JP2010221437A - Printing apparatus, printing method, and method for forming lookup table - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To perform high-resolution printing of an achromatic color ink at a high speed. <P>SOLUTION: The printing apparatus prints on the basis of output image data by performing color conversion of input image data in which the color of each pixel is expressed by a color vector of an input color space to the output image data in which each pixel has an ink amount related to a plurality of kinds of ink. The printing apparatus includes: a preliminary conversion means which converts the color vector to a scalar by a linear function; a first color conversion means which converts the color vector to an achromatic color ink amount by referring to a first lookup table which regulates a corresponding relationship between the scalar and the achromatic color ink amount as the ink amount of the achromatic color ink; and a second color conversion means which converts the color vector to a chromatic color ink amount by referring to a second lookup table which regulates a corresponding relationship between the color vector and the chromatic color ink amount as the ink amount of a chromatic color ink. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a printing apparatus, a printing method, and a lookup table creation method.

  In a printer, K (black) ink is used more frequently than other inks and is more conspicuous than other inks, so it is desirable to print at high resolution. In the above document, ink nozzles that discharge K ink are arranged at a higher density than other inks, and high-resolution printing is performed for K ink.

JP 2004-25545 A

However, when high-resolution printing is performed for K ink, the number of pixels to be processed by color conversion processing and halftone processing increases, and there is a problem that high-speed printing cannot be performed. In particular, there is a problem that a printing speed that satisfies the user cannot be obtained because printing of a document or the like that uses a lot of K ink requires high speed.
The present invention has been made in view of the above problems, and an object thereof is to perform high-resolution printing of achromatic ink at high speed.

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

[Application Example 1]
Input image data in which the color of each pixel is represented by a color vector in the input color space is color-converted into output image data in which each pixel has an ink amount related to a plurality of types of ink, and printing is performed based on the output image data A printing device to perform,
Preliminary conversion means for converting the color vector into a scalar by a conversion formula;
A first color conversion that converts the color vector into the achromatic color ink amount by referring to a first lookup table that defines a correspondence relationship between the scalar and the achromatic color ink amount that is the ink amount of the achromatic color ink. Means,
A second color that converts the color vector into the chromatic color ink amount by referring to a second look-up table that defines a correspondence relationship between the color vector and the chromatic color ink amount that is the ink amount of the chromatic color ink. A printing apparatus comprising: conversion means;
According to this configuration, the conversion from the color vector to the achromatic ink amount can be performed at high speed. The scalar may be calculated based on a luminance formula.

[Application Example 2]
The first color conversion means outputs first color conversion image data in which each pixel has the achromatic color ink amount,
The second color conversion means outputs second color conversion image data in which each pixel has the chromatic color ink amount, and
The printing apparatus in which the first color conversion image data has a higher resolution than the second color conversion image data.
According to this configuration, the achromatic color ink amount can be controlled with high resolution, and high-definition printing can be realized. The resolution is reflected in the number of conversions to be converted by the first color conversion means, but since each conversion is performed at high speed, the overall processing time does not become a problem.

[Application Example 3]
In the first lookup table, the achromatic ink amount corresponding to all the scalars that can be converted from the color vector is stored.
According to this configuration, since the first color conversion unit does not need to perform an interpolation operation, it is possible to realize faster color conversion.

[Application Example 4]
A printing apparatus in which a relationship between the scalar and the achromatic ink amount in the first look-up table is defined by a sigmoid function.
According to this configuration, the achromatic ink amount can be smoothly changed by a sigmoid function.

[Application Example 5]
Create a lookup table that is referenced when color conversion is performed on input image data in which the color of each pixel is represented by a color vector in the input color space to output image data in which each pixel has ink amounts relating to a plurality of types of ink. A lookup table creation method,
Converting the color vector to a scalar;
Creating a first look-up table defining a correspondence relationship between the scalar and the achromatic ink amount that is the ink amount of the achromatic ink obtained by substituting the scalar into a conversion function;
Creating a second look-up table that defines the correspondence between the color vector and the chromatic color ink amount that is the ink amount of the chromatic color ink;
In creating the second look-up table, the chromatic color ink amount is optimized so that an optimal print result is obtained when printing is performed in combination with the achromatic color ink amount based on the first look-up table. A lookup table creation method characterized by the above.
According to this configuration, the first look-up table and the second look-up table used in the printing apparatus can be prepared.

  The present invention can be realized in various forms. For example, a printing apparatus and method, a lookup table creation method and apparatus therefor, and a printing apparatus manufacturing method and manufacturing in which the lookup table is incorporated in the printing apparatus. The present invention can be realized in the form of a system, a computer program for realizing the functions of those methods or apparatuses, a recording medium on which the computer program is recorded, and the like.

1 is a block diagram illustrating a configuration of a printer according to an embodiment of the present invention. It is a schematic diagram explaining the printing system of a printer. FIG. 2 is a block diagram illustrating a software configuration of a printer. It is a flowchart which shows a printing process. It is a schematic diagram explaining a color conversion process and a halftone process. It is a block diagram which shows the structure of the lookup table preparation apparatus in one Example of this invention. It is a flowchart which shows the whole process sequence of an Example. It is explanatory drawing which shows the processing content in the case of producing 3D-LUT by step S100-S300 of FIG. It is explanatory drawing which shows the correspondence of the color point of RGB color system which is an input color system, and the color point of L ^* a ^* b ^* color system. It is a flowchart which shows 1D-LUT creation processing. It is a graph which shows the sigmoid function which sets K ink amount. It is explanatory drawing which shows the dynamic model utilized for the smoothing process of an Example. It is a flowchart which shows the typical process sequence of a smoothing process. It is a flowchart which shows the detailed procedure of step T100 of FIG. It is explanatory drawing which shows the processing content of step S120-S150 of FIG. It is a flowchart which shows the detailed procedure of an optimization process (step T130 of FIG. 13).

Next, embodiments of the present invention will be described in the following order.
A. Configuration of printing device:
B. Printing process:
C. Configuration of LUT creation apparatus and overall LUT creation processing procedure:
D. Procedure for creating 1D-LUT:
E. Dynamic model:
F. Smoothing processing (smoothing / optimization processing) procedure:
G. Contents of optimization process:
H. Variation:

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

  In this embodiment, four cartridge holders 11a, 11a,... Are provided, and cyan (C) ink, magenta (M) ink, yellow (Y) ink, and black are provided in the cartridge holders 11a, 11a,. (K) Ink cartridges 12, 12,... For ink are attached. The CMY ink corresponds to the chromatic ink of the present invention, and the K ink corresponds to the achromatic ink of the present invention. The carriage 11 includes a print head 19 that ejects ink supplied from the ink cartridges 12, 12... From a large number of ink nozzles Nz.

FIG. 2 schematically shows a printing method of the printer 10 of the present embodiment. The printer 10 includes a print head 19 having a plurality of nozzles Nz... For each CMYK ink, and a process for controlling the amount of ink ejected by the nozzles Nz. Based on the data. In the present embodiment, the number and arrangement density of the ink nozzles Nz for K ink in the main scanning direction / sub-scanning direction are double that of the ink nozzles Nz for other CMY inks. That is, the K ink has a printing resolution (dot formation density) twice that of the other CMY inks. In the present embodiment, it is assumed that the print resolution is specified to be 1440 × 1440 dpi for CMY ink and 2880 × 2880 dpi for K ink. It is not always necessary to arrange the nozzles Nz of the K ink at a high density in the main scanning direction / sub-scanning direction, and the K ink has a high resolution by increasing the discharge frequency of the K ink compared to other inks. You may make it print with. The ink droplets ejected by the nozzles Nz... Become fine dots on the printing paper, and a print image having an ink coverage corresponding to each ink amount I _j is formed on the printing paper by the collection of a large number of dots. It becomes. The ink amount of each ink is represented as I _j, and the subscript j is a natural number (j = 1 to 4) for identifying the type of each ink. Here, j = 1 corresponds to C ink, j = 2 corresponds to M ink, j = 3 corresponds to Y ink, and j = 4 corresponds to K ink. In this specification, printing based on the ink amount I _j means that the image of the ink coverage in accordance with the ink amount I _j is reproduced on the printing paper. The printer 10 in the present embodiment is an ink jet printer, but the present invention can be applied to various printers in addition to the ink jet method. In this embodiment, each ink amount I _j is given by 8 bits from 0 to 255.

  FIG. 3 shows a software configuration of the firmware FW. The firmware FW includes an image data acquisition unit FW1, a rendering unit FW2, a color conversion unit FW3, a halftone unit FW4, and a rasterization unit FW5. Furthermore, the color conversion unit FW3 includes a first color conversion unit FW3a and a second color conversion unit FW3b. The image data acquisition unit FW1 acquires the print data PD stored in the memory card MC as a print target. The print data PD may be document data, graphic data, or photographic image data. The rendering unit FW2 generates input image data ID used for printing based on the print data PD. The input image data ID is composed of pixels having the number of pixels (printing resolution × printing actual size) corresponding to the printing resolution (2880 × 2880 dpi) of K ink, and each pixel has an RGB value of 8 bits (0 to 255). The color information expressed by In this embodiment, the input color space is an RGB color space, and the combination of RGB values is a color vector representing a color in the RGB color space.

The color conversion unit FW3 acquires the input image data ID and performs color conversion on the input image data ID. Specifically, the RGB value of each pixel is sequentially converted into each ink amount I _j of CMYK ink. First color conversion section FW3a converts the RGB values of each pixel in the ink amount I ₄ of K ink, the ink amount I ₁ of the second color conversion section FW3b the CMY inks of RGB values of each pixel, I _2, I ₃ Convert to At that time, the first color conversion unit FW3a refers to the 1D-LUT 15b, and the second color conversion unit FW3b refers to the 3D-LUT 15c. Further, the second color conversion unit FW3b performs an interpolation operation while referring to the 3D-LUT 15c when converting the RGB values into the respective ink amounts I ₁ , I ₂ , and I ₃ . The halftone unit FW4 performs halftone processing on the ink amount I _{4 of} K ink output from the one-color conversion unit FW3a and the ink amounts I ₁ , I ₂ , and I _{3 of} CMY ink output from the second color conversion unit FW3b. Execute. The rasterizing unit FW5 allocates each pixel (dischargeability) of the halftone data after the halftone process to each main scan and each ink nozzle Nz of the print head 19, and generates drive data. The drive data is output to the ASIC 22, and the ASIC 22 generates drive signals for the paper feed mechanism 17, the carriage motor 18, and the print head 19. As a result, printing is executed.

B. Printing process:
FIG. 4 shows the flow of the printing process. In Step P100, the image data acquisition unit FW1 acquires the print data PD stored in the memory card MC as a print target. In step P110, the rendering unit FW2 generates an input image data ID used for printing based on the print data PD. Based on the layout information and drawing commands included in the print data PD, bitmap data composed of each pixel having RGB values is generated, and the resolution is converted to correspond to the K ink print resolution (2880 × 2880 dpi). To generate the input image data ID. As described above, because of the difference in the number and density of the ink nozzles Nz, the K ink has a printing resolution that is twice that of the other CMY inks, and therefore the input image data ID has a resolution that is twice that of the CMY inks. In step P130, the color conversion unit FW3 acquires the input image data ID and performs color conversion on the input image data ID.

ステップＰ１３０ｃにおいて、第１色変換部ＦＷ３ａは１Ｄ−ＬＵＴ１５ｂを参照し、逆輝度値Ｂｒに対応するＫインクのインク量Ｉ₄を取得する。 FIG. 5 schematically shows the flow of color conversion processing and halftone processing. First, in Step P130a, the first color conversion unit FW3a selects one pixel of the input image data ID. In Step P130b, the first color conversion unit FW3a as the preliminary conversion means of the present invention acquires the RGB value of the selected pixel, and preliminarily converts the RGB value to the inverse luminance value Br. The RGB value is a color vector having elements of R gradation, G gradation, and B gradation and representing arbitrary coordinates in the RGB color space. In Step P130b, the following (1) and (2) The color vector is converted into an inverse luminance value Br as a scalar. The inverse luminance value Br is a value obtained by subtracting the luminance value normalized to 0 to 1 from 1, and is a scalar representing that the darker the value is, the brighter the value is.

In Step P130c, the first color conversion unit FW3a refers to the 1D-LUT 15b and acquires the ink amount I ₄ of K ink corresponding to the reverse luminance value Br.

In FIG. 5, a 1D-LUT 15b is shown. In the 1D-LUT 15b, a correspondence relationship between each value of each reverse luminance value Br and each value of the ink amount I ₄ of K ink is defined. In this embodiment, since each RGB has 8 bits, the ink amount I ₄ of K ink may be stored for 256 ³ reverse luminance values Br that can be combined. Therefore, the 1D-LUT 15b can acquire the ink amount I ₄ of K ink without performing an interpolation calculation. In Step P130d, the first color conversion unit FW3a determines whether or not all the pixels have been selected. If all the pixels have not been selected, the next pixel is selected in Step P130a. On the other hand, when all the pixels are selected, the color conversion process of the K ink to the ink amount I ₄ ends. As a result, color-converted image data CD1 including pixels having the number of pixels corresponding to the printing resolution of K ink and each pixel having the ink amount I ₄ of K ink is generated.

Next, in Step P130e, the second color conversion unit FW3b performs size conversion (reduction) by reducing the number of pixels in the vertical and horizontal directions of the input image data ID to half (a quarter of the total number). Here, simple thinning may be performed, or interpolation based on the RGB values of surrounding pixels may be performed. Since the input image data ID is generated in advance with the number of pixels corresponding to the resolution twice as high as the printing resolution of the CMY ink, the number of pixels of the input image data ID is changed to CMY by converting the size of the input image data ID to half. This corresponds to the original print resolution of the ink. In Step P130f, the second color conversion unit FW3b selects one pixel of the input image data ID after size conversion. In Step P130g, the second color conversion unit FW3b acquires the RGB value of the selected pixel, and converts the RGB value into the ink amounts I ₁ , I ₂ , and I ₃ of CMY ink. Specifically, the RGB values are converted into the ink amounts I ₁ , I ₂ , and I ₃ of CMY ink by performing an interpolation calculation while referring to the 3D-LUT 15c.

In FIG. 5, the 3D-LUT 15c is schematically shown. In the 3D-LUT 15c, the correspondence relationship between RGB values and ink amounts I ₁ , I ₂ , and I ₃ of CMY inks is defined for 17 ³ input grid points distributed in the RGB color space. When the second color conversion unit FW3b obtains the RGB value, it identifies which small space the RGB value belongs to in the RGB space and corresponds to each lattice point constituting the vertex of the small space. by each ink amount I _1, I _2, I ₃ of CMY ink attached to a linear combination (linear interpolation), to calculate the ink amount I _1, I _2, I ₃ of CMY ink corresponding to the RGB values . The weight for linear combination is set based on the positional relationship between the RGB value in the RGB color space and each vertex in the small space. For example, the weight is set based on the RGB value and the volume of a tetrahedron or hexahedron partitioned by each vertex of the small space. In this way, it is possible to convert arbitrary RGB values into CMY ink amounts I ₁ , I ₂ , and I ₃ while suppressing the data capacity of the 3D-LUT 15c. In Step P130h, the second color conversion unit FW3b determines whether or not all the pixels have been selected. If all the pixels have not been selected, the next pixel is selected in Step P130f. On the other hand, when all the pixels are selected, the color conversion process ends. As a result, color-converted image data CD2 to CD4 that are composed of pixels having the number of pixels corresponding to the printing resolution of the CMY ink and each pixel has the ink amounts I ₁ , I ₂ , and I ₃ of the CMY ink are generated. Become. When the color conversion process is completed as described above, the halftone unit FW4 executes the halftone process in step P140.

The color conversion image data CD1 to CD4 in which each pixel has the ink amounts I ₄ , I ₁ , I ₂ , and I _{3 of} KCMY ink are obtained by the color conversion process of Step P130. As described above, the color conversion image data CD1 in which each pixel has the ink amount I4 of K ink has the number of pixels corresponding to the printing resolution twice that of the color conversion image data CD2 to ₄ of other CMY inks (as the number of pixels). 4 times). In Steps P140a to P140d, halftone processing is sequentially performed on the color converted image data CD1 to CD4 after color conversion. For example, the color-converted image data CD1 to CD4 are binarized and sequentially converted into halftone data HD1 to HD4 by sequentially performing a dither method and an error diffusion method. Of course, an error diffusion method may be applied. In the halftone data HD1 to HD4, the K ink halftone data HD1 has four times as many pixels as the other halftone data HD2 to HD4.

In Step P150, the rasterizing unit FW5 assigns each pixel (two gradations indicating whether ejection is possible) of the halftone data HD1 to HD4 after the halftone process to each main scan and each ink nozzle Nz of the print head 19, and drives it. Generate data. The K ink halftone data HD1 has four times the number of pixels of the other halftone data HD2 to HD4, but the arrangement number and density of the K ink ink nozzles Nz in the main scanning direction / sub-scanning direction are different. Since it is twice that of CMY ink, the print size of each ink is matched. The drive data after the rasterization process is output to the ASIC 22 in step P160, and the ASIC 22 generates drive signals for the paper feed mechanism 17, the carriage motor 18, and the print head 19. As a result, printing is executed. As a result, an ink amount corresponding to the ink amount I _j of the CMYK ink in the color conversion image data CD1 to CD4 is ejected onto the print medium, and an image corresponding to the input image data ID is formed on the print medium. It becomes.

As described above, in the present embodiment, the printing resolution of K ink is higher than that of other CMY inks, so that characters and the like can be printed with high definition. The color conversion to the CMY gradation by the 3D-LUT 15c involves an interpolation operation, but the color conversion to the CMY gradation is performed after reducing the number of pixels, so that the processing load can be reduced. On the other hand, the color conversion of the K ink to the ink amount I ₄ is performed for a large number of pixels. However, since it is only necessary to refer to the simple calculation of the above equations (1) and (2) and the 1D-LUT 15b, The load can be reduced. Therefore, the printing process can be executed smoothly without increasing the processing capacity and storage capacity of the CPU 13 and RAM 14 of the printer 10.

C. Configuration of LUT creation apparatus and overall LUT creation processing procedure:
FIG. 6 is a block diagram showing the configuration of the lookup table creation device in one embodiment of the present invention. This apparatus includes a 3D-LUT creation module 100, a 1D-LUT creation module 200, a forward model converter 300, and an LUT storage unit 400. “LUT” is an abbreviation for lookup table. The functions of the modules 100 and 200 and the converter 300 are realized by the computer executing a computer program stored in the memory. The LUT storage unit 400 is realized by a recording medium such as a hard disk device.

  The 3D-LUT creation module 100 includes a smoothing processing initial value setting module 120, a smoothing processing module 130, and a table creation module 140. The smoothing processing module 130 includes a color point movement module 132, an ink amount optimization module 134, an image quality evaluation index calculation module 136, and a K ink amount acquisition module 137. The 1D-LUT creation module 200 includes an inverse luminance conversion module 210, a conversion function setting module 220, and a table creation module 240. The forward model converter 300 includes a spectral printing model converter 310 and a color calculation unit 320. The functions of these parts will be described later.

  The LUT storage unit 400 is for storing the 1D-LUT 15b, the 3D-LUT 15c, and the like. The 3D-LUT 15c is a color conversion lookup table that receives an RGB color system and outputs an ink amount. “1D” and “3D” mean the number of input values. The RGB color system, which is the input color system of the 3D-LUT 15c, is not a so-called device-dependent color system, but a virtual color system (or an abstract color system) set independently of a specific device. is there.

FIG. 7 is a flowchart illustrating the overall processing procedure of the embodiment. In step S50 of FIG. 7, the 1D-LUT 15b is created, and then the 3D-LUT 15c is created by steps S100 to S300 of FIG. As described above, in the 1D-LUT 15b, the correspondence relationship between the inverse luminance value Br obtained by substituting arbitrary RGB values into the equations (1) and (2) and the ink amount I _{4 of} K ink is stored. Yes.

FIGS. 8A to 8C are explanatory diagrams showing processing contents when the 3D-LUT 15c is created in steps S100 to S300 of FIG. In step S100, the forward model converter 300 is prepared. Here, the “forward model” means a conversion model that converts an ink amount into a color value (colorimetric value) of a device independent color system. In the embodiment, the CIE-L ^* a ^* b ^* color system is used as the device independent color system. Hereinafter, the color value of the CIE-L ^* a ^* b ^* color system is also simply referred to as “L ^* a ^* b ^* value” or “Lab value”.

As shown in FIG. 8A, the spectral printing model converter 310 that forms the preceding stage of the forward model converter 300 is configured to print the ink amounts of a plurality of types of ink according to the ink amounts (by the printer 10). The spectral reflectance R (λ) of the patch is converted. In the present specification, the term “color patch” is used in a broad sense including not only a chromatic color patch but also an achromatic color patch. In the present embodiment, a color printer that can use four types of inks of cyan (C), magenta (M), yellow (Y), and black (K) is assumed, and the spectral printing model converter 310 also has these four types. The ink amount I _j of the ink is input. However, an arbitrary ink set can be used as the plurality of types of ink used in the printer. The color calculation unit 320 calculates the color value of the L ^* a ^* b ^* color system from the spectral reflectance R (λ). For the calculation of the color value, a light source (for example, standard light D50) selected in advance is used as a color patch observation condition. As a method for creating the spectral printing model converter 310, for example, a method described in JP-T-2007-511175 can be employed.

In step S200 of FIG. 7, an initial input value for creating a 3D-LUT is set by the user. FIG. 8B shows an example of the configuration of the 3D-LUT 15c and its initial input value setting. As the input value of the 3D-LUT 15c, values at substantially equal intervals determined in advance as RGB values are set. Since a set of RGB values is considered to represent a point in the RGB color space, the set of RGB values is also referred to as an “input grid point”. In this embodiment, the input grid points intersection of orthogonal grating for each 16 divides the RGB shaft (17 ^3). In step S200, the user inputs initial values (initial input ink amounts) of ink amounts for a small number of input lattice points selected in advance from among a plurality of input lattice points. It is preferable to select at least an input grid point corresponding to a vertex of a three-dimensional color solid in the RGB color space as the input grid point where the initial input ink amount is set. At the apex of this three-dimensional color solid, each RGB value takes the minimum value or the maximum value of the definition range. Specifically, (R, G, B) = (0,0,0), (0,0,255), (0,255,0), (255,0,0), (0,255, 255), (255, 0, 255), (255, 255, 0), and (255, 255, 255), the initial input ink amount is set for the eight input grid points. The ink amounts for the input grid points of (R, G, B) = (255, 255, 255) are all set to zero. The initial input ink amount for the other input grid points is arbitrary, and is set to 0, for example.

In step S300 of FIG. 7, the smoothing processing module 130 (FIG. 6) executes smoothing processing (smoothing / optimization processing) based on the initial input value set in step S200. In the first stage of the smoothing process, the initial ink amount I _{j (} for each initial input value in the RGB color space set in step S200 (other than the small number of initial input values to which the initial input ink amount was input in step S200). _{R, G, B)} is set by the smoothing process initial value setting module 120 (FIG. 6). However, for the initial ink amount I _{4 (R, G, B)} for K ink, those obtained by converting the respective initial input values (RGB values) by the above formulas (1), (2) and 1D-LUT 15b are applied. To do. In the smoothing process (smoothing / optimization process), the initial ink amount I _{4 (R, G, B)} for K ink is excluded from the optimization target, and the initial ink amount I as shown in FIG. _{4 (R, G, B)} is maintained until the end of the smoothing process (smoothing / optimization process). For other CMY inks, in the smoothing process (smoothing / optimization process), the ink amounts I ₁ , I ₂ , and I ₃ are varied so as to be optimized. FIG. 8C shows the processing content of step S300. On the left side of FIG. 8C, the distribution of a plurality of color points in a state before the smoothing process is indicated by double circles and white circles. These color points constitute a three-dimensional color solid CS in the L ^* a ^* b ^* space. The L ^* a ^* b ^* coordinate values of each color point are converted into L ^* a ^* b ^* values by using the forward model converter 300 (FIG. 8A) from the ink amounts at a plurality of input grid points of the 3D-LUT 15c. It is the value.

The three-dimensional color solid CS of the L ^* a ^* b ^* color system has the following eight vertices (double circle points in FIG. 8C).
Point P _K : Paper black point corresponding to (R, G, B) = (0, 0, 0).
Point P _W : Paper white point corresponding to (R, G, B) = (255, 255, 255).
Point P _C : cyan point corresponding to (R, G, B) = (0, 255, 255).
Point P _M : Magenta point corresponding to (R, G, B) = (255, 0, 255).
Point P _Y : Yellow point corresponding to (R, G, B) = (255, 255, 0).
Point P _R : Red point corresponding to (R, G, B) = (255, 0, 0).
Point P _G : Green point corresponding to (R, G, B) = (0, 255, 0).
Point P _B : Blue point corresponding to (R, G, B) = (0, 0, 255).

The right side of FIG. 8C shows the distribution of color points after the smoothing process. The smoothing process is a process of moving a plurality of color points in the L ^* a ^* b ^* space and smoothing the distribution of these color points at nearly equal intervals. In the smoothing process, the ink amounts I ₁ , I ₂ , and I ₃ of CMY inks that are optimal for reproducing the L ^* a ^* b ^* values of the respective color points after movement are also determined. On the other hand, since the ink amount I ₄ of K ink has already been determined by the 1D-LUT 15b, the ink amount I ₄ of K ink is not an object of optimization. That is, using the ink amount I ₄ of the K ink that has already been determined, the L * a * b * value of each color point after movement can be reproduced, and the optimum ink amount I _{1 of the} CMY ink , I ₂ , I ₃ are searched. When the optimum ink amounts I ₁ , I ₂ , and I ₃ of CMY inks are registered as output values of the 3D-LUT 15c, the 3D-LUT 15c is completed.

FIGS. 9A to 9C show the correspondence between the color points of the input color system (that is, the input grid points) and the color points of the L ^* a ^* b ^* color system. The vertices of the L ^* a ^* b ^* color system 3D color solid CS correspond one-to-one with the vertices of the 3D color solid of the input color system of the 3D-LUT 15c. Also, the sides (ridge lines) connecting the vertices can be considered to correspond to each other in both color solids. Each color point of the L ^* a ^* b ^* color system before the smoothing process is associated with each input grid point of the 3D-LUT 15c. Therefore, each color of the L ^* a ^* b ^* color system after the smoothing process The points are also associated with the input grid points of the 3D-LUT 15c. Note that the input grid points of the 3D-LUT 15c are not changed by the smoothing process. The 3D color CS of the L ^* a ^* b ^* color system after the smoothing process corresponds to the entire color gamut (color gamut) that can be reproduced by the ink set constituting the output color system of the 3D-LUT 15c. Yes. Therefore, the input color system of the 3D-LUT 15c has significance as a color system that represents the entire color gamut that can be reproduced by this ink set.

The reason for performing the smoothing process in the L ^* a ^* b ^* space when creating the 3D-LUT 15c is as follows. In the 3D-LUT 15c, there is a demand for setting the amount of ink in the output color system so that a color gamut as large as possible can be reproduced. The color gamut that can be reproduced with a specific ink set is determined in consideration of predetermined limiting conditions such as ink duty limitation (limitation of the amount of ink that can be ejected to a certain area). On the other hand, the forward model converter 300 described above is created regardless of the reproducible color gamut without taking these restrictions into consideration. Therefore, if the range that can be taken by the color point in the L ^* a ^* b ^* space is determined in consideration of limiting conditions such as ink duty limitation during the smoothing process, a color gamut that can be reproduced with a specific ink set is determined. It becomes possible to do. As an algorithm for moving the color point, for example, an algorithm using a dynamic model described later is used.

In step S400 of FIG. 7, the table creation module 140 creates the 3D-LUT 15c using the result of the smoothing process. In other words, the table creation module 140 determines the optimal ink amount for reproducing the color points of the L ^* a ^* b ^* color system associated with each input grid point in the 3D-LUT 15c (FIG. 8C). Register as an output value. In the smoothing process, in order to reduce the calculation load, it is also possible to select only the color points corresponding to only a part of the input grid points of the 3D-LUT 15c as the processing target. For example, if the RGB value interval at the input grid point of the 3D-LUT 15c is 16, setting the RGB value interval at the input grid point to be smoothed to 32 reduces the load of the smoothing process by half. Can do. In this case, the table creation module 140 determines and registers the ink amount for all the input grid points of the 3D-LUT 15c by interpolating the smoothing processing result. In the following, after briefly explaining the dynamic model used in the smoothing process (smoothing / optimization process) of the embodiment, the processing procedure of the smoothing process and the contents of the optimization process will be described sequentially.

D. Procedure for creating 1D-LUT:
FIG. 10 is a flowchart of the 1D-LUT creation process in step S50 of FIG. In step S52, the conversion function setting module 220 of the 1D-LUT creation module 200 sets a conversion function for converting an RGB value, which is a three-dimensional color vector, into a one-dimensional scalar. In this embodiment, as shown in the above-described equations (1) and (2), a conversion function for calculating the inverse luminance value Br as the scalar is set. In step S54, a conversion function for converting the inverse luminance value Br into the ink amount I ₄ of K ink is set.

ここで、Ｋ_DutyはＫインクの使用量の上限に対応するＫインクのインク量Ｉ₄であり、例えばＫインクのインク物性や印刷媒体の物性によって決定される値である。ａは、シグモイド関数の振幅を微調整するためのパラメータであり、ａを１に近い範囲で調整することにより、シグモイド関数の振幅はＫ_Dutyを中心として微調整される。ｋ_sはシグモイド関数の傾きを調整するパラメータである。逆輝度値Ｂｒの増加とともに（暗くなるほど）Ｋインクのインク量Ｉ₄を増加させる必要があるため、ｋ_sは正値となる。ｘ１とｙ１は、シグモイド関数の中心位置（対称点）の位置をそれぞれＢｒ軸方向とインク量Ｉ₄軸方向に調整するパラメータである。ステップＳ５４において、上述したパラメータａ，ｋ_s，ｘ１，ｂ，ｙ１は、シグモイド関数の最大値がＫ_Duty以下となるように設定される。また、ステップＳ５４において、上述したパラメータａ，ｋs，ｘ１，ｂ，ｙ１は、点Ｐ_Rに対応するＫインクのインク量Ｉ₄が０となるように設定される。 FIG. 11 shows an example of the conversion function set in step S54 and the setting procedure. In this embodiment, the ink amount I ₄ of K ink is defined by a sigmoid function (conversion function) of the inverse luminance value Br (0 to 1). The sigmoid function is expressed by the following equation (3).

Here, K _Duty is the ink amount I ₄ of K ink corresponding to the upper limit of the amount of K ink used, and is a value determined by, for example, the physical properties of the K ink and the physical properties of the printing medium. a is a parameter for finely adjusting the amplitude of the sigmoid function, and by adjusting a within a range close to 1, the amplitude of the sigmoid function is finely adjusted around K _Duty . k _s is a parameter for adjusting the slope of the sigmoid function. Since it is necessary to increase the ink amount I ₄ of K ink as the reverse luminance value Br increases (becomes darker), k _s becomes a positive value. x1 and y1 are parameters for adjusting the position of the center position (symmetry point) of the sigmoid function in the Br axis direction and the ink amount I ₄ axis direction, respectively. In step S54, the parameters a, k _s , x1, b, and y1 described above are set so that the maximum value of the sigmoid function is equal to or less than K _Duty . Further, in step S54, the above-mentioned parameters a, ks, x1, b, y1 is the ink amount I ₄ of K ink corresponding to the point P _R is set to be 0.

As shown in FIG. 8 (C), when the point P _R and the point P _G and the point P _B is constitutes the apex of a color gamut, K ink is discharged when printing color indicated such vertices The color becomes dull and the color gamut becomes narrow. Of the point P _R and the point P _G and the point P _B, wherein (1) the inverse luminance value Br is maximized by formula is a point P _R. Since the sigmoid function is a monotonically decreasing function, if as the output value of the sigmoid function is 0 for inverse luminance value Br of the point P _R, conversely luminance value Br corresponding to another point P _G and the point P _B In contrast, the output value of the sigmoid function can be guaranteed to be zero. Therefore, if the output value obtained when substituting the inverse luminance value Br of the point P _R to the sigmoid function does not become 0, for example readjust equal to sigmoid function to reduce the parameter b and the parameter a. Incidentally, as long as the the ink amount I ₄ is 0 when the output value need not be strictly 0, which quantizes the output value obtained when substituting the inverse luminance value Br of the point P _R to the sigmoid function Good. For example, when rounding off, it may be less than 0.5.

When the sigmoid function of the equation (3) can be set as described above, the inverse luminance conversion module 210 sequentially substitutes each inverse luminance value Br into the equation (3) in step S56, and the ink of the K ink. The quantity I ₄ is calculated. In step S58, the table creation module 240 quantizes the calculated ink amount I ₄ of K ink into 8 bits, and stores the correspondence between the inverse luminance value Br and the ink amount I ₄ in the 1D-LUT 15b. According to the 1D-LUT 15b based on the sigmoid function, smooth gradation with K ink can be realized.

ここで、Ｆ_gは着目色点ｇが隣接色点ｇｎ（ｎは１〜Ｎ）から受ける引力の合計値、Ｖ_gは着目色点ｇの速度ベクトル、−ｋ_vＶ_gは速度に応じた抵抗力、Ｘ_gは着目色点ｇの位置ベクトル、Ｘ_gnは隣接色点ｇｎの位置ベクトル、ｋ_p，ｋ_gは係数である。係数ｋ_p，ｋ_gは予め一定の値に設定される。なお、文中では、ベクトルを示す矢印は省略される。 E. Dynamic model:
FIG. 12 is an explanatory diagram illustrating a dynamic model used in the smoothing process (smoothing / optimization process) according to the embodiment. Here, a state in which a plurality of color points (white circles and double circles) are arranged in the L ^* a ^* b ^* color space is shown. However, for convenience of explanation, the arrangement of the color points is drawn two-dimensionally here. In this dynamic model, it is assumed that virtual force Fp _g of the following formula with respect to focus color point g is according.

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

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

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

F. Smoothing processing (smoothing / optimization processing) procedure:
FIG. 13 is a flowchart showing a typical processing procedure of the smoothing process (step S300 in FIG. 7). In step T100, the smoothing process initial value setting module 120 (FIG. 6) initializes a plurality of color points to be subjected to the smoothing process.

ここで、Ｉ _j(R,G,B)は、入力格子点のＲＧＢ値に対するインクセット全体のインク量を表している。ここでも下付文字ｊは、インクの種類を示す１〜４の自然数を表す。ＲＧＢ値が０または２５５を取る入力格子点に対するインク量は、図５のステップＳ２００においてユーザによって予め入力された初期入力インク量である。前記（５）式および（６）式によれば、いわゆる６面体補間により、任意のＲＧＢ値における初期インク量Ｉ _j(R,G,B)を求めることできる。 FIG. 14 is a flowchart showing a detailed procedure of Step T100. In step T102, the smoothing process initial value setting module 120 determines the initial ink amount of each ink of each color point to be smoothed from the initial input ink amount (FIG. 8B). For example, in the smoothing process for 3D-LUT, the initial ink amount I _{j (R, G, B)} for each input grid point is determined according to the following equations (5) and (6).

Here, I _{j (R, G, B)} represents the ink amount of the entire ink set with respect to the RGB values of the input grid points. Again, the subscript j represents a natural number between 1 and 4 indicating the type of ink. The ink amount for the input grid point where the RGB value takes 0 or 255 is the initial input ink amount input in advance by the user in step S200 of FIG. According to the equations (5) and (6), the initial ink amount I _{j (R, G, B)} at an arbitrary RGB value can be obtained by so-called hexahedral interpolation.

In step T104 in FIG. 14, the K ink amount acquisition module 137 calculates the inverse luminance value Br by substituting the RGB values of the respective input grid points into the equations (1) and (2). Then, the K ink amount acquisition module 137 acquires the ink amount I ₄ of K ink corresponding to the inverse luminance value Br with reference to the 1D-LUT 15b, and uses the acquired ink amount I ₄ to obtain the initial ink amount of K ink. Replace I _{4 (R, G, B)} . That is, for K ink, the values are based on the equations (1), (2) and 1D-LUT 15b.

ここで、Ｌ^* _(R,G,B)、ａ^* _(R,G,B)、ｂ^* _(R,G,B)は変換後の色彩値Ｌ^*ａ^*ｂ^*を示しており、関数ｆ_L*FM、ｆ_a*FM、ｆ_b*FMはフォワードモデルコンバーター３００による変換を意味している。なお、これらの式からも理解できるように、この変換後の色彩値Ｌ^*ａ^*ｂ^*は、３Ｄ−ＬＵＴ１５ｃの入力値であるＲＧＢ値に対応付けられている。なお、インク量Ｉ_j（Ｉ _j(R,G,B)，ΔＩ_j，Ｉ_jr，ｈ_jも含む）を下付文字ｊを付すことなく示す場合は、各インク（ｊ＝１〜４またはｊ＝１〜３）のインク量Ｉ_jを各行要素として有する行列（ベクトル）を意味することとする。 In step T106 of FIG. 14, the color value L ^* a ^* b ^* corresponding to the initial ink amount I _{j (R, G, B)} is obtained using the forward model converter 300. This calculation can be expressed by the following equation (7).

Here, L ^* _{(R, G, B)} , a ^* _{(R, G, B)} and b ^* _{(R, G, B)} indicate the color values L ^* a ^* b ^* after conversion, f _{L * FM} , f _{a * FM} , and f _{b * FM} mean conversion by the forward model converter 300. As can be understood from these equations, the converted color value L ^* a ^* b ^* is associated with the RGB value that is the input value of the 3D-LUT 15c. In addition, when the ink amount I _j (including I _{j (R, G, B)} , ΔI _j , I _jr , h _j ) is indicated without the subscript j, each ink (j = 1 to 4 or It means a matrix (vector) having an ink amount I _j of j = 1 to 3) as each row element.

As a result of the process in step T100 described above, the following initial values are determined for the color points to be subjected to the smoothing process.
(1) Input grid point value of base LUT: (R, G, B)
(2) Initial coordinate values of color points in the L ^* a ^* b ^* space corresponding to each input grid point: (L ^* _{(R, G, B)} , a ^* _{(R, G, B)} , b ^* _{(R , G, B)} )
(3) Initial ink amount corresponding to each input grid point: I _{j (R, G, B)}
As can be understood from the above description, the initial value setting module 120 has a function of setting initial values related to other input grid points from input initial values related to typical input grid points. Of the initial ink amount I _{j (R, G, B)} , I _{4 (R, G, B)} of K ink is a value based on the above formulas (1), (2) and 1D-LUT 15b. The initial value setting module 120 may be included in the smoothing processing module 130. In step T120 of FIG. 13, the color point moving module 132 moves the color point in the L ^* a ^* b ^* space according to the dynamic model described above.

FIGS. 15A to 15D are explanatory diagrams showing the processing contents of steps T120 to T150 in FIG. As shown in FIG. 15A, there is a considerable bias in the distribution of color points before the smoothing process. FIG. 15B shows the position of each color point after a minute time has elapsed. The L ^* a ^* b ^* value of each color point after this movement is referred to as “target value LAB _t ”. This is because the value “LAB _t” is used as a target value in the search process of the optimum value of the ink amount described below.

In Step T130, the ink amount optimization module 134 searches for an optimum value of the ink amount I _j with respect to the target value LAB _t using a preset objective function E (see FIG. 15C). However, the ink amount I ₄ of K ink is not optimized, and the initial ink amount I _{4 (R, G, B)} remains unchanged. That is, the values based on the formula (1), the formula (2) and the 1D-LUT 15b are maintained. In the optimization using the objective function E, a plurality of ink amounts I _j that reproduce L ^* a ^* b ^* values close to the coordinate value LAB _t of the color point after moving by a minute amount in the dynamic model. The ink amount that is as small as possible is determined as the optimum ink amount with the sum of the square errors of the parameters ΔL ^* , Δa ^* , ΔGI, ΔCII, and ΔTI. The search for the optimum ink amount is started from the initial ink value I _{j (R, G, B) of} each input grid point set in step T100. Accordingly, the ink amount obtained by the search is a value obtained by correcting the initial ink amount I _{j (R, G, B)} . As will be described in detail later, the objective function E given by the equation (EQ1) can be written as a quadratic function relating to the ink amount vector I as in the equation (EQ2). The optimization of the ink amount is performed according to the quadratic programming method using the quadratic objective function E. The detailed procedure of step T130 and the contents of the objective function E will be described later.

In step T140 of FIG. 13, the L ^* a ^* b ^* value corresponding to the ink amount I _j searched in step T130 is recalculated by the forward model converter 300 (see FIG. 15D). Here, the reason why the L ^* a ^* b ^* value is recalculated is that the searched ink amount I _j is the ink amount that minimizes the objective function E, and therefore L ^* a ^* b reproduced with the ink amount I _j. ^{This is because the *} value slightly deviates from the target value LAB _t of the optimization process. The L ^* a ^* b ^* values recalculated in this way are used as coordinate values after the movement of each color point.

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

  In this way, in the typical smoothing process (smoothing / optimization process) of the present embodiment, the optimum ink amount corresponding to the color point after the movement is obtained while moving each color point at a minute time interval by the dynamic model. Is searched with an optimization method. Then, these processes are continued until the movement amount of the color point becomes sufficiently small. As a result, as shown in FIG. 8C, a smooth color point distribution can be obtained by the smoothing process.

G. Contents of optimization process:
The optimization function E (see FIG. 15C) should be expressed using the Jacobian matrix J relating to the color value (L ^* a ^* b ^* value), which is a function of the ink amount I _j , and the image quality evaluation index. Is possible. The Jacobian matrix J is expressed by the following equation (8), for example.

The first to third lines on the right side of the equation (8) show values obtained by partial differentiation of the color values L ^* a ^* b ^* with the ink amounts I _j (j = 1 to 3) of CMY inks. In this embodiment, since the K ink is not optimized, the ink amount I ₄ of the K ink is not allowed. Therefore, the partial differentiation at the ink amount I ₄ does not make sense, and the Jacobian matrix J is composed of column elements that are partially differentiated at the ink amount I _j (j = 1 to 3). In the fourth and following lines, an image quality evaluation index (graininess index GI (Graininess Index) representing color image quality of a color patch printed with a set of ink amounts I _j (j = 1 to 4) and color non-constancy The index CII (Color Inconstancy Index) and the total ink amount TI are values obtained by partial differentiation of the individual ink amounts I _j with the CMY ink amounts I _j (j = 1 to 3). The indices GI, CII, and TI are indices indicating that the smaller the value, the better the image quality of the color patch reproduced with the ink amount I _j .

The color value L ^* a ^* b ^* is converted from the ink amount I _j (ink amount vector I) by the following equation (9) using the forward model converter 300.

The image quality evaluation indexes GI, CII, and TI can also be expressed as functions of the ink amount I _j (ink amount vector I), respectively.

Note that the subscript “ill” of the color non-constancy index CII _{ill in} the equation (11) represents the type of light source. In the above equation (8), standard light A and standard light F12 are used as the types of light sources. An example of a method for calculating the color non-constancy index CII will be described later. As the color non-constant index CII, one relating to one or a plurality of arbitrary standard light sources can be used. The ink amount vector I substituted as a variable in the equations (9) to (11) includes the ink amount I _{4 of} K ink. Also in the equation (12), the ink amount I _j is summed in the range of j = 1 to 4. In this embodiment, the ink amount I ₄ of the K ink is not targeted for optimization, but the color value L ^* a ^* b ^* and the image quality evaluation indexes GI and CII are also taken into account in consideration of the ink amount I ₄ of the K ink. , TI is obtained. That is, the color values L ^* a ^* b ^* and the image quality evaluation index GI when printing is performed by combining the ink amounts I ₁ , I ₂ , and I ₃ of the optimization target CMY inks with the ink amount I ₄ of the K ink. CII and TI are evaluated.

ここで、ａＬは明度補正係数、ＷＳ（ｕ）はカラーパッチの印刷に利用されるハーフトーンデータが示す画像のウイナースペクトラム、ＶＴＦ（ｕ）は視覚の空間周波数特性、ｕは空間周波数である。ハーフトーンデータは、カラーパッチのインク量Ｉ_jからハーフトーン処理（プリンター１０が実行するハーフトーン処理と同一のものとする）によって決定される。前記（１３）式は一次元で表現しているが、空間周波数の関数として二次元画像の空間周波数を算出することは容易である。粒状性指数ＧＩの計算方法としては、例えば、本出願人により開示された特表２００７−５１１１６１号公報に記載された方法や、Makoto Fujino， Ｉmage Quality Evaluation of Ｉnkjet Prints， Japan Hardcopy '99， p.291-294に記載された方法を利用することができる。 The graininess index GI can be calculated using various graininess prediction models. For example, the graininess index GI can be calculated by the following equation (13).

Here, aL is a brightness correction coefficient, WS (u) is a winner spectrum of an image indicated by halftone data used for printing a color patch, VTF (u) is a visual spatial frequency characteristic, and u is a spatial frequency. The halftone data is determined from the ink amount I _j of the color patch by halftone processing (same as the halftone processing executed by the printer 10). Although the expression (13) is expressed in one dimension, it is easy to calculate the spatial frequency of the two-dimensional image as a function of the spatial frequency. As a method for calculating the graininess index GI, for example, the method described in Japanese Patent Application Publication No. 2007-511116 disclosed by the applicant, Makoto Fujino, Image Quality Evaluation of Inkjet Prints, Japan Hardcopy '99, p. The method described in 291-294 can be used.

ここで、ΔＬ^*は２つの異なる観察条件下（異なる光源下）におけるカラーパッチの明度差、ΔＣ^* _abは彩度差、ΔＨ^* _abは色相差を示す。色非恒常性指数ＣＩＩの計算時には、２つの異なる観察条件下でのＬ^*ａ^*ｂ^*値は、色順応変換（ＣＡＴ）を用いて標準観察条件（例えば標準の光Ｄ６５の観察下）に変換される。ＣＩＩについては、Billmeyer and Saltzman's Principles of Color Technology， 3rd edition， John Wiley & Sons， Ｉnc， 2000， p.129， pp. 213-215を参照。 The color non-constancy index CII is given by the following equation (14), for example.

Here, ΔL ^* is the lightness difference of the color patch under two different observation conditions (under different light sources), ΔC ^* _ab is the chroma difference, and ΔH ^* _ab is the hue difference. When calculating the color non-constant index CII, the L ^* a ^* b ^* values under two different viewing conditions are converted to standard viewing conditions (eg, under the observation of standard light D65) using chromatic adaptation transformation (CAT). Converted. For CII, see Billmeyer and Saltzman's Principles of Color Technology, 3rd edition, John Wiley & Sons, Inc, 2000, p.129, pp.213-215.

ここで、ｆ_L*FMは、フォワードモデルによるインク量ＩからＬ^*値への変換関数、Ｉ_rはインク量Ｉの現在値（平滑化／最適化処理前のインク量）、分母のｈ_jはｊ（ｊ＝４は除く）番目の各インク量Ｉ_jの微少変動量である。一方、分子のｈは、微少変動量ｈ_jを行要素とする行列（ベクトル）であり、Ｋインクについての微少変動量ｈ₄＝０を有している。他の成分も同じ形式で表される。 Of the plurality of components (also referred to as “elements”) of the Jacobian matrix J, for example, the component relating to the L ^* value is given by equation (15).

Here, f L _{* FM,} the conversion function from the ink amount I by the forward model to the L ^* value, the current value of I _r is the ink amount I (smoothing / optimization process before the ink amount), the denominator of h _j is j (j = 4 are excluded) th minute variation of the ink amount I _j of. On the other hand, the numerator h is a matrix (vector) having the minute fluctuation amount h _j as a row element, and has a minute fluctuation amount h ₄ = 0 for K ink. Other components are also represented in the same format.

ここで、右辺の各項の最初に記載されているｗ _L*，ｗ _a*等は、各項の重みである。各項の重みは、予め設定されている。 The optimization objective function E is given by the following equation (16), for example.

Here, w _{L *} , w _{a * and the} like described at the beginning of each term on the right side are the weights of each term. The weight of each term is set in advance.

The first term w _{L *} (ΔL ^* −ΔL ^* _t ) ^{2 on} the right side of the equation (16) is a square error with respect to the variations ΔL ^* and ΔL ^* _t of the color value L ^* . These fluctuation amounts ΔL ^* and ΔL ^* _t are given by the following equations.

The partial differential value on the right side of the equation (17) is a value given by the Jacobian matrix (equation (8)), I _j is the ink amount obtained as a result of the optimization process, and I _jr is the current ink amount. It is. The first variation amount ΔL ^* is an amount obtained by linearly converting the variation amount ΔI _j = (I _j −I _jr ) of the ink amount by the optimization process using the partial differential value that is an element of the Jacobian matrix. On the other hand, the second variation amount ΔL ^* _t is the target value L ^* _t obtained by the smoothing process in step T120 and L ^* given by the forward model for the current ink amount I _jr (ink amount vector I _r ). Difference. The second fluctuation amount ΔL ^* _t can be considered as a difference between L ^* values before and after the smoothing process.

The terms after the second term on the right side of the equation (16) are also given by the same equations as the equations (17) and (18). That is, the objective function E includes the first variation amounts ΔL ^* , Δa ^* , Δb ^* , ΔGI, etc. obtained by linearly transforming the variation amount ΔI _j of the ink amount by the optimization processing with the Jacobian matrix components, and the parameter L Is given as a sum of square errors of second variation amounts ΔL ^* _t , Δa ^* _t , Δb ^* _t , ΔGI _t ... Before and after the smoothing process regarding ^* , a ^* , b ^* , GI. .

The first fluctuation amounts ΔL ^* , Δa ^* , Δb ^* , ΔGI,... Can be written in the following formulas (19) and (20).

ここで、（２１）式の最後の３個の項ｗ_Ｉ1（Ｉ₁−Ｉ_1t）²…ｗ_Ｉ3（Ｉ₃−Ｉ_3t）²は、前記（１６）式から追加された成分であり、最適化処理の前後での各インク量Ｉ_jの滑らかさを維持するために導入されたものである。ここで、Ｉ_1t〜Ｉ_3tは、注目している入力格子点に関するターゲットインク量（最適化処理において目標とするインク量）を意味している。ターゲットインク量Ｉ_jtは、現在のインク量Ｉ_jrに依存する所定の関数に従って決定された値を利用することができる。例えば、ターゲットインク量Ｉ_jtとして、その入力格子点に関する現在のインク量Ｉ_jrそのものの値や、その入力格子点の現在インク量Ｉ_jrとその周囲の入力格子点における現在インク量の加重平均などを利用することが可能である。（２１）式で追加された項ｗ_Ｉ1（Ｉ₁−Ｉ_1t）²…ｗ_Ｉ3（Ｉ₃−Ｉ_3t）²は、最適化処理の結果として得られるインク量Ｉ_jと、ターゲットインク量Ｉ_jtの２乗誤差である。このような項を導入すれば、最適化処理の前後でインク量が過度に変化してしまうことを防止できるという利点がある。 Since the ink amount I ₄ for K ink is not changed, ΔI ₄ need not be considered. Therefore, the variation vector ΔI is composed of only components from j = 1 to 3 corresponding to CMY inks. As the objective function E, a function given by the following equation (21) may be used.

Here, the last three terms w _I1 (I ₁ −I _1t ) ² ... W _I3 (I ₃ −I _3t ) ² in the equation (21) are components added from the equation (16), This is introduced in order to maintain the smoothness of each ink amount I _j before and after the optimization process. Here, I _{1t to} I _3t mean the target ink amount (target ink amount in the optimization process) regarding the input grid point of interest. As the target ink amount I _jt , a value determined according to a predetermined function depending on the current ink amount I _jr can be used. For example, as the target ink amount I _jt , the value of the current ink amount I _jr itself regarding the input grid point, the weighted average of the current ink amount I _jr of the input grid point and the current ink amount at the surrounding input grid points, etc. Can be used. The term w _I1 (I ₁ −I _1t ) ² ... W _I3 (I ₃ −I _3t ) ² added in the equation (21) is the ink amount I _j obtained as a result of the optimization process and the target ink amount I. _This is the square error of _jt . If such a term is introduced, there is an advantage that the ink amount can be prevented from changing excessively before and after the optimization process.

The expression (21) can be expressed as an expression (22) using a matrix.

Here, the superscript T represents transposition of the matrix. Matrixes W _M and W _I are diagonal matrices (see equations (23) and (24)) in which weights are arranged on the diagonal elements, respectively, and matrix ΔM is a target variation vector (see equation (25) for each parameter). ). Further, (22) the ink quantity relating the vector (matrix) in the formula I, I _r, I _t are each composed of only a component of up to j = 1 to 3 corresponding to the CMY inks. That is, the ink amount I ₄ of K ink is not an object of optimization.

(25) the right side of the equation, the parameters ^{L *, a *, b *} , and the target values for CII ... (also referred to as "element"), each parameter is given by the current ink amount I _r L ^*, a ^*, b ^* , CII... The ink amount I ₄ of K ink is not subject to optimization, but the ink amount I ₄ of K ink is also considered when calculating each parameter L ^* , a ^* , b ^* , CII. That is, the current ink amount I _r on the right side of the equation (25) includes I ₄ as a row element. In this respect, it differs from the current ink amount I _{r in the} equation (22). Among the target values of each parameter, the color values L ^* _t , a ^* _t , and b ^* _t are determined by the smoothing process (step T120). There are several determination methods for the target values GI _t , CII _t , and TI _t of the image quality evaluation index. The first method uses a predetermined constant (for example, GI _t = −2, CII _t = −1, TI _t = −1) as the target values GI _t , CII _t , and TI _t . The reason why negative values are used as constants is that these image quality evaluation indices are indices indicating that the smaller the image quality evaluation index, the higher the image quality. Note that the target value GI _t of the graininess index GI is preferably set to zero. In the second method, target values GI _t , CII _t , and TI _t are defined as functions of color value target values L ^* _t , a ^* _t , and b ^* _t . As described above, since the target value of each parameter is determined before the optimization process, all components of the target variation vector ΔM are constants.

The (22) of each term of the expression on the right side third term _{^{(I r T J T + ΔM}} T) W M (JI r + ΔM), and Section 6 _{I t ^T} W I I _t is optimized Since the ink amount I obtained as a result of the processing is not included, it is a constant. In general, no constant term is required as the objective function E for optimization. Therefore, when the constant term is deleted from the equation (25) and the whole is multiplied by ½, the following equation (26) is obtained.

Here, when the matrix A and the vector g are defined as in the following formulas (27) and (28), the formula (26) can be written as the formula (29).

  It can be understood that the objective function E given by the equation (29) is a quadratic form related to the ink amount vector I obtained by the optimization. In addition, when the objective function given by the above equation (16) is used instead of the objective function given by the above equation (21), it can be written in the same secondary form as the equation (29). The equations (EQ1) and (EQ2) shown in FIG. 15C are the same as the equations (16) and (29), respectively.

  In the optimization process of the present embodiment, the quadratic objective function E as shown in the equation (29) is used, so that the quadratic programming method can be used as the optimization method. Here, “secondary programming” means narrowly-ordered secondary programming that does not include sequential quadratic programming. Using quadratic programming with a quadratic objective function will greatly speed up processing compared to using other nonlinear programming methods such as quasi-Newton and sequential quadratic programming. Is possible.

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

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

ここで、ベクトルｂは、デューティ制限の対象となるインク種類を識別するための係数であり、要素に０か１を持つベクトルである。例えば、１種類のインクに関するデューティ制限の場合には、ベクトルｂの１個の要素のみが１となる。一方、全インクの合計インク量に関するデューティ制限の場合には、ベクトルｂのすべての要素が１となる。（３０）式の右辺のｌｉｍ_Ｉは、デューティ制限値である。 The ink duty limit can be expressed by the following equation (30).

Here, the vector b is a coefficient for identifying the ink type that is the target of duty limitation, and is a vector having 0 or 1 as an element. For example, in the case of a duty limit relating to one type of ink, only one element of the vector b is 1. On the other hand, in the case of the duty limit related to the total ink amount of all inks, all elements of the vector b are 1. Lim _{I on} the right side of the equation (30) is a duty limit value.

There is also a restriction that each ink amount I _j is not negative. This non-negative limit can be expressed by the following equation (31).

When the above equation (30) and equation (31) are combined, the ink duty limit is given by the following equation (32).

  The constraint expressed by the equation (32) is a linear inequality constraint. In general, quadratic programming can be performed under linear constraints. That is, in the optimization processing in the present embodiment, the optimization is performed by executing quadratic programming using the quadratic objective function E given by the above equation (29) under the constraint of the equation (32). Search for the correct ink amount. As a result, it is possible to execute the ink amount search at high speed while strictly satisfying this linear constraint. Since the 1D-LUT 15b is created so as to satisfy the ink duty limit for K ink (j = 4), the fourth and eighth lines need not be substantially considered in the optimization process.

FIG. 16 is a flowchart showing a detailed procedure of the optimization process (step T130 in FIG. 13). In step T132, first, a target fluctuation amount ΔM given by the above equation (28) is obtained. The target variation ΔM, as described above, the target value L ^* _t obtained in step T120 (smoothing processing), a ^* _t, are determined based on the b ^* _t and the current ink amount I _r.

In step T134, the Jacobian matrix J given by the equation (11) is calculated. Each component of the Jacobian matrix J is a value calculated with respect to the current ink amount I _r (value before smoothing / optimization), as exemplified by the equation (18).

In step T136, the difference between the linear transformation results ΔL ^* , Δa ^* , Δb ^* , ΔGI... And the target fluctuation amount ΔM (ΔL ^* _t , Δa ^* _t , Δb ^* _t , ΔGI _t ...) Is obtained. The ink amount I _j (j = 1 to 3) is optimized so as to be minimized. This optimization is realized by executing a quadratic programming method using a quadratic objective function E given by the above equation (29). The ink amount I ₄ of K ink is not optimized, and the initial ink amount I _{4 (R, G, B)} is maintained. The correspondence relationship between each input grid point in the RGB color space and the optimized ink amount I _j (j = 1 to 3) of the CMY ink is stored in the 3D-LUT 15c. The 1D-LUT 15b and the 3D-LUT 15c created as described above are stored in the ROM 15 of the printer 10 and referred to in the above-described printing process.

  As already described in the flowchart of FIG. 13, after the optimization process in step T130, if it is determined that the convergence is insufficient, the smoothing process (step T120) and the optimization process (step T130) are performed. Will be executed again. At this time, the value obtained by the previous smoothing / optimization process is used as the initial value of the smoothing / optimization process. Note that such repeated processing is not essential, and at least one smoothing / optimization processing may be performed. As described above, in this embodiment, since the optimal ink amount is searched by executing the quadratic programming method using the objective function E of the quadratic form, the ink amount search can be executed at high speed. . According to the actual measurement by the inventors, it has been found that the processing can be completed in about one-tenth of the time when the conventional quasi-Newton method is used.

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

前記（３３），（３４）式によればＵＣＲ（Under Color Remove）に基づく手法によって、Ｋインクのインク量Ｉ₄を得ることができる。以上のようにスカラーへの変換関数を異ならせた場合、変換されるスカラーの特性も異なることとなるため、各スカラーの特性に応じてシグモイド関数の各パラメータを設定する必要がある。 H1. Modification 1:
In the above embodiment, the RGB value (color vector) is converted to a scalar based on the luminance equation as in the equation (1), but other conversion functions may be used. Further, when the RGB values are linearly combined as in the equation (1), a weighting factor different from that in the equation (1) may be adopted. For example, when the preferable ink amount I _{4 of} K ink is obtained statistically and empirically, each weighting factor may be set so as to be converted into the preferable ink amount I ₄ of K ink. . In addition, it is not always necessary to linearly combine the RGB values. For example, the G value may be used as the luminance equivalent value. In this way, faster color conversion can be realized. Further, it may be converted into a scalar by the following equations (33) and (34).

According to the equations (33) and (34), the ink amount I ₄ of K ink can be obtained by a technique based on UCR (Under Color Remove). As described above, when the conversion function to the scalar is varied, the characteristics of the converted scalar are also different. Therefore, it is necessary to set each parameter of the sigmoid function according to the characteristics of each scalar.

  In the above description, the scalar input to the 1D-LUT 15b is illustrated as a linear function of RGB values. However, the scalar may be calculated by a nonlinear function of RGB values. For example, the conversion characteristics to scalars can be finely adjusted by using functions such as quadratic and cubic equations for RGB values. Therefore, for example, adjustment that matches the K ink ejection characteristics of the printer 10 can be realized by a conversion function to a scalar.

H2. Modification 2:
In the embodiment described above, in the 1D-LUT 15b, the ink amount I ₄ of K ink is stored for 256 ³ reverse luminance values Br that can be calculated by the above equations (1) and (2), thereby eliminating the need for an interpolation operation. , Speeding up the color conversion process. Since the 1D-LUT 15b is one-dimensional on both the input side and the output side, even if an interpolation operation is performed, the processing load is small. Accordingly, the 1D-LUT 15b may be set to about 17 grids, and interpolation calculation may be used together.

H3. Modification 3:
In the above embodiment, the CIE-L ^* a ^* b ^* color system is used as the device-independent color system. However, the CIE-XYZ color system, the CIE-L ^* u ^* v ^* color system, etc. Any device independent color system can be used. However, from the viewpoint of realizing smooth color reproduction, device independent color systems that are uniform color spaces such as CIE-L ^* a ^* b ^* color system and CIE-L ^* u ^* v ^* color system are used. It is preferable to use it.

H4. Modification 4:
In the embodiment, the process using the dynamic model is adopted as the smoothing process, but other kinds of smoothing processes may be adopted. For example, it is possible to employ a smoothing process in which the distance between adjacent color points is measured and the individual distance is adjusted so as to be as close as possible to the average value.

H5. Modification 5:
In the present specification, “ink” is used in a broad sense including not only liquid ink used for ink jet printers and offset printing, but also toner used for laser printers. As other terms having such a broad meaning of “ink”, “coloring material”, “coloring material”, and “coloring agent” can also be used.

H6. Modification 6:
In the above-described embodiment, the method and apparatus for creating color conversion correspondence information such as a lookup table has been described. However, the present invention provides a printing apparatus that includes a built-in unit that incorporates the color conversion correspondence information thus obtained in the printing apparatus. It is also applicable to the system. The color conversion correspondence information creating apparatus that creates the color conversion correspondence information may be included in this printing apparatus manufacturing system, or may be included in another system or apparatus. The built-in part of the manufacturing system can be realized as a printer driver installer (installation program), for example.

  DESCRIPTION OF SYMBOLS 10 ... Printer, 13 ... CPU, 14 ... RAM, 15 ... ROM, 20 ... Memory card slot, 21 ... Bus, 22 ... ASIC, 15a ... Program data, 15b ... 1D-LUT, 15c ... 3D-LUT, 100 ... 3D -LUT creation module, 120 ... smoothing process initial value setting module, 130 ... smoothing process module, 132 ... color point movement module, 134 ... ink amount optimization module, 136 ... image quality evaluation index calculation module, 140 ... table creation module, 200 ... 1D-LUT creation module, 300 ... Forward model converter, 310 ... Spectral printing model converter, 320 ... Color calculation unit, 400 ... LUT storage unit

Claims (7)

Input image data in which the color of each pixel is represented by a color vector in the input color space is color-converted into output image data in which each pixel has an ink amount related to a plurality of types of ink, and printing is performed based on the output image data A printing device to perform,
Preliminary conversion means for converting the color vector into a scalar by a conversion formula;
A first color conversion that converts the color vector into the achromatic color ink amount by referring to a first lookup table that defines a correspondence relationship between the scalar and the achromatic color ink amount that is the ink amount of the achromatic color ink. Means,
A second color that converts the color vector into the chromatic color ink amount by referring to a second look-up table that defines a correspondence relationship between the color vector and the chromatic color ink amount that is the ink amount of the chromatic color ink. A printing apparatus comprising: a conversion unit.   The printing apparatus according to claim 1, wherein the scalar is based on a luminance formula. The first color conversion means outputs first color conversion image data in which each pixel has the achromatic color ink amount,
The second color conversion means outputs second color conversion image data in which each pixel has the chromatic color ink amount, and
The printing apparatus according to claim 1, wherein the first color conversion image data has a higher resolution than the second color conversion image data.   4. The achromatic color ink amount corresponding to all the scalars that can be converted from the color vector is stored in the first look-up table. 5. The printing apparatus as described.   5. The printing apparatus according to claim 1, wherein a relationship between the scalar and the achromatic ink amount in the first look-up table is defined by a sigmoid function. Input image data in which the color of each pixel is represented by a color vector in the input color space is color-converted into output image data in which each pixel has an ink amount related to a plurality of types of ink, and printing is performed based on the output image data A printing method to execute,
Converting the color vector into a scalar by a conversion formula;
By converting the color vector into the achromatic color ink amount by referring to a first lookup table that defines the correspondence between the scalar and the achromatic color ink amount that is the ink amount of the achromatic color ink,
The color vector is converted to the chromatic color ink amount by referring to a second look-up table that defines a correspondence relationship between the color vector and the chromatic color ink amount that is the ink amount of the chromatic color ink. Printing method. Create a lookup table that is referenced when color conversion is performed on input image data in which the color of each pixel is represented by a color vector in the input color space to output image data in which each pixel has ink amounts relating to a plurality of types of ink. A lookup table creation method,
Converting the color vector into a scalar by a conversion formula;
Creating a first look-up table that defines the correspondence between the scalar and the achromatic ink amount that is the ink amount of the achromatic ink obtained by substituting the scalar into a conversion function;
Creating a second look-up table that defines the correspondence between the color vector and the chromatic color ink amount that is the ink amount of the chromatic color ink;
In creating the second look-up table, the chromatic color ink amount is optimized so that an optimum print result is obtained when printing is performed in combination with the achromatic color ink amount based on the first look-up table. A lookup table creation method characterized by the above.

Images