JP2010245966A - Color conversion profile generation device, method, program, and printer - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a technology for quickly performing optimization processing in the case of creating a color conversion profile. <P>SOLUTION: An initial value-setting part sets the initial value of an ink color system and the initial position of an equipment independent color system color point as the color point of an equipment independent color system corresponding to an input color system as an initial value associated with each of a plurality of input color system color points as the prescribed color points of an input color system. A smoothing/optimization processing part executes: a smoothing processing for smoothing the distribution of a plurality of equipment independent color system color points from the initial position; and an optimization processing for determining the ink quantity of the ink color system corresponding to the plurality of smoothed equipment independent color system color points by optimization using the preliminarily set objective functions. The objective functions include ink quantity adjustment items using adjustment coefficients corresponding to the color region to which the equipment independent color system color points corresponding to the type of ink and ink quantity vectors belongs as the secondary coefficients of the quantity of ink. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a technique for creating a color conversion profile, and more particularly to a technique for creating a color conversion profile using a smoothing process.

The color conversion profile is information indicating a correspondence relationship between the input color system and the output color system, and is used in a format such as a color conversion lookup table or a color conversion function, for example. The coordinate value of the input color system in the color conversion lookup table represents the position of a point in the color space of the input color system, and the coordinate value of the output color system is a point in the color space of the output color system. Represents the position. In the present specification, points in an arbitrary color space are also referred to as “color points” or “grid points”. Further, the color point represented by the input value and the color point represented by the output value registered in the color conversion lookup table are also referred to as “input grid point” and “output grid point”, respectively.
As a technique for smoothing the arrangement of input grid points and output grid points in the color conversion lookup table, for example, there is one described in Patent Document 1 disclosed by the applicant of the present application. In this smoothing, after moving the grid point of the Lab color system, an optimum ink amount corresponding to the moved L ^* a ^* b ^* grid point is obtained using an optimization process using an objective function. Has been decided. This optimum ink amount is determined as an ink amount that minimizes the objective function. As an optimization processing method, a nonlinear programming method such as a quasi-Newton method or a sequential quadratic programming method is used.
However, the conventional method has a problem that it takes considerable processing time for the optimization processing using the nonlinear programming method.
In view of such problems, the present inventor has made it possible to execute an optimum ink amount search at high speed by making the objective function a quadratic form and performing a quadratic programming method using the objective function. The inventors have found that the processing can be completed in about one-tenth of the time when using the conventional quasi-Newton method.
On the other hand, Patent Document 2 proposes a method of creating a color conversion profile by imposing a restriction that suppresses the amount of ink for ink with a small amount of ink. The limitation is realized by adding a term obtained by linearly combining the ink amounts of the individual inks to the objective function having a linear form. By adjusting the weight of each ink amount in the linear combination, it was possible to suppress the ink amount for a specific ink.

Japanese Patent Laid-Open No. 2006-197080 JP 2008-230050 A

  However, when the objective function is in a quadratic form in view of speeding up, there is a problem that a term obtained by linearly combining the ink amounts of individual inks cannot be simply added to the objective function.

  An object of the present invention is to provide a technique capable of performing an optimization process in creating a color conversion profile at a high speed while adjusting the balance of the ink amounts of the respective inks.

  SUMMARY An advantage of some aspects of the invention is to solve at least a part of the problems described above, and the invention can be implemented as the following forms or application examples.

[Application Example 1]
A device for creating a color conversion profile for converting an input color system coordinate value into an ink color system ink amount composed of a plurality of types of ink,
As an initial value associated with each of a plurality of input color system color points that are predetermined color points of the input color system, an initial value of the ink color system and a device corresponding to the input color system An initial value setting unit for setting the initial position of the device independent color system color point, which is the color point of the independent color system;
A smoothing process for smoothing the distribution of the plurality of device independent color system color points from an initial position, and an amount of ink of the ink color system corresponding to the smoothed plurality of device independent color system color points A smoothing / optimization processing unit for performing optimization processing determined by optimization using a predetermined objective function,
Color conversion profile creation for creating a color conversion profile for converting the coordinate value of the input color system into the ink amount of the ink color system based on the ink amount determined by the smoothing / optimization processing unit And comprising
The smoothing / optimization processing unit performs the optimization process using a quadratic programming method using a quadratic function related to an ink amount vector represented by an ink amount obtained by the optimization process as the objective function. Run,
The objective function is an ink amount having an adjustment coefficient corresponding to a color gamut to which the device independent color system color point corresponding to the ink type and the ink amount vector belongs as a secondary coefficient of the ink amount. A color conversion profile creation device including an adjustment term.
According to this configuration, since the ink amount optimization processing is executed using a quadratic programming method using a quadratic objective function, other nonlinear programming methods such as a quasi-Newton method and a sequential quadratic programming method are used. The optimization process can be performed at a higher speed than the case of using it. Since this objective function reflects the value of the adjustment coefficient according to the ink type and the color gamut to which the device independent color system color point belongs, the device independent color system color point is used in the smoothing / optimization process. The increase in the amount of ink of each ink can be suppressed or promoted according to the color gamut to which.

[Application Example 2]
The color conversion profile creation device according to claim 1,
The objective function is
(I) Defined with respect to coordinate conversion in which the ink amount is a coordinate value of the first coordinate system, and a plurality of parameters including the coordinate value of the device independent color system and the image quality evaluation index are the coordinate values of the second coordinate system. A first variation amount of the plurality of parameters calculated by multiplying the Jacobian matrix by the variation amount of the ink amount,
(Ii) A color conversion profile creation device including a sum of square errors of differences between the second variation amounts of the plurality of parameters before and after the smoothing process.
According to this configuration, it is possible to obtain a quadratic objective function suitable for quadratic programming by a relatively simple calculation.

[Application Example 3]
The color conversion profile creation device according to claim 2,
A color conversion profile creation device in which the adjustment coefficient is added as a matrix element to the Jacobian matrix.
According to this configuration, it is possible to obtain the ink amount adjustment term while using the Jacobian matrix.

[Application Example 4]
The color conversion profile creation device according to claim 1,
The smoothing / optimization processing unit is more optimal as the objective function is smaller,
The adjustment coefficient relating to dark ink having a density higher than that of the other inks is such that the ink amount of the dark ink increases as the color gamut to which the device independent color system color point corresponding to the ink amount vector belongs becomes high. A color conversion profile creation device that is set so that the amount of increase in the objective function corresponding to a unit increase increases.
According to this configuration, it is possible to suppress the amount of ink having a high density at high brightness.

  The present invention can be realized in various forms. For example, a color conversion profile creation method and apparatus, a smoothing / optimization processing method and apparatus therefor, and printing in which a color conversion profile is incorporated in a printing apparatus The present invention can be realized in the form of a device manufacturing method and system, a computer program for realizing the functions of the method or device, a recording medium on which the computer program is recorded, and the like. Furthermore, the usefulness of the present invention can be realized also in a printing apparatus in which a color conversion profile is incorporated.

It is a block diagram which shows the structure of the lookup table preparation apparatus in one Example of this invention. It is a flowchart which shows the whole process sequence of an Example. It is explanatory drawing which shows the processing content in the case of producing a base 3D-LUT by step S100-S300 of FIG. It is explanatory drawing which shows the correspondence of the color point of RGB color system which is an input color system, and the color point of Lab color system. It is explanatory drawing which shows the processing content in the case of producing a base 4D-LUT by step S100-S300 of FIG. It is explanatory drawing which shows the preparation method of the color correction LUT using base LUT. It is explanatory drawing which shows the dynamic model utilized for the smoothing process of an Example. It is a flowchart which shows the typical process sequence of a smoothing process. It is a flowchart which shows the detailed procedure of step T100 of FIG. It is explanatory drawing which shows the processing content of step S120-S150 of FIG. It is explanatory drawing which shows the example of a setting of an adjustment coefficient. It is a flowchart which shows the detailed procedure of an optimization process (step T130 of FIG. 8). 1 is a block diagram illustrating a configuration of a printer according to an embodiment of the present invention. It is a schematic diagram explaining the printing system of a printer. FIG. 2 is a block diagram illustrating a software configuration of a printer.

Next, embodiments of the present invention will be described in the following order.
A. Equipment configuration and overall processing procedure:
B. Dynamic model:
C. Smoothing processing (smoothing / optimization processing) procedure:
D. Contents of optimization process:
E. Configuration of printing device:
F. Variation:

A. Equipment configuration and overall processing procedure:
FIG. 1 is a block diagram showing the configuration of a lookup table creation apparatus in an embodiment of the present invention. This apparatus includes a base LUT creation module 100, a color correction LUT creation module 200, a forward model converter 300, and an LUT storage unit 400. “LUT” is an abbreviation for a lookup table as a color conversion profile. The functions of the modules 100 and 200 and the converter 300 are realized by the computer executing a computer program stored in the memory. The LUT storage unit 400 is realized by a recording medium such as a hard disk device.

  The base LUT creation module 100 includes a smoothing process initial value setting module 120 and a table creation module 140. The smoothing processing module 130 includes a color point movement module 132, an ink amount optimization module 134, and an image quality evaluation index calculation module 136. The forward model converter 300 includes a spectral printing model converter 310 and a color calculation unit 320. The functions of these parts will be described later.

  The LUT storage unit 400 stores the inverse model initial LUT 410, the base 3D-LUT 510, the base 4D-LUT 520, the color correction 3D-LUT 610, the color correction 4D-LUT 620, and the like. However, LUTs other than the inverse model initial LUT 410 are created by the base LUT creation module 100 and the color correction LUT creation module 200. The base 3D-LUT 510 is a color conversion lookup table that receives an RGB color system and outputs an ink amount. On the other hand, the base 4D-LUT 520 is a color conversion lookup table that receives the CMYK color system and outputs the ink amount. “3D” and “4D” mean the number of input values. The RGB color system and the CMYK color system, which are the input color systems of these base LUTs 510 and 520, are not so-called device-dependent color systems, but are virtual color systems (or other than a specific device) (or Abstract color system). These base LUTs 510 and 520 are used when creating the color correction LUTs 610 and 620, for example. This is because the name “base LUT” is used as a basis for creating a color correction LUT. The color correction LUTs 610 and 620 are look-up tables for converting a standard device-dependent color system (for example, an sRGB color system or a JAPAN COLOR 2001 color system) into an ink amount of a specific printer. The inverse model initial LUT 410 will be described later.

FIG. 2 is a flowchart showing an overall processing procedure of the embodiment. 3A to 3C are explanatory diagrams showing processing contents when a base 3D-LUT is created by steps S100 to S300 of FIG. In step S100, a forward model converter 300 and an inverse model initial LUT 410 are prepared. Here, the “forward model” means a conversion model that converts the ink amount into a color value (colorimetric value) of the device independent color system. In contrast, the “inverse model” is a device independent color system. This means a conversion model that converts the color value of the ink into an ink amount. In the embodiment, the CIE-Lab color system is used as the device independent color system. Hereinafter, the color value of the CIE-Lab color system is also simply referred to as “L ^* a ^* b ^* value” or “Lab value”.

  As shown in FIG. 3A, the spectral printing model converter 310 that forms the preceding stage of the forward model converter 300 is configured such that a plurality of types of ink amounts are converted into spectral reflectances of color patches that are printed according to the ink amounts. Convert to R (λ). In the present specification, the term “color patch” is used in a broad sense including not only a chromatic color patch but also an achromatic color patch. In this embodiment, cyan (C), magenta (M), yellow (Y), black (K), light cyan (Lc), light magenta (Lm), light black (Lk), and very light black (LLk). A color printer that can use eight types of ink is assumed, and the spectral printing model converter 310 also receives the ink amounts of these eight types of ink. However, an arbitrary ink set can be used as the plurality of types of ink used in the printer. The color calculation unit 320 calculates a color value of the Lab color system from the spectral reflectance R (λ). For the calculation of the color value, a light source (for example, standard light D50) selected in advance is used as a color patch observation condition. As a method for creating the spectral printing model converter 310, for example, a method described in JP-T-2007-511175 can be employed.

The inverse model initial LUT 410 is a look-up table having an L ^* a ^* b ^* value as an input and an ink amount as an output. The initial LUT 410 is obtained by, for example, dividing an L ^* a ^* b ^* space into a plurality of small cells and selecting and registering an optimum ink amount for each small cell. This selection is performed in consideration of, for example, the image quality of the color patch printed with the ink amount. In general, there are many combinations of ink amounts that reproduce a certain L ^* a ^* b ^* value. Therefore, in the initial LUT 410, one that selects an optimum ink amount from a desired viewpoint such as image quality is registered from among a large number of ink amount combinations that reproduce substantially the same L ^* a ^* b ^* value. The L ^* a ^* b ^* value that is the input value of the initial LUT 410 is a representative value of each small cell. On the other hand, the ink amount as an output value reproduces any L ^* a ^* b ^* value in the cell. Therefore, in the initial LUT 410, the input value L ^* a ^* b ^* values between the ink amount and is not a thing which exactly correspond to the output value, the forward model converter 300 the amount of ink output value L ^When converted to a ^* a ^* b ^* value, a value slightly different from the input value of the initial LUT 410 is obtained. However, as the initial LUT 410, an input value and an output value that completely correspond to each other may be used. It is also possible to create a base LUT without using the initial LUT 410. As a method for creating the initial LUT 410 by selecting an optimal ink amount for each small cell, for example, the method described in the Japanese translations of PCT publication No. 2007-511175 can be employed.

  In step S200 of FIG. 2, an initial input value for creating a base LUT is set by the user. FIG. 3B shows an example of the configuration of the base 3D-LUT 510 and its initial input value setting. As the input values of the base 3D-LUT 510, values at substantially equal intervals predetermined as RGB values are set. Since a set of RGB values is considered to represent a point in the RGB color space, the set of RGB values is also referred to as an “input grid point”. In step S200, the initial value of the ink amount for some small number of input grid points selected in advance from among the plurality of input grid points is input by the user. It is preferable to select at least an input grid point corresponding to a vertex of a three-dimensional color solid in the RGB color space as the input grid point to which the initial input value is set. At the apex of this three-dimensional color solid, each RGB value takes the minimum value or the maximum value of the definition range. Specifically, when each RGB value is expressed by 8 bits, (R, G, B) = (0, 0, 0), (0, 0, 255), (0, 255, 0) , (255, 0, 0), (0, 255, 255), (255, 0, 255), (255, 255, 0), (255, 255, 255). The initial input value is set. The ink amounts for the input grid points of (R, G, B) = (255, 255, 255) are all set to zero. The initial input value of the ink amount for the other input grid points is arbitrary, and is set to 0, for example. In the example of FIG. 3B, the ink amount for the input grid point of (R, G, B) = (0, 0, 32) is a value other than 0. This is when this LUT 510 is completed. Is the value of

In step S300 of FIG. 2, the smoothing processing module 130 (FIG. 1) executes smoothing processing (smoothing / optimization processing) based on the initial input value set in step S200. FIG. 3C shows the processing content of step S300. On the left side of FIG. 3C, the distribution of a plurality of color points in a state before the smoothing process is indicated by double circles and white circles. These color points constitute a three-dimensional color solid CS in the L ^* a ^* b ^* space. The L ^* a ^* b ^* coordinate value of each color point is obtained by converting the ink amount at a plurality of input grid points of the base 3D-LUT 510 into an L ^* a ^* b ^* value using the forward model converter 300 (FIG. 3A). This is the converted value. As described above, in step S200, the initial input value of the ink amount is set only for some small number of input grid points. Therefore, the initial value of the ink amount for other input grid points is set from the initial input value by the smoothing process initial value setting module 120 (FIG. 1). This initial value setting method will be described later.

The three-dimensional color solid CS of the Lab color system has the following eight vertices (double circle points in FIG. 3C).
Point P _K : Paper black point corresponding to (R, G, B) = (0, 0, 0).
Point P _W : Paper white point corresponding to (R, G, B) = (255, 255, 255).
Point P _C : cyan point corresponding to (R, G, B) = (0, 255, 255).
Point P _M : Magenta point corresponding to (R, G, B) = (255, 0, 255).
Point P _Y : Yellow point corresponding to (R, G, B) = (255, 255, 0).
Point P _R : Red point corresponding to (R, G, B) = (255, 0, 0).
Point P _G : Green point corresponding to (R, G, B) = (0, 255, 0).
Point P _B : Blue point corresponding to (R, G, B) = (0, 0, 255).

The right side of FIG. 3C shows the distribution of color points after the smoothing process. The smoothing process is a process of moving a plurality of color points in the L ^* a ^* b ^* space and smoothing the distribution of these color points at nearly equal intervals. In the smoothing process, an optimum ink amount is also determined for reproducing the L ^* a ^* b ^* values of the respective color points after movement. When this optimum ink amount is registered as the output value of the base LUT 510, the base LUT 510 is completed.

  4A to 4C show the correspondence between the color point of the input color system (that is, the input grid point) and the color point of the Lab color system. The vertices of the Lab color system three-dimensional color solid CS correspond one-to-one with the vertices of the input color system three-dimensional color solid of the base LUT 510. Also, the sides (ridge lines) connecting the vertices can be considered to correspond to each other in both color solids. Each color point of the Lab color system before the smoothing process is associated with each input grid point of the base LUT 510. Therefore, each color point of the Lab color system after the smoothing process also corresponds to each input grid point of the base LUT 510. Attached. Note that the input grid points of the base LUT 510 are not changed by the smoothing process. The Lab color system three-dimensional color solid CS after the smoothing process corresponds to the entire color gamut (color gamut) reproducible with the ink set constituting the output color system of the base LUT 510. Therefore, the input color system of the base LUT 510 has significance as a color system that represents the entire color gamut that can be reproduced with this ink set.

The reason for performing the smoothing process in the L ^* a ^* b ^* space when creating the base LUT 510 is as follows. In the base LUT 510, there is a demand for setting an output color system ink amount so that a color gamut as large as possible can be reproduced. The color gamut that can be reproduced with a specific ink set is determined in consideration of predetermined limiting conditions such as ink duty limitation (limitation of the amount of ink that can be ejected to a certain area). On the other hand, the forward model converter 300 described above is created regardless of the reproducible color gamut without taking these restrictions into consideration. Therefore, if the range that can be taken by the color point in the L ^* a ^* b ^* space is determined in consideration of limiting conditions such as ink duty limitation during the smoothing process, a color gamut that can be reproduced with a specific ink set is determined. It becomes possible to do. As an algorithm for moving the color point, for example, an algorithm using a dynamic model described later is used.

  In step S400 of FIG. 2, the table creation module 140 creates the base LUT 510 using the result of the smoothing process. That is, the table creation module 140 registers the optimum ink amount for reproducing the color point of the Lab color system associated with each input grid point as the output value of the base LUT 510 (FIG. 3C). In the smoothing process, in order to reduce the calculation load, it is possible to select only the color points corresponding to only a part of the input grid points of the base LUT 510 as the processing target. For example, when the RGB value interval at the input grid point of the base LUT 510 is 16, if the RGB value interval at the input grid point to be smoothed is set to 32, the load of the smoothing process can be halved. it can. In this case, the table creation module 140 determines and registers the ink amount for all the input grid points of the base LUT 510 by interpolating the smoothing processing result.

  FIGS. 5A to 5C are explanatory diagrams showing processing contents when the base 4D-LUT 520 is created by steps S100 to S300 of FIG. FIG. 5A is the same as FIG. A base 4D-LUT 520 shown in FIG. 5B is different from the base 3D-LUT 510 shown in FIG. 3B in that the input is a CMYK color system. As an initial input value of the base 4D-LUT 520, (C, M, Y, K) = (0, 0, 0, 0), (0, 0, 255, 0), (0, 255, 0, 0) ), (0, 255, 255, 0), (255, 0, 0, 0), (255, 0, 255, 0), (255, 255, 0, 0), (255, 255, 255, 0) ), (0, 0, 0, 255), (0, 0, 255, 255), (0, 255, 0, 255), (0, 255, 255, 255), (255, 0, 0, 255) ), (255, 0, 255, 255), (255, 255, 0, 255), (255, 255, 255, 255), the initial value of the ink amount is set for 16 input lattice points. The initial input value of the ink amount for the other input grid points is arbitrary, and is set to 0, for example.

FIG. 5C shows a state of the smoothing process. As the color solid corresponding to the base 4D-LUT 520 in the L ^* a ^* b ^* space, as shown at the right end of FIG. 5C, there is one color solid for each K value of the input values. There is a three-dimensional color solid CS. In this example, a plurality of color solids CS including a color solid of K = 0 and a color solid of K = 32 are illustrated. In the present specification, these individual color solids CS are also referred to as “K layers”. This is because each color solid CS can be considered to correspond to an input layer in which the K value among the CMYK values is constant and the C, M, and Y values are variable. The plurality of color solids CS represent a dark color gamut as the K value increases. The plurality of color solids CS can be realized by determining the ink amount of the dark black ink K so that the ink amount of the dark black ink K increases as the K value of the input color system increases. As described above, the reproducible color gamut is limited by the ink duty limit value. As the ink duty limit value, two limit values are generally imposed, that is, the ink amount of each ink and the total ink amount of all inks. On the other hand, methods for reproducing dark colors include a method using achromatic ink such as dark black ink K and a method using composite black. However, since composite black has a large total ink amount, it is more likely to conflict with the ink duty limit value than dark black ink K, which is disadvantageous for reproducing dark colors. Therefore, a color solid having a large K value in the input color system and a large amount of dark black ink K is more than a color solid having a small K value in the input color system and a small amount of dark black ink K. Dark colors can be reproduced.

6A and 6B are explanatory diagrams illustrating a method for creating a color correction LUT using a base LUT. As shown in FIG. 6A, the base 3D-LUT 510 converts the RGB value into the ink amount I _j . The ink amount I _j represents the amount of ink 8 types of ink shown in Figure 3 (B). At this time, the subscript _j of the ink amount I j is 1 to 8. The converted ink amount I _j is converted into an L ^* a ^* b ^* value by the forward model converter 300. On the other hand, the sRGB values are converted into L ^* a ^* b ^* values according to a known conversion formula. The L ^* a ^* b ^* value after this conversion is gamut-mapped so that the color gamut matches the color gamut of the L ^* a ^* b ^* value converted by the forward model converter 300. On the other hand, through the base 3D-LUT 510 and the forward model converter 300, an inverse conversion LUT 511 is created using the L ^* a ^* b ^* values converted from the RGB values as a reverse lookup table. The gamut-mapped L ^* a ^* b ^* values are converted into RGB values by the inverse conversion LUT511. This RGB value is further converted again into the ink amount I _j by the base 3D-LUT 510. The color correction 3D-LUT 610 can be created by registering the correspondence between the last ink amount I _j and the first sRGB value in the lookup table. The color correction 3D-LUT 610 is a color conversion table for converting the sRGB color system to the ink color system.

FIG. 6B shows a method for creating the color correction 4D-LUT 620. The difference from FIG. 6A is that, instead of the 3D-LUT 510 and its inverse transformation LUT 511, the 4D-LUT 520 and its inverse transformation LUT 521 are used, and the sRGB color system is changed to an L ^* a ^* b ^* value. Instead of the known conversion formula for converting to ## EQU3 ## a known conversion formula for converting the JAPAN COLOR color system (shown as “jCMYK” in the figure) into L ^* a ^* b ^* values is used. As is well known, JAPAN COLOR is a color system composed of four colors of CMYK. In the method of FIG. 6B, when converting the L ^* a ^* b ^* value into the CMYK value in the inverse transformation LUT 521, the K value of the inverse transformation LUT 521 is calculated from the first K value of the jCMYK value before the known transformation. A layer (a portion where the K value is constant) is selected. Therefore, it is possible to create a color correction 4D-LUT 620 that reflects the characteristics of the K layer in the base 4D-LUT 520.

  Normally, the base LUTs 510 and 520 are mounted on the printer driver, and are used for processes other than the color correction LUT creation process. However, description of other utilization examples is omitted here. In the following, after briefly explaining the dynamic model used in the smoothing process (smoothing / optimization process) of the embodiment, the processing procedure of the smoothing process and the contents of the optimization process will be described sequentially.

ここで、Ｆ_gは着目色点ｇが隣接色点ｇｎ（ｎは１〜Ｎ）から受ける引力の合計値、Ｖ_gは着目色点ｇの速度ベクトル、−ｋ_vＶ_gは速度に応じた抵抗力、Ｘ_gは着目色点ｇの位置ベクトル、Ｘ_gnは隣接色点ｇｎの位置ベクトル、ｋ_p，ｋ_gは係数である。係数ｋ_p，ｋ_gは予め一定の値に設定される。なお、文中では、ベクトルを示す矢印は省略される。 B. Dynamic model:
FIG. 7 is an explanatory diagram illustrating a dynamic model used for the smoothing process (smoothing / optimization process) of the present embodiment. Here, a state in which a plurality of color points (white circles and double circles) are arranged in the L ^* a ^* b ^* color space is shown. However, for convenience of explanation, the arrangement of the color points is drawn two-dimensionally here. In this dynamic model, it is assumed that virtual force Fp _g of the following formula with respect to focus color point g is according.

Here, F _g is a total value of the attractive force received by the target color point g from the adjacent color points gn (n is 1 to N), V _g is a velocity vector of the target color point g, and −k _v V _g is a velocity. Resistance, X _g is a position vector of the target color point g, X _gn is a position vector of the adjacent color point gn, and k _p and k _g are coefficients. The coefficients k _p and k _g are set to constant values in advance. In the text, the arrow indicating the vector is omitted.

This model is a damped vibration model of mass points connected to each other by springs. That is, the virtual force Fp _g according to the target color point g is a focusing color point g and the spring force F _g, which distance increases larger with adjacent color points gn, increases as the speed of the target color point g is large resistance -K _v V _g and the total value. In this dynamic model, for each color point, after setting the initial value of the position vector X _g and the velocity vector F _g, it slides into successively calculates the position vector X _g and the velocity vector F _g minute time lapse. Note that the initial value of the velocity vector V _g for a plurality of color points is set to 0, for example. By using such a dynamic model, each color point moves gradually, and a smooth color point distribution can be obtained.

Note that forces other than the spring force F _g and the resistance force −k _v V _g may be used as the force related to each color point. For example, various other forces described in Japanese Patent Laid-Open No. 2006-197080 disclosed by the present applicant may be used in this dynamic model. Further, when moving each color point by applying a dynamic model, a specific color point can be handled as a constraint point that does not move by the dynamic model.

C. Smoothing processing (smoothing / optimization processing) procedure:
FIG. 8 is a flowchart showing a typical processing procedure of the smoothing process (step S300 in FIG. 2). In step T100, the smoothing process initial value setting module 120 (FIG. 1) initializes a plurality of color points to be smoothed.

ここで、Ｉ_(R,G,B)は、入力格子点のＲＧＢ値に対するインクセット全体のインク量（図３の例では８種類のインクのインク量）を表している。ＲＧＢ値が０または２５５を取る入力格子点に対するインク量は、図２のステップＳ２００においてユーザによって予め入力された値である。前記（２）式および（３）式によれば、任意のＲＧＢ値における仮インク量Ｉ_(R,G,B)を求めることが可能である。 FIG. 9 is a flowchart showing a detailed procedure of Step T100. In step T102, a temporary ink amount for each color point to be subjected to the smoothing process is determined from the initial input value of the ink amount (FIGS. 3B and 5B). For example, in the smoothing process for 3D-LUT, the temporary ink amount I _{(R, G, B)} for each input grid point is determined according to the following equations (2) and (3).

Here, I _{(R, G, B)} represents the ink amount of the entire ink set with respect to the RGB values of the input lattice points (in the example of FIG. 3, the ink amounts of eight types of ink). The ink amount for the input grid point where the RGB value is 0 or 255 is a value input in advance by the user in step S200 of FIG. According to the equations (2) and (3), the temporary ink amount I _{(R, G, B)} at an arbitrary RGB value can be obtained.

In the smoothing process for 4D-LUT, the temporary ink amount I _{(C, M, Y, K)} for each input grid point is determined according to the following equations (4) and (5).

ここで、Ｉ_(C,M,Y,0)は、Ｋ＝０の８個の頂点におけるインク量の初期入力値から、前記（２）式と同様の式で算出されたインク量である。（６）式の関数ｆ _D1は値Ｉ_(C,M,Y,0)と値Ｉ_(0,0,0,255)の合計値がインクデューティ制限値をオーバーする場合に、値Ｉ_(C,M,Y,0)を減じることによって、インク量Ｉ_(C,M,Y,255)がインクデューティ制限値内に納まるようにする関数である。また、（７）式の関数ｆ _D2は、値Ｉ_(C,M,Y,0)と値Ｉ_(0,0,0,255)の合計値がインクデューティ制限値をオーバーする場合に、合計値（Ｉ_(C,M,Y,0)＋Ｉ_(0,0,0,255)）の全体を減じることによって、インク量Ｉ_(C,M,Y,255)がインクデューティ制限値内に納まるようにする関数である。なお、インク量Ｉ_j（Ｉ _j(R,G,B)，ΔＩ_j，Ｉ_jr，ｈ_jも含む）を下付文字ｊを付すことなく示す場合は、各インクのインク量Ｉ_jを各行要素として有する行列（ベクトル）を意味することとする。 As can be understood from the equation (4), since there are 16 initial input values of the ink amount for 4D-LUT, setting of the initial input value is complicated. Therefore, for example, the input grid points for setting the initial input value of the ink amount are eight vertices of K = 0, that is, (C, M, Y, K) = (0, 0, 0, 0), ( 0,0,255,0), (0,255,0,0), (0,255,255,0), (255,0,0,0), (255,0,255,0), ( 8 vertices of 255, 255, 0, 0), (255, 255, 255, 0) and 1 vertex of K = 255, for example, (C, M, Y, K) = (0, 0) , 0, 255) only, and the ink amount of the color point of K = 255 may be determined by the following equation (6) or (7).

Here, I _{(C, M, Y, 0)} is an ink amount calculated from the initial input value of the ink amount at eight vertices of K = 0 by the same expression as the expression (2). (6) the function f _D1 is the value I _{(C, M, Y, 0)} if the total value of the value I _{(0, 0, 0, 255)} is over the ink duty limit value I _{(C, M , Y, 0)} is a function for keeping the ink amount I _{(C, M, Y, 255)} within the ink duty limit value. Further, (7) the function f _D2, the value I _{(C, M, Y, 0)} and if the total value of the values I _{(0, 0, 0, 255)} is over the ink duty limit value, the total value ( A function for _keeping the ink amount I _{(C, M, Y, 255)} within the ink duty limit value by subtracting the total of I _{(C, M, Y, 0)} + I _{( 0, 0, 0 , 255))} It is. In addition, when the ink amount I _j (including I _{j (R, G, B)} , ΔI _j , I _jr , h _j ) is indicated without the subscript j, the ink amount I _j of each ink is indicated in each row. It means a matrix (vector) having elements.

ここで、Ｌ^* _(R,G,B)、ａ^* _(R,G,B)、ｂ^* _(R,G,B)、Ｌ^* _(C,M,Y,K)、ａ^* _(C,M,Y,K)、ｂ^* _(C,M,Y,K)は変換後の色彩値Ｌ^*ａ^*ｂ^*を示しており、関数ｆ_L*FM、ｆ_a*FM、ｆ_b*FMはフォワードモデルコンバーター３００による変換を意味している。なお、これらの式からも理解できるように、この変換後の色彩値Ｌ^*ａ^*ｂ^*は、ベースＬＵＴの入力値であるＲＧＢ値またはＣＭＹＫ値に対応付けられている。 In Step T104 of FIG. 9, the forward model converter 300 is used to obtain a color value L ^* a ^* b ^* corresponding to the temporary ink amount. This calculation can be expressed by the following equation (8) or (9).

Here, L ^* _{(R, G, B)} , a ^* _{(R, G, B)} , b ^* _{(R, G, B)} , L ^* _{(C, M, Y, K)} , a ^* _{(C, M, Y, K)} and b ^* _{(C, M, Y, K)} indicate the color values L ^* a ^* b ^* after conversion, and the functions f _{L * FM} , f _{a * FM} , f _{b * FM} Means conversion by the forward model converter 300. As can be understood from these equations, the converted color value L ^* a ^* b ^* is associated with an RGB value or a CMYK value that is an input value of the base LUT.

In step T106 in FIG. 9, the color value L ^* a ^* b ^* obtained in step T104 is converted again into an ink amount using the inverse model initial LUT 410 (FIG. 3A). Here, the reason why the ink amount is converted again using the inverse model initial LUT 410 is that the initial input value of the ink amount or the temporary ink amount determined in step T102 is the ink amount that reproduces the L ^* a ^* b ^* value. This is because the ink amount is not always preferable. On the other hand, in the inverse model initial LUT 410, a preferable ink amount that takes image quality and the like into consideration is registered. If this value is used to convert the L ^* a ^* b ^* value back into the ink amount, the L ^* a ^* b ^* A preferable ink amount for realizing the value can be obtained as an initial value. However, step T106 may be omitted.

As a result of the process in step T100 described above, the following initial values are determined for the color points to be subjected to the smoothing process.
(1) Input grid point value of base LUT: (R, G, B) or (C, M, Y, K)
(2) Initial coordinate values of color points in the L ^* a ^* b ^* space corresponding to each input grid point: (L ^* _{(R, G, B)} , a ^* _{(R, G, B)} , b ^* _{(R , G, B)} ) or (L ^* _{(C, M, Y, K)} , a ^* _{(C, M, Y, K)} , b ^* _{(C, M, Y, K)} )
(3) Initial ink amount corresponding to each input grid point: I _{(R, G, B)} or I _{(C, M, Y, K)}
As can be understood from the above description, the initial value setting module 120 has a function of setting initial values related to other input grid points from input initial values related to typical input grid points. The initial value setting module 120 may be included in the smoothing processing module 130.

In Step T120 of FIG. 8, the color point moving module 132 moves the color point in the L ^* a ^* b ^* space according to the dynamic model described above.

10A to 10D are explanatory diagrams showing the processing contents of steps T120 to T150 in FIG. As shown in FIG. 10A, there is a considerable bias in the distribution of color points before the smoothing process. FIG. 10B shows the position of each color point after the minute time has elapsed. L ^* a ^* b ^* values of each color point after this movement is referred to as a "target value _{^{(L t * a t * b}} t * value)". The modifier "target" is because this _{^{L t * a t * b t}} * value is used as a target value during the process of searching for the optimum value of the ink amount described below.

In Step T130, the ink amount optimizing module 134 searches for the optimum value of the ink amount with respect to the target value LAB _t using the preset objective function E (see FIG. 10C). In the optimization using the objective function E, a plurality of ink amounts I _j that reproduce L ^* a ^* b ^* values close to the coordinate value LAB _t of the color point after moving by a minute amount in the dynamic model. The ink amount that is as small as possible is determined as the optimum ink amount with the sum of the square errors of the parameters ΔL ^* , Δa ^* , ΔGI, ΔCII, and ΔTI. The search for the optimum ink amount is started from the initial ink value of each input grid point set in step T100. Therefore, the ink amount obtained by the search is a value obtained by correcting this initial ink amount. As will be described in detail later, the objective function E given by the equation (EQ1) can be written as a quadratic function relating to the ink amount vector I as in the equation (EQ2). The optimization of the ink amount is performed according to the quadratic programming method using the quadratic objective function E. The detailed procedure of step T130 and the contents of the objective function E will be described later.

In step T140 in FIG. 8, the L ^* a ^* b ^* value corresponding to the ink amount I _j searched in step T130 is recalculated by the forward model converter 300 (see FIG. 10D). Here, the reason why the L ^* a ^* b ^* value is recalculated is that the searched ink amount I _j is the ink amount that minimizes the objective function E, and therefore L ^* a ^* b reproduced with the ink amount I _j. ^{This is because the *} value slightly deviates from the target value LAB _t of the optimization process. The L ^* a ^* b ^* values recalculated in this way are used as coordinate values after the movement of each color point.

In step T150, it is determined whether or not the average value (ΔLab) _ave of the movement amount of the coordinate value of each color point is equal to or less than a preset threshold value ε. When the average value (ΔLab) _{ave of the} movement amount is larger than the threshold value ε, the process returns to step T120 and the smoothing process of steps T120 to T150 is continued. On the other hand, when the average value (ΔLab) _{ave of} the moving amount is equal to or smaller than the threshold value ε, the color point distribution is sufficiently smoothed, and thus the smoothing process ends. Note that an appropriate value for the threshold ε is experimentally determined in advance.

  As described above, in the typical smoothing process (smoothing / optimization process) of the present embodiment, the optimum ink amount corresponding to the color point after the movement is obtained while moving each color point at every minute time interval by the dynamic model. Is searched with an optimization method. Then, these processes are continued until the movement amount of the color point becomes sufficiently small. As a result, as shown in FIG. 3C, a smooth color point distribution can be obtained by the smoothing process.

D. Contents of optimization process:
The optimization processing objective function E (see FIG. 10C) can be expressed using a Jacobian matrix J relating to color values (L ^* a ^* b ^* values), which are functions of the ink amount, and an image quality evaluation index. It is. The Jacobian matrix J is expressed by, for example, the following equation (10).

The first to third lines on the right side of the equation (10) indicate values obtained by partial differentiation of the color values L ^* a ^* b ^* with the individual ink amounts I _j . In the fourth and subsequent rows, an image quality evaluation index (graininess index GI (Graininess Index) representing the image quality of a color patch printed with one set of ink amount I _j (j = 1 to 8) and color non-constancy. An index CII (Color Inconstancy Index) and a value obtained by partial differentiation of the total ink amount TI with respect to each ink amount I _j are shown, and the image quality evaluation indexes GI, CII, and TI indicate that the smaller the value, the more the ink amount. This is an index indicating that the image quality of the color patch reproduced with I _j tends to be good.

The color value L ^* a ^* b ^* is converted from the ink amount I _j by the following equation (11) using the forward model converter 300.

The image quality evaluation indexes GI and CII can also be expressed as functions of the ink amount I _{j in} general.

In addition, the subscript “ill” of the color non-constancy index CII _{ill in} the equation (13) represents the type of light source. In the above-described equation (10), standard light A and standard light F12 are used as the types of light sources. An example of a method for calculating the color non-constancy index CII will be described later. As the color non-constant index CII, one relating to one or a plurality of arbitrary standard light sources can be used.

ここで、ａＬは明度補正係数、ＷＳ（ｕ）はカラーパッチの印刷に利用されるハーフトーンデータが示す画像のウイナースペクトラム、ＶＴＦ（ｕ）は視覚の空間周波数特性、ｕは空間周波数である。ハーフトーンデータは、カラーパッチのインク量Ｉ_jからハーフトーン処理（プリンター１０が実行するハーフトーン処理と同一のものとする）によって決定される。前記（１５）式は一次元で表現しているが、空間周波数の関数として二次元画像の空間周波数を算出することは容易である。粒状性指数ＧＩの計算方法としては、例えば、本出願人により開示された特表２００７−５１１１６１号公報に記載された方法や、Makoto Fujino， Ｉmage Quality Evaluation of Inkjet Prints， Japan Hardcopy '99， p.291-294に記載された方法を利用することができる。 The graininess index GI can be calculated using various graininess prediction models. For example, the graininess index GI can be calculated by the following equation (15).

Here, aL is a brightness correction coefficient, WS (u) is a winner spectrum of an image indicated by halftone data used for printing a color patch, VTF (u) is a visual spatial frequency characteristic, and u is a spatial frequency. The halftone data is determined from the ink amount I _j of the color patch by halftone processing (same as the halftone processing executed by the printer 10). Although the equation (15) is expressed in one dimension, it is easy to calculate the spatial frequency of the two-dimensional image as a function of the spatial frequency. As a method for calculating the graininess index GI, for example, a method described in Japanese Patent Application Publication No. 2007-511161 disclosed by the applicant, Makoto Fujino, Image Quality Evaluation of Inkjet Prints, Japan Hardcopy '99, p. The method described in 291-294 can be used.

ここで、ΔＬ^*は２つの異なる観察条件下（異なる光源下）におけるカラーパッチの明度差、ΔＣ^* _abは彩度差、ΔＨ^* _abは色相差を示す。色非恒常性指数ＣＩＩの計算時には、２つの異なる観察条件下でのＬ^*ａ^*ｂ^*値は、色順応変換（ＣＡＴ）を用いて標準観察条件（例えば標準の光Ｄ６５の観察下）に変換される。ＣＩＩについては、Billmeyer and Saltzman's Principles of Color Technology， 3rd edi_tion， John Wiley & Sons， Ｉnc， 2000， p.129， pp. 213-215を参照。 The color non-constancy index CII is given by the following equation (16), for example.

Here, ΔL ^* is the lightness difference of the color patch under two different observation conditions (under different light sources), ΔC ^* _ab is the chroma difference, and ΔH ^* _ab is the hue difference. When calculating the color non-constant index CII, the L ^* a ^* b ^* values under two different viewing conditions are converted to standard viewing conditions (eg, under the observation of standard light D65) using chromatic adaptation transformation (CAT). Converted. For the CII, Billmeyer and Saltzman's Principles of Color Technology, 3rd edi t ion, John Wiley & Sons, Inc, 2000, p.129, see pp. 213-215.

ここで、ｆ_L*FMは、フォワードモデルによるインク量ＩからＬ^*値への変換関数、Ｉ_rはインク量Ｉの現在値（平滑化／最適化処理前のインク量）、ｈ_jはｊ番目のインク量Ｉ_jの微小変動量である。ヤコビ行列Ｊの最下行を除く他の成分も同じ形式で表される。前記（１４）、（１７）式に準じて、ヤコビ行列Ｊの最下行の要素を算出すると、ヤコビ行列Ｊの最下行の要素はすべて１となる。あるインクのインク量Ｉ_jが微小変動量ｈ_jだけ変動した場合の合計インク量ＴＩの変動量もｈ_jとなるからである。しかしながら、本実施例では、（１８）式に示すように、ヤコビ行列Ｊの最下行の要素を１とせず、調整係数Ｕ_jを使用することとする。

前記（１８）式右辺は、合計インク量ＴＩに関する成分を除いた本来のヤコビ行列の最下行に調整係数Ｕ_jの行を追加したものであると捉えることができる。また、前記（１８）式右辺は、前記（１４）式に示した現実の合計インク量ＴＩではなく、下記（１９）式に示す仮想的な合計インク量ＴＩについての偏微分要素を最下行に有するヤコビ行列Ｊであるとも捉えることができる。本明細書では、前記（１８）式の右辺全体をヤコビ行列Ｊと称呼するものとする。

Of the plurality of components (also referred to as “elements”) of the Jacobian matrix J, for example, the component relating to the L ^* value is given by equation (17).

Here, f _{L * FM} is a conversion function from the ink amount I to the L ^* value according to the forward model, I _r is the current value of the ink amount I (ink amount before smoothing / optimization processing), and h _j is j This is a minute fluctuation amount of the first ink amount I _j . Other components except the bottom row of the Jacobian matrix J are also expressed in the same format. When the elements in the bottom row of the Jacobian matrix J are calculated according to the equations (14) and (17), all the elements in the bottom row of the Jacobian matrix J are 1. This is because the fluctuation amount of the total ink amount TI when the ink amount I _j of a certain ink fluctuates by the minute fluctuation amount h _j is also h _j . However, in this embodiment, as shown in the equation (18), the element in the bottom row of the Jacobian matrix J is not set to 1, and the adjustment coefficient U _j is used.

The right side of the equation (18) can be considered to be obtained by adding the row of the adjustment coefficient U _j to the lowest row of the original Jacobian matrix excluding the component related to the total ink amount TI. The right side of the equation (18) is not the actual total ink amount TI shown in the equation (14) but the partial differential element for the virtual total ink amount TI shown in the following equation (19) It can also be understood that it is a Jacobian matrix J having. In this specification, the entire right side of the equation (18) is referred to as a Jacobian matrix J.

FIGS. 11A and 11B schematically show an example of the adjustment coefficient U _j . Figure 11 (A) shows the CIE-Lab color space, indicates the position indicated by the target value ^{_{L t * a t * b t}} * in CIE-Lab color space by a double circle. Incidentally, the target value ^{_{L t * a t * b t}} *, is based on the dynamic model described above. Reference plane B1 that divides the CIE-Lab color space generally vertically (high brightness side and the low brightness side), B2 are provided, parallel to the L ^* axis passing through the target value ^{_{L t * a t * b t}} * The intersections between the straight line L and the reference planes B1 and B2 are indicated by white circles as control points CP1 and CP2, respectively. Figure 11 (B) is the target value ^{_{L t * a t * b t}} * (2 double circle) and passes through the control points CP1, CP2 (open circles), L ^* adjustment factor along the axis and a straight line parallel U _j ( j = 1, 5: C ink, Lc ink).

The adjustment coefficient U ₁ for C ink is a constant positive value U _c1 in a region with a lightness lower than the control point CP1, and decreases linearly from the positive value U _c1 as the lightness increases in a region with a higher lightness than the control point CP1. I will do it. Then, in the region where the brightness is higher than the predetermined brightness, the adjustment coefficient U ₁ becomes a constant negative value U _c2 . On the other hand, the adjustment coefficient U ₅ for Lc ink is a constant positive value U _c1 in a region having a higher brightness than the control point CP2, and is linear from the positive value U _c1 as the brightness decreases in a region having a lower brightness than the control point CP2. It will decrease to. Then, the adjustment factor U ₅ is in the region of the lower brightness than a predetermined brightness, adjustment coefficient U ₅ is a constant negative value U _c2. In FIG. 11B, the C ink and the Lc ink are taken as an example, but the adjustment coefficient U _j is set to a value larger than the light ink in the low lightness region for the dark ink, and in the high lightness region for the light ink. The value is larger than that of dark ink. The reference plane B1, B2, since L ^* is not perpendicular to the axis, the brightness of the control points CP1, CP2 varies depending on the target value ^{_{L t * a t * b t}} * is hue and shows saturation . In the example of FIG. 11A, the reference planes B1 and B2 are parallel to each other, but they are not limited to being parallel to each other. When the reference planes B1 and B2 are non-parallel, the magnitude relationship between the brightness levels of the control points CP1 and CP2 may be reversed depending on the hue and saturation.

ここで、右辺の各項の最初に記載されているｗ _L*，ｗ _a*等は、各項の重みである。各項の重みｗ _L*、ｗ _a*…は、予め設定されている。ヤコビ行列Ｊの最下行の合計インク量ＴＩに対する重みｗ_TIは、１としておく。 The optimization objective function E is given by the following equation (20), for example.

Here, w _{L *} , w _{a * and the} like described at the beginning of each term on the right side are the weights of each term. The weights w _{L *} , w _{a *} ... For each term are set in advance. The weight w _TI for the total ink amount TI in the bottom row of the Jacobian matrix J is set to 1.

The first term w _{L *} (ΔL ^* −ΔL ^* _t ) ^{2 on} the right side of the equation (20) is a square error with respect to the variations ΔL ^* and ΔL ^* _t of the color value L ^* . These fluctuation amounts ΔL ^* and ΔL ^* _t are given by the following equations.

The partial differential value on the right side of the equation (21) is a value given by the Jacobian matrix (equation (10)), I _j is the ink amount obtained as a result of the optimization process, and I _jr is the current ink amount. . The first variation amount ΔL ^* is an amount obtained by linearly converting the variation amount ΔI _j of the ink amount by the optimization processing with a partial differential value that is a component of the Jacobian matrix. On the other hand, the second variation amount [Delta] L ^* _t is the difference between the target value L ^* _t obtained in the smoothing process of step T120, the color values are given in the current ink amount I _r L ^* and (I _r) . The second fluctuation amount ΔL ^* _t can be considered as a difference between L ^* values before and after the smoothing process.

The terms after the second term on the right side of the equation (20) are also given by the same equations as the equations (21) and (22). That is, the objective function E includes the first variation amounts ΔL ^* , Δa ^* , Δb ^* , ΔGI, etc. obtained by linearly transforming the variation amount ΔI _j of the ink amount by the optimization processing with the Jacobian matrix components, and the parameter L Is given as a sum of square errors of second variation amounts ΔL ^* _t , Δa ^* _t , Δb ^* _t , ΔGI _t ... Before and after the smoothing process regarding ^* , a ^* , b ^* , GI. .

By the way, the first fluctuation amounts ΔL ^* , Δa ^* , Δb ^* , ΔGI,... Can be written in the following formulas (23) and (24) using a matrix.

Expression (20) can be expressed as Expression (25) using a matrix.

Here, T represents transposition of the matrix. The matrix W _M is a diagonal matrix (see formula (26)) in which weights are arranged on the diagonal elements, and the matrix ΔM is a target variation vector (see formula (27)) for each parameter.

(27) the right side of the equation, the parameters ^{L *, a *, b *} , is the difference between the target values for CII ... (also referred to as "element"), and each parameter values given the current ink amount I _r . Among the target values of each parameter, the color values L ^* _t , a ^* _t , and b ^* _t are determined by the smoothing process (step T120). Set w _IT = 1 of the matrix W _{M in} the equation (26).
Image quality evaluation index of the target value and the current target variation DerutaGI _t obtained from image quality evaluation index, DerutaCII _t, for .DELTA.TI _t, there are several determination methods. The first method, the target variation ΔGI _t, ΔCII _t, predetermined constant as .DELTA.TI _t (e.g. _{ΔGI t = -2, ΔCII t =} -1, ΔTI t = 1) is a method to use. The reason why negative values are used as constants is that these image quality evaluation indices are indices indicating that the smaller the image quality evaluation index, the higher the image quality. In addition, the target value GI _t of the graininess index GI is preferably set to zero. In the second method, target values GI _t , CII _t , and TI _t are defined as functions of color value target values L ^* _t , a ^* _t , and b ^* _t . As described above, since the target value of each parameter is determined before the optimization process, all components of the target variation vector ΔM are constants.

Of the terms on the right side of the equation (25), the third term (I _r ^T J ^T + ΔM ^T ) W _M (JI _r + ΔM) includes the ink amount I obtained as a result of the optimization process. Since there is no constant. In general, no constant term is required as the optimization objective function E. Therefore, when the constant term is deleted from the equation (25) and the whole is multiplied by 1/2, the following equation (28) is obtained.

Here, when the matrix A and the vector g are defined as in the following formulas (29) and (30), the formula (28) can be written as in the formula (31).

  It can be understood that the objective function E given by the equation (31) is a quadratic form related to the ink amount vector I obtained by the optimization. The expressions (EQ1) and (EQ2) shown in FIG. 10C are the same as the expressions (20) and (31), respectively.

  In the optimization process of the present embodiment, the quadratic objective function E as shown in the equation (31) is used, so that the quadratic programming method can be used as the optimization method. Here, “secondary programming” means narrowly-ordered secondary programming that does not include sequential quadratic programming. Using quadratic programming with a quadratic objective function will greatly speed up processing compared to using other nonlinear programming methods such as quasi-Newton and sequential quadratic programming. Is possible.

ここで、Ｚはインク量調整項を表す。ｗ_TI＝１，ΔＴＩ_t＝１であるため、前記（３２）式は下記（３３）式で表すことができる。

前記（３３）式が示すようにインク量調整項Ｚは、現在のインク量Ｉ_jrからインク量Ｉ_jへの変動量（Ｉ_j−Ｉ_jr）を、調整係数Ｕ_jを重みとして線形結合した値の２乗に応じた値である。前記（３３）式をさらに展開した場合、調整係数Ｕ_jの２乗が各インクのインク量変動量（Ｉ_j−Ｉ_jr）の２次の係数となることが理解できる。 Next, a term including the adjustment coefficient U _j in the objective function E is examined. If only the term including the adjustment coefficient U _j is extracted from the right side of the equation (25), the following equation is obtained.

Here, Z represents an ink amount adjustment term. Since w _TI = 1 and ΔTI _t = 1, the equation (32) can be expressed by the following equation (33).

As shown in the equation (33), the ink amount adjustment term Z is a linear combination of the fluctuation amount (I _j −I _jr ) from the current ink amount I _jr to the ink amount I _j using the adjustment coefficient U _j as a weight. It is a value corresponding to the square of the value. When the expression (33) is further developed, it can be understood that the square of the adjustment coefficient U _j becomes a second-order coefficient of the ink amount fluctuation amount (I _j −I _jr ) of each ink.

Here, when the adjustment coefficient U _j of a certain ink is a positive value, the larger the amount of increase from the current ink amount I _jr to the ink amount I _j in the optimization, the greater the amount of ink that is caused by the ink amount I _j of the ink. Thus, the ink amount adjustment term Z becomes a small value. If the ink amount adjustment term Z is small, the value of the objective function E is also small, so that the increase of the ink amount I _j of the ink is promoted in the optimization. Furthermore, it can be said that the greater the positive ink adjustment coefficient U _j , the greater the contribution to the ink amount adjustment term Z and the objective function E, and thus the greater the degree of promotion for the ink amount I _j of the ink. On the other hand, when the adjustment coefficient U _j of a certain ink is a negative value, the larger the amount of increase from the current ink amount I _jr to the ink amount I _j in the optimization, the greater is the attribute of the ink amount I _j of the ink. Thus, the ink amount adjustment term Z becomes a large value. If the ink amount adjustment term Z is large, the value of the objective function E is also large, so that an increase in the ink amount I _j of the ink is suppressed in the optimization. Furthermore, the larger the absolute value of the negative ink adjustment coefficient U _j , the greater the contribution to the ink amount adjustment term Z and the objective function E, and the greater the degree of suppression of the increase in the ink amount I _j of the ink. I can say. At this time, the above equation (33) is such that the linear combination of the ink amount fluctuation amount (I _j −I _jr ) and the adjustment coefficient U _j is 1, so that Z is minimized, but U _j is a positive value. When the ink amount I _j increases on average, the linear combination approaches 1; when U _j is a negative value, the ink amount I _j decreases on average and the linear combination approaches 1.

As described above, as the adjustment coefficient U _j is larger, the increase in the ink amount I _j in the optimization is promoted. Accordingly, the adjustment coefficient U _j may be set to a large value for ink that is desired to be used for printing. In the present embodiment, for the C ink having a relatively high density, the adjustment coefficient U _j is set large in the low lightness region, and the adjustment coefficient U _j is set small in the high lightness region. Therefore, the ink amount I _j of the C ink in the high brightness area can be suppressed. For the Lc ink in which the adjustment coefficient U _j is set so as to have the opposite tendency, the ink amount I _j can be increased in the high brightness region. In addition, since the adjustment coefficient U _j is gradually changed as shown in FIG. 11, it is possible to prevent the tendency of the ink amount I _j from changing suddenly and to realize smooth gradation. As described above, in this embodiment, the adjustment coefficient U _j is individually set for each ink, so that the relative balance of the ink amount I _j can be adjusted between the inks.

Matrix W _M shown in the above (26), each image quality evaluation index GI, CII, but it is possible to set the weight for the entire TI, it is not possible to set a weight for each of the ink by weight w _TI. It is conceivable to set a target ink amount with respect to the ink amount I _j of each ink, and add a term obtained by weighting these square errors with a weight corresponding to each ink to the objective function E. Complicated and increased processing load. On the other hand, the element (the partial differential value of the total ink amount TI) in the lowermost row of the original Jacobian matrix of the equation (10) as in this embodiment is set to the adjustment coefficient U _j as in the equation (18). By replacing it, it is possible to easily adjust the relative balance of the ink amount I _j of each ink.

By the way, the search for the ink amount by the optimization process in the present embodiment is executed under the following conditions.
(Optimization condition) The objective function E is minimized.
(Restrictions) Observe ink duty limits.

As the ink duty limit value, for example, the maximum allowable value of the ink amount of each ink and the maximum allowable value of the total ink amount are used. For example, when the ink amount of each ink is expressed by 8 bits, the maximum allowable value of the ink amount I _j of eight types of individual inks is set to 180, and the maximum allowable value of the total ink amount ΣI _j is set to 240. May be.

ここで、ベクトルｂは、デューティ制限の対象となるインク種類を識別するための係数であり、要素に０か１を持つベクトルである。例えば、１種類のインクに関するデューティ制限の場合には、ベクトルｂの１個の要素のみが１となる。一方、全インクの合計インク量に関するデューティ制限の場合には、ベクトルｂのすべての要素が１となる。（３４）式の右辺のlim_Iは、デューティ制限値である。 The ink duty limit can be expressed by the following equation (34).

Here, the vector b is a coefficient for identifying the ink type that is the target of duty limitation, and is a vector having 0 or 1 as an element. For example, in the case of a duty limit relating to one type of ink, only one element of the vector b is 1. On the other hand, in the case of the duty limit related to the total ink amount of all inks, all elements of the vector b are 1. Lim _{I on} the right side of the equation (34) is a duty limit value.

There is also a restriction that each ink amount I _j is not negative. This non-negative limit can be expressed by the following equation (35).

When the formula (34) and the formula (35) are combined, the ink duty limit is given by the following formula (36).

  The constraint expressed by the equation (36) is a linear inequality constraint. In general, quadratic programming can be performed under linear constraints. In other words, in the optimization processing in the present embodiment, the optimization is performed by executing the quadratic programming method using the quadratic objective function E given by the equation (31) under the constraint of the equation (36). Search for the correct ink amount. As a result, it is possible to execute the ink amount search at high speed while strictly satisfying this linear constraint.

FIG. 12 is a flowchart showing a detailed procedure of the optimization process (step T130 in FIG. 8). In step T132, first, the target fluctuation amount ΔM given by the above equation (27) is obtained. The target variation ΔM, as described above, the target value L ^* _t obtained in step T120 (smoothing processing), a ^* _t, are determined based on the b ^* _t and the current ink amount I _r.

In step T134, the Jacobian matrix J given by the equation (10) is calculated. Each component of the Jacobian matrix J is a value calculated with respect to the current value I _r (value before smoothing / optimization) of the ink amount, as exemplified by the equation (17).

In step T136, the difference between the linear transformation results ΔL ^* , Δa ^* , Δb ^* , ΔGI... And the target fluctuation amount ΔM (ΔL ^* _t , Δa ^* _t , Δb ^* _t , ΔGI _t ...) Is obtained. The ink amount is optimized so as to be minimized. This optimization is realized by executing a quadratic programming method using the objective function E of the quadratic form given by the equation (31).

  As already described in the flowchart of FIG. 8, when it is determined that the convergence is insufficient after the optimization process in step T130, the smoothing process (step T120) and the optimization process (step T130) are performed. Will be executed again. At this time, the value obtained by the previous smoothing / optimization process is used as the initial value of the smoothing / optimization process. Note that such repeated processing is not essential, and at least one smoothing / optimization processing may be performed.

  As described above, in this embodiment, since the optimal ink amount is searched by executing the quadratic programming method using the objective function E of the quadratic form, the ink amount search can be executed at high speed. . According to the actual measurement by the inventors, it has been found that the processing can be completed in about one-tenth of the time when the conventional quasi-Newton method is used.

E. Configuration of printing device:
FIG. 13 shows the configuration of the printer 10. In FIG. 1, the printer 10 includes a CPU 13, a RAM 14, a ROM 15, a memory card slot 20, a bus 21 and an ASIC 22. The firmware FW for controlling the printer 10 is executed by the CPU 13 performing calculations according to the program data 15a while expanding the program data 15a stored in the ROM 15 into the RAM 14. The firmware FW generates drive data based on the print data PD stored in the memory card MC installed in the memory card slot 20. The ASIC 22 acquires drive data and generates drive signals for the paper feed mechanism 17, the carriage motor 18, and the print head 19. In the ROM 15, a color correction 3D-LUT 610 is stored. The printer 10 includes a carriage 21, and the carriage 11 includes cartridge holders 11 a to which ink cartridges 12 can be attached. .. Can be inserted and fixed in the cartridge holders 11a, 11a.

  In this embodiment, four cartridge holders 11a, 11a,... Are provided, and cyan (C), magenta (M), yellow (Y), and black (K) are provided in the cartridge holders 11a, 11a,. , 8 ink cartridges 12, 12... Filled with light cyan (Lc), light magenta (Lm), light black (Lk), and very light black (LLk) inks, respectively. The CMY ink corresponds to the chromatic ink of the present invention, and the K ink corresponds to the achromatic ink of the present invention. The carriage 11 includes a print head 19 that ejects ink supplied from the ink cartridges 12, 12... From a large number of ink nozzles Nz.

FIG. 14 schematically shows the printing method of the printer 10 of the present embodiment. The printer 10 includes a print head 19 having a plurality of nozzles Nz... For each CMYK ink, and a process for controlling the amount of ink ejected by the nozzles Nz. Based on the data. The ink droplets ejected by the nozzles Nz... Become fine dots on the printing paper, and a print image having an ink coverage corresponding to each ink amount I _j is formed on the printing paper by the collection of a large number of dots. It becomes. Note that the ink amount of each ink is represented as I _j, and the subscript j is a natural number (j = 1 to 8) for identifying the type of each ink. In this specification, printing based on the ink amount I _j means that the image of the ink coverage in accordance with the ink amount I _j is reproduced on the printing paper. The printer 10 in the present embodiment is an ink jet printer, but the present invention can be applied to various printers in addition to the ink jet method. In this embodiment, each ink amount I _j is given by 8 bits from 0 to 255.

  FIG. 15 shows the software configuration of the firmware FW. The firmware FW includes an image data acquisition unit FW1, a rendering unit FW2, a color conversion unit FW3, a halftone unit FW4, and a rasterization unit FW5. The image data acquisition unit FW1 acquires the print data PD stored in the memory card MC as a print target. The print data PD may be document data, graphic data, or photographic image data. The rendering unit FW2 generates input image data ID used for printing based on the print data PD. The input image data ID is composed of pixels having the number of pixels (print resolution × print actual size) corresponding to the print resolution (for example, 2880 × 2880 dpi), and each pixel is an 8-bit (0 to 255) CIE-sRGB color. It is expressed by RGB values conforming to space.

The color conversion unit FW3 acquires the input image data ID and performs color conversion on the input image data ID. Specifically, the color conversion unit FW3 converts the RGB value into the ink amount I _j of each ink by performing an interpolation operation while referring to the color correction 3D-LUT 610. The halftone unit FW4 executes halftone processing based on the ink amount I _j of each ink output from the color conversion unit FW3. The rasterizing unit FW5 allocates each pixel (dischargeability) of the halftone data after the halftone process to each main scan and each ink nozzle Nz of the print head 19, and generates drive data. The drive data is output to the ASIC 22, and the ASIC 22 generates drive signals for the paper feed mechanism 17, the carriage motor 18, and the print head 19. As a result, printing is executed. As a result, the ink coverage of each ink reflecting the adjustment coefficient U _j is reproduced on the printing paper.
F. Variation:
The present invention is not limited to the above-described examples and embodiments, and can be implemented in various modes without departing from the gist thereof. For example, the following modifications are possible.

F1. Modification 1:
In the above-described embodiment, the reference planes B1 and B2 that substantially divide the CIE-Lab color space up and down are provided. However, the adjustment coefficient U _j may be controlled according to the hue. For example, for a certain hue, the use of the ink amount I _j of a certain ink can be promoted more than other inks.

F2. Modification 2:
In the above embodiment, the CIE-Lab color system is used as the device independent color system. However, any other device independent such as the CIE-XYZ color system or the CIE-L ^* u ^* v ^* color system is used. It is possible to use a color system. However, from the viewpoint of realizing smooth color reproduction, it is preferable to use a device independent color system that is a uniform color space such as the CIE-Lab color system or the CIE-L ^* u ^* v ^* color system.

F3. Modification 3:
In the embodiment, the process using the dynamic model is adopted as the smoothing process, but other kinds of smoothing processes may be adopted. For example, it is possible to employ a smoothing process in which the distance between adjacent color points is measured and the individual distance is adjusted so as to be as close as possible to the average value.

F4. Modification 4:
In the present specification, “ink” is used in a broad sense including not only liquid ink used for ink jet printers and offset printing, but also toner used for laser printers. As other terms having such a broad meaning of “ink”, “coloring material”, “coloring material”, and “coloring agent” can also be used.

F5. Modification 5:
In the above embodiment, the method and apparatus for creating a color conversion profile such as a look-up table has been described. However, the present invention provides a printing apparatus manufacturing system that includes a built-in unit that incorporates the color conversion profile thus obtained in the printing apparatus. Is also applicable. A color conversion profile creation apparatus that creates a color conversion profile may be included in the printing apparatus manufacturing system, or may be included in another system or apparatus. The built-in part of the manufacturing system can be realized as a printer driver installer (installation program), for example.

  DESCRIPTION OF SYMBOLS 10 ... Printer, 13 ... CPU, 14 ... RAM, 15 ... ROM, 20 ... Memory card slot, 21 ... Bus, 22 ... ASIC, 15a ... Program data, 100 ... Base LUT creation module, 120 ... Smoothing processing initial value setting module , 130 ... smoothing processing module, 132 ... color point movement module, 134 ... ink amount optimization module, 136 ... image quality evaluation index calculation module, 140 ... table creation module, 200 ... color correction LUT creation module, 300 ... forward model converter, 310 ... Spectral printing model converter, 320 ... Color calculation unit, 400 ... LUT storage unit, 410 ... Inverse model initial LUT, 510 ... Base 3D-LUT, 511 ... Inverse conversion LUT, 520 ... Base 4D-LUT, 21 ... inverse transform LUT, 610 ... color correction 3D-LUT, 620 ... color correction 4D-LUT

Claims (8)

A color conversion profile creation device for converting an input color coordinate system coordinate value into an ink color system ink amount composed of a plurality of types of ink,
As an initial value associated with each of a plurality of input color system color points that are predetermined color points of the input color system, an initial value of the ink color system and a device corresponding to the input color system An initial value setting unit for setting the initial position of the device independent color system color point, which is the color point of the independent color system;
A smoothing process for smoothing the distribution of the plurality of device independent color system color points from an initial position, and an amount of ink of the ink color system corresponding to the smoothed plurality of device independent color system color points A smoothing / optimization processing unit for performing optimization processing determined by optimization using a predetermined objective function,
Color conversion profile creation for creating a color conversion profile for converting the coordinate value of the input color system into the ink amount of the ink color system based on the ink amount determined by the smoothing / optimization processing unit And comprising
The smoothing / optimization processing unit performs the optimization process using a quadratic programming method using a quadratic function related to an ink amount vector represented by an ink amount obtained by the optimization process as the objective function. Run,
The objective function is an ink amount having an adjustment coefficient corresponding to a color gamut to which the device independent color system color point corresponding to the ink type and the ink amount vector belongs as a secondary coefficient of the ink amount. A color conversion profile creation device including an adjustment term. The color conversion profile creation device according to claim 1,
The objective function is
(I) Defined with respect to coordinate conversion in which the ink amount is a coordinate value of the first coordinate system, and a plurality of parameters including the coordinate value of the device independent color system and the image quality evaluation index are the coordinate values of the second coordinate system. A first variation amount of the plurality of parameters calculated by multiplying the Jacobian matrix by the variation amount of the ink amount,
(Ii) A color conversion profile creation device including a sum of square errors of differences between the second variation amounts of the plurality of parameters before and after the smoothing process. The color conversion profile creation device according to claim 2,
A color conversion profile creation device in which the adjustment coefficient is added as a matrix element to the Jacobian matrix. The color conversion profile creation device according to claim 1,
The smoothing / optimization processing unit is more optimal as the objective function is smaller,
The adjustment coefficient relating to dark ink having a density higher than that of the other inks is such that the ink amount of the dark ink increases as the color gamut to which the device independent color system color point corresponding to the ink amount vector belongs becomes high. A color conversion profile creation device that is set so that the amount of increase in the objective function corresponding to a unit increase increases. A method of creating a color conversion profile for converting an input color system coordinate value into an ink color system ink amount composed of a plurality of types of ink, comprising: (a) a predetermined input color system predetermined value; As an initial value associated with each of a plurality of input color systems that are color points, an initial value of the ink color system and a color point of a device independent color system corresponding to the input color system A step of setting a certain device independent color system color point position; (b) a smoothing process for smoothing a distribution of the plurality of device independent color system color points from an initial position; A smoothing / optimization processing unit that executes an optimization process for determining an ink amount of the ink color system corresponding to the device independent color system color point by optimization using a preset objective function And (c) the input table based on the ink amount determined in the step (b). And a step of creating a color conversion profile for converting the coordinate values of the system to the ink amount of the ink color system,
The step (b) is a step of executing the optimization process using a quadratic programming method having a quadratic function related to an ink amount vector represented by the ink amount obtained by the optimization process as the objective function. Including
The objective function is an ink amount having an adjustment coefficient corresponding to a color gamut to which the device independent color system color point corresponding to the ink type and the ink amount vector belongs as a secondary coefficient of the ink amount. A method for creating a color conversion profile including an adjustment term. A program that causes a computer to create a color conversion profile for converting input color system coordinate values into ink color system ink amounts composed of a plurality of types of ink including achromatic ink and chromatic ink And (a) the computer uses the initial value of the ink color system as an initial value associated with each of a plurality of input color system color points that are predetermined color points of the input color system. And a device independent color system color point position that is a color point of a device independent color system corresponding to the input color system, and (b) the computer is configured to output the plurality of device independent color systems. A smoothing process for smoothing the distribution of the system color points from the initial position, and an ink amount of the ink color system corresponding to the plurality of device-independent color system color points that have been smoothed are set in advance. Optimization determined by optimization using (C) the computer converts the coordinate values of the input color system based on the ink amount determined in the step (b) to the ink color specification. Creating a color conversion profile for conversion to a system ink amount, and causing the computer to execute the program,
The step (b) is a step of executing the optimization process using a quadratic programming method having a quadratic function related to an ink amount vector represented by the ink amount obtained by the optimization process as the objective function. Including
The objective function is an ink amount having an adjustment coefficient corresponding to a color gamut to which the device independent color system color point corresponding to the ink type and the ink amount vector belongs as a secondary coefficient of the ink amount. Color conversion profile creation program including adjustment terms. A printing device,
A printing apparatus incorporating a color conversion profile created by the color conversion profile creation apparatus according to claim 1. A printing device,
A printing apparatus incorporating a color conversion profile formed by the color conversion profile creation method according to claim 5.

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