement value and the predetermined color measurement value, the coefficient of the color correction equation is adjusted so that the color difference is smaller than the predetermined value, and M (<N) pieces are used as the second step. And the color patch colorimetric values based on the M (<N) sample values, the conversion relationship is obtained, and the inverse conversion relationship of the sample values with respect to the colorimetric values is obtained from the conversion relationship. The sample value determined from the inverse transformation relationship with respect to the colorimetric value is determined in the first step. By using the coefficient of the Dell equation as an initial value as an input of the nonlinear model equation, a colorimetric value is obtained as the output, and according to the color difference between the obtained colorimetric value and the predetermined colorimetric value, The nonlinear model equation is determined by adjusting the coefficient of the nonlinear model equation so that the color difference is smaller than a predetermined value, the predetermined colorimetric value is input to the correction equation, and the value of the color space obtained by the input Is input to the nonlinear model formula to obtain a colorimetric value, and the color correction formula is set so that the color difference is smaller than a predetermined value according to the color difference between the calculated colorimetric value and the predetermined colorimetric value. And adjusting the coefficient to determine the color correction formula.

  Further, a measurement value for other sample values in the printing device is obtained from a conversion relationship between a sample value that is a color space value depending on the printing device and a colorimetric value of a color patch printed by the printing device based on the sample value. An image processing apparatus for estimating a color value, comprising a nonlinear model equation representing an input / output characteristic of a printing apparatus that receives a color space value as an input and outputs a colorimetric value corresponding to the value. As the step, the conversion relationship between the N sample values and the colorimetric values of the color patches based on the N sample values is obtained, and the inverse conversion relationship of the sample values with respect to the colorimetric values is obtained from the conversion relationship, A sample value determined from the inverse transformation relationship with respect to the colorimetric value is input to the nonlinear model equation to obtain a colorimetric value as the output. According to the color difference from the color value, the nonlinear model equation is determined by adjusting the coefficient of the nonlinear model equation so that the color difference is smaller than a predetermined value, and the colorimetric value is estimated by the determined nonlinear model equation. As a second step, the conversion relationship between the M (<N) sample values and the colorimetric values of the color patches based on the M (<N) sample values is obtained, and the colorimetry is obtained from the conversion relationship. An inverse transformation relationship of the sample value with respect to the value is obtained, and a sample value determined from the inverse transformation relationship for a predetermined colorimetric value is determined in the first step as an initial value as a coefficient of the nonlinear model equation; The colorimetric value is obtained as the output, and the coefficient of the nonlinear model equation is set so that the color difference is smaller than the predetermined value according to the color difference between the calculated colorimetric value and the predetermined colorimetric value. To determine the nonlinear model formula and A process for estimating a colorimetric value using a determined nonlinear model formula is executed.

  Also, a device profile of the printing device is created from the conversion relationship between the sample value that is a color space value depending on the printing device and the colorimetric value of the color patch printed by the printing device based on the sample value. A non-linear model expression representing an input / output characteristic of a printing apparatus that receives a color space value as an input and outputs a colorimetric value corresponding to the value, and receives the colorimetric value as an input A color correction expression that outputs the value of the color space that is input to the nonlinear model expression is prepared. As a first step, N sample values and color patch colorimetric values based on the N sample values are calculated. Obtaining the conversion relationship, obtaining an inverse transformation relationship of the sample value with respect to the colorimetric value from the transformation relationship, and inputting a sample value determined from the inverse transformation relationship with respect to a predetermined colorimetric value to the nonlinear model equation The colorimetric value is obtained as the output, and the coefficient of the nonlinear model equation is set so that the color difference is smaller than the predetermined value according to the color difference between the calculated colorimetric value and the predetermined colorimetric value. To determine the nonlinear model equation, input a predetermined colorimetric value into the correction equation, and input the color space value obtained by the input into the nonlinear model equation to obtain a colorimetric value, According to the color difference between the obtained colorimetric value and the predetermined colorimetric value, the coefficient of the color correction formula is adjusted so that the color difference is smaller than the predetermined value, and M (<N ) Sample values and the color patch colorimetric values based on the M (<N) sample values, and the inverse relationship of the sample values with respect to the colorimetric values is obtained from the conversion relationship. The sample value determined from the inverse transformation relationship for a predetermined colorimetric value is determined in the first step. By using the coefficient of the nonlinear model equation as an initial value as an input of the nonlinear model equation, a colorimetric value is obtained as the output, and according to the color difference between the obtained colorimetric value and the predetermined colorimetric value, The nonlinear model equation is adjusted by adjusting a coefficient of the nonlinear model equation so that the color difference is smaller than a predetermined value, a predetermined colorimetric value is input to the correction equation, and the color space obtained by the input A color measurement value is obtained by inputting a value into the nonlinear model formula, and the color correction is performed so that the color difference is smaller than a predetermined value according to a color difference between the obtained color measurement value and the predetermined color measurement value. A process of adjusting the coefficient of the formula to determine the color correction formula is executed.

  According to the above configuration, the printing apparatus prints N patches as the first step, and based on the colorimetric values obtained from the patches, the nonlinear model equation representing the input / output characteristics of the printing apparatus is obtained. Other colorimetric values can be estimated by this non-linear model formula, and M (<N) patches are printed as the second step, and based on the colorimetric values obtained from this patch, Since a nonlinear model expression representing the input / output characteristics of the printing apparatus with the coefficient of the nonlinear model expression in the first step as an initial value is determined, and other colorimetric values can be estimated by this nonlinear model expression, Even if the number of M patches to be output is not large, colorimetric values can be estimated with relatively high accuracy, and color correction data can be created using this. That.

  As described above, according to the present invention, a predetermined number of patches are printed by the printing apparatus, and a model equation representing the input / output characteristics of the printing apparatus is determined based on the colorimetric values obtained from the patches. Since other colorimetric values can be estimated by this model formula, if the parameters of the model formula are determined by N patches in the first step, N parameters are determined from the second step onward. Using the model formula parameters determined by the patch as the initial value, colorimetric values can be estimated with relatively high accuracy using M (<N) patches, and color correction data can be created using this. Can also be done.

  As a result, it is not always necessary to use color patches that are equally spaced, and any color patch can be used.

  Further, after the second step, by using the parameters determined in the first step, it is possible to estimate colorimetric values with high accuracy with a small number of color patches.

  Furthermore, it is possible to reduce the colorimetric error due to the variation of the colorimeter due to disturbance and the uneven operation.

  Furthermore, since it is a global approximation, a smooth estimation result can be obtained, and noise during preview can be reduced.

  Furthermore, it is possible to increase the speed by storing the estimation result of the colorimetric value based on the model and the parameter in the LUT.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

(Embodiment 1)
FIG. 1 is a conceptual diagram of an image processing system according to an embodiment of the present invention, and FIG. 2 is a block diagram showing a configuration for colorimetric value estimation in this system.

  In FIG. 1, a color patch image 11 to be printed by a printer 13 as an output device is generated when an operator inputs sample values in a host computer 12, and the data is output to the printer 13. Then, a color patch 14 is printed out by the printer 13, and the color patch 14 is measured by a colorimeter (not shown) to obtain colorimetric data.

  The system shown in FIG. 1 is a system in which a scanner or digital camera is connected as an input device, a monitor, and a copying machine are connected as input devices in addition to the above-described devices. Of course, normal printing is performed.

  The configuration shown in FIG. 2 is configured by a host computer 12, a printer 13, and a colorimeter. More specifically, it is constituted by CPU processing in the host computer 12 and memories such as ROM and RAM, input means such as a keyboard, CPU processing in the printer 13, and printing mechanisms such as memory and print head. .

  In FIG. 2, 21 is a sample value input means for inputting N sample values on the color space of the printer 13 for generating a color patch, and 22 is an N sample value input by the sample value input means 21. Color patch image generating means 24 for generating the corresponding patch image data 11 for each of them, 24 is a color patch reading means for reading the generated color patch image data 11 provided with a memory, and these means are the host computer. 12.

  Reference numeral 25 denotes color patch image printing means for printing out the color patch 14 based on the color patch image data 11 output from the color patch image reading means, and this means is constituted by the printer 13. The printed color patch 14 is measured by the color patch colorimetric means 27.

  28 is a non-linear model / parameter determining means for determining parameters of a non-linear printer model from N sample values in the color space of the printer as an output device and its colorimetric values, as will be described later, and 29 is a non-linear model. A nonlinear model / parameter storage means for storing the nonlinear model and parameters obtained by the parameter determination means 28.

  In FIG. 5, reference numeral 1001 denotes sample value input means for inputting M (<N) sample values on the color space of the printer 13 for generating a color patch, and reference numeral 1002 denotes M inputted by the sample value input means 1001. A color patch image generation unit 1004 that generates patch image data 11 corresponding to each of (<N) sample values, and a color patch reading unit 1004 that includes a memory and reads the generated color patch image data 11. These means are configured in the host computer 12.

  Reference numeral 1005 denotes a color patch image print unit that prints out the color patch 14 based on the color patch image data 11 output from the color patch image reading unit. The printed color patch 14 is measured by the color patch colorimetric means 1007.

  Reference numeral 1008 denotes a non-linear model parameter initial setting that reads a non-linear model and a parameter obtained from N sample values in the color space of the printer as an output device and the colorimetric value, and sets them as initial values of the non-linear model parameters. Means 1009 is a non-linear model / parameter determining means for determining non-linear printer model parameters from M (<N) sample values in the color space of the printer as an output device and their colorimetric values as will be described later. Reference numeral 1010 denotes colorimetric value estimation means for estimating colorimetric values for M (<N) sample values from the nonlinear model and parameters obtained by the nonlinear model / parameter determination means 1008. These means are: The host computer 12 is used.

  The processing in the above configuration will be described more specifically. When selecting sample values on the printer color space such as RGB or CMYK, these sample values are mapped onto a uniform color space such as the Lab color space. At this time, a plurality of sample values are selected so as to be substantially equal in this space, and are input by the sample value input means 21. Specifically, individual sample values may be set by an operator's operation of a keyboard or the like, or may be selected and set from predetermined sample values. When it is difficult to select a uniform sample in the uniform color space, the sample values may be equally spaced in the output device. For example, N sample values are configured by 9x9x9, and M sample values are configured by 5x5x5. Next, the plurality of sample values input by the color patch image generating means 22 are temporarily taken into the memory by the color patch reading means 24 for output to the printer 13. Then, a color patch image 26 is printed out by the color patch image printing means 25 constituted by the printer 13.

  The output color patch image 26 is measured by color patch colorimetric means 27 such as a colorimeter, and colorimetric values in a device-independent color space such as XYZ and Lab are obtained for each patch. As a result, sample values such as RGB and CMYK in the color patch and colorimetric values such as XYZ and Lab are related, and the parameters of the nonlinear model are determined by the nonlinear model / parameter determining means 28 based on this.

  The nonlinear model used in the nonlinear model / parameter determining means 28 differs depending on the type of color space of the output device, but in this embodiment, an electrophotographic printer using a laser beam using CMY toners as color materials is used. Explained as an example. Of course, the present invention is not limited to the method of this printer. For example, the printer uses a method in which bubbles are generated in ink using thermal energy and each ink of YMC is ejected by the pressure of the bubbles. May be.

  In the first step, the parameters of a highly accurate nonlinear model of a specific printer are obtained from N sample values, and in the second step, individual differences between printers of the same type are determined by M sample values, which are smaller than N samples. It is intended to compensate for fluctuations due to aging. In other words, by using the nonlinear model parameters determined in the first step as initial values and optimizing the nonlinear model again in the second step, it is possible to optimize the characteristics of the printer of the same type while retaining the original characteristics.

  In addition, the parameters of the nonlinear model determined in the first step are stored in the printer profile shipped from the factory, and the user can optimize the printer characteristics with a small number of samples in the second step. User burden and color measurement time can be reduced.

  The non-linear model of the printer according to the present embodiment has a coefficient matrix of 3 × 20 as follows, for example, with CMY values as inputs and XYZ values as outputs, and a maximum third-order term for C, M, and Y. Can be modeled by a non-linear matrix consisting of a product with a 1 × 20 matrix including.

ところで、Neugebauer方程式はＣＭＹの各面積率からＣＭＹ値に対するＸＹＺの値を推定する例えば以下のような方程式である。

By the way, the Neugebauer equation is, for example, the following equation for estimating the value of XYZ with respect to the CMY value from each area ratio of CMY.

ここで、（Ｘｃ，Ｙｃ，Ｚｃ），（Ｘｍ，Ｙｍ，Ｚｍ），（Ｘｙ，Ｙｙ，Ｚｙ），（Ｘｒ，Ｙｒ，Ｚｒ），（Ｘｇ，Ｙｇ，Ｚｇ），（Ｘｂ，Ｙｂ，Ｚｂ），（Ｘｋ，Ｙｋ，Ｚｋ），（Ｘｗ，Ｙｗ，Ｚｗ）は基本色８点に対するＸＹＺ値を示す。

Here, (Xc, Yc, Zc), (Xm, Ym, Zm), (Xy, Yy, Zy), (Xr, Yr, Zr), (Xg, Yg, Zg), (Xb, Yb, Zb) , (Xk, Yk, Zk), (Xw, Yw, Zw) indicate XYZ values for eight basic colors.

And if this equation is expressed by a functional expression, it becomes as follows.
X = f (CMY, CM, MY, YC, C, M, Y) (3)
Y = g (CMY, CM, MY, YC, C, M, Y) (4)
Z = h (CMY, CM, MY, YC, C, M, Y) (5)
Comparing Equation (3), Equation (4), and Equation (5) with Equation (1), it can be seen that the nonlinear model of the printer represented by Equation (1) includes the Neugebauer equation. In other words, if the XYZ values for the CMY values can actually be estimated by the Neugebauer equation, the XYZ values for the arbitrary CMY values are estimated by determining the model by obtaining the coefficients of the 3 × 20 matrix in the nonlinear matrix of equation (1). Will be able to.

  As described above, when the nonlinear model / parameter determining means 28 obtains the coefficient of the nonlinear matrix and the model is determined, an arbitrary CMY value can be inputted by the measured value estimating means 29 and an XYZ value corresponding to this can be obtained.

  The coefficient (parameter) determination process by the nonlinear model / parameter determination means 28 will be described in detail with reference to FIGS.

  FIG. 3 is a diagram conceptually showing this determination process. In FIG. 3, 31 is a table corresponding to the inverse conversion of the relationship 30 between the sample value input by the sample value input means 21 (see FIG. 2) and the colorimetric value actually obtained by the colorimetry means 27. And a table storing the relationship from the device-independent color XtYtZt to the output device-dependent color CMY. Reference numeral 32 denotes a non-linear printer model shown in the above equation (1) in which the output device-dependent color CMY is input and the device-independent color XaYaZa is output. 33 is obtained by converting the Lab color value obtained by converting the actual colorimetric value (target value) (XtYtZt) by the conversion 34 and the colorimetric value (estimated value) XaYaZa estimated by the nonlinear model by the conversion 35. This is a process for obtaining a color difference ΔEab between the Lab value and optimizing the parameters (coefficients) aij (i = 1..., 3 and j = 1... 20) of the nonlinear model based on the magnitude of the color difference.

  FIG. 4 is a flowchart showing the procedure of the parameter determination process.

  In this process, first, the nonlinear model 32 is initialized in step S401.

  This initialization is performed by assigning, for example, the following values as initial values of coefficients for N sample values in the nonlinear printer model according to the above equation (1).

(A11, a21, a31) = (Xc, Yc, Zc)
(A12, a22, a32) = (Xm, Ym, Zm)
(A13, a23, a33) = (Xy, Yy, Zy)
(A121, a221, a321) = (Xw, Yw, Zw)
Here, (Xc, Yc, Zc), (Xm, Ym, Zm), (Xy, Yy, Zy), (Xw, Yw, Zw) are XYZ values for Cyan, Magenta, Yellow, and White, respectively. All coefficients that are not used are zero.

  Further, the initial value of the coefficient for the M (<N) sample values is assigned with the coefficient determined for the N sample values.

  Next, the relationship table 30 from CMY values to XYZ values obtained by colorimetry in step S402 is read. In step S403, the inverse relationship of the obtained relationship table 30 is obtained, and the relationship table from XtYtZt values to CMY values. 31 is created. In order to obtain this inverse transformation, CMY and XYZ may be simply exchanged so that the correspondence between CMY and XYZ is not lost. As a result, the sample value in the CMY color space can be obtained based on the XYZ value, so that the XYZ value can be used as the target value. Next, in step S404, a plurality of target values XtYtZt obtained as described above are input in a predetermined order. As a result, it is determined whether or not the parameters are appropriate for each target as shown below, and finally, parameters that appropriately represent the printer model can be obtained.

  That is, first, in step S405, the CMY value for the target value (XtYtZt) is obtained from the XtYtZt → CMY relationship table 31 obtained in step S403. An estimated value (XaYaZa) is obtained. That is, the estimated value (XaYaZa) is obtained by substituting the respective CMY values into the expression (1) initialized in step S401. Then, the XYZ values (estimated values) obtained as described above in step S407 are converted into coordinates in the Lab space by the conversion 35 in order to evaluate the color difference. On the other hand, in step S408, the XtYtZt value input as the target value is converted into coordinates in the Lab space by the conversion 34 in order to evaluate the color difference.

  In step S409, a color difference ΔEab between the Lab value obtained from the target value (XtYtZt) and the Lab value obtained from the estimated value (XaYaZa) is obtained. In step S413, whether or not the color difference has been computed for all target values. to decide. If color differences have not been calculated for all target values, the target value input order is shifted in step S414, and the process returns to step S404. On the other hand, if it is determined that color differences have been obtained for all target values, in step S410, these color differences are evaluated, and the accuracy of the obtained printer model is determined.

  That is, in step S410, for example, it is determined whether or not the average color difference for all the obtained target values is smaller than a predetermined threshold value. If the average of the color differences is smaller than the predetermined threshold value, the process is terminated assuming that a highly accurate printer model can be obtained. On the other hand, when the average of the color differences is larger than the predetermined threshold, the above optimization process is repeated.

  Note that an upper limit of the number of times the optimization process is repeated may be obtained. If the average of the color differences does not fall below the predetermined threshold even after reaching the repeated upper limit, an error is notified to the user. Furthermore, the average of the final color difference is notified and the user is asked to make a decision.

  When the optimization process is repeated, the printer model is changed based on the change in the previous average color difference and the current average color difference. For example, if the average color difference is greater than the previous time, the change amount of the printer model is reduced. Thus, the change amount of the printer model is adjusted so that the optimization process is converged.

  In the above description, CMY is an example of an output device color space, and of course, it may be RGB or CMYK. Similarly, XYZ is an example of a device-independent color space, which may be a color space such as Lab or Luv, and of course the color difference is not limited to ΔEab.

  As described above, when a CMY value is obtained such that the target value can be obtained as a colorimetric value, and the same CMY value is also input to the nonlinear printer model, the output is the same (close) value as the actual system (target value). Whether or not is indicated. If the values are the same (close), the nonlinear model can be regarded as almost the same as the actual system. If they are different, the parameters of the nonlinear model are corrected and the same is repeated. That is, a target value is input to a system obtained by combining a known inverse transformation system (colorimetric value inverse transformation 31) and an unknown forward transformation system (nonlinear model 32), and whether the output matches the target value (near neighborhood). Whether or not) will be determined. Here, in order to evaluate how close the estimated value (output) is to the target value, the present embodiment uses a color difference. By evaluating with the color difference, it can be assured that the visual approximation error is small for the estimation result. Further, if the degree of fine adjustment of the parameter is changed according to the difference in the color difference, the parameter can be converged quickly.

  In addition, when sample values at equal intervals on the printer color space are selected as input by the sample value input means 21, generally, the distribution of the XYZ values with respect to the sample values is not uniform but biased on the Lab color space. As a result, when optimization is performed using such XYZ values as target values, the estimation accuracy for sample values corresponding to regions that are densely distributed in Lab space is high, but the distribution is sparsely distributed in Lab space. The sample estimation accuracy corresponding to a certain region is low. As a method for solving this problem, it is conceivable to increase the number of sample values corresponding to a sparsely distributed region in the Lab space, or to add a point in the vicinity of a CMY value with low conversion accuracy as a sample value. .

  Furthermore, in addition to the method of increasing the number of samples, when determining the degree of fine adjustment of the parameter, the target value that becomes a dense distribution is used for the evaluation result of the target value that becomes a sparse distribution in the Lab space. A method of making it heavier can be considered.

  The overall accuracy can be improved by adjusting the weight distribution for the sample distribution and each target value.

(Embodiment 2)
The present embodiment relates to the determination of the nonlinear model described in the first embodiment and storing the result in the LUT and calculating the colorimetric result at high speed when the estimation result by the model is used. is there.

  The more complex the nonlinear model described above, the longer the computation time for estimation by that model. For this reason, in the present embodiment, the estimation result of the colorimetric value can be speeded up by storing the estimation result by the non-linear model in the LUT. This LUT is generated by storing the result calculated based on the obtained nonlinear model in the lattice points of the LUT.

  Such an LUT can be used, for example, when an image created on a host computer is previewed on a monitor before being printed out.

  Here, the LUT depends on the number of components of the output device, such as a three-dimensional LUT when the input is RGB or CMY, and a four-dimensional LUT when the input is CMYK.

  In the method of performing linear interpolation by storing the colorimetric values in the LUT without using the method of the present invention, even if the number of grids is larger than the number of grids when the colorimetric values are stored, the number is increased by linear interpolation. The accuracy does not change because it only supplements the grid. For example, when sampling on the output device color space with 9 × 9 × 9 sample values and storing the colorimetric values directly in the 9 × 9 × 9 LUT to obtain an arbitrary colorimetric value, the output device color space Even if the result of linear interpolation for the 33 × 33 × 33 sample value is stored again in the 33 × 33 × 33 LUT and linear interpolation is performed using the 33 × 33 × 33 LUT, the accuracy is 9 × 9. This is the same as when a × 9 LUT is used.

  On the other hand, in the model approximation using the nonlinear model parameter to which the present invention is applied, the accuracy is determined by the parameter instead of the number of grids. Therefore, if the accuracy of the model is directly reflected in the value of the grid and an LUT having a large number of grids is used, A more accurate interpolation result can be obtained.

(Embodiment 3)
The present embodiment relates to a method for creating a device profile by using a measurement value estimation result by a non-linear model.

  Using the CMY-> XYZ nonlinear printer model and parameters obtained as described above, the nonlinear masking parameters that are the unknown inverse transformation system (XYZ-> CMY) are determined, and a printer profile can be created. it can.

  FIG. 6 is a block diagram showing a configuration for creating a profile. In FIG. 6, the same elements as those shown in FIG. 2 are denoted by the same reference numerals.

  In FIG. 6, 27 is a color patch colorimetric means for reading the colorimetric values for the output patch 14, and 28 is for determining a nonlinear model parameter for colorimetric value estimation from the read colorimetric values. The non-linear model parameter determining means 29 is a calorimetric value estimating means 29 for estimating the calorimetric value using the parameters obtained by the non-linear model parameter determining means 28, and these are the same as the elements described in the first embodiment. Is.

  65 is an LUT (CMY → XYZ) creation means for storing the result of the colorimetric value estimation means 29 in the LUT, and 66 is a linear interpolation value of the LUT obtained by the LUT (CMY → XYZ) creation means 65. These are non-linear masking parameter determining means for determining non-linear masking parameters which are the inverse transformations, and will be described in detail with reference to FIGS.

  67 is a device output value estimation means for estimating the printer output value using the parameter obtained by the non-linear masking parameter determination means, and 68 is in accordance with the color reproduction range obtained from the colorimetric values for the output patch 14. The color space compression means 69 for applying color space compression inputs XYZ values for sampling the XYZ space at equal intervals with respect to the color space compression performed by the color space compression creation means 68, and outputs the XYZ values as device output values. This is an LUT (XYZ → CMY) creation means for creating an XYZ → CMY conversion LUT including color space compression by using the estimation means 67 as an input.

  Reference numeral 610 denotes a device-dependent color conversion from a device-dependent color obtained by the LUT (CMY → XYZ) creating unit 65 to a device-independent color and a device-independent color obtained by the LUT (XYZ → CMY) creating unit 69. This is a profile output means for writing the color conversion LUT as an output device profile 611.

  In the ICC profile that is standard in the technical field of the present invention, AtoBxTag for converting from device-dependent colors to device-independent colors and BtoAxTag for converting from device-independent colors to device-dependent colors are used. Each LUT is to be stored. By storing the estimation results using the nonlinear model and nonlinear masking in AtoBxTag and BtoAxTAg as LUTs respectively, it is possible to perform proofing with high accuracy.

  The parameter determination by the above-described nonlinear masking parameter determination means 66 will be described below with reference to FIGS.

  In FIG. 7, reference numeral 71 denotes a target value included in the color reproduction range of the printer that is the output device, and 72 is a nonlinear masking model for obtaining a relationship from the output device-independent color to the device-dependent color. An estimated value (CaMaYa) is output on the basis of the XYZ value obtained by converting the value by the conversion 75.

  73 is an LUT for estimating the colorimetric value obtained by the LUT (CMY → XYZ) creating means 65, and 74 is a colorimetric value (estimated value) estimated from the target value 71 and the non-linear masking 72 via the LUT 73. This is a process of obtaining a color difference and changing a non-linear masking parameter according to the magnitude of the color difference.

  FIG. 8 is a flowchart showing a procedure of parameter determination processing for nonlinear masking.

  First, in step S801, initialization is performed for the nonlinear masking parameters.

  For example, as a nonlinear masking, for example, when assuming a 3 × 20 matrix shown in the following equation (6),

初期化は、例えば、以下の値を係数の初期値として割り当てる。

For initialization, for example, the following values are assigned as initial values of coefficients.

(b11, b21, b31) = (0, 0.5, 0.5)
(b12, b22, b32) = (0.5, 0, 0.5)
(b13, b23, b33) = (0.5, 0.5, 0)
(b120, b220, b320) = (1, 1, 1)
Here, all the coefficients not shown are set to zero.

  Next, in step S802, as described in the first embodiment, the parameters of the nonlinear model of the printer are determined based on the contents of the table 30. On the other hand, in step S804, the target value (Lt at bt) 71 is set and inputted in a predetermined order within the color reproduction range of the printer as the output device. As a result, for each target value (Lt at bt), it is determined whether or not the nonlinear masking parameters are appropriate as follows.

  That is, in step S804, the target value (Lt at bt) is converted into an XYZ value by conversion 75 (see FIG. 7), and in step S805, the non-linear masking of equation (6) initialized as described above is converted into XYZ. An operation for inputting a value and outputting an estimated value CaMaYa is performed. Next, in step S806, the estimated value (CaMaYa) is converted into the colorimetric value estimated value (XaYaZa) using the LUT 73 created by the LUT creating means 65, and in step S807 this is converted into 76 (FIG. 7). To the value of Lab.

  In step S808, the color difference between the target value Ltat bt set and input in step S803 and the Lab obtained as described above is calculated. Then, similarly to steps S410 to S414 in FIG. 4 according to the first embodiment, the parameter adjustment of the nonlinear masking 72 is performed until the color difference becomes smaller than a predetermined threshold value for all target values.

  As described above, by using the nonlinear printer model as described in the first embodiment, it is possible to determine the parameters of nonlinear masking for correcting the color of the input data, which is suitable for the printer model. Masking processing can be performed.

  The masking set in this way can be used as a table as an LUT, as in the case of the printer model, as described in the second embodiment.

<Other embodiments>
As described above, the present invention can be applied to a system composed of a plurality of devices (for example, a host computer, an interface device, a reader, a printer, etc.) but also to an apparatus composed of a single device (for example, a copying machine, a facsimile machine). May be.

  In addition, a program code of software for realizing the functions of the embodiment is provided in an apparatus or a computer in the system connected to the various devices so as to operate the various devices so as to realize the functions of the above-described embodiments. What is implemented by operating the various devices in accordance with a program stored in a computer (CPU or MPU) of the system or apparatus supplied is also included in the scope of the present invention.

  Further, in this case, the program code of the software itself realizes the functions of the above-described embodiments, and the program code itself and means for supplying the program code to the computer, for example, a storage storing the program code The medium constitutes the present invention.

  As a storage medium for storing the program code, for example, a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a nonvolatile memory card, a ROM, or the like can be used.

  Further, by executing the program code supplied by the computer, not only the functions of the above-described embodiments are realized, but also the OS (operating system) in which the program code is running on the computer, or other application software, etc. It goes without saying that the program code is also included in the embodiment of the present invention even when the functions of the above-described embodiment are realized in cooperation with the embodiment.

  Further, after the supplied program code is stored in a memory provided in a function expansion board of a computer or a function expansion unit connected to the computer, a CPU provided in the function expansion board or function storage unit based on an instruction of the program code However, it is needless to say that the present invention also includes a case where the function of the above-described embodiment is realized by performing part or all of the actual processing.

1 is a diagram illustrating a configuration of a print system according to an embodiment of the present invention. It is a block diagram which shows the structure for a 1st nonlinear model parameter determination from N patches based on Embodiment 1 of this invention. It is a figure which shows the concept of the said nonlinear model parameter determination process. It is a flowchart which shows the procedure of the said nonlinear model parameter determination process. It is a block diagram which shows the structure for a 2nd nonlinear model parameter determination from M (<N) patches based on Embodiment 1 of this invention. It is a block diagram which shows the structure for the parameter determination of the nonlinear masking which concerns on Embodiment 2 of this invention. It is a figure which shows the concept of the parameter determination process of the said nonlinear masking. It is a flowchart which shows the procedure of the parameter determination process of the said nonlinear masking. It is a figure for demonstrating one prior art example of colorimetric value estimation using a color patch.

Claims (10)

  As a first step, colorimetric values for N color patches are approximated by a printing apparatus model and the parameters of the model, the parameters of the model are stored, and the parameters obtained in the first step are stored as a second step. A colorimetric value for an arbitrary color patch is estimated by approximating a colorimetric value for M (<N) color patches with the model and the parameter of the model, with model parameters as initial values. A method for estimating colorimetric values for color patches. A colorimetric value for other sample values in the printing device from a conversion relationship between a sample value that is a color space value depending on the printing device and a colorimetric value of a color patch printed by the printing device based on the sample value Is a method of estimating
A non-linear model equation representing an input / output characteristic of a printing apparatus that takes a value of the color space as an input and outputs a colorimetric value corresponding to the value is prepared,
As a first step, the conversion relationship between N sample values and colorimetric values of color patches based on the N sample values is obtained,
From the conversion relationship, the inverse conversion relationship of the sample value with respect to the colorimetric value is obtained,
By taking a sample value determined from the inverse transformation relationship for a predetermined colorimetric value as an input of the nonlinear model equation, a colorimetric value is obtained as the output,
According to the color difference between the obtained colorimetric value and the predetermined colorimetric value, the nonlinear model equation is determined by adjusting the coefficient of the nonlinear model equation so that the color difference is smaller than the predetermined value, Save the parameters of the determined nonlinear model equation,
As the second step, the conversion relationship between M (<N) sample values and the colorimetric values of the color patches based on the M (<N) sample values is obtained.
From the conversion relationship, the inverse conversion relationship of the sample value with respect to the colorimetric value is obtained,
A sample value determined from the inverse transformation relationship with respect to a predetermined colorimetric value is used as an input of the nonlinear model equation with the parameter of the nonlinear model equation determined in the first step as an initial value. Find the value
According to the color difference between the obtained colorimetric value and the predetermined colorimetric value, the nonlinear model equation is determined by adjusting the coefficient of the nonlinear model equation so that the color difference is smaller than the predetermined value,
A colorimetric value is estimated by the determined nonlinear model equation;
A method for estimating a colorimetric value relating to a color patch characterized by comprising a step.   The first step is to approximate the colorimetric values for the N color patches by the model of the printing device and the parameters of the model, store the parameters of the model, and the second step is M (<N) colors Estimating a colorimetric value relating to an arbitrary color patch by approximating the colorimetric value relating to the patch with the model parameter determined in the first step as an initial value using the model of the printing apparatus and the parameter of the model. A device profile creation method characterized by: A method for creating a device profile of a printing apparatus from a conversion relationship between a sample value that is a color space value depending on the printing apparatus and a colorimetric value of a color patch printed by the printing apparatus based on the sample value Because
A non-linear model equation representing an input / output characteristic of a printing apparatus that takes a value of the color space as an input and outputs a colorimetric value corresponding to the value is prepared,
Prepare a color correction equation that takes the colorimetric value as input and outputs the value of the color space that is input to the nonlinear model equation,
As a first step, the conversion relationship between N sample values and colorimetric values of color patches based on the N sample values is obtained,
From the conversion relationship, the inverse conversion relationship of the sample value with respect to the colorimetric value is obtained,
By taking a sample value determined from the inverse transformation relationship for a predetermined colorimetric value as an input of the nonlinear model equation, a colorimetric value is obtained as the output,
According to the color difference between the obtained colorimetric value and the predetermined colorimetric value, the nonlinear model equation is determined by adjusting the coefficient of the nonlinear model equation so that the color difference is smaller than the predetermined value, Save the parameters of the nonlinear model equation,
As the second step, the conversion relationship between M (<N) sample values and the colorimetric values of the color patches based on the M (<N) sample values is obtained.
From the conversion relationship, the inverse conversion relationship of the sample value with respect to the colorimetric value is obtained,
A sample value determined from the inverse transformation relationship with respect to a predetermined colorimetric value is used as an output of the nonlinear model equation by setting the parameter of the nonlinear model equation determined in the first step as an initial value. Find the colorimetric value,
According to the color difference between the obtained colorimetric value and the predetermined colorimetric value, the nonlinear model equation is determined by adjusting the coefficient of the nonlinear model equation so that the color difference is smaller than the predetermined value,
A predetermined colorimetric value is input to the color correction formula, and the color space value obtained by the input is input to the nonlinear model formula to obtain a colorimetric value.
In accordance with the color difference between the calculated colorimetric value and the predetermined colorimetric value, adjusting the coefficient of the color correction expression so that the color difference is smaller than the predetermined value, and determining the color correction expression A method of creating a device profile characterized by having   An image processing apparatus comprising the nonlinear model equation determined in the second step by the colorimetric value estimation method according to claim 2 as a lookup table.   5. An image processing apparatus comprising: the nonlinear model formula and / or the color correction formula determined in the second step determined by the device profile creation method according to claim 4 as a look-up table. A colorimetric value for other sample values in the printing device from a conversion relationship between a sample value that is a color space value depending on the printing device and a colorimetric value of a color patch printed by the printing device based on the sample value An image processing apparatus for estimating
A non-linear model equation representing an input / output characteristic of a printing apparatus that takes a value of the color space as an input and outputs a colorimetric value corresponding to the value is prepared,
As a first step, the conversion relationship between N sample values and colorimetric values of color patches based on the N sample values is obtained,
From the conversion relationship, the inverse conversion relationship of the sample value with respect to the colorimetric value is obtained,
By taking a sample value determined from the inverse transformation relationship for a predetermined colorimetric value as an input of the nonlinear model equation, a colorimetric value is obtained as the output,
According to the color difference between the obtained colorimetric value and the predetermined colorimetric value, the nonlinear model equation is determined by adjusting the coefficient of the nonlinear model equation so that the color difference is smaller than the predetermined value, Save the parameters of the nonlinear model equation,
As the second step, the conversion relationship between M (<N) sample values and the colorimetric values of the color patches based on the M (<N) sample values is obtained.
From the conversion relationship, the inverse conversion relationship of the sample value with respect to the colorimetric value is obtained,
A sample value determined from the inverse transformation relationship with respect to a predetermined colorimetric value is measured as the output by setting the parameter of the nonlinear model equation determined in the first step as an initial value and inputting the nonlinear model equation. Find the color value,
According to the color difference between the obtained colorimetric value and the predetermined colorimetric value, the nonlinear model equation is determined by adjusting the coefficient of the nonlinear model equation so that the color difference is smaller than the predetermined value, Estimate the colorimetric value using the determined nonlinear model formula.
An image processing apparatus that executes processing. An image for creating a device profile of the printing apparatus from a conversion relationship between a sample value that is a color space value depending on the printing apparatus and a colorimetric value of a color patch printed by the printing apparatus based on the sample value A processing device comprising:
A non-linear model equation representing an input / output characteristic of a printing apparatus that takes a value of the color space as an input and outputs a colorimetric value corresponding to the value is prepared,
Prepare a color correction equation that takes the colorimetric value as input and outputs the value of the color space that is input to the nonlinear model equation,
As a first step, the conversion relationship between N sample values and colorimetric values of color patches based on the N sample values is obtained,
From the conversion relationship, the inverse conversion relationship of the sample value with respect to the colorimetric value is obtained,
By taking a sample value determined from the inverse transformation relationship for a predetermined colorimetric value as an input of the nonlinear model equation, a colorimetric value is obtained as the output,
According to the color difference between the obtained colorimetric value and the predetermined colorimetric value, the nonlinear model equation is determined by adjusting the coefficient of the nonlinear model equation so that the color difference is smaller than the predetermined value, Save the parameters of the nonlinear model equation,
As the second step, the conversion relationship between M (<N) sample values and the colorimetric values of the color patches based on the M (<N) sample values is obtained.
From the conversion relationship, the inverse conversion relationship of the sample value with respect to the colorimetric value is obtained,
A sample value determined from the inverse transformation relationship with respect to a predetermined colorimetric value is measured as the output by setting the parameter of the nonlinear model equation determined in the first step as an initial value and inputting the nonlinear model equation. Find the color value,
According to the color difference between the obtained colorimetric value and the predetermined colorimetric value, the nonlinear model equation is determined by adjusting the coefficient of the nonlinear model equation so that the color difference is smaller than the predetermined value,
A predetermined colorimetric value is input to the color correction formula, and the color space value obtained by the input is input to the nonlinear model formula to obtain a colorimetric value.
Processing for determining the color correction formula by adjusting the coefficient of the color correction formula so that the color difference is smaller than the predetermined value according to the color difference between the calculated color measurement value and the predetermined color measurement value An image processing apparatus that executes the image processing apparatus. A colorimetric value for other sample values in the printing device from a conversion relationship between a sample value that is a color space value depending on the printing device and a colorimetric value of a color patch printed by the printing device based on the sample value A storage medium storing a processing program for estimating
The program
A non-linear model equation representing an input / output characteristic of a printing apparatus that takes a value of the color space as an input and outputs a colorimetric value corresponding to the value is prepared,
As a first step, the conversion relationship between N sample values and colorimetric values of a color patch based on the N sample values is obtained,
From the conversion relationship, the inverse conversion relationship of the sample value with respect to the colorimetric value is obtained,
By taking a sample value determined from the inverse transformation relationship for a predetermined colorimetric value as an input of the nonlinear model equation, a colorimetric value is obtained as the output,
According to the color difference between the obtained colorimetric value and the predetermined colorimetric value, the nonlinear model equation is determined by adjusting the coefficient of the nonlinear model equation so that the color difference is smaller than the predetermined value, Save the parameters of the nonlinear model equation,
As a second step, the conversion relationship between M (<N) sample values and the colorimetric values of the color patch based on the M (<N) sample values is obtained.
From the conversion relationship, the inverse conversion relationship of the sample value with respect to the colorimetric value is obtained,
The sample value determined from the inverse transformation relationship with respect to a predetermined colorimetric value is set as the initial value of the parameter of the nonlinear model equation determined in the first step, and is input as the nonlinear model equation. Find the colorimetric value,
In accordance with the color difference between the obtained colorimetric value and the predetermined colorimetric value, adjusting the coefficient of the nonlinear model equation so as to make the color difference smaller than the predetermined value, and determining the nonlinear model equation A storage medium characterized by having. Processing for creating a device profile of a printing apparatus from a conversion relationship between a sample value that is a color space value depending on the printing apparatus and a colorimetric value of a color patch printed by the printing apparatus based on the sample value A storage medium readable by an information processing device,
The program
A non-linear model equation representing an input / output characteristic of a printing apparatus that takes a value of the color space as an input and outputs a colorimetric value corresponding to the value is prepared,
Prepare a color correction equation that takes the colorimetric value as input and outputs the value of the color space that is input to the nonlinear model equation,
As a first step, the conversion relationship between N sample values and colorimetric values of color patches based on the N sample values is obtained,
From the conversion relationship, the inverse conversion relationship of the sample value with respect to the colorimetric value is obtained,
By taking a sample value determined from the inverse transformation relationship for a predetermined colorimetric value as an input of the nonlinear model equation, a colorimetric value is obtained as the output,
According to the color difference between the obtained colorimetric value and the predetermined colorimetric value, the nonlinear model equation is determined by adjusting the coefficient of the nonlinear model equation so that the color difference is smaller than the predetermined value, Save the parameters of the nonlinear model equation,
As the second step, the conversion relationship between M (<N) sample values and the colorimetric values of the color patches based on the M (<N) sample values is obtained.
From the conversion relationship, the inverse conversion relationship of the sample value with respect to the colorimetric value is obtained,
The sample value determined from the inverse transformation relationship with respect to a predetermined colorimetric value is set as the initial value of the parameter of the nonlinear model equation determined in the first step, and is input as the nonlinear model equation. Find the colorimetric value,
According to the color difference between the obtained colorimetric value and the predetermined colorimetric value, the nonlinear model equation is determined by adjusting the coefficient of the nonlinear model equation so that the color difference is smaller than the predetermined value,
A predetermined colorimetric value is input to the correction equation, and the color space value obtained by the input is input to the nonlinear model equation to obtain a colorimetric value.
In accordance with the color difference between the calculated colorimetric value and the predetermined colorimetric value, adjusting the coefficient of the color correction expression so that the color difference is smaller than the predetermined value, and determining the color correction expression A storage medium characterized by having.

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