JP6565761B2 - Color conversion table creation program, color conversion table creation device, and color conversion table creation method - Google Patents

Description

  The present invention relates to a method for creating a color conversion table for determining the amount of ink ejected by a printer.

  In the printing apparatus, the amount of ink to be ejected is determined according to the input color image data. The relationship between the color data of the color image and the amount of each color ink is stored in advance as a color conversion table (color conversion LUT (LUT: Look Up Table)). At the time of printing, each color position at each pixel position is determined according to the color conversion table. The ink amount is determined (see, for example, Patent Documents 1 and 2).

JP 2008-302699 A JP2011-223392A

  According to the technique described in the above-mentioned patent document, when achromatic colors are expressed by mixing a plurality of chromatic inks used in a printing apparatus, the achromatic colors may not appear on an actual printed matter.

  The present invention has been made to solve the above-described problems, and can be realized as the following modes in order to achieve both the ink amount and the gradation of the color value.

(1) According to one aspect of the present invention, a step of creating a color conversion table for converting an input value of an input color system into an ink amount set of an ink color system composed of a plurality of types of ink A program for executing the program is provided. This program creates a replacement ratio vector for generating a replacement ratio vector for converting the ink amounts of the plurality of types of inks into a virtual color space constituted by predetermined three ink types of the plurality of types of inks. Creating a virtual color value of the virtual color space corresponding to an ink amount of the ink color system corresponding to an input value of the input color system at a plurality of grid points of the color conversion table; And a virtual color value determination step for determining using the virtual color value, and an ink amount determination step for determining a combination of the ink amounts allocated to each of the plurality of grid points using the determined virtual color value. And executing the replacement ratio vector creating step in a composite vector in which the virtual color value of each axis of the virtual color space is equal. Le, creates the substitution ratio vector so as to approach a predetermined achromatic vector in the device-independent color space.

  According to the color conversion table creation program of this aspect, when determining the virtual color value corresponding to the ink amount, the composite vector in which the virtual color value of each axis of the virtual color space is equal is the device independent table. The color system is adjusted so as to approach an achromatic color vector (representing a vector of virtual color values corresponding to an achromatic color, hereinafter also referred to as a virtual achromatic color vector). As a result, when the input value of the input color system is converted into an ink amount set using the color conversion table created by this program, a printed material can be used to express an achromatic color by combining a plurality of chromatic inks. The achromatic color can be appropriately expressed above (in a color that a person perceives as an achromatic color). An achromatic color expressed by a combination of a plurality of chromatic inks is also referred to as “composite gray” and “composite black”.

(2) In the color conversion table creation program according to the above aspect, the replacement ratio vector creation step changes the size of a reference vector in each axial direction constituting the composite vector to change the composite vector into the achromatic color vector. It may be close to. In this way, it is possible to easily create a replacement ratio vector in which the colors of composite gray and composite black are adjusted.

(3) In the color conversion table creation program of the above aspect, the replacement ratio vector creation step brings the composite vector closer to the achromatic color vector by rotating a reference vector in each axial direction constituting the composite vector. Also good. Even in this way, it is possible to easily create a replacement ratio vector in which the colors of composite gray and composite black are adjusted.

(4) In the color conversion table creation program of the above aspect, the predetermined achromatic color vector may be a vector corresponding to a color value obtained by subtracting a predetermined saturation value from the color value of the print medium color. If it does in this way, composite gray and composite black will be easily recognized as an achromatic color on printed matter.

(5) In the color conversion table creation program according to the above aspect, the predetermined achromatic color vector includes the virtual color value selected from a color circle having three colors of cyan, magenta, and yellow as axes in the virtual color space. It may be a vector. When the value selected in this way is regarded as a virtual color value and selected, the colors of composite gray and composite black can be adjusted according to the user's preference.

  The present invention can also be realized in various forms other than the color conversion table creation program. For example, a color conversion table creation method, various apparatuses for performing the method, a system having these various apparatuses, a control method for these various apparatuses and a computer program for realizing the system, a recording medium on which the computer program is recorded, It can be realized in the form of a data signal or the like embodied in a carrier wave including the computer program.

It is a block diagram which shows the structure of the color conversion table production apparatus of 1st Embodiment. It is explanatory drawing which shows the processing content of a converter. It is explanatory drawing which shows the structure of an inverse model initial table. It is explanatory drawing which shows the example of a structure of a color conversion table, and its initial input value setting. It is a flowchart which shows the flow of the creation process of a color conversion table. It is a figure which represents the classification | category of an input lattice point notionally. It is a flowchart which shows the flow of the preparation process of a substitution ratio matrix. It is explanatory drawing for demonstrating the correction method of a base substitution ratio matrix. It is a flowchart which shows the detail of a 1st virtual color value determination process. It is a flowchart which shows the detail of a 1st ink amount determination process. It is a flowchart which shows the detail of a process of a 2nd virtual color value determination process. It is a flowchart which shows the detail of a 2nd ink amount determination process. It is explanatory drawing explaining the 2nd ink amount determination process. It is explanatory drawing which shows the processing content in step S610. It is a figure showing the input color system color space. It is a flowchart which shows the detail of step S620. It is a flowchart which shows the detail of step S630 in a 2nd ink amount determination process. It is explanatory drawing which shows the dynamic model utilized for the 2nd ink amount determination process. It is explanatory drawing explaining the process which is made to correspond substantially with an achromatic color vector by rotating a composite vector.

A. First embodiment:
A1. Configuration of color conversion table creation device:
FIG. 1 is a block diagram showing the configuration of the color conversion table creation device 100 according to the first embodiment of the present invention. The color conversion table creation apparatus 100 according to the present embodiment converts a device color system coordinate value representing an input value to a device into a combination of ink amounts of each color of a plurality of types of ink installed in a printer. Create In this embodiment, a CMYK space is exemplified as the device color system.

  The color conversion table creation apparatus 100 includes a color conversion table creation unit 10, a memory 12, a converter 60, a table storage unit 70, an input I / F unit 82, and an output I / F unit 84. . The function of each unit is realized by the computer executing the program 14 stored in the memory 12. The table storage unit 70 is realized by a recording medium such as a hard disk device. An operation unit 92 such as a keyboard or a mouse is connected to the input I / F unit 82, and a display unit 94 such as a liquid crystal display is connected to the output I / F unit 84.

The color conversion table creation unit 10 includes a replacement ratio vector creation unit 20, a virtual color value determination unit 30, an ink amount determination unit 40, and a table creation unit 50. The replacement ratio vector creation unit 20 creates a replacement ratio matrix by creating a replacement ratio vector. The replacement ratio vector is a vector for converting the ink amount into a virtual color space. In the present 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”. Further, in the present embodiment, as the ink colors constituting the virtual color space, three colors of dark cyan (C), dark magenta (M), and yellow (Y), which are the three primary colors of subtractive color mixing, are selected, and the virtual CMY space is selected. Is configured. The replacement ratio matrix in this embodiment is created so that an achromatic color can be appropriately expressed on a printed material when an achromatic color is expressed by a combination of a plurality of chromatic inks (so-called composite gray and composite black). ing. The creation process of the substitution ratio matrix will be described in detail later.

  The virtual color value determining unit 30 uses the replacement ratio matrix 610 to determine the color value (virtual color value) of the virtual CMY space corresponding to the ink amount.

  The ink amount determination unit 40 determines an ink amount appropriate for representing the input coordinate value of the grid point of the color conversion table 720 using the virtual color value.

  The table creation unit 50 registers the ink amount determined by the ink amount determination unit 40 in the color conversion table 720 and completes the color conversion table 720.

  The converter 60 includes a replacement ratio matrix 610, and converts the ink amount set into virtual CMY values based on the replacement ratio matrix 610. The functions of these parts will be described later.

  The table storage unit 70 stores an inverse model initial table 710 and a color conversion table 720. The inverse model initial table 710 is a color conversion table that receives a color value (virtual CMY value) in a virtual CMY space and outputs an ink amount. For example, the ink amount is expressed by a gradation value of 0 to 255 when expressed by 8 bits. The “inverse model” means a conversion model that converts color values in a virtual CMY space, which will be described in detail later, into ink amounts. The inverse model initial table 710 is stored in the table storage unit 70 in advance. The inverse model initial table 710 will be described in detail later.

  The color conversion table 720 is a color conversion table in which the CMYK color system is input and the ink amount is output. Since the color conversion table 720 is created by the color conversion table creation unit 10 and stored in the table storage unit 70, it is indicated by a broken line in FIG.

FIG. 2 is an explanatory diagram showing the processing contents of the converter 60. The converter 60 refers to the replacement ratio matrix 610 and converts the ink amounts of a plurality of types of ink into V _C , V _M , and V _Y that are color points (coordinates) of the virtual CMY space that is a virtual color space. To do. Hereinafter, the color points V _C , V _M , and V _Y in the virtual CMY space are referred to as virtual CMY values. In this embodiment, cyan (C), magenta (M), yellow (Y), black (K), light cyan (Lc), light magenta (Lm), light black (Lk), very light black (LLk), Assuming color separation in a color printer that can use 10 types of inks of orange (Or) and green (Gr), the converter 60 also converts the ink amounts of these 10 types of ink into color points in the virtual CMY space. . However, an arbitrary ink set can be used as the plurality of types of ink used in the printer. In addition to the CMY, a virtual color space constituted by LcLmY or the like may be adopted as the virtual color space to be output from the converter 60, and any of a plurality of inks mounted on the printer may be arbitrarily selected. A virtual color space configured by the three selected ink types can be used. The construction of the virtual color space will be described in detail later.

FIG. 3 is an explanatory diagram showing the configuration of the inverse model initial table 710. The inverse model initial table 710 is a color conversion table having a virtual CMY value as an input and an ink amount as an output. In the inverse model initial table 710, for example, the virtual CMY space is divided into a plurality of small cells, and an optimum ink amount is selected and registered 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 virtual CMY value. Therefore, in the inverse model initial table 710, a table in which an optimal ink amount is selected from a desired viewpoint such as image quality from among a large number of combinations of ink amounts that reproduce substantially the same virtual CMY values is registered. A virtual CMY value that is an input value of the inverse model initial table 710 is a representative value of each small cell. On the other hand, the ink amount as an output value reproduces any virtual CMY value in the cell. Therefore, in the inverse model initial table 710, the virtual CMY value that is the input value and the ink amount that is the output value do not correspond exactly, and the converter 60 converts the ink amount of the output value to the virtual CMY value. When converted, a value slightly different from the input value of the inverse model initial table 710 is obtained. However, as the inverse model initial table 710, a table in which input values and output values completely correspond may be used. Also, it is possible to create a color conversion table without using the inverse model initial table 710. As a method of creating the inverse model initial table 710 by selecting an optimal ink amount for each small cell, for example, a small cell in the L ^* a ^* b ^* space corresponding to each small cell in the virtual CMY space may be used. The ink amount selected by adopting the method described in Table 2007-511175 can be created by associating it with each small cell in the virtual CMY space.

  FIG. 4 is an explanatory diagram showing a configuration of the color conversion table 720 and an example of setting an initial input value thereof. As input values of the color conversion table 720, values at substantially equal intervals that are predetermined as CMYK values are set. Since a set of CMYK values is considered to represent a point in the CMYK color space, the set of CMYK values is also referred to as an “input grid point”. In the present embodiment, 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 via the operation unit 92 by the user. The input grid point to which the initial input value is set is an input grid point corresponding to the vertex of a four-dimensional color cube in the CMYK color space (a grid point having a value of only 0 or 255 when expressed in 8 bits). It is preferable to select at least all of the above. At the apex of the four-dimensional color cube, each value of CMYK takes the minimum value or the maximum value of the definition range. Specifically, when each value of CMYK is expressed by 8 bits, (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), Ink quantity with respect to 16 input lattice points (255, 0, 0, 255), (255, 0, 255, 255), (255, 255, 0, 255), (255, 255, 255, 255) The initial input value of the ink amount for the other input grid points is arbitrary, and is set to 0, for example. In this example, the ink amount for the input grid point of (C, M, Y, K) = (0, 0, 0, 32) is a value other than 0. This is the completion of this color conversion table 720. This is the value when

A2. Color conversion table creation process:
A2-1. Flow of the entire color conversion table creation process:
FIG. 5 is a flowchart showing the flow of the color conversion table creation process of the present embodiment. When a color conversion table creation process start instruction is input to the color conversion table creation apparatus 100, the color conversion table creation process is started.

  In step S100, the replacement ratio vector creation unit 20 creates a replacement ratio matrix by creating a replacement ratio vector. The creation process of the substitution ratio matrix will be described in detail later.

  In step S150, the input grid points existing in the color conversion table to be created are classified into a plurality of groups having different dimensions. Steps S300 to S600, which will be described later, are executed in ascending order of the dimensionality of the classification determined in step S150. The determination of the grid point classification will be described in detail later.

  In step S <b> 200, the table creation unit 50 temporarily registers the initial input value of the ink amount in the color conversion table 720 via the operation unit 92 by the user in the color conversion table 720. As described above, the user can select (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), and (255, 255, 255, 255), the ink amount values are input to the color conversion table 720. An input value is set (FIG. 4).

  In step S300, the virtual color value determination unit 30 uses the converter 60 (FIG. 2) to determine the initial input values (16 grid points) set in step S200 with reference to the replacement ratio matrix 610 and the virtual CMY values. Convert to (color point). In other words, a first virtual color value determination process for determining virtual color values corresponding to a plurality (16) of input grid points of the color conversion table 720 is performed. This will be described in detail later.

  In step S400, the ink amount determination unit 40 modifies the initial input value set in step S200 by using the virtual color value obtained in step S300, so that 16 grid points (hereinafter also referred to as vertex grid points). The first ink amount determination process is performed to determine the optimal ink amount in (1). This will be described in detail later.

  In step S500, the virtual color value determination unit 30 uses the ink amounts at the 16 grid points (vertex grid points) determined in step S400 to ink a plurality of grid points (intermediate grid points) between the vertex grid points. A second virtual color value determination process is performed for obtaining the amount and a corresponding virtual CMY value (virtual color value). This will be described in detail later.

  In step S600, the ink amount determination unit 40 uses the virtual CMY values of the plurality of intermediate grid points determined in step S500 to determine an appropriate ink amount at the plurality of intermediate grid points. I do. This will be described in detail later.

  In step S700, the table creation unit 50 registers the ink amount determined in steps S400 and S600 as the output value of the color conversion table 720. Thereby, the color conversion table 720 is completed.

A2-2. Grid point classification processing:
Color conversion table as vertices (also called small vertices) of multiple small cubes (small hypercubes) when a cube (hypercube) representing the input color system color space is divided into multiple small cubes (small hypercubes) In step S150, the input grid points are classified according to the positions of the dimensional number cube corresponding to the dimensional number of the input grid points. For example, a CMYK four-dimensional space is classified into “vertex”, “side”, “surface”, “cube (3D)”, and “hypercube (4D)”. In step S150, classification 1 based on the number of dimensions of the grid points and classification 2 for further subdividing the grid points classified in each dimension obtained by classification 1 are performed.

  FIG. 6 is a diagram conceptually showing the classification of input grid points in the present embodiment. FIG. 6 shows an input color system color space when K = 0. When the input color system color space is represented as a cube, the input grid points of the color conversion table 720 are represented as vertices of a plurality of small cubes obtained by dividing the cube representing the input color system color space. In FIG. 6, in order to clearly show lattice points, lattice points on a plane of C = 0, a plane of M = 0, and a plane of Y = 255 are shown, and the display of other lattice points is omitted. In FIG. 6, the lattice points classified as “vertices” are hatched circles, the lattice points classified as “sides” are white circles smaller than “vertices”, and the lattice points classified as “faces” are represented as “sides”. "Is indicated by a black circle having the same size as". " As shown in the figure, the grid points classified as “sides” are grid points excluding the vertices (8 points) among the grid points on the sides (12 sides) of the cube representing the input color system. The grid points classified as “plane” are grid points obtained by removing the grid points (44 points) on the side from the grid points on the cube plane (six planes) representing the input color system. The lattice points classified as “cube” are all lattice points except the lattice points on the outer surface of the cube representing the input color system, that is, lattice points inside the cube.

A2-2-1 Category 1:
In classification 1, the “number of dimensions” is calculated for each input grid point in the table, and all grid points are classified according to the number of dimensions. In the present embodiment, the CMYK color space is exemplified as the input color system color space (also referred to as “input space”). In this case, all the grid points of the table are classified into one of “vertex”, “side”, “surface”, “cube (3D)”, and “hypercube (4D)”. The number of dimensions of the grid points is obtained from the CMYK values possessed by each grid point. In this embodiment, the CMYK value of the input grid point is expressed by an 8-bit value of 0 or more and 255 or less. At this time, the number of dimensions of each input grid point is determined as the number of input space dimensions−the number of values where the grid point CMYK value is 0 or 255. For example, the lattice point A (C, M, Y, K) = (0, 0, 0, 0) in FIG. Since the input color space (CMYK space) of the input grid point is four-dimensional, the number of dimensions of the grid point A is 0 at 4-4. Similarly, in the lattice point B (C, M, Y, K) = (255, 0, 255, 128), the number of values of 0 or 255 is 3, and the number of dimensions is 4-3 = 1. . In the grid point (C, M, Y, K) = (64, 255, 64, 64) (not shown), the number of values of 0 or 255 is 1, and the number of dimensions is 4-1 = 3. Become. The number of dimensions is obtained for all the grid points in the table, and the grid points having the same number of dimensions are represented as 0 = “vertex”, 1 = “side”, 2 = “surface”, 3 = “cube (three-dimensional)”, 4 = classify as “hypercube (4 dimensions)”

A2-2-2 Category 2:
The lattice point group classified according to the number of dimensions by classification 1 is subdivided for each related lattice point on the table. The subdivision is performed for each permutation of values that are 0 or 255 of the CMYK values of each grid point. Specifically, for example, when a certain grid point C (C, M, Y, K) classified as “side” = (255, 64, 255, 0), only a value of 0 or 255 is considered. For example, C = 255, Y = 255, and K = 0. Similarly, when lattice point C (C, M, Y, K) classified as “side” = (255, 128, 255, 0), if only the value of 0 or 255 is considered, C = 255, Y = 255 and K = 0. At this time, the lattice point C and the lattice point D are classified as “belonging to the same side S1”. Conceptually, since C = 255, Y = 255, and K = 0, it can be said that the lattice points belong to “the side connecting G (CY) and composite (CMY)”. Here, the “vertices” where the number of dimensions = 0 are not required to be subdivided by classification 2. This is because it is determined that all lattice point groups classified as vertices belong to independent vertices even in classification 2.

  As with the above, subdivision processing is performed for each classification from 1 to 4 dimensions. According to the classification 2, the input grid points constituting the color conversion table 720 (four-dimensional table) are 16 vertices, 32 sides, 24 faces, 8 cubes (3D), 1 super It is subdivided into one of the cubes (four dimensions). The first virtual color value determining process S300 and the first ink amount determining process S400, which will be described in detail later, are executed for the grid points classified as “vertices”. In the second virtual color value determination process S500 and the second ink amount determination process S600, lattice points classified into “side”, “surface”, “cube (3D)”, and “hypercube (4D)” Are executed in the order of “side”, “surface”, “cube”, and “hypercube”.

A2-3. Replacement ratio matrix creation process:
A2-3-1. Overall flow of the replacement ratio matrix creation process:
FIG. 7 is a flowchart showing a flow of processing for creating the replacement ratio matrix 610. In step S102, the user prints a color patch of a specific ink amount gradation value for each color ink mounted on the printer, measures the print result with a colorimeter, and operates the color measurement result. Input via the unit 92. The colorimetric values obtained here are obtained using the color values of the device-independent color space, and in this embodiment are obtained as L ^* a ^* b ^* values. As this specific ink amount gradation value, for example, when the printer can print with 256 gradations, any gradation of 0 to 255 can be adopted. However, as the specific gradation value, the same gradation value is adopted for each color ink.

  In step S104, the replacement ratio vector creation unit 20 creates a vector (color development characteristic vector) representing the color development of each ink color. The color development characteristic vector can be represented as a difference vector between the color value of paper white and the colorimetric value obtained for a specific ink amount gradation value in the L * a * b * space. The base point of the vector is not limited to paper white but may be another point. The color development characteristic vector created in this way is a vector representing the color development characteristics of each ink.

In step S106, the replacement ratio vector creation unit 20 selects three types of ink representing the virtual color space, and defines a virtual color space based on the coloring characteristic vector of the selected ink type. The three types of ink selected in step S106 constitute dimensions of the work space when performing the ink amount determination process described later. In this embodiment, as described above, the three subtractive primary colors, dark cyan (C), dark magenta (M), and yellow (Y), are selected, and the color development characteristic vectors of these three colors of ink are selected. A unit vector that is the basis of the virtual color space is constructed. This virtual color space is called a virtual CMY space. In the following description, the virtual dark cyan, virtual dark magenta, and virtual yellow vectors, which are components of the virtual CMY space, are represented as V _C , V _M , and V _Y , respectively, and coordinate values designated by these components. (Virtual color point) is called a virtual CMY value.
Note that C, M, Y, K, Lc, Lm, Lk, Llk, which are ink types mounted on the printer, are combinations that can form a base necessary for expressing a three-dimensional space. A virtual color space constructed based on unit vectors of three colors arbitrarily selected from Or and Gr can also be used. In the present embodiment, the ten colors are shown, but the ink type mounted on the printer is not limited to this.

  In step S108, the replacement ratio vector creation unit 20 creates a base replacement ratio matrix X. The base replacement ratio matrix X is a matrix for converting the ink amount of each color into a virtual CMY value, and is a matrix that is used as a basis when the replacement ratio matrix 610 is created. A method for creating the base substitution ratio matrix X will be described in detail later.

In step S110, the substitution ratio vector generating unit 20 uses the matrix for the virtual CMY values the orientation of the equivalent amount of the composite vector V _CO, close to achromatic vector V _A representing the achromatic color, based substitution ratio matrix X To obtain a replacement ratio matrix 610. A method for creating the substitution ratio matrix 610 will be described in detail later.

A2-3-2. Create base substitution ratio matrix X:
First, a permutation matrix M ₀ for converting a CMY color development characteristic vector into a base vector in a virtual CMY space can be expressed by the following equation (1).

In the above equation (1), xc is the color development characteristic vector of C ink, xm is the color development characteristic vector of M ink, and xy is the color development characteristic vector of Y ink. Further, “t” added to the upper right of the vector represents transposition of a matrix / vector, and indicates a column vector obtained by transposing the coloring characteristic row vector.

The permutation matrix M ₀ represented in this way converts the unit vectors U _C , U _M , U _Y in the virtual CMY space into color development characteristic vectors xc, xm, xy, as shown in the following equation (2). It can be regarded as a matrix.

In addition, from the above equation (2), the inverse matrix M ₀ ⁻¹ normalizes the color development characteristic vector of each color of C, M, and Y, which is the basis of the virtual CMY space, to the unit vector of each base of the virtual CMY space. The vector obtained by converting the color development characteristic vector of each color ink with the inverse matrix M ₀ ⁻¹ is a replacement ratio vector for replacing the ink amount of each color with the virtual CMY. . When the replacement ratio vectors obtained for the respective colors are arranged in this way, a base replacement ratio matrix X shown in the following equation (3) is obtained. The base substitution ratio matrix X is used when creating the substitution ratio matrix 610 included in the converter 60. This is because the name “base replacement ratio matrix X” is used as a basis for creating the replacement ratio matrix 610.

In the above equation (3), I _C , I _M , I _Y , I _K , I _Lc , I _Lm , I _Lk , I _Llk , I _Or , and I _Gr represent the ink amount of each color at the lattice point in the ink amount space. Show. According to the base replacement ratio matrix X shown in the above equation (3), the ink amount data can be replaced with virtual CMY.

  Hereinafter, the creation of the base substitution ratio matrix X will be described with a specific example.

  For the ink types C, M, and Y that form the basis vector, the Lab value obtained with a certain ink amount is set to a three-column vector, and the following 3 × 3 matrix is obtained by arranging three colors (Equation (4)).

When each column vector is taken as a difference from the white point (also referred to as paper white) of the medium (paper), a permutation matrix M ₀ (Equation (5) below) is obtained.

Obtains the inverse matrix _M ^{0 -1} of M ₀ (below (6)), is multiplied from the right, a unit matrix E is obtained (following equation (7)). This can be considered as three vectors having a magnitude of 1 for only one element in each row direction, and can be regarded as the above-described basis vector.

For each of the remaining seven ink colors other than CMY, as in CMY, the difference between the Lab value obtained by measuring the color patch and the white point (paper white) is obtained and used as a color development characteristic vector. Multiplying the transposed matrix of the color development characteristic vector of each ink color by the inverse matrix M ₀ ⁻¹ from the right provides a replacement ratio vector (column vector) for replacing the ink amount of each color with virtual CMY. When the replacement ratio vectors for the respective colors thus obtained are arranged, a base replacement ratio matrix X shown in the following equation (8) is obtained.

  As described above, the base replacement ratio matrix X can be said to convert the ink amount of each color into color values (virtual CMY values) in the virtual CMY space using the color development characteristic vector of the CMY ink as a base vector. .

A2-3-3. Creation of substitution ratio matrix 620:
FIG. 8 is an explanatory diagram for explaining a method of correcting the base replacement ratio matrix X. In the present embodiment, with respect to the substitution ratio vectors constituting the base substitution ratio matrix X, the composite vector V _CO virtual CMY values equal amount, the same processing as to approach the achromatic vector V _A representing the achromatic color By doing so, the base replacement ratio matrix X is corrected to generate a replacement ratio matrix 610. Here, by correcting the magnitude of the reference vectors forming a composite vector V _CO (consistent with the basis vectors), the composite vector V _CO, close to achromatic vector V _A. Each reference _{vector, V 0C = (1,0,0),} V 0M = (0,1,0), a V 0Y = (0,0,1). In the present embodiment, as the achromatic color vector V _A , a vector calculated from a color value of saturation 0 obtained by subtracting L ^* from the color value of paper white is used. The color value for calculating the achromatic color vector V _A may be, for example, a color value obtained by merely decimating L * from the color value of paper white, or a Lab value indicated when K ink is actually printed at the duty limit value. . _A virtual CMY vector obtained from the color value is set as v _A = [V _CA V _MA V _YA ] ^t . _A matrix having each element of v _A diagonally is denoted by V _A.

As shown in the upper part of FIG. 8, the composite vector _VCO and the achromatic color vector V _A do not match. In other words, when C, M, and Y inks are mixed in equal amounts, they should theoretically be achromatic, but when they are actually printed on media (paper), they may not appear achromatic. In many cases, the color value of the color measurement result also has a certain degree of saturation. That is, when C, M, and Y inks are mixed in equal amounts, it can be said that an achromatic color does not occur in the device-independent color space. Therefore, in this embodiment, by correcting the size of each reference vector, the corrected composite vector V ′ _CO , which is a combined vector of the corrected reference vectors, is brought close to the achromatic color vector V _A (FIG. 8). Bottom). In accordance with the size of the reference vector before correction, the size of the achromatic color vector V _A is converted to ^3½ to create an achromatic color vector V ′ _A , and the corrected composite vector V ′ _CO and the achromatic color vector V ′ _A are made to coincide. In order to match the orientation of the composite vector V _CO and achromatic vector V _A, it corrects the composite vector V _CO using matrix as shown below. Note that they may not completely match due to calculation errors or the like in the correction processing. Including such a case, it is expressed as “composite vector V _CO is brought close to achromatic vector V _A ”.

If the reference vector V _0C = [VC _C VM _C VY _C ] ^t , V _0M = [VC _M VM _M VY _M ] ^t , V _0Y = [VC _Y VM _Y VY _Y ] ^t , then the composite vector V _CO is It is expressed by equation (9).

When the matrix for transforming the composite vector _{V CO} achromatic vector V _'A and _{M C,} the following equation (10) the relation holds.

Here, when multiplied by the inverse matrix _M ^{C -1} of _{M C} from the right, the following equation (11).

Since the reference vector is equal to the unit matrix, it can be said from formula (11) that M _C ⁻¹ is equal to the inverse matrix of V ′ _A. That, V 'obtains the _M ^{C -1} serving inverse matrix of _A, when multiplied by _M ^{C -1} composite vector _{V CO} from the right, the composite vector V after _{correction' CO (VC ', VM'} , VY ') is As a result, the direction of the achromatic color vector V _A and the corrected composite vector V ′ _CO can be matched.

Here, when the virtual color value in the virtual CMY space is replaced with the CMY ink amount, the composite vector _VCO is equal to the replacement ratio of each CMY ink color in the base replacement ratio matrix X ′. In this case, for example, is 'VC is a virtual C value of _CO' composite vector V after correction, be one or more, C ink amount with respect to the value = 1 virtual C of virtual CMY space is 1 or less (e.g. If the replacement ratio is 2.0, virtual CMY = 1.0 is indicated when C ink is 0.5). Similarly, 'is a virtual C value of _CO VC' composite vector V after correction, is less than 1, C ink amount with respect to the value = 1 virtual C of virtual CMY space is greater than 1. That is, when the replacement ratio matrix is created so that the virtual CMY vector (composite vector V _CO ) corresponding to the same amount of CMY ink matches the direction of the achromatic color vector V _A , the vector (C, It can be seen that the amount of CMY ink generated when M, Y) = (1, 1, 1) is not equal. In uncorrected composite vector V _CO, if the C direction of the color was stronger VC 'has a value of 1 or more. In this case, the C ink amount with respect to the virtual C value is smaller than when the base replacement ratio matrix is used. In this way, color correction of composite gray and composite black (achromatic color expression by mixing chromatic colors) is realized.

Therefore, when the ink amount is converted using the replacement ratio matrix X ′ obtained by converting the base replacement ratio matrix X using the inverse matrix M _C ⁻¹ , the colors of the composite gray and the composite black are more improved. It can be brought close to an achromatic color in an independent color space.

Hereinafter, a specific method for correcting the base replacement ratio matrix X and creating the replacement ratio matrix 610 will be described with a specific example. Here, the achromatic color development characteristic vector is a difference vector between a color value of saturation 0 obtained by subtracting L ^* from a color value of paper white and a color value of paper white.

The achromatic color development characteristic vector is (L *, a *, b *) = (− 5.00, −0.31, 0.04). The achromatic color development characteristic vector is converted into a virtual CMY space vector using the above-described inverse matrix M ₀ ⁻¹ to obtain an achromatic color vector V _A (formula (12) below).

The achromatic color vector V _A is corrected so as to have a size of 3 ^1/2 to obtain an achromatic color vector V ′ _A. The achromatic color vector V ′ _A can be expressed by the following equation (13).

Using this achromatic color vector V ′ _A , an inverse matrix M _C ⁻¹ is obtained by the equation (11) (the following equation (14)).

Check here. When the achromatic color vector V ′ _A in the virtual CMY space before correction (virtual CMY space based on the base replacement matrix X) is converted using the inverse matrix M _C ⁻¹ , the following equation (15) is obtained.

According to the equation (15), the achromatic color vector V ″ _A after conversion is a vector with a virtual CMY value = (1.0, 1.0, 1.0). The achromatic color vector V ″ _A in the CMY space matches the combined vector of the base vectors V _C , V _M , and V _Y that define the virtual CMY space before correction. Therefore, when the replacement ratio matrix X ′ obtained by converting the base replacement ratio matrix X using the inverse matrix M _C ⁻¹ is used, the composite region in the virtual CMY space after correction (the virtual CMY values are equal in quantity) The ink amount corresponding to (region) can be associated with an appropriate ink amount that is not equal.

Therefore, the base replacement ratio matrix X is corrected by multiplying each column vector of the base replacement ratio matrix X by the inverse matrix M _C ⁻¹ to create the replacement ratio matrix 610.

  As described above, the base substitution ratio matrix X can be expressed by the following equation (16). Expression (16) is the same as Expression (8).

When each column vector of the base replacement ratio matrix X is multiplied by the inverse matrix M _C ⁻¹ , the replacement ratio vector is corrected for each of the 10 ink colors. When the replacement ratio vectors after correction are arranged, a replacement ratio matrix X ′ shown in the following equation (17) is obtained. This replacement ratio matrix X ′ becomes the replacement ratio matrix 610 included in the converter 60.

As described above, when the replacement ratio matrix X ′ obtained by converting the base replacement ratio matrix X using the inverse matrix M _C ⁻¹ is used, the composite area in the virtual CMY space (the virtual CMY values are equal in quantity). In the device-independent color space can be associated with an ink amount set that represents a color very close to an achromatic color. As a result, when an achromatic color is expressed with a plurality of chromatic color ink sets, it is possible to express a color very close to the achromatic color of the device-independent color system on the printed matter.

A2-4. First virtual color value determination process:
FIG. 9 is a flowchart showing details of the first virtual color value determination process (FIG. 5: step S300). In the first virtual color value determination process, virtual color values of input grid points (16 points) (hereinafter also referred to as vertex color points) classified as “vertices” in the grid point classification process (step S150) are determined. . In step S302, the virtual color value determination unit 30 determines the temporary ink amount for each input grid point (vertex color point) from the initial input value of ink amount (FIG. 4) according to the following equations (18) and (19). I (C, M, Y, K) is determined.

  Here, I (C, M, Y, K) represents the ink amount of the entire ink set with respect to the CMYK value of the input grid point (in the example of FIG. 4, the ink amount of 10 types of ink). The ink amount for the input grid point where the CMYK value is 0 or 255 is a value input in advance by the user in step S200 of FIG. According to the above equations (18) and (19), it is possible to obtain the temporary ink amount I (C, M, Y, K) at an arbitrary CMYK value.

  In step S304, the converter 60 is used to obtain a virtual CMY value corresponding to the temporary ink amount. This calculation can be expressed by the following equation (20).

Here, V _C (C, M, Y, K), V _M (C, M, Y, K), and V _Y (C, M, Y, K) indicate virtual CMY values after conversion. , X ′ means conversion by the substitution ratio matrix 610 described above. As can be understood from these equations, the converted virtual CMY values are associated with CMYK values that are input values of the color conversion table 720.

  In step S306, the virtual CMY values obtained in step S304 are converted back into ink amounts using the inverse model initial table 710 (FIG. 3). Here, the reason why the ink amount is converted again using the inverse model initial table 710 is that the initial input value of the ink amount or the temporary ink amount determined in step S302 is always preferable as the ink amount for reproducing the virtual CMY value. This is because it is not the amount of ink. On the other hand, in the inverse model initial table 710, since a preferable ink amount considering image quality and the like is registered, if the virtual CMY value is converted again into the ink amount using this, it is preferable for realizing the virtual CMY value. The ink amount can be obtained as an initial value. However, step S306 may be omitted.

As a result of the processing in step S300 described above, the following initial values are determined for the vertex color points (color points of 16 cube vertices in the input color system color space).
(1) Value of input grid point of color conversion table: (C, M, Y, K)
(2) Initial coordinate values of color points in the virtual CMY space corresponding to each input grid point: (V _C (C, M, Y, K), V _M (C, M, Y, K), V _Y (C , M, Y, K))
(3) Initial ink amount corresponding to each input grid point: I (C, M, Y, K)

A2-5. First ink amount determination process:
FIG. 10 is a flowchart showing details of the first ink amount determination process (step S400 in FIG. 5).

In step S420, the ink amount determination unit 40 searches for an optimum value of the ink amount with respect to the virtual CMY value determined in step S300, using a preset objective function E (Equation (21) below). In the optimization using the objective function E, a plurality of parameters ΔV _C , ΔV _M , ΔV _Y , ΔGI among the ink amounts Ij (j = 1 to 10) for reproducing the virtual CMY values determined in step S300. , ΔCII, ΔTI, the ink amount that is as small as possible is determined as the optimum ink amount. The search for the optimum ink amount is started from the initial ink amount at each input grid point obtained in step S306. Therefore, the ink amount obtained by the search is a value obtained by correcting this initial ink amount. The objective function E given by the equation (21) can be written as a quadratic function relating to the ink amount vector I as in the following equation (22). The optimization of the ink amount of the vertex color point is executed according to the quadratic programming method using the objective function E having such a quadratic form.

Here, w _VC , w _VM, etc. described at the beginning of each term on the right side are the weights of each term. The weights w _VC , w _VM ... For each term are set in advance. The first term w _VC (ΔV _C −ΔV _Ct ) ^{2 on} the right side of the equation (21) is a square error related to the fluctuation amounts ΔV _C and ΔV _Ct of the virtual cyan V _C. Here, the first variation amount ΔV _C is a partial differential value that is a component of the Jacobian matrix, representing the variation amount ΔI _j of the ink amount in step S420 (the difference between the ink amount in step S300 and the ink amount in step S420). This is a linearly converted quantity. On the other hand, the second variation amount ΔV _Ct is the difference between the virtual cyan value obtained by the process of step S300 and the virtual cyan value given by the current ink amount Ir. Note that the second variation amount ΔV _Ct can be considered as a difference between the virtual cyan values before and after the process of step S420. The same applies to the second and subsequent terms on the right side of equation (21). That is, the objective function E includes the first variation amounts ΔV _C , ΔV _M , ΔV _Y , ΔGI... Obtained by linearly converting the variation amount ΔIj of the ink amount by the processing of step S420 with the Jacobian matrix component, and the parameter V. _This is given as the sum of square errors of the second fluctuation amounts ΔV _Ct , ΔV _Mt , ΔV _Yt , ΔGI _t ... Before and after the process of step S420 regarding _C , V _M , V _Y , GI. Here, GI, CII, and TI are image quality evaluation indexes, which are respectively a graininess index GI (Graininess Index), a color non-constancy index CII (Color Inconstancy Index), and a set of inks (10 types in the present embodiment). ) Of the total ink amount TI. The image quality evaluation indexes GI, CII, and TI are indexes indicating that the smaller the value, the better the image quality of the color patch reproduced with one set of ink amounts Ij (j = 1 to 10). . The subscript of the color non-constant index CII represents the type of light source when observing the color patch. In the above equation (21), standard light A and standard light F12 are used as the types of light sources. The objective function E can be obtained by the method described in Japanese Patent Application Laid-Open No. 2011-223392 disclosed by the present applicant.

  The objective function E given by the equation (22) is a quadratic form related to the ink amount vector I obtained in the first ink amount determination process (step S400).

  In step S430, the virtual CMY values corresponding to the ink amounts Ij (j = 1 to 10) searched in step S420 are recalculated by the converter 60. Here, the reason why the virtual CMY value is recalculated is that the searched ink amount Ij is the ink amount that minimizes the objective function E, and therefore the virtual CMY value reproduced with the ink amount Ij is determined in step S300. This is because it deviates somewhat from the virtual CMY value. The virtual CMY value recalculated in this way is used as the coordinate value after the movement of each color point.

  In step S440, it is determined whether or not the average value (ΔVCMY) ave of the movement amount of the coordinate value of each color point is equal to or less than a preset threshold value ε. Here, the movement amount is a difference between the virtual CMY value obtained in step S300 and the virtual CMY value recalculated in step S430. When the average value (ΔVCMY) ave of the movement amount is larger than the threshold value ε, the process returns to step S420 and the processes of steps S420 to S430 are continued. On the other hand, when the average value (ΔVCMY) ave of the movement amount is equal to or smaller than the threshold value ε, step S450 is executed. Note that an appropriate value for the threshold ε is experimentally determined in advance.

  In step S450, the ink amount determination unit 40 determines whether the processing has been completed for all the vertices. Steps S420 to S440 are sequentially repeated for the color points of each vertex, and when the processing is completed for all the vertices, the first ink amount determination process is terminated.

  As described above, if it is determined that the convergence is insufficient after step S430, steps S420 to S430 are executed again. At this time, the value obtained in the previous process is used as the initial value. Such repeated processing is not essential, and the processing of steps S420 to S430 may be performed at least once. The process for determining the ink amount of the vertex color point may be determined by a known method other than the first ink amount determination process S400 described here.

A2-6. Second virtual color value determination process:
FIG. 11 is a flowchart showing details of the second virtual color value determination process (FIG. 5: Step S500). In the second virtual color value determination process, virtual color values are determined for each class of grid point groups from “side” to “hypercube” classified in the grid point classification process (step S150). The At this time, the processing is performed in the order of the number of dimensions from the lattice point group classified as the “side” having the low number of dimensions to the lattice point classified as the “hypercube” having the high number of dimensions. That is, processing is performed in the order of “side”, “surface”, “cube”, and “hypercube”. In the present embodiment, the second virtual color value determination process for a certain “side” is exemplified. Hereinafter, the color points of the grid points constituting the side excluding the “vertex” grid points corresponding to the end points of the side to be processed are referred to as intermediate color points. Although omitted in this example, the same applies to other dimensions, and the intermediate color point of a certain surface is the color point of the lattice points constituting the surface, excluding the “vertex” and “side” lattice points included in the surface. The same applies to cubes and hypercubes.

  In step S502, the virtual color value determining unit 30 calculates each input grid from the ink amount of the vertex color point obtained in step S400 according to the above equations (18) and (19) as in step S302 (FIG. 9). The temporary ink amount I (C, M, Y, K) for the point (corresponding to the intermediate color point) is determined.

  In step S504, similarly to the above-described step S304, the converter 60 is used to obtain virtual CMY corresponding to the temporary ink amount.

  As a result of the processing in step S500 described above, the same initial value as that of the vertex color point is determined for each intermediate color point.

A2-7. Second ink amount determination process:
FIG. 12 is a flowchart showing details of the second ink amount determination process (step S600 in FIG. 5). FIG. 13 is an explanatory diagram for explaining the second ink amount determination process. In the following, in order to simplify the description, the ink amount determination process for the grid point group classified as “side”, which is the grid point classification process (step S150), will be described. Here, the description will be made assuming that the grid points constituting the side are five points and the control points of the Bezier curve are four points. FIG. 13 shows the ink amount of magenta ink corresponding to five input grid points (V0 to V4). The grid point positions (input color system coordinate values) of the input grid points V0 to V4 are V0 (C, M, Y, K) = (255, 0, 0, 0), V1 (C, M, Y). , K) = (255, 64, 0, 0), V2 (C, M, Y, K) = (255, 128, 0, 0), V3 (C, M, Y, K) = (255, 192) , 0, 0), V4 (C, M, Y, K) = (255, 255, 0, 0). In the second ink amount determination process (step S600 in FIG. 5), the Bezier curve BC is defined using the control points P0 to P3 shown in FIG. 13, and the ink amounts I _V1 to _{V 3} corresponding to the input grid points _V1 to V3 are defined. I _V3 is obtained.

  As shown in FIG. 13, the Bezier curve BC is defined by end points P0 and P3 and intermediate control points P1 and P2, and mediates a function t of a virtual input value obtained by the coordinate value of the input color system of each control point. It is a parametric function that uses a variable and the ink amount as a dependent variable. Here, the virtual input value is represented using one coordinate axis among a plurality of coordinate axes defining the input color system color space. Specifically, a coordinate axis whose input value (coordinate value) changes is used in the grid point group to be processed. For example, at the above-described input grid points V0 to V4, only the value of magenta (M) changes at the grid point position (coordinate value of the input color system). Therefore, the coordinate axis (coordinate value) of magenta (M) is used as the virtual input value. As the virtual input value, the same value is used for all ink colors (in this embodiment, 10 colors). The number of Bezier curves corresponding to the number of ink colors (10 in the present embodiment) is defined for the input grid points V0 to V4, but all of the virtual input values in each Bezier curve are input grid points V0 to V0. The coordinate value of magenta (M) of V4 is used. Since there are two coordinate value (coordinate axis) axes that change for the lattice point group classified into the same “plane”, two types of coordinate axes are used as virtual input values.

  The control points P0 and P3 shown in FIG. 13 are grid points that exist on the color conversion table and the ink amount has already been determined, but the control points P1 and P2 do not exist on the color conversion table and the ink amount is determined. These are grid points that are virtually defined on the input color space for processing. The virtual input values of these virtual control points are, for example, coordinate values that substantially divide the virtual input values of P0 and P3 by the number of virtual control points. In the example shown in FIG. 13, P1 = 85 and P2 = 170.

  In step S610 (FIG. 12), the ink amount determination unit 40 performs color points (grid points) in the virtual CMY space determined in the second virtual color value determination process (FIG. 5: step S500) according to a dynamic model described later. (Color points corresponding to V1 to V3) are moved.

  FIG. 14 is an explanatory diagram showing the processing contents in step S610. As shown on the left side of FIG. 14, before the color point is moved, the distribution of the color point is considerably biased. The right side of FIG. 14 shows the position of each color point after the minute time has elapsed. The virtual CMY value of each color point after the movement is referred to as “target value (VCMYt)”. This is because the modifier “target” is used as a target value in the search process of the optimum value of the ink amount described below.

  In step S620 (FIG. 12), the ink amount determination unit 40 obtains the objective function E2, and uses the objective function E2 to determine the ink amount of the control point for determining the Bezier curve for calculating the ink amount of the intermediate color point. Search for the optimum value. The detailed procedure of step S620 and the contents of the objective function E will be described later.

  In step S630, the ink amount determination unit 40 defines a Bezier curve using the control point ink amount obtained in step S620, and calculates the ink amount Ij of the grid point group to be processed. Details will be described later.

In step S640, the virtual CMY value (V _C V _M V _Y ) corresponding to the ink amount Ij calculated in step S630 is recalculated by the converter 60. The virtual CMY value recalculated in this way is used as the coordinate value after the movement of each color point.

In step S650, it is determined whether or not the average value (ΔVCMY) ave of the movement amount of the coordinate value of each color point is equal to or less than a preset threshold value ε. Here, the movement amount is a difference between the target value VCMYt obtained in step S610 and the virtual CMY value (V _C V _M V _Y ) recalculated in step S640. If the average value (ΔVCMY) ave of the movement amount is larger than the threshold value ε, the process returns to step S610 and the processes of steps S610 to S640 are continued. On the other hand, if the average value (ΔVCMY) ave of the movement amount is equal to or smaller than the threshold value ε, the second ink amount determination process is ended. That is, in step S640, it can be said that it is determined whether or not the virtual CMY value corresponding to the ink amount calculated in step S630 substantially matches the target virtual CMY value. Note that an appropriate value for the threshold ε is experimentally determined in advance.

Details of steps S620 and 630 will be described with reference to FIGS.
FIG. 15 is a diagram illustrating an input color system color space in the present embodiment. FIG. 15 shows an input color system color space when K = 0. When the input color system color space is represented as a cube, the input grid points of the color conversion table 720 are the input grid points of the color conversion table 720 when the input color system color space is represented as a cube. Represented as vertices of a plurality of small cubes obtained by dividing a cube representing a color system color space. It is represented as an intersection of a plurality of grid lines GL that divide the input color system color space into a plurality of small cubes. Here, each side of the cube is also defined as a grid line GL. In FIG. 15, in order to clearly show lattice points, lattice points IP on a plane of C = 0, a plane of M = 0, and a plane of Y = 255 are shown, and the display of other lattice points is omitted. Further, only a part of the lattice point IP is provided with a reference numeral, and other reference numerals are omitted. Among the input lattice points, the lattice points IP corresponding to the vertex lattice points are indicated by hatching circles, and the lattice points IP corresponding to the intermediate lattice points are indicated by white circles smaller than the lattice point IP corresponding to the vertex lattice points. In FIG. 15, the side GL1 in which the C coordinate is 255, the Y coordinate is 0, the K coordinate is 0, and the value of the M coordinate is changed is indicated by a bold line. In the following description, the case where the amount of magenta ink corresponding to the grid points V0 to V4 on the side GL1 is obtained will be described as an example. In the present embodiment, one Bezier curve is defined for a group of lattice points classified as one “side”.

  FIG. 16 is a flowchart showing details of step S620. In step S621, the ink amount determination unit 40 selects vertex lattice points on the processing target side GL1 as a plurality of (two in this example) end points that define a Bezier curve. In the example of FIG. 13, grid points V0 and V4 are selected as the end points P0 and P3. The ink amounts corresponding to the grid points V0 and V4 are determined by the first ink amount determination process. Step S621 in the present embodiment is also referred to as an end point selection step. In the present embodiment, the Bezier curve is defined by a plurality of “end points” and “intermediate control points” between the plurality of end points. The “end points” and “intermediate control points” are also simply referred to as “control points”.

  In step S622, the ink amount determination unit 40 selects an arbitrary virtual input value between the two end points P0 and P3 as the virtual input value of the intermediate control point. In the example of FIG. 13, virtual input values at arbitrary points P1 and P2 between the two end points P0 and P3 (V3) are selected as virtual input values of the intermediate control points. In the example shown in FIG. 13 of this embodiment, four control points (P0 to P3 in FIG. 13) are selected. In this embodiment, a Bezier curve is used as a parametric curve used for the ink amount determination process. Since the curve does not necessarily pass through the intermediate control point in the Bezier curve, the coordinates of the input grid points of the color conversion table 720 are used as virtual input values of the intermediate control points P1 and P2 among the control points that are independent variables of the ink amount determination process. Uses irrelevant virtual values (coordinates). In the case where the curve passes through the intermediate control point, such as a spline curve, the virtual input value of the intermediate control point may be matched with the coordinates of the input grid point of the color conversion table 720.

  In step S624 (FIG. 16), the ink amount determination unit 40 calculates the ink amount of the lattice point (the lattice point classified as “vertex”) determined in the first ink amount determination process (FIG. 5: step S400). Using the equations (18) and (19), the initial ink amounts at the intermediate control points P1 and P2 are obtained.

  In step S626, the ink amount determination unit 40 obtains the objective function E2 using the initial ink amounts at the control points P1 and P2. The objective function E2 is expressed by the following equation (23), for example.

Here, I _p1p2 is the ink amount at the control points P1 and P2, GV _C is the virtual C gradation evaluation index value with respect to the ink amount, and GV _M and GV _Y are the virtual M and virtual Y gradation evaluation indexes. The value, GI, is an evaluation index value of graininess with respect to the ink amount. The evaluation index value will be described later. w _vC , w _vM , w _vY , and w _GI are weighting factors for each term, and are set in advance.

Using the initial ink amounts of the control points P1 and P2 obtained in step S624, the evaluation index values GV _C , GV _M , GV _Y , and GI of the equation (23) are obtained. A specific procedure will be described below. First, using the initial ink amounts at the control points P1 and P2 and the ink amounts at the control points P0 and P3 (determined in the first ink amount determination process), the general equation (Equation (24)) of the Bezier curve is used. Let us define a Bezier curve.

  When function t is a parameter, N is the number of control points, i is a subscript of a control point, and P is a control point, a value P (t) at an arbitrary t on the curve is expressed by the above equation (24). . Here, the parametric variable t is a function of a virtual input value, and is represented by t = virtual input value of a grid point to be processed / (virtual input value of end point−virtual input value of start point). Of the two end points of the control point, the one with a small virtual input value is called a “start point”, and the other is called an “end point”.

  Using the initial ink amounts of the control points P1 and P2 and the ink amounts of the control points P0 and P3 (determined in the first ink amount determination process), the grid point V1 of the color conversion table 720 is obtained by the equation (24). The ink amount (temporary ink amount) of .about.V3 is obtained.

For example, P0 ink amount I _P0 = 0, P3 ink amount I _P3 = 200 (determined by the first ink amount determination process), P1 ink amount I _P1 = 150, P2 ink amount I _P2 = 180 (step) In this case, the ink amount I _V1 of _V1 can be obtained as follows. The parameter t of V1 is t = 64 / 255≈0.251. By using this, the ink amount _IV1 of _V1 can be obtained by the following equation (25).

In particular,
I _V1 = 0.251 ³ × 200 + 3 × 0.251 ² × (1−0.251) × 150 + 3 × 0.251 × (1−0.251) ² × 180 + (1−0.251) ³ × 0
Thus, I _V1 = 92.0 is obtained.

Similarly, I _V2 = 149,1, I _V3 = 181.7 is obtained.

Using the ink amounts I _{V1 to} I _V3 of the respective grid points of the color conversion table 720 thus obtained, the values of the respective terms (evaluation index values GV _C , GV _M , GV _Y , GI) of the objective function E2 Ask for. Evaluation index value GV _C is obtained by the following expression (26).

Here, as X, the substitution ratio matrix 610 obtained in step S100 (FIG. 5) is used. Similarly, values of evaluation index values GV _M and GV _Y are obtained. The granularity evaluation index can be calculated by the method described in JP2011-223392A disclosed by the present applicant.

  For each term of the objective function E2, the sum of the indices of the grid points V1 to V3 of the color conversion table 720 to be processed is used. That is, the objective function E2 can be expressed by the following equation (27).

In step S628, starting from the objective function E2 obtained in step S626, the values of the ink amounts I _P1 and I _P2 at the control points P1 and P2 are changed, and the objective function E2 is changed accordingly. The ink amounts I _P1 and I _P2 of the control points P1 and P2 that minimize E2 are searched. That is, the optimized optimum ink amount is used as the ink amount at the control points P1 and P2. Steps S622 to S628 in the present embodiment are also referred to as intermediate control point selection steps. In the description of step S620, magenta ink has been described as an example, but the same calculation is performed for all ink colors (10 colors in the present embodiment) of the printer to be processed. The objective function in this case is that the independent variable in each term of the objective function is not one color of M (magenta) ink but all the ink colors of the printer (10 colors in this embodiment), and all the ink colors of the printer (this embodiment). In this case, the sum of the evaluation index values obtained for 10 colors (the following equation (28)) is used.

FIG. 17 is a flowchart showing details of step S630 (FIG. 12) in the second ink amount determination process. In step S632, the ink amount determination unit 40 determines the ink amounts I _P1 and I _{P2 of} the control points P1 and P2 obtained in step S620 and the control point obtained in the first ink amount determination process S400 (FIG. 5). by using the P0, the ink amount _I P0 of _{P3, I P3,} the general formula of the Bezier curve (the formula (24)), to define a Bezier curve BC (Fig. 13). The ink amounts I _P0 and I _{P3 at} the control points P0 and P3 are equal to the ink amounts I _V0 and I _{V4 at} the input grid points V0 and V4 (vertex grid points) of the color conversion table 720, respectively.

  In step S634, the ink amounts of the input grid points V1 to V3 of the color conversion table 720 are obtained using the Bezier curve BC determined in step S632.

  In the description of steps S620 and S630 described above and FIG. 13, an example in which the ink amount of magenta ink is obtained is shown. However, other ink types can be obtained similarly.

  In the above description, an example in which the lattice point group classified into the side GL1 in FIG. Similarly, the above processing is performed for each lattice point group classified into all the remaining “sides” of the hypercube representing the input color system color space. Next, a grid point group classified as “side” is selected as an “end point”, and a Bezier for calculating the ink amount of the grid point group classified as the “surface” of the hypercube representing the input color system color space. The curved surface is obtained, and the ink amount of the lattice point group classified as “surface” is obtained. Next, the grid point group classified as “surface” is selected as “end point”, and the grid point group classified as “cube (three-dimensional)” representing the input color system color space (inside the cube) A Bezier function (three-dimensional) for determining the ink amount of (grid points) is obtained, and the ink amount of the lattice point group classified as “cube” is obtained. Finally, the grid point group classified as “cube” is selected as “end point”, and the ink amount of the grid point group classified as “super cube” of the hypercube representing the input color system color space is obtained. The Bezier function (four-dimensional) is obtained, and the ink amount of the lattice point group classified as “hypercube” is obtained. That is, the second ink amount determination process (FIG. 12) is repeatedly executed to obtain corresponding ink amounts for all the input grid points of the color conversion table 720. Here, as the “Bézier function” in the flowchart of FIG. 17, a Bezier function having a number of dimensions corresponding to the classification of the processing target grid point group is defined.

A2-8. Dynamic model:
FIG. 18 is an explanatory diagram showing a dynamic model used for the second ink amount determination process of the present embodiment. Here, a state is shown in which a plurality of color points (white circles and double circles) are arranged in the virtual CMY color space. However, for convenience of explanation, the arrangement of the color points is drawn two-dimensionally here. In this dynamic model, it is assumed that the virtual force Fpg of the equation (EQ1) (shown in FIG. 18) is applied to the target color point g. 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 resultant force Fpg related to the target color point g is larger as the distance between the target color point g and the adjacent color point gn increases, and the resistance force −kvVg increases as the speed of the target color point g increases. And the total value. In this dynamic model, the initial values of the position vector Xg and the velocity vector Fg are set for each color point, and then the position vector Xg and velocity vector Fg after a minute time are sequentially calculated. The initial value of the velocity vector Vg 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 Fg and the resistance force -kvVg may be used as the force relating 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.

A3. Effects of the embodiment:
According to the color conversion table creation apparatus 100 of the present embodiment, when creating a replacement ratio matrix (replacement ratio vector) that associates ink amounts with virtual CMY values, a composite area vector is converted into a device-independent color space. Correction processing is performed in accordance with an achromatic color vector representing a color very close to the achromatic color. In other words, the replacement ratio matrix created by performing this correction processing corresponds to an appropriate ink amount set in which the ink amount corresponding to the composite region in the virtual CMY space (the region where the virtual CMY values are equal) is not equal. Can be attached. For this reason, when the ink amount is determined using the color conversion table created using the color conversion table creating apparatus 100, when an achromatic color is expressed by a plurality of chromatic color ink sets, the device-independent table is displayed on the printed matter. It is possible to express a color very close to an achromatic color.

B. Second Embodiment of Replacement Ratio Vector Generation Method:
The color conversion table creation apparatus of the second embodiment is different from the first embodiment in the replacement ratio vector creation method (specifically, step S110 in FIG. 7) in the replacement ratio vector creation unit 20. Other configurations are the same as those of the first embodiment.

  In the replacement ratio matrix creation process (FIG. 7) according to the first embodiment, in step S110, the composite vector is corrected by correcting the size of the reference vector (the vector matching the base vector in the virtual CMY space). Although the direction of the vector is adjusted, in this embodiment, the direction of the composite vector is adjusted by rotating the reference vector. This will be specifically described below.

In the replacement ratio matrix creation processing of this embodiment, a virtual CMY space is defined with the color development characteristic vector of CMY ink as a base vector, as in the first embodiment, and a base replacement ratio matrix X is created (FIG. 7). Steps S102 to S108). Here, the achromatic color vector V _A as in the first embodiment does not match the composite vector V _{CO in} which the virtual CMY values in the virtual CMY space are equal (upper part of FIG. 8). Therefore, by rotating the composite vector V _CO, achromatic vector V _A and substantially aligned, create a substitution ratio vector as the color of achromatic color is adjusted when converting the amount of ink to the virtual CMY space .

19, by rotating the composite vector V _CO, is an explanatory diagram for explaining a process of achromatic vector V _A and to substantially coincide. FIG. 19 shows a composite vector _VCO and an achromatic color vector _{VA as} viewed from the C-axis direction with the virtual CMY value = (0, 0, 0) as the origin. In FIG. 19, θ _C represents the rotation angle around the VC axis, and a, b, and c represent the magnitudes of V _A , (V _A −V _CO ), and V _CO , respectively.

Although it is possible to uniquely determine the rotation axis and the rotation angle for matching the composite vector _VCO and the achromatic color vector V _A by a single rotation process from a known vector, in the present embodiment, the process is performed. For the sake of simplification, one of the virtual CMY axes or a combination thereof is used as a rotation axis, and the rotation is repeated a plurality of times. Specifically, the rotation process is performed twice with the virtual C axis and the axis obtained by combining the virtual M axis and the virtual Y axis.

A rotation process around the virtual C axis will be described as an example. In FIG. 19, each axis is shown as VC, VM, VY. In the following description, the rotation matrix is expressed by 4 rows and 4 columns, but this is virtual CMY three-dimensional homogeneous coordinates, and in the representation of a space (for example, virtual CMYK space) obtained by expanding the virtual CMY space into four dimensions. Absent. It should be noted that the composite vector _VCO and the achromatic color vector V _A are normalized so as to be 1 respectively.

In the example shown in FIG. 19, Cosθ _C is expressed by the following equation (29) from the cosine theorem.

Arccos (Cos? _C) from the rotation angle theta _C is sin [theta _C from 1-Cos ² θ _C is obtained respectively.

When the rotation angle is θ _C , the matrix T _C that rotates the angle θ _C around the virtual C axis is expressed by the following equation (30).

Cos [theta] _C, sin [theta _C, more, it is possible to obtain the matrix _{T C,} by multiplying the left matrix _{T C} achromatic vector _{V A,} to obtain an achromatic vector V _'A after the rotation (provided that this calculation The achromatic vector V _A is also changed to the homogeneous coordinate system in advance).

Next, the same rotation conversion is performed with the rotation axis as the direction perpendicular to the virtual C axis. This rotation axis is assumed to be equal to an axis obtained by combining the negative direction of the virtual M and the direction of the virtual Y. This axis is called a virtual MY axis for convenience. The methods described above as well as the rotational angle theta _MY, and Cos? _MY, calculates the sin [theta _MY. Matrix _{T MY} to theta _MY rotated about imaginary MY axis, when the direction vector of the virtual MY axis _ev MY ₌ a ^{_{[e C e M e Y]}} t, is expressed by the following equation (31).

Multiplying T _MY left achromatic vector V _'A rotated about the imaginary axis, the vector V _"A consistent with the composite vector V _CO is obtained.

By multiplying the rotation matrices T _C and T _MY obtained here by the reference vector in the virtual CMY axis direction in order from the left, a correction reference vector to be obtained is obtained. With the above method, the directions of the composite vector _VCO and the achromatic color vector _VA can be matched.

  Here, when the virtual color value is replaced with the CMY ink amount, unlike the first embodiment, the relationship in which the virtual CMY value changes by 1 when the ink amount changes by 1 is the same as before the correction. However, since the direction has changed due to the rotation process, the increase in the ink color used as the basis vector does not simply match the increase in the virtual CMY value (for example, even if the C ink increases by 1, the virtual CMY The value does not increase by 1). In addition, since the corrected reference vector (3 rows and 3 columns) is no longer a diagonal matrix, the change in the ink amount affects the change in the virtual CMY value. For example, if the virtual M value and the virtual Y value of the C reference vector are negative, considering that the virtual CMY value is the same, the virtual Y value and the virtual M value decrease as C ink is generated. In order to compensate for this, the ink amounts of the M ink and the Y ink are increased, and the C ink is smaller than before the correction. In this way, color correction of composite gray and composite black (achromatic color expression by mixing chromatic colors) is realized.

  Each of the reference CMY vectors obtained as a result of the correction process has not changed in magnitude from 1, and the direction of the reference CMY vector does not coincide with the direction of the virtual CMY axis.

Hereinafter, a specific method for correcting the base replacement ratio matrix X and creating the replacement ratio matrix 610 will be described with a specific example. The achromatic color vector V _A is a vector calculated from the color value of saturation 0 obtained by subtracting L ^* from the color value of paper white. Since the rotation angle is small, the effective number is expressed by four digits for this example. Note that the virtual CMY and the calculation process matrix are represented by 4 rows and 4 columns, but this is a representation of a space (for example, a virtual CMYK space) that is a virtual CMY three-dimensional homogeneous coordinate and is expanded from the virtual CMY space to four dimensions. is not.

The color value of saturation 0 obtained by subtracting L ^* from the color value of paper white is set to (L *, a *, b *) = (89.1600, 0.0000, 0.0000). From this, the achromatic color vector V _A = [0.6660 0.5149 0.5398] ^t is obtained.

V _CO = [0.5774 0.5774 0.5774] From ^t , distances a = 0.7459, b = 0.0729, and c = 0.8165 (FIG. 19) when viewed around the virtual C axis are obtained. It is done.
As a result, cos θ _C = 0.9997, θ _C = 0.0236, and sin θ _C = 0.0236.

Using the cos [theta] _C, sin [theta _C, and the above (30), the matrix _{T C} is required to angle theta _C rotated around the virtual axis C (below (32) below).

Achromatic vector V _'A rotated theta _C achromatic color vector V _A and around a virtual C-axis using the matrix T _C is expressed by the following equation (33).

Achromatic color vector V _'A and the composite vector _{V CO,} a distance a = 1.0000 when viewed around virtual MY axis, b = 1.0000, c = 1.0000 is obtained. Than this,
cos θ _MY = 0.0036, θ _MY = 0.1134, sin θ _MY = 0.1131
It becomes.

By the equation (31), the matrix _{T MY} to angle theta _MY rotated around the virtual MY axis is calculated (the following equation (34) below).

Achromatic vector V _"A who theta _MY rotated about imaginary MY axis achromatic vector V _'A with the matrix _{T MY} is expressed by the following equation (35).

As described above, the achromatic vector V _"A coincides with the composite vector _{V CO.}

  Therefore, the corrected reference vector is expressed by the following equation (36).

That is, each column vector of the base substitution ratio matrix X, by multiplying the matrix T _C and matrix T _MY, by correcting the base substitution ratio matrix X, it is possible to create a substitution ratio matrix 610.

  Even when the color conversion table 720 is created using the substitution ratio matrix created by the substitution ratio vector creation processing of the present embodiment, the color of the achromatic region is adjusted, and the achromatic color is appropriately expressed on the printed matter. can do.

C. Variations:
The present invention is not limited to the above-described embodiments and embodiments, and can be carried out in various modes without departing from the gist thereof. For example, the following modifications are possible.

(1) The achromatic color vector used when creating the replacement ratio matrix is not limited to the above embodiment. For example, L ^* is reduced by -5 from the color value of paper white, a value that holds the saturation, a value based on a patch printed with the ink amount of K (black) ink equal to the duty limit value, and (L ^* , A ^* , b ^* ) = (0, 0, 0) may be used. Further, the color selected by the user via the operation unit 92 from the color circle centered on three colors of cyan, magenta, and yellow displayed on the display unit 94 (FIG. 1) is regarded as a virtual color value, and the virtual A virtual CMY vector having color values in the virtual color space may be used.

(2) In the replacement ratio matrix creation process of the above embodiment, the example in which the replacement ratio vector creation unit 20 executes steps S104 to S110 (FIG. 6) has been shown. However, the replacement ratio vector creation unit 20 has at least step S110 ( FIG. 6) may be executed. For example, a base replacement ratio matrix creating unit that executes steps S104 to S108 (FIG. 6) to create the base replacement ratio matrix X may be provided separately from the replacement ratio vector creating unit 20. The base storage ratio matrix X created in advance may be provided in the table storage unit 70, and the replacement ratio vector creation unit 20 may create the replacement ratio matrix 610 by correcting the base replacement ratio matrix X. .

(3) The process of determining the ink amount (FIG. 5: Steps S300 to S600) is not limited to the above embodiment, and the ink amount can be determined by various known methods. Even in this case, when the color value of the input color system is converted into an ink amount set of an ink color system composed of a plurality of types of ink using the color conversion table 720, the color of the composite area is changed. Can be adjusted.

(4) “Ink” is not limited to liquid ink used in ink jet printers and offset printing, but is used in a broad sense including toner used in laser printers. As other terms having such a broad meaning of “ink”, “coloring material”, “coloring material”, and “coloring agent” can also be used.

(5) In the above-described embodiment, the program, method, and apparatus for creating a color conversion table have been described. However, a printing apparatus manufacturing system that includes a built-in unit that incorporates the color conversion table obtained as described above into a printing apparatus. Applicable. The color conversion table creating apparatus 100 that creates the color conversion table 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.

(6) The program, method, and apparatus for creating the color conversion table have been described, but the above-described color conversion table creating apparatus is provided, and the input print data is based on the color conversion table created by the color conversion table creating apparatus. This can also be realized by a printing apparatus that performs conversion and printing. Furthermore, such a printing apparatus may be configured to have a colorimetric function. The printing apparatus having a colorimetric function may be configured to include a program for executing step S102 in the replacement ratio matrix creating process (FIG. 6) in the above embodiment and a processing unit.

(7) An arbitrary ink set can be used as the plurality of types of ink used in the printer. For example, it may be composed of ink obtained by adding a special color R to CMYK.

(8) Although the color conversion table in which the input color system is CMYK is illustrated, a color conversion table in which the input color system is RGB may be used.

V A _... achromatic vector, V _'A ... achromatic vector, V _{CO ...} composite vector, V' _{CO ...} corrected composite _{vector, V 0C, V 0M, V} 0Y ... reference _{vector, V '0C, V' 0M} , _V'0Y : Reference vector after correction, g: Point of interest, P0 to P4 ... Control point, V0-V4 ... Input grid point, 10 ... Color conversion table creation unit, 12 ... Memory, 14 ... Program, 20 ... Replacement ratio vector Creation unit, 30 ... virtual color value determination unit, 40 ... ink amount determination unit, 50 ... table creation unit, 60 ... converter, 70 ... table storage unit, 82 ... input I / F unit, 84 ... output I / F unit, 92 ... operation unit, 94 ... display unit, 100 ... color conversion table creation device, 610 ... substitution ratio matrix, 710 ... inverse model initial table, 720 ... color conversion table

Claims (7)

A program for causing a computer to execute a step of creating a color conversion table for converting an input value of an input color system into an ink amount set of an ink color system composed of a plurality of types of ink,
Replacement ratio vector creation for creating a replacement ratio vector for converting the respective ink amounts of the plurality of types of inks into virtual color values of a virtual color space constituted by predetermined three ink types of the plurality of types of inks Steps,
Using the replacement ratio vector, the virtual color value of the virtual color space corresponding to the ink amount of the ink color system corresponding to the input value of the input color system at a plurality of grid points of the color conversion table. A virtual color value determination step determined by
Using the determined virtual color value to cause the computer to execute an ink amount determination step of determining a combination of the ink amounts assigned to each of the plurality of grid points;
The replacement ratio vector creation step includes:
A program that creates the replacement ratio vector so that a composite vector in which the virtual color values of the respective axes of the virtual color space are equal to each other approaches a predetermined achromatic color vector in a device-independent color space. The program according to claim 1,
The replacement ratio vector creation step includes:
The program which makes the said composite vector approach the said predetermined achromatic color vector by changing the magnitude | size of the reference | standard vector of each axial direction which comprises the said composite vector. The program according to claim 1,
The replacement ratio vector creation step includes:
A program for bringing the composite vector closer to the predetermined achromatic color vector by rotating a reference vector in each axial direction constituting the composite vector. A program according to any one of claims 1 to 3,
The predetermined achromatic color vector is a program corresponding to a color value obtained by subtracting a predetermined saturation value from a color value of a print medium color. A program according to any one of claims 1 to 3,
The predetermined achromatic vector is a vector having, in the virtual color space, a color selected from a color circle having three colors of cyan, magenta, and yellow as axes. An apparatus for creating a color conversion table for converting an input value of an input color system into an ink amount set of an ink color system comprising a plurality of types of ink,
Replacement ratio vector creation for creating a replacement ratio vector for converting the respective ink amounts of the plurality of types of inks into virtual color values of a virtual color space constituted by predetermined three ink types of the plurality of types of inks And
Using the replacement ratio vector, the virtual color value of the virtual color space corresponding to the ink amount of the ink color system corresponding to the input value of the input color system at a plurality of grid points of the color conversion table. A virtual color value determination unit determined by
An ink amount determination unit that determines a combination of the ink amounts allocated to each of the plurality of grid points using the determined virtual color value;
The replacement ratio vector creation unit includes:
An apparatus for creating the replacement ratio vector so that a composite vector in which the virtual color value of each axis of the virtual color space is equal is approximated to a predetermined achromatic color vector in a device-independent color space. A method of creating a color conversion table for converting an input value of an input color system into an ink amount set of an ink color system composed of a plurality of types of ink,
Creating a replacement ratio vector for converting the amount of each of the plurality of types of ink into a virtual color value of a virtual color space configured by predetermined three ink types of the plurality of types of ink;
Using the replacement ratio vector, the virtual color value of the virtual color space corresponding to the ink amount of the ink color system corresponding to the input value of the input color system at a plurality of grid points of the color conversion table. The process of determining
Using the determined virtual color value to determine a combination of the ink amounts assigned to each of the plurality of grid points, and
The step of creating the substitution ratio vector includes:
A method of creating the replacement ratio vector so that a composite vector having an equal amount of the virtual color value of each axis of the virtual color space approaches a predetermined achromatic color vector in a device-independent color space.

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