JPH11132850A - Conversion of color-expressing data and simulation of color printed matter with using the same - Google Patents

Abstract

PROBLEM TO BE SOLVED: To faithfully reproduce a part of an optional dot percent of a color printed matter disposed in a three-dimensional space, by setting a basic reference color on four sides of a virtual secondary color plane, and determining each reflection coefficient to the basic reference color. SOLUTION: For instance, in a tertiary color printed matter of three, i.e., cyan, magenta and yellow inks, a coordinate point of an object color (object point) is projected on four sides constituting a virtual secondary color plane PTP perpendicular to a cyan axis, thereby setting four reference points (indicated by black quadrangles). Then, a diffuse reflection coefficient Sb at each reference point on each of four planes PTP1 -PTP4 (color planes, namely, secondary color spaces) including the respective reference points is determined by linear coupling. A diffuse reflection coefficient Sb(dC/ M/ Y, λ) at an optional dot percent dC/ M/ Y of cyan, magenta and yellow is determined by linear coupling of the diffuse reflection coefficients Sb at four reference points.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

[0001] 1. Field of the Invention [0002] The present invention relates to a technology for converting color expression data and a technology for reproducing a color print using an output device such as a display device or a printer using the same.

[0002]

2. Description of the Related Art When a color print is reproduced by various output devices such as a display device and a printer, it is desirable to reproduce a color as close as possible to a real print. Conventionally, Murray-Davis's formula, Yule-Nielsen's formula, Neugebauer's formula, and the like are known as methods of color reproduction of printed matter. For example, Neugebauer's equation is calculated from the dot area ratios of four colors of YMCK ink in RGB.
Is an expression used when the value of each color component is determined.

[0003]

However, since the above-mentioned conventional conversion formula is set based on an idealized model, there is a problem that an actual color cannot be reproduced in many cases. In particular, when reproducing a state of observing a printed matter arranged in a three-dimensional space, there is a problem that the model cannot be applied in many cases.

On the other hand, as a method of reproducing a printed matter arranged in a three-dimensional space, there is a method disclosed in Japanese Patent Application Laid-Open No. Hei 7-234158 by the present applicant. in this way,
Illuminance spectrum I (θ, ρ,
λ) (θ is the reflection angle, ρ is the deviation angle, λ is the wavelength) is determined from the specular reflection coefficient Ss (λ) and the internal reflection coefficient Sb (λ), and based on this illuminance spectrum I (θ, ρ, λ). To reproduce color prints. According to this method, a color print having a specific halftone dot area ratio (for example, 100%) printed in a single color can be faithfully reproduced, but a faithful reproduction of a color print having an arbitrary halftone dot area ratio and a plurality of inks can be performed. It was not clear how to apply it when faithfully reproducing color prints printed with.

SUMMARY OF THE INVENTION The present invention has been made to solve the above-mentioned problems in the prior art, and has a portion having an arbitrary halftone dot area ratio in a color print printed with a plurality of inks arranged in a three-dimensional space. It is a first object of the present invention to provide a technique capable of reproducing the image more faithfully as compared with the related art.

It is a second object of the present invention to provide a technique for converting color expression data by applying a method of determining a reflection coefficient used in a color reproduction technique for color printed matter.

[0007]

In order to solve at least a part of the above-mentioned problems, a simulation method according to the present invention employs an N-dimensional simulation method arranged in a three-dimensional space.
A method of reproducing a color print by an output device by performing a rendering process on a color print of a next color (N is an integer of 3 or more), and (a) a predetermined brightness is set at a target point on the color print. A step of defining the illuminance spectrum I of the reflected light observed at a predetermined observation point when the light of the spectrum φ is radiated by the formula 1, and In the three-dimensional color space, (N-
2) ΔN (N−1) obtained when the dot area ratio of each type of ink is fixed to a value equal to the dot area ratio of the target color.
(C) projecting the coordinate points of the target color on four sides of the selected virtual secondary color plane. , Said 4
Setting four basic reference colors on one side; (d)
Determining a first reflection coefficient Sb and a second reflection coefficient Ss included in Equation 1 for each of the four basic reference colors; and (e) the first and second reflections for the target color. Determining the values of the coefficients Sb and Ss by a linear combination of the values of the first and second reflection coefficients Sb and Ss for the four reference colors, respectively; and (f) first and second values for the target color. Determining the illuminance spectrum I of the reflected light according to Equation 1 using the reflection coefficients Sb and Ss of (a), and (g) using the illuminance spectrum I of the reflected light in a color system suitable for the output device. Obtaining color data representing the target color.

According to the above simulation method, the reflection coefficients Sb and Ss of the target color, which is the N-th color having an arbitrary dot area ratio d ₁ → _N , are determined by the linear combination of the reflection coefficients of the four basic reference colors. Therefore, the illuminance spectrum I (d ₁ → _N , θ, ρ, λ) of the target color can be obtained with a relatively small amount of calculation. Also, this illuminance spectrum can be converted into color data of a color system of the output device. Therefore,
An arbitrary halftone dot area portion in an N-th color printed matter arranged in a three-dimensional space can be reproduced more faithfully than in the past. In addition, reproduction can be performed with a smaller amount of calculation than when five or more reference colors are used.

In the above simulation method, when the N is 4 or more, the step (d) includes (1) changing a parameter n (n is an integer equal to or less than (N-1) and 3 or more) to (N
-1) repeating a first process while sequentially changing from 3 to 3, wherein the first process regards each of the four basic reference colors as a virtual n-th reference color, and In the n-dimensional color space including the halftone dot area ratio of the (n-2) types of inks among the n types of inks constituting the virtual nth order reference color, ｛N (n-1) / obtained when fixed to the same value
By selecting one of the 2｝ virtual secondary color planes and projecting the coordinate points of the virtual n-th reference color onto four sides of the selected virtual secondary color plane, This is a process of setting four virtual (n-1) secondary reference colors on one side, and the step (1) is a process of setting a plurality of virtual secondary reference colors by repeating the first process. Yes,
The step (d) further includes (2) repeating a second process while sequentially changing a parameter m (m is an integer of 3 or more and N or less) from 3 to N, wherein the second process comprises: 4 set by the projection of each virtual m-th reference color
The first and second reflection coefficients Sb, Ss for each virtual m-th reference color are determined by a linear combination of the first and second reflection coefficients Sb, Ss for one virtual (m-1) -th reference color. Preferably, the step (2) is a step of obtaining the first and second reflection coefficients Sb and Ss for the four basic reference colors by repeating the second processing.

[0010] By repeating the second process of obtaining the reflection coefficient of the virtual m-th order color from the reflection coefficients of the four virtual (m-1) order reference colors, the reflection coefficients of the four basic reference colors are obtained. Therefore, the reflection coefficient of the target color can be determined by the linear combination of the reflection coefficients of these four basic reference colors. This second processing also includes four virtual (m-1)
Since the reflection coefficient of the virtual m-th order color is obtained from the reflection coefficient of the next reference color, the reflection of the virtual m-th order color can be reduced with a smaller amount of calculation than in the case where a larger number of virtual (m-1) next reference colors are used. The coefficients can be determined.

Note that the characteristics fb (θ) and fs (ρ)
Preferably have the form of Equation 2 respectively.

[0012] The simulation system of the present invention comprises:
A system that reproduces the color print by an output device by performing a rendering process on a color print of an N-th color (N is an integer of 3 or more) arranged in a three-dimensional space. Means for defining an illuminance spectrum I of reflected light observed at a predetermined observation point when the light of the predetermined luminance spectrum φ is irradiated, and a target color of the target point which is an N-order color. In the N-dimensional color space, when the dot area ratio of (N-2) kinds of inks among the N kinds of inks constituting the Nth color is fixed to a value equal to the dot area rate of the target color. Means for selecting one of the obtained {N (N-1) / 2} virtual secondary color planes, and 4 of the selected virtual secondary color planes
Means for setting four basic reference colors on the four sides by projecting the coordinate points of the target color on the two sides, and a first reflection coefficient Sb and a second reflection coefficient Basic reference color determining means for determining Ss for each of the four basic reference colors; and setting the values of the first and second reflection coefficients Sb and Ss for the target color in the fourth reference color. Using a means for determining by a linear combination of the values of the first and second reflection coefficients Sb and Ss, and the first and second reflection coefficients Sb and Ss for the target color,
Means for determining the illuminance spectrum I of the reflected light according to Equation 3, means for using the illuminance spectrum I of the reflected light to determine color data representing the target color in a color system suitable for an output device, And an output device for outputting the target color according to data.

The recording medium used in the simulation of the present invention is used in a computer having an output device,
A computer readable recording of a computer program for reproducing the color print on the output device by performing a rendering process on a color print of Nth color (N is an integer of 2 or more) arranged in a three-dimensional space. A function of defining an illuminance spectrum I of reflected light observed at a predetermined observation point by a mathematical expression 4 when the target point on the color print is irradiated with light having a predetermined luminance spectrum φ. , In the N-dimensional color space including the target color of the target point, which is the N-th color, the dot area ratio of (N−2) types of ink among the N types of inks constituting the N-order color is set as the target. A function of selecting one from {N (N-1) / 2} virtual secondary color planes obtained when the value is fixed to a value equal to the halftone dot area ratio of the color; Next color plane A function of setting four basic reference colors on the four sides by projecting coordinate points of the target color on the two sides, and a first reflection coefficient Sb and a second reflection coefficient included in Equation 4 A basic reference color determination function for determining the Ss for each of the four basic reference colors, and the values of the first and second reflection coefficients Sb and Ss for the target color are determined by the fourth reference color. A function to be determined by a linear combination of the values of the first and second reflection coefficients Sb and Ss, and a first and second reflection coefficient S for the target color.
b, Ss, the function of determining the illuminance spectrum I of the reflected light according to Equation 4; and, using the illuminance spectrum I of the reflected light, a color representing the target color in a color system suitable for the output device. A function for obtaining data, a function for outputting the target color to the output device according to the color data,
Is a computer-readable recording medium on which a computer program for causing a computer to realize the above is recorded.

In the above-described simulation system and recording medium, similarly to the above-described simulation method,
An arbitrary halftone dot area portion in an N-th color printed matter arranged in a three-dimensional space can be reproduced more faithfully than in the past. In addition, reproduction can be performed with a smaller amount of calculation than when five or more reference points are used.

The process of determining the reflection coefficient used in the above-described simulation can be applied to a color expression data conversion technique such as conversion of a color system.

According to the color expression data conversion method of the present invention, a specific target color which is an N-order color reproduced by N (N is an integer of 3 or more) primary colors included in the first color system is used. A method for converting first color expression data representing the densities of N types of primary colors into second color expression data related to the target color, comprising: (a) in an N-dimensional color space including the target color, {N (N-1) / 2} virtual secondary colors obtained when the densities of (N-2) primary colors of the N primary colors are fixed to values equal to the density of the target color (B) projecting the coordinate points of the target color on four sides of the selected virtual secondary color plane, thereby selecting four planes on the four sides. Setting a basic reference color; and (c) converting the value of the second color expression data into the four basic reference colors. And determining respectively,
(D) determining the value of the second color expression data for the target color by a linear combination of the values of the second color expression data for the four reference colors, respectively. .

As a conventional color conversion method, for example, there is a method described in FIG. 4 of Japanese Patent No. 2666523. In this conventional method, a color space is divided into a plurality of unit cubes, and these unit cubes are further divided into unit tetrahedrons including a target color. The value of the converted color expression data for the target color has been obtained by performing an interpolation process using a unit tetrahedron. In such a conventional conversion method, the values of the converted color expression data at the vertices of many small unit cubes must be measured and obtained in advance.
There was a problem that an extremely large number of data was required.

According to the method for converting color expression data according to the present invention, the second color expression data for an arbitrary target color, which is the Nth color, is determined by a linear combination of the color expression data of the four basic reference colors. So, based on relatively little data,
Second color expression data of the target color can be obtained.

In the above color expression data conversion method, when the N is 4 or more, the step (c) includes the step of (1) setting the parameter n (n is an integer of (N-1) to 3 or more) to (N
-1) repeating a first process while sequentially changing from 3 to 3, wherein the first process regards each of the four basic reference colors as a virtual n-th reference color, and When the density of the (n-2) primary colors of the n primary colors constituting the virtual n-th reference color is fixed to a value equal to the density of the virtual n-th reference color in the n-dimensional color space including Is selected from among {n (n-1) / 2} virtual secondary color planes, and the virtual n-th reference color is placed on four sides of the selected virtual secondary color plane. Are projected on the four sides by four virtual (n-
1) A process for setting a next reference color, the process (1)
Is a step of setting a plurality of virtual secondary reference colors by repeating the first processing, and the step (c) comprises:
Further, (2) a step of repeating the second process while sequentially changing the parameter m (m is an integer of 3 or more and N or less) from 3 to N, wherein the second process is performed for each virtual m-th reference color Four virtual (m-1) set by the projection
The process of determining the second color expression data for each virtual m-th reference color by linearly combining the second color expression data for the next reference color, and the step (2) is a process for determining the second process. Calculating the second color representation data for the four basic reference colors by repeating
Is preferred.

By repeating the second process of obtaining the second color expression data of the virtual m-th color from the second color expression data for the four virtual (m-1) next reference colors,
Second color expression data for one basic reference color is obtained. Therefore, the linear combination of the second color expression data for these four basic reference colors results in the second color representation data for the target color.
Can be determined. In the second processing, the second color expression data for the virtual m-th color is obtained from the second color expression data for the four virtual (m-1) next reference colors. 1) Compared with the case where the next reference color is used, the color expression data for the virtual m-th color can be obtained with a smaller amount of calculation.

When the above-described conversion of the color expression data is applied to a simulation of a color print, the target color is a color of a specific target point existing on the color print reproduced by the N types of primary colors. And the second color expression data is a reflection observed at a predetermined observation point when the target point on the color printed matter arranged in a three-dimensional space is irradiated with light having a predetermined luminance spectrum. It is a reflection coefficient component included in the illuminance spectrum of light.

In the case where the above conversion of the color expression data is applied to the conversion of the color system, the second color expression data is a second color system different from the first color system. Are colorimetric values.

The color expression data conversion device according to the present invention comprises:
Regarding a specific target color that is an N-order color reproduced by N types (N is an integer of 3 or more) of primary colors included in the first color system,
First color expression data representing the densities of the N primary colors is
An apparatus for converting into second color expression data related to the target color, wherein in an N-dimensional color space including the target color,
{N (N-1) / 2} virtual secondary colors obtained when the densities of (N-2) primary colors of the N primary colors are fixed to values equal to the density of the target color Means for selecting one of the planes, and a fourth one of the selected virtual secondary color planes
Basic reference color setting means for setting four basic reference colors on the four sides by projecting the coordinate points of the target color on the four sides, and setting the value of the second color expression data to the four Means for determining each of the three basic reference colors;
Means for respectively determining the value of the second color expression data for the target color by a linear combination of the values of the second color expression data for the four reference colors.

The recording medium used for the conversion of the color expression data of the present invention is a specific medium which is an N-order color reproduced by N (N is an integer of 3 or more) primary colors included in the first color system. For a target color, a computer-readable recording medium storing a computer program for converting first color expression data representing the densities of the N primary colors into second color expression data relating to the target color. Then, in the N-dimensional color space including the target color, ΔN obtained when the density of the (N−2) primary colors among the N primary colors is fixed to a value equal to the density of the target color. A function of selecting one from (N-1) / 2} virtual secondary color planes, and projecting coordinate points of the target color on four sides of the selected virtual secondary color plane Thus, four basic reference colors are set on the four sides. A basic reference color setting function, a function of determining the value of the second color expression data for each of the four basic reference colors, and a value of the second color expression data for the target color. A computer-readable recording medium that stores a computer program for causing a computer to perform a function of determining each of the values of the second color expression data in four reference colors by a linear combination.

With these conversion devices and recording media,
Similarly to the above-described conversion method, the second color expression data of the target color can be obtained based on relatively few data.

[0026]

Other Embodiments of the Invention The present invention includes the following other embodiments. A first aspect is a program supply device which, when executed by a computer, supplies a computer program for realizing each step or each means of the above-described invention via a communication path.

[0027]

BEST MODE FOR CARRYING OUT THE INVENTION

A. Outline of Color Data Generation Method: Next, embodiments of the present invention will be described based on examples. FIG. 1 is an explanatory diagram showing a state in which incident light is reflected by ink applied on printing paper. As shown in FIG. 1, the incident light Li on the ink
Is reflected in two different paths. The first reflected light is
Specularly reflected light Ls reflected at the boundary between the surface of the ink and the air layer. The second reflected light is diffuse reflected light (also referred to as “internal reflected light”) Lb emitted to the outside after light passing through the surface of the ink is scattered by the ink and particles in the paper.

FIG. 2 shows a light source, printed matter, and visual system (observer).
FIG. 4 is an explanatory diagram showing a relationship with the above. As shown in FIG. 2, the position of the visual system is shifted from the direction of the specular reflected light Ls by an angle ρ (hereinafter, referred to as an angle ρ).
(Referred to as "shift angle"). The direction (observation direction) connecting the reflection point of light on the surface of the printed material and the visual system may not exist on a plane formed by the incident light Li and the reflected light Ls. An angle between Ls and the observation direction is defined as a shift angle ρ.

The illuminance of the reflected light observed by the observer in FIG. 2 is a linear combination of the illuminance of the specular reflected light Ls, the illuminance of the diffusely reflected light Lb, and the illuminance of the ambient light, as shown in the following Expression 5. It is considered to be represented by

[0030]

(Equation 5)

Here, λ is the wavelength of light, I (θ, ρ, λ)
Is the illuminance spectrum of the observed reflected light, Ib (θ, ρ,
λ) is the illuminance spectrum of the diffuse reflected light Lb, and Is (θ,
ρ, λ) is the illuminance spectrum of specular reflected light Ls, Ie
(Λ) is the spectrum of ambient light. Illuminance spectrum I
(Θ, ρ, λ), Is (θ, ρ, λ) and Ib (θ,
ρ, λ) depends on the reflection angle θ, the shift angle ρ, and the wavelength λ. On the other hand, the illuminance spectrum Ie (λ) of the ambient light is a component derived from the ambient light observed at the observation point such as natural light in addition to the standard light source, and does not depend on the reflection angle θ or the shift angle ρ. It depends only on the wavelength λ.

In Equation 5, the illuminance spectrum Is
Assuming that (θ, ρ, λ) and Ib (θ, ρ, λ) can be separated into an angle component and a wavelength component, respectively, as in the following equation 6, equation 5 is rewritten as equation 7.

[0033]

(Equation 6)

[0034]

(Equation 7)

Here, Sb (λ) is the diffuse reflection coefficient, Ss
(Λ) is the specular reflection coefficient, and φ (λ) is the luminance spectrum of the incident light.

Angle-dependent characteristic fb (θ) of diffuse reflected light Lb
Is known to be represented by cos θ. The illuminance of the specular reflected light Ls is the strongest when observed in the reflection direction (the direction of ρ = 0) along the reflection angle θ, and decreases sharply as it deviates from this direction. Characteristic fs in Equation 7
(Ρ) represents such a phenomenon. Therefore, the function fs (ρ) becomes fs (ρ) = 1 when ρ = 0, and 0 ≦
In the range of ρ ≦ 90 °, the characteristics can be considered to be such that the characteristics monotonously decrease as ρ increases. As the characteristic fs (ρ), for example, it is known that cosρ raised to the power of n ₀ (n ₀ is a constant obtained experimentally) can be used. However, in this embodiment, as will be described later, the function form of the characteristic fs (ρ) is determined based on the measurement of the reflected light.

In the above equation 7, the dot area ratio of the color print is not taken into account. Therefore, in the following, a color print is painted with four color inks of C (cyan), M (magenta), Y (yellow), and K (sumi), and the halftone dot area ratio is (d _C , d _M). , D _Y , d _K ). In the following, the dot area ratios of the four CMYK inks will be collectively referred to as “d _{C / M / Y / K} ”. In the right-hand side of the above-described Expression 7, the dot area ratio d
Only the diffuse reflection coefficient Sb and the specular reflection coefficient Ss depend on _{C / M / Y / K.} Therefore, Expression 7 is rewritten as Expression 8 below.

[0038]

(Equation 8)

The illuminance spectrum I (d _{C / M / Y / K} , θ, ρ, λ) of the reflected light in the printed portion having the dot area ratio d _{C / M / Y / K.}
Is obtained, the tristimulus values X (d _{C / M / Y / K} ), Y (d _{C / M / Y / K} ), and Z (d) in the CIE-XYZ color system
_{C / M / Y / K} ) is given by the following equation 9 according to the definition.

[0040]

(Equation 9)

Here, x (λ), y (λ), and z (λ) are color matching functions (note that, in sentences other than mathematical expressions, bars on characters x, y, and z are omitted for convenience. doing).

That is, the tristimulus values X (d _{C / M / Y / K} ), Y (d _{C / M / Y / K} ), and Z (d
_{C / M / Y / K} ) or their chromaticity coordinate values (x, y,
z) is converted into color data of the color system (for example, RGB color system) of the output device, and the color of the print portion of the dot area ratio d _{C / M / Y / K} is faithfully reproduced in the output device. It is possible to reproduce.

The above equation 8 can be easily extended to a printed matter generally printed with N kinds of inks. That is, if the halftone dot area ratios of the N types of inks are represented by the symbol “d ₁ → _N ”, the symbol “d _{C / M / Y / K} ” in Expression 8 is used.
Is replaced by “d ₁ → _N ” to obtain the following equation (10).
Can be expanded to the general formula shown in

[0044]

(Equation 10)

However, in the following description, Equation 8 is mainly used.
Is applied (that is, a case where a printed matter printed with four colors of CMYK inks is reproduced) will be described. In this specification, colors printed with N types of inks are referred to as “N-order colors”.

The illuminance spectrum Ie (λ) of the ambient light, which is the third term on the right side of the above equation 8, is determined to be a constant value according to the observation environment of the color print. Therefore, in Expression 8, if a term other than the illuminance spectrum Ie (λ) of the environment light is obtained, the illuminance spectrum I of the reflected light in an arbitrary observation environment can be obtained. Therefore, a method of obtaining the illuminance spectrum I of the reflected light when the illuminance spectrum Ie (λ) of the ambient light is 0 will be described below.

When the illuminance spectrum Ie (λ) of the ambient light is 0, the above equation 8 can be rewritten as the following equation 11.

[0048]

[Equation 11]

What we want to know here is the dot area ratio d.
_{C / M / Y / K} in the diffuse reflection coefficient _{Sb (d C / M / Y} / K, λ)
And the specular reflection coefficient Ss (dC _{/ M / Y / K} , λ) and the characteristic fs (ρ) depending on the shift angle ρ. How to determine a specific form of the characteristic fs (ρ) depending on the shift angle ρ will be described later in detail. Below, first, the dot area ratio d
_{C / M / Y / K} in the diffuse reflection coefficient _{Sb (d C / M / Y} / K, λ)
An outline of how to determine the specular reflection coefficient Ss (d _{C / M / Y / K} , λ) will be described.

B. Outline of Method of Determining Reflection Coefficient for Nth Color: FIG. 3 is an explanatory diagram showing a method of calculating the reflection coefficient for colors from the primary color to the tertiary color. FIG. 3A shows how to calculate the reflection coefficient for the primary color. For example, the diffuse reflection coefficient Sb (d _C , λ) for the primary color of cyan is determined according to the following equation (12).

[0051]

(Equation 12)

Here, α _C (d _C ), β _C (d _C ), γ
_C (d _C ) is a weight coefficient. In other words, diffuse reflection in an arbitrary dot percent d _C of cyan coefficient Sb (d _C,
λ) are the three standard halftone dot area ratios (d _C = 0%, 50%,
100%), the diffuse reflection coefficient Sb (d _C = 0%,
λ), Sb (d _C = 50%, λ), Sb (d _C = 100
%, Λ). Weight coefficient α _C (d
_C ), β _C (d _C ), γ _C (d _C ) and reference diffuse reflection coefficient values Sb (d _C = 0%, λ), Sb (d _C = 50%,
λ) and Sb (d _C = 100%, λ) will be described later.

The specular reflection coefficient Ss (d _C , λ) at an arbitrary halftone dot area ratio d _C of cyan is determined by the following equation 13 similar to the equation 12.

[0054]

(Equation 13)

The weighting factors α _C , β _C , and γ in Expression 13
_{As C} , the weighting factors α _C , β _C , γ in Equation 12
_The same as _C may be used. Of course, the weight coefficient for the diffuse reflection coefficient Sb (d _C , λ) and the weight coefficient for the specular reflection coefficient Ss (d _C , λ) may be determined separately. It should be noted that the reflection coefficients Sb and Ss can be determined for the primary colors of the inks other than cyan by the same expressions as Expressions 12 and 13.

FIG. 3B shows how to calculate the reflection coefficient for the secondary color. For example, the diffuse reflection coefficient Sb (d _{C / M} , λ) for the secondary colors of cyan and magenta is determined according to the following equation (14).

[0057]

[Equation 14]

Here, C _{1 to} C ₄ are weight coefficients. The method of determining the weight coefficients C _{1 to} C ₄ will be described later. As can be understood from the form of Expression 14, the diffuse reflection coefficient Sb (d _{C / M} , _{C at} an arbitrary dot area ratio d _{C / M} of cyan and magenta
λ) is a target point of a secondary color (indicated by a black square) on four sides constituting a two-dimensional color space (color plane) shown in FIG.
Are projected at four reference points (indicated by white squares), the diffuse reflection coefficients Sb (d _{0 / M} , λ), Sb (d _{100 / M} , λ),
It is given by a linear combination of Sb (d _{C / 0} , λ) and Sb (d _{C / 100} , λ). Here, for example, “d _{0 / M} ” indicates that the dot area ratio of cyan is 0% and the dot area ratio of magenta is d.
_M means Note that the diffuse reflection coefficient Sb at the reference point on each side is:
It is determined according to the primary color determination method shown in FIG. Accordingly, the diffuse reflection coefficient Sb of the secondary color (d _{C / M} , λ)
Is given by a linear combination of the reference diffuse reflection coefficients at both ends (black circles) and midpoints (white circles) of each side of the two-dimensional color space shown in FIG. Among the reference colors giving the reference reflection coefficient, particularly, the reference color at the midpoint of the side (white circle) is called “quasi-standard color”, and the reference colors at both end points of the side (black circle) are called “reference color in a narrow sense”. May be called.

Among the four reference points (open squares) in FIG. 3B, the reference point having a dot area ratio of d _{100 / M and} the reference point having a dot area ratio of d _{C / 100} are as follows. , In a strict sense, a secondary color (2
Color printed with different types of ink). However, in this specification, in order to obtain the reflection coefficient of the secondary color, the secondary color is placed on the one-dimensional color space (that is, each side) constituting the outer edge of the two-dimensional color space including the secondary color. The color of the reference point set by projecting each coordinate point is called a “virtual primary color”. In this specification, generally, in order to obtain the reflection coefficient of the N-order color, the reflection coefficient is defined on an (N-1) -dimensional color space (that is, each side) constituting the outer edge of the N-dimensional color space including the N-order color.
The color of the reference point set by projecting the coordinate points of the N-th color is called "virtual (N-1) -th color".

Specular reflection coefficient Ss (d _{C / M} , λ) at an arbitrary halftone dot area ratio d _{C / M} of the secondary colors of cyan and magenta
Is determined by the same expression as Expression 14, and is omitted here. The weight coefficient C ₁ for the diffuse reflection coefficient Sb
And -C _4, weight coefficient C ₁ -C relative specular reflection coefficient Ss
₄ may be determined separately, or the same weighting factor may be used. Regarding the secondary colors other than the combination of cyan and magenta, the reflection coefficients Sb and Ss can be determined by the same expression as Expression 14.

FIG. 3C shows how to calculate the reflection coefficient for the tertiary color. For example, the diffuse reflection coefficient Sb (d _{C / M / Y} , λ) for a tertiary color composed of three inks of cyan, magenta and yellow is determined according to the following equation (15).

[0062]

(Equation 15)

The four diffuse reflection coefficients S included in Equation 15
b (d _{C / M / 0} , λ), Sb (d _{C / 0 / Y} , λ), Sb (d
_{C / M / 100} , λ) and Sb (d _{C / 100 / Y} , λ) are shown in FIG.
As shown in (C), a virtual secondary color plane PT including the target color of the tertiary color (indicated by a white triangle) and perpendicular to the cyan axis
The diffuse reflection coefficients at four reference points (indicated by black squares) where the coordinate points of the target color are projected on the four sides of P. The value of the diffuse reflection coefficient Sb at each reference point is determined by applying the method for determining the diffuse reflection coefficient of the secondary color shown in FIG. 3B on _four surfaces PTP _{1 to} PTP 4 including each reference point. Respectively.

On the virtual secondary color plane PTP, the halftone dot area ratio of cyan is constant, and the halftone dot area ratios of magenta and yellow change. In this specification, a surface in which only the dot area ratios of two kinds of inks are changed and the dot area ratios of other inks are constant is generally called a virtual secondary color plane. FIG. 3 (C)
The virtual secondary color plane PTP among the six planes of the color solid shown in
Four surfaces PTP including four sides each ₁ ～PTP ₄
In both cases, the dot area ratio of cyan and the dot area ratio of another ink (magenta or yellow) change,
This is a virtual secondary color plane in which the halftone dot area ratio of the remaining one ink (yellow or magenta) is constant (0% or 100%). In other words, the four sides of the virtual secondary color plane PTP including the target color and having a constant halftone dot area ratio of cyan are cyan and the other one of the three inks constituting the tertiary color. dot percent is included in each of the four virtual secondary color plane PTP ₁ ~PTP ₄ that varies with. Thus, the reflection coefficients at the four reference points (black squares), in each of the virtual secondary color plane PTP ₁ ~PTP _4,
It can be obtained according to the method of determining the reflection coefficient shown in FIG.

The above equation (15) has the same format as the above equation (14), but the values of the weighting factors C ₁ -C ₄ are determined independently by the equations (14) and (15). As can be understood from the form of Expression 15, the diffuse reflection coefficient S at an arbitrary dot area ratio d _{C / M / Y} of cyan, magenta, and yellow
b (d _{C / M / Y} , λ) is a coordinate point (also referred to as a target point) of a target color of a tertiary color on four sides constituting the virtual two-dimensional color space PTP shown in FIG. To determine the four reference points and determine the linear combination of the diffuse reflection coefficients Sb at these four reference points. Note that “projecting a coordinate point on a side constituting the color space” is equivalent to setting one coordinate value of the coordinate point to 0% or 100%.

As the virtual secondary color plane used for obtaining the reflection coefficient of the target color, instead of using the virtual secondary color plane PTP perpendicular to the cyan axis, a virtual secondary color plane perpendicular to the magenta axis is used. It is also possible to use a plane or a virtual secondary color plane perpendicular to the yellow axis. That is, as a virtual secondary color plane used when calculating the reflection coefficient of the target color as the tertiary color, the dot area ratio of one ink is fixed to a value equal to the dot area ratio of the target color. Any one of the three resulting virtual secondary color planes can be used.

The specular reflection coefficient Ss (d _{C / M / Y} , λ) at an arbitrary halftone dot area ratio d _{C / M / Y} of the tertiary color is determined by the same equation as the above-mentioned equation (15). Here, it is omitted.
The weighting factors C _{1 to} C for the diffuse reflection coefficient Sb
₄ and the weighting factors C _{1 to} C ₄ for the specular reflection coefficient Ss may be determined separately, or the same weighting factor may be used. Also, for tertiary colors other than the combination of cyan, magenta, and yellow, the reflection coefficients Sb and Ss can be determined by the same formula as Expression 15.

As described above, in this embodiment, the reflection coefficient of the target color (the white triangle point in FIG. 3C), which is a tertiary color having an arbitrary halftone dot area ratio, is the virtual coefficient including the target color. By projecting the coordinate points of the target color on the four sides of the secondary color plane PTP, four reference points (black square points in FIG. 3C) are determined, and the reflection coefficients of these four reference points are determined. Determined by finding a linear combination.

The diffuse reflection coefficient Sb (d _{C / M / Y / K} , λ) for the target color of the quaternary color composed of the four inks of cyan, magenta, yellow and black is determined according to the following equation (16). You.

[0070]

(Equation 16)

As can be inferred from the above description regarding the tertiary color, four diffuse reflection coefficients Sb (d _{C / M / 0 / K} , λ),
Sb (d _{C / 0 / Y / K} , λ), Sb (d _{C / M / 100 / K} , λ),
Sb (d _{C / 100 / Y / K} , λ) is a virtual secondary color obtained by fixing the dot area ratios of cyan and black to values equal to the dot area ratios d _c and d _K of the target color. It is a diffuse reflection coefficient at four reference points projected on four sides of a plane. In other words, the dot area ratio d of these four reference points
Regarding _{C / M / 0 / K} , dC _{/ 0 / Y / K} , dC _{/ M / 100 / K} , and dC _{/ 100 / Y / K} , the dot area ratio of cyan and black is the halftone of the target color. The value is the same as the value of the dot area ratio, and one of magenta and yellow is 0% or 100%. That is, the virtual secondary color plane used when calculating the reflection coefficient of the target color, which is the quaternary color, has the same dot area ratio of two colors (for example, cyan and black) of the four inks as the target color. This is a virtual secondary color plane that is fixed to a value and changes the dot area ratio of the other two colors (for example, magenta and yellow). The four reference points have a halftone dot area ratio of one of the four inks equal to 0% or 100%, and the halftone dot area ratios of the other three inks have the same value as the target color. It corresponds to such a color. Therefore, these four reference colors are assumed to be target colors of the tertiary colors, and
By applying the method of determining the reflection coefficient for the target color of the next color, the reflection coefficients for the four reference colors can be obtained.

By generalizing Equations (14) to (16), the diffuse reflection coefficient Sb (d ₁ → _n , _n ) for the target color of the n-th color (n is an integer of 2 or more) having an arbitrary halftone dot area ratio
λ) is given by the following equation (17).

[0073]

[Equation 17]

Here, Sb (d _i = 0, λ), Sb (d
_i = 100, λ) indicates that the halftone dot area ratio of the i-th ink is 0.
% And 100%, respectively, which means the diffuse reflection coefficient when the dot area ratio of the other inks is set equal to the dot area ratio of the target color. Also, Sb (d _j = 0,
λ) and Sb (d _j = 100, λ) are respectively set the dot area ratio of the j-th ink to 0% and 100%, and set the dot area ratio of the other ink to the dot area ratio of the target color. Means the diffuse reflection coefficient when set equal to That is, n
The reflection coefficient of the target color of the next color is given by a linear combination of the reflection coefficients of four reference colors obtained by fixing one of two specific inks of the n kinds of inks to 0% or 100%.

Equations (14) to (16) correspond to examples of equations in the case where n is set to 2, 3, and 4 in Equation (17).

The specular reflection coefficient Ss (d ₁ → _N , λ) for the n-th color (n is an integer of 2 or more) having an arbitrary halftone dot area ratio is given by the following equation 18 similar to the above equation 17.

[0077]

(Equation 18)

In general, the reflection coefficient of a target color, which is an N-order color (N is an integer of 3 or more), is expressed by the coordinates of the target color of the N-order color on four sides of a virtual secondary color plane including the target color. The four reference points are determined by projecting the points, and are determined by determining a linear combination of the reflection coefficients at these four reference points. At this time, the virtual secondary color plane is obtained when the value of the dot area ratio of the (N-2) color in the N inks constituting the Nth color is fixed to the same value as the target color. ｛N
Any one of (N-1) / 2} virtual secondary color planes can be selected and used. The four reference points for the Nth color can be considered as the (N-1) th color. At this time, when the value of (N-1) is 3 or more, the colors at these four reference points are regarded as the target colors of the (N-1) -order color, and each (N-1) -order color is regarded as the target color. Each (N-1) -order color is projected onto the four sides of the included virtual secondary color plane to determine reference points of the four (N-2) -order colors. In this way, by successively decreasing the order of the reference points, it is possible to finally obtain a plurality of secondary color reference points. The value of the reflection coefficient for these secondary color reference points can be determined by the method shown in FIG. Thereafter, by sequentially calculating the reflection coefficients at the third or higher order reference points, the reflection coefficient of the target color, which is the Nth color, can be finally determined. That is, the reflection coefficient Sb (d ₁ → _n , λ) of the _n-th color is calculated according to the expressions in which n is sequentially changed from 2 to N in Expressions 17 and 18.
By sequentially determining Ss (d ₁ → _n , λ), N
The reflection coefficients Sb (d ₁ → _n , λ) and Ss (d ₁ → _n ,
λ) can be obtained. Expressions 17 and 18
The value of the weighting factor C ₁ -C ₄ in is not constant, different values depending on the actual value of the halftone dot area ratio used in the values and the expression of n is used, respectively.

In the following, details of a method of determining a reflection coefficient for a primary color and a method of determining a reflection coefficient for a secondary color or higher color will be sequentially described.

C. Determination method of reflection coefficient for primary color:
The diffuse reflection coefficient Sb and the specular reflection coefficient Ss at an arbitrary halftone dot area ratio of the primary color are given by Expressions 12 and 13, respectively.

FIG. 4 is an explanatory diagram showing a method for determining the diffuse reflection coefficient Sb of the primary color according to equation (12). However, in FIG. 4, in order to indicate that an arbitrary ink is targeted, codes “d” and “α, β, γ” having no subscripts are respectively added to the dot area ratio and the weighting coefficient. Used.

Reference diffuse reflection coefficient value Sb (0%, λ), S
b (50%, λ) and Sb (100%, λ) are diffuse reflection coefficient values experimentally determined in advance at the reference halftone dot area ratio (0%, 50%, 100%), as described later. It is. Reference diffuse reflection coefficient values Sb (0%, λ), Sb (50
%, Λ) and Sb (100%, λ) depend on the wavelength λ of the light, and are determined for a plurality of values of the wavelength λ as described later. For example, the wavelength of visible light (about 380 nm
When about 780 nm is divided into about 60 wavelength regions, the reference diffuse reflection coefficient value Sb (0%,
λ), Sb (50%, λ), and Sb (100%, λ) are obtained in advance. Reference diffuse reflection coefficient value Sb (0%, λ),
A method for obtaining Sb (50%, λ) and Sb (100%, λ) will be described later.

Each weight coefficient α (d), β (d), γ (d)
Depends on the dot area ratio d, as shown in FIG. Weight coefficient α for reference diffuse reflection coefficient value Sb (0%, λ)
The value of (d) is 1 when the dot area ratio d of the target print portion is 0%, and is 0 when the dot area ratio d is 50% and 100%. Thus, each weight coefficient α, β, γ is
Dot percent d of the target print portion, the reference diffuse reflection coefficient Sb (d _i, lambda) associated with the weighting coefficient becomes 1 when equal to the dot percent d _i in the other reference diffuse reflection coefficient Sb (d _j, λ) 0 become in equal to the dot percent d _j in.

In FIG. 4, the change of the weighting coefficient α (d) is represented by 11 points (indicated by black circles) in the range of 0 ≦ d ≦ 100%. Any dot area ratio d
Is determined by interpolating these 11 coefficient values α. For example, the weighting coefficient α (d) may be determined by linearly interpolating the two coefficient values α at the two halftone dot rates closest to the target halftone dot rate d. Of course, the weight coefficient α (d) may be determined by nonlinearly interpolating the coefficient values α at three or more points. This is the same for the other weighting factors β (d) and γ (d).

FIG. 5 shows three reference reflection coefficient values Sb (0%, λ), Sb (50%, λ) and Sb (10
0%, λ) to obtain an arbitrary dot area ratio d
FIG. 5 is a conceptual diagram showing an advantage of a method for determining a reflection coefficient Sb (d, λ) in FIG. The dotted line at the bottom of FIG.
It shows a reproduction value obtained by interpolating two points of 0%. The dashed line indicates the actually measured value. In a reproduction value obtained by interpolation of two points, a reproduction error tends to increase when the dot area ratio d is about 50%. Therefore, in this embodiment, a point where the halftone dot area ratio is 50% is added, and 0% and 5% are added.
A linear combination of three values of 0% and 100% (the above-described equation 1)
2, 13) approximates a reproduction value at an arbitrary halftone dot area ratio. As a result, it is possible to reduce the reproduction error when the dot area ratio is about 50%.

To obtain the illuminance spectrum I (d, θ, ρ, λ) of the reflected light of the printed portion at an arbitrary halftone dot area ratio d for the primary colors of the respective inks according to the above-mentioned equations 11 to 13, It is understood that it is only necessary to determine the item in advance. (1) Reference diffuse reflection coefficient values Sb (0%, λ), Sb (5
0%, λ), Sb (100%, λ). (2) Reference specular reflection coefficient values Ss (0%, λ), Ss (5
0%, λ), Ss (100%, λ). (3) Changes in weight coefficients α (d), β (d), and γ (d) (FIG. 4). (4) The shape of the characteristic fs (ρ) depending on the angle ρ. Hereinafter, a method of determining the above items (hereinafter, referred to as “reference data”) and reproducing a printed matter based on these reference data will be described.

D. Procedure of the embodiment: FIGS. 6 and 7 are explanatory diagrams showing the procedure of the embodiment. In step S1 of FIG. 6, a gradation including a reference color and a plurality of primary colors other than the reference color was created for each of the inks constituting the Nth color, and the spectral reflectance was measured. Here, the “reference color” refers to the color of the color chart of the halftone dot area ratio (that is, 0%, 50%, 100%) related to the reference reflection coefficient in Expressions 12 and 13. The reference color is a color having a halftone dot area ratio related to the reference reflection coefficient among the primary colors. “Gradation” is a printed matter in which color patches of the reference color and the primary color are arranged in the order of the dot area ratio. In the embodiment, N · 2 ^(N−1) constituting an N-dimensional color space Gradients were created for all sides of the book. For example, when tertiary color simulation is performed, twelve gradations on twelve sides of the color solid shown in FIG.

FIG. 8 is an explanatory diagram showing the contents of the processing in step S1. As a gradation, FIG.
As shown in (A), a printing ink (for example, cyan) of one color was printed every 10% from 0% to 100%. FIG. 8B shows the measurement conditions of the spectral reflectance. The spectral reflectance is represented by an illuminance spectrum I (d,
θ, ρ, λ) normalized by the luminance spectrum φ (λ) of the incident light, and therefore I (d, θ, ρ, λ) / φ
(Λ). As shown in FIG. 8B, in this embodiment, two points of 8 ° and 10 ° are set as the reflection angle θ. Further, as the shift angle ρ, an angle of 2 ° was set in a range from −10 ° to 34 °, and 35 ° was set. In the above equation 11, the only component that depends on the reflection angle θ is cos θ. Therefore, it is sufficient to set one value as the measurement condition of the reflection angle θ. However, in this embodiment, two values are set as the reflection angle θ in order to improve the accuracy. On the other hand, regarding the shift angle ρ, in order to determine the dependency of the component fs (ρ) on the shift angle ρ (that is, the function form of fs (ρ)),
The angle was set relatively finely.

In step S1, the 11 shown in FIG.
For each of the color chips, the spectral reflectance as shown in FIG. 8C was measured under the measurement conditions shown in FIG. 8B.
FIG. 9 is a conceptual diagram illustrating a measuring apparatus for spectral reflectance. Place the colorimetric sample 20 on a sample table (not shown),
The illuminance spectrum I (d, θ, ρ, λ) of the reflected light was measured by the spectrophotometer 24 while irradiating the light with the light source 22. As the colorimetric sample 20, a standard white plate was used in addition to the gradation color patches shown in FIG. The standard white plate used in the examples has a spectral reflectance substantially equal to 1. Therefore, the illuminance spectrum of the reflected light of the standard white plate is
This corresponds to the luminance spectrum φ (λ) of the incident light. Therefore,
Illuminance spectrum I (d, θ, ρ, λ) of reflected light of each color chart
Was normalized by the illuminance spectrum φ (λ) of the standard white plate to calculate the spectral reflectance. In addition, the standard white plate has almost no specular reflection component, and thus its measured value does not depend on the deviation angle ρ. Therefore, as the measurement conditions of the standard white plate, the same incident angle θ (at least one of 8 ° and 10 °) as the other colorimetric samples is set, and the shift angle ρ is −
It was set to 10 °.

The measurement data was analyzed by a personal computer. As the light source 22, a daylight flood lamp with standard light D65 was used. Also, the measurement is performed in a dark room,
An ideal observation state without ambient light was realized.

FIG. 10 is an enlarged graph showing the measured values of the spectral reflectance shown in FIG. This graph shows that the halftone dot area ratio d is 50% and the incident angle θ is 8 °.
A plurality of measurement results with different shift angles ρ are shown. The level where the reflectance is 1.0 indicates a level equal to the illuminance spectrum of the standard white plate. The reason why the spectral reflectance of the colorimetric sample may exceed 1.0 is that the measured value of the standard white plate does not include the specular reflection component, so the measured value of the colorimetric sample including the specular reflection component is larger. This is because there are cases.

In step S2 of FIG. 6, the diffuse reflection component Ib of equation 11 is calculated from the measured value of the spectral reflectance of the primary color.
(D, θ, λ), and the specular reflection component Is
(D, ρ, λ) was estimated. FIG. 11 is an explanatory diagram showing a procedure for determining the diffuse reflection component and the specular reflection component from the spectral reflectance, and further determining the weighting factors α, β, and γ. In step S2, the diffuse reflection component shown in FIG. 11B was extracted from the spectral reflectance shown in FIG. 11A, and the specular reflection component shown in FIG. 11C was estimated.

To extract the diffuse reflection component, ρ = 35 °, θ
= 8 ° spectral reflectance was used. Incident angle θ
Since it is known that the dependence on is given by cos θ, the value of the incident angle θ may be selected from either 8 ° or 10 °. As the shift angle ρ, 35 ° which is the largest value among the measurement conditions was selected. The reason is as follows. As described above, the dependence fs (ρ) on the shift angle ρ included in Expression 11 is fs (ρ) = 1 when ρ = 0, and sharply increases with increasing ρ in the range of 0 ≦ ρ ≦ 90 °. This characteristic is such that it decreases monotonously. As can be understood from Equation 11, ρ is sufficiently large and the angle component fs (ρ)
Can be regarded as 0, the specular reflection component Is
(D, ρ, λ) / φ (λ) = Ss (d, λ) · fs
(Ρ) becomes 0. Under this condition, the measured value of the spectral reflectance is the diffuse reflection component Ib (d, θ, λ) / φ (λ) = Sb
(D, λ) · cos θ. The angle component fs (ρ) is
Since it shows a value close to cos ⁿ ρ (n is about 300 to 400),
Even if the value of fs (35 °) is regarded as 0, the error is negligible.

FIG. 12 is a graph plotting the diffuse reflection component Sb (d, λ) · cos θ extracted under the conditions of ρ = 35 ° and θ = 8 °. In this graph, the dot area ratio d
The diffuse reflection component Sb (d, λ) · cos
The wavelength dependence of θ is shown. In the embodiment, as shown in the following Expression 19, the diffuse reflection component is divided by cos θ to calculate the diffuse reflection coefficient Sb (d, λ).

[0095]

[Equation 19]

For the estimation of the specular reflection component Is (d, ρ, λ), a spectral reflectance of ρ = 0 ° and θ = 8 ° was used. As the incident angle θ, the same value as the condition under which the diffuse reflection component is extracted is used. The deviation angle ρ was set to 0 ° because fs (ρ)
This is for selecting a condition that satisfies = 1. The detailed shape of the shift angle dependency fs (ρ) is unknown, but it is known from the definition that fs (0) = 1. That is, when the shift angle ρ is 0, the specular reflection component Is (d, ρ
= 0, λ) is equal to the specular reflection coefficient Ss (d, λ) multiplied by the incident light spectrum φ (φ). Therefore, ρ =
Specular reflection component Is (d, ρ = 0, λ) under the condition of 0
Is obtained, it means that the specular reflection coefficient Ss (d, λ) has been obtained.

From the above equation (11), the spectral reflectance I (d, θ, ρ = 0, λ) / φ (λ) where the shift angle ρ is 0 ° is given by the following equation (20).

[0098]

(Equation 20)

By transforming Equation 20, the specular reflection coefficient Ss
(D, λ) is given by the following equation (21).

[0100]

(Equation 21)

FIG. 13 is a graph plotting the specular reflection coefficient Ss (d, λ) estimated according to Equation 21 under the condition of θ = 8 °. In this graph, the specular reflection coefficient Ss is set for each color chart of primary colors having different halftone dot area ratios d.
The wavelength dependence of (d, λ) is shown.

In step S3 in FIG. 6, the shape of the dependence fs (ρ) of the specular reflection component on the shift angle ρ (also referred to as “specular reflection attenuation coefficient”) is determined. Equation 11 described above
As can be seen from FIG. 5, the dot area ratio d, the incident angle θ, and the wavelength λ
Is constant, the spectral reflectance I / φ is equal to the shift angle ρ
Only depends on. Therefore, the dot area ratio d and the incident angle θ
And the spectral reflectance I / φ under the condition that the wavelength λ is constant.
The function form was determined by examining the dependence of the shift angle ρ on. Specifically, fs (ρ) has been found to have a Gaussian distribution function as shown in Equation 22 below.

[0103]

(Equation 22)

Here, the constant σ is a value in the range of about 70 to about 90. The unit of the shift angle ρ is radian. In the example, σ = 80 was obtained using the least squares method.

The function form of fs (ρ) is given by the following equation (2).
It is also possible to use 3.

[0106]

(Equation 23)

[0107] Here, the index n ₀ is a value in the range of from about 350 to about 400. Dependency fs given by equation 22
(Ρ), and the dependency fs (ρ) given by Equation 23,
In any case, fs (ρ) = 1 when ρ = 0, and 0 ≦ ρ ≦ 9
In the range of 0 °, the characteristic is such that it monotonously decreases as ρ increases.

In step S4 of FIG.
Weighting factors α, β, and γ used in 2, 13 were determined (FIG. 11D). In this embodiment, from the diffuse reflection coefficient Sb (d, λ) obtained in step S2,
β and γ were determined as follows. First, Expression 12 described above was extended to a simultaneous equation relating to a plurality of values of the wavelength λ, and this simultaneous equation was written using a matrix as in the following Expression 24 and Expression 25.

[0109]

(Equation 24)

[0110]

(Equation 25)

As shown in Equation 25, the matrix V
org represents the value of the diffuse reflection coefficient Sb (d, λ) for a plurality of wavelength values in the visible light wavelength range (λmin to λmax) for an arbitrary dot area ratio d. Also, the matrix K
Represents weighting factors α (d), β (d), γ (d).
The matrix Vprim has a reference diffuse reflection coefficient Sb (0%, λ) for a plurality of wavelength values in the visible light wavelength range (λmin to λmax).
λ), Sb (50%, λ), and Sb (100%, λ). Here, λmin is the minimum value of the wavelength λ of visible light,
λmax is the maximum value. For example, if the wavelength λ of visible light is divided into 60 wavelength regions, Equation 24 corresponds to a simultaneous equation including 60 equations.

The eleven values of the dot area ratio d (0%, 10%
.. 100%) is obtained in step S2 described above.
The matrix Vorg on the left side of Equation 24 is known for these eleven dot area ratio values. For the same reason, Equation 2
The second matrix Vprim on the right side of 4 is also known. Therefore,
The unknowns on the right side of Equation 24 are α (d), β
There is only a matrix K indicating (d) and γ (d). As described above, when the simultaneous equations (Equation 24) in which the number of unknowns is smaller than the number of equations are solved for the matrix K of unknowns, the unknowns α
A result equivalent to that obtained by approximating (d), β (d), and γ (d) by the least square method is obtained. Specifically, for each value (0%, 10%... 100%) of the 11 halftone dot area ratios d, a matrix K given by the following equation 26 is obtained.
11 sets of weighting coefficients α (d), β (d), γ (d) (d =
0%, 10%... 100%).

[0113]

(Equation 26)

FIG. 14 shows the weight coefficient α thus obtained.
It is a graph which shows the change of (d), (d), and (g). The weighting factors α (d), β (d), γ shown in FIG.
(D) has the same properties as those shown in FIG. However, FIG. 4 shows the outline of the change of the weight coefficient, whereas FIG. 14 shows the values actually obtained in the embodiment.

At step S5 in FIG.
Using the various results obtained in S4, a simulation of the reflectance of the Nth color (N is an integer of 3 or more) was performed. FIG. 7 shows a detailed procedure of step S5. In step S11, the parameter n is set equal to N. In step S12, the reference points of the four virtual (n-1) -order colors are determined by projecting the target colors on the four sides of the virtual secondary color plane including the target color of the n-th color. Here, the “virtual (n−1) -order color” means that the halftone dot area ratio of one of the n types of inks of the target color that is the n-th color is set to 0% or 100%. Say the color.

In step S13, it is determined whether (n-1) is equal to 1. When (n-1) is equal to 1, the flow shifts to step S16 described later. On the other hand, (n-
When 1) is not equal to 1, each reference point is regarded as a new target color (step S14), and 1
Is subtracted (step S15), and the aforementioned step S12
Return to Steps S12 to S15 are repeated until the reference point of the virtual primary color is obtained. As a result, reference points of virtual (N−k) -th order colors (where k is an integer from 1 to (N−1)) are determined by 4 × 4 ^(k−1) pairs. For example, when simulating the target color of the tertiary color, 4 × 1 sets of reference points of the virtual secondary color are determined, and 4 × 4 sets of reference points of the virtual primary color are determined. . Also, when simulating the target color of the quaternary color,
4 × 1 set of reference points of the virtual tertiary color is determined,
4 × 4 sets of reference points for the virtual secondary color and 4 × 16 sets of reference points for the virtual primary color are determined. However, among the 4 × 4 ^(k−1) virtual (N−k) -th order colors, the same color may actually overlap.

In this way, the virtual (N-1) -th order color is converted to the virtual 1
When all the reference points up to the next color are determined, step S1
At 6, the parameter m is set to 2. This parameter m is the same as the parameter n in steps S11 to S15, but another symbol is used for convenience of explanation. In step S17, the reflection coefficients Sb and Ss at the reference point of the virtual (m-1) -order color are calculated by using the above-described equation (1).
2, 13 (when m = 2) or Equations 17, 18 (when m is 3 or more). In step S18, it is determined whether (m-1) is equal to N. If not, the parameter m is increased by one in step 19. Then, returning to step S17, the reflection coefficients Sb and Ss at one higher-order reference point are determined. Steps S17 to S19 are repeated until the reflection coefficients Sb and Ss of the N-order color are obtained. N-order color reflection coefficient Sb,
After Ss is obtained, in step S19, the illuminance spectrum I (or the spectral reflectance I / φ) of the N-th color is calculated by using the above-described Expression 10 (or Expression 11).

When determining the reflection coefficient of the virtual primary color in step 16, first, the weighting factors α (d), β
(D), γ (d) and the reference diffuse reflection coefficient value Sb (0%,
λ), Sb (50%, λ), and Sb (100%, λ), and in accordance with Equation 12 described above, an arbitrary halftone dot area ratio d
At step Sb (d, λ). Similarly, the specular reflection coefficient Ss (d, λ) is calculated according to the above-described equation (13).

FIG. 15 shows the diffuse reflection component Sb (d, λ) ·
13 is a graph comparing an actually measured value of cos θ (shown by a solid line) and a simulation result (shown by a broken line) by Expression 12. The solid line and the dashed line almost coincide with each other, and it can be seen that both coincide well. Similarly, it was confirmed that the actual measurement value and the simulation result of the specular reflection component were in good agreement.

The determination of the reference diffuse reflection coefficient and the reference specular reflection coefficient according to the procedures of steps S1 to S4 in FIG. 6 is performed for each of the inks constituting the Nth color. Also,
Weights α, β, and γ are also obtained for each ink.

As shown in FIG. 3B, when it is desired to obtain the reflection coefficient of the target color as the secondary color, the two-dimensional color space (the rectangular plane in FIG. 3B) including the target color is used. Make up 4
The reference reflection coefficients at both end points (reference colors) and midpoints (quasi-reference colors) of the sides of the book are determined in advance. Therefore, in this case, the reference reflection coefficient on each of the four sides is determined according to the procedure of steps S1 to S4 in FIG. For example, in FIG.
When determining the reference reflection coefficient at both ends (black circles) and midpoint (white circles) of the side A _M2 of 0%, cyan is constant at 100%, and magenta changes every 10% from 0% to 100%. Create a gradient. Since this gradation is printed in cyan and magenta, it is a secondary color. However, the reference reflection coefficient and the weighting coefficients α, β, and γ can be determined according to the procedure of steps S1 to S4 in FIG. . It is preferable that the weighting coefficients α, β, and γ are individually obtained on each of the four sides. However,
Parallel sides (in FIG. 3B, sides A _C1 , A _C2 and sides A _M1 ,
A _M2 ) may use the same value as the weighting factors α, β, and γ.

As shown in FIG. 3C, when it is desired to obtain the reflection coefficient of the target color as the tertiary color, each of the 12 sides constituting the three-dimensional color space (color solid) including the target color is used. The reference reflection coefficients at both end points and the middle point are obtained in advance. In this case, the reference reflection coefficient and the weighting coefficients α, β, and γ on each of the 12 sides are determined in accordance with the procedures of steps S1 to S4 in FIG. As described above, it is preferable that the weighting factors α, β, and γ are individually obtained on each of the 12 sides. However, for the sides parallel to each other, the same value may be used as the weighting coefficients α, β, and γ.

The above description of the reference reflection coefficient to be obtained for the secondary color and the tertiary color can be easily generalized to the case of the N-order color. That is, when it is desired to obtain the reflection coefficient of the target color that is the N-order color, the end points and the midpoint of each of the N · 2 ^(N−1) sides forming the N-dimensional color space including the target color are calculated. Reflection coefficient and weighting coefficient α, β, γ in
May be obtained in accordance with the procedures of steps S1 to S4 in FIG. Then, by executing the processing of step S5 (FIG. 7), the reflection coefficient, the spectral reflectance, and the illuminance spectrum of the target color, which is the N-order color, can be obtained.

When the reflection coefficient of the target color, which is the N-order color, is to be obtained, N · 2 which forms the N-dimensional color space including the target color is used.
N.2 ^(N-1) virtual primary colors obtained by projecting target colors on ^(N-1) sides are used. For these virtual primary colors, the dot area ratio of one of the N types of inks of the target color is set to a value equal to the target color, and the dot area ratio of the other ink is set to 0.
% Or 100%. As described above, since the virtual primary color used when obtaining the reflection coefficient of the target color, which is the N-order color, is uniquely determined from the dot area ratio of the target color, the above-described step S12 in FIG. ,
After determining the combination of the reference points of the virtual secondary colors in S13, the process may proceed to step S16 or later immediately.

E. Details of Method of Determining Reflection Coefficient for Secondary Color: As described above, the diffuse reflection coefficient at an arbitrary halftone dot area ratio of the secondary color of magenta and cyan is given by Expression 14. The problem here is that the four weighting factors C ₁ included in equation (14). ~C is a value of _4. Four weighting factors C ₁ -C _4, for example given by the following equation 27.

[0126]

[Equation 27]

Here, ξ _M and η _M are weighting factors that depend on the halftone dot area ratio d _M of magenta, and ξ _C and η _C are weighting factors that depend on the halftone dot area ratio d _C of cyan. Also, m
Is a constant. The value of m is preferably 1, 2, 0.5 or the like, and particularly preferably m = 2. Four weighting factors C ₁ ~
The denominator of C ₄ is common, and the weight coefficient C ₁ ＣC ₄ are set to be 1. The values of the weighting factors ξ _M , η _M , ξ _C , and η _C depending on the dot area ratio are determined as follows.

FIG. 16 is an explanatory diagram showing a method for determining the diffuse reflection coefficient Sb of the secondary color using the equations (14) and (27). FIG. 16A shows substantially the same contents as FIG. 3B described above. The diffuse reflection coefficient Sb (d _{C / M} , λ) at an arbitrary halftone dot area ratio d _{C / M} is obtained by projecting a target point (black square) of a secondary color onto four sides of a secondary color plane. Diffuse reflection coefficient Sb at four determined reference points (white squares)
(D _{0 / M} , λ), Sb (d _{100 / M} , λ), Sb (d
_{C / 0} , λ) and Sb (d _{C / 100} , λ). The same applies to the specular reflection coefficient. The reflection coefficients at the four reference points are determined according to the above-described method of determining the reflection coefficient of the primary color.

FIGS. 16B and 16C show the weighting factors ξ _M , η _M , which depend on the dot area ratios d _M , d _C of each ink.
It shows changes in ξ _C and η _C. FIG. 16 (B), (C)
, The weighting factors ξ _M (d _M ), η _M
The values of (d _M ), ξ _C (d _C ), and η _C (d _C ) only depend on the dot area ratios d _M and d _C of the respective inks constituting the secondary color.

FIG. 16D is an explanatory diagram showing the meaning of the weight coefficient. Weighting factors ξ _M (d _M ), η _M (d _M ), ξ
_C (d _C ) and η _C (d _C ) are coordinate systems for correcting the reflection coefficient Sb (d _{C / M} , λ) of the target point (black square) from the reflection coefficient of the reference point (white square). (Referred to as a “correction coordinate system”). That is, the weighting factor associated with the dot percent d _C of cyan _{ξ C (d C), η} C (d C) represents the position of the reference point on the cyan axis A _C of the correction coordinate system.
Here, eta _C (d _C), the origin of the cyan axis A _C reference point from (point dot percent corresponding to 0%) corresponds to the distance to the (open squares), xi] _C (d _C) corresponding to the distance from the reference point (white square) to the end of the cyan axis a _C (point dot percent corresponding to 100%). Note that the weight coefficient ξ _C (d
The sum of _C ) and η _C (d _C ) does not necessarily have to be equal to 1.0, but is approximately a value close to 1.0. The same applies to the magenta axis A _M. Equations (14) and (27) represent the distances ξ _M , η _M , の between the target point (black square) and the reference point (white square) in the corrected coordinate system of FIG.
_It can be understood that this is an equation for calculating the reflection coefficient Sb (d _{C / M} , λ) of the target point by interpolating the reflection coefficient of the reference point based on _C and η _C.

The reflection coefficient at the reference point (open square) in FIG. 16D can be obtained according to the above-described method for determining the primary color reflection coefficient. Therefore, the weight coefficient ξ _M (d
_M ), η _M (d _M ), ξ _C (d _C ), and changes in η _C (d _C ) (FIGS. 16 (B), (C)) can be obtained in advance by using the above-described equations (14) and (27). Thus, the reflection coefficient of the target point (black square) of an arbitrary halftone dot area ratio d _{C / M} can be obtained.

Note that instead of Equation 27, the following Equation 28
Can also be used.

[0133]

[Equation 28]

Here, the value of m is particularly preferably 1. Expression 28 is almost the same as Expression 27, and distances ξ _M , η _M , ξ _C , η between the target point (black square) and the reference point (white square).
_This means that by interpolating the reflection coefficient of the reference point based on _C , the reflection coefficient Sb (d _{C / M} , λ) of the target point can be obtained.

The changes in the weighting factors ξ _M , η _M , ξ _C , and η _C are determined as follows in the same manner as the method of determining the weighting factors α, β, and γ of the primary colors described above. First, the weighting factors ξ _M ,
For η _M , ξ _C , and η _C , the primary color weighting factors α,
The following equation 29, similar to equations 24 and 25 for β and γ,
30 holds.

[0136]

(Equation 29)

[0137]

[Equation 30]

As shown in Equation 30, the matrix V
_{org #} is the wavelength range of visible light (λmin to λmin) for an arbitrary halftone dot area ratio d _k (subscript k means one type of ink).
λ max) for multiple wavelength values
represents the value of b (d _k , λ). The matrix K in Equations 29 and 30 represents the weighting factors ξ _k (d _k ) and η _k (d _k ). The matrix V _{prim #} has a wavelength range of visible light (λmin to λma
x), the reference diffuse reflection coefficients Sb (0%, λ) and Sb (100%,
λ). For example, if the wavelength λ of visible light is divided into 60 wavelength regions, Equation 29 is equivalent to a simultaneous equation including 60 equations.

Equations 29 and 30 hold for each ink constituting the target secondary color. For example, among the four sides constituting the two-dimensional color space of FIG. 16A, on the side (cyan axis) A _C where magenta is 0%, Equations 29 and 30 (where the subscript k means cyan) Are satisfied, and also on the side (magenta axis) A _M where cyan is 0%, Equations 29 and 30 (at this time, the subscript k
Means magenta) independently. Then, on each of these sides, when a matrix K given by the following equation 31 is obtained, 11 sets of weighting factors ξ _k (d _k ), η _k
(D _k ) (d = 0%, 10%... 100%) are obtained.

[0140]

(Equation 31)

FIGS. 16B and 16C show the changes in the weighting factors 重 み_k (d _k ) and η _k (d _k ) thus obtained.

As shown in FIGS. 16B and 16C, instead of calculating the changes of the weighting factors ξ _M , η _M , ξ _C , and η _C used in Expression 27 or Expression 28, ,
Weighting coefficient C ₁ used in Expression 14 It is also possible to previously obtained a change in -C ₄ directly. Where weighting factor ξ
Changes in _M , η _M , ξ _C , and η _C are represented by weight coefficients C ₁ Since moderate compared to the change of -C _4, weight coefficient _{ξ M, η M, ξ C} ,
Using the change in η _C has the advantage that the reflection coefficient can be more accurately interpolated.

The weighting factors ξ _k (d _k ) and η _k (d _k ) obtained for the diffuse reflection coefficient Sb can be used for the specular reflection coefficient Ss. Of course, the weighting factors ξ _k (d _k ) and η _k (d _k ) for the specular reflection coefficient Ss are
The weight coefficient of the diffuse reflection coefficient may be obtained separately.

As described above, if the weighting factors ξ _k (d _k ) and η _k (d _k ) are determined in advance for each ink of the target secondary color, the above-described equations (14) and (27) (or 14 and Equation 28), the diffuse reflection coefficient Sb of a secondary color having an arbitrary halftone dot area ratio can be obtained. Similarly, the specular reflection coefficient Ss can be obtained. Therefore, by substituting these reflection coefficients Sb and Ss into the above-described equation 8, the illuminance spectrum I of the secondary color is determined, and the color data X,
Y and Z can be calculated.

FIG. 17 shows the diffuse reflection component S for the secondary color.
It is the graph which compared the measured value of b (d, (lambda)) * cos (theta) (shown by a solid line) with the simulation result (shown by a broken line) by Formula 14 and Formula 27. FIG. 17 shows the result regarding the secondary color in which the halftone dot area ratio d _{M of} magenta is constant at 50% and the halftone dot area ratio d _{C of} cyan takes a value from 0% to 100% every 10%. . The solid line and the dashed line almost coincide with each other, and it can be seen that both coincide well. Similarly, it was confirmed that the actual measurement value and the simulation result of the specular reflection component were in good agreement.

F. More Accurate Method of Determining Reflection Coefficient for Secondary Color: FIG. 18 is an explanatory diagram showing a method of more accurately determining the reflection coefficient of a secondary color. In order to more accurately determine the reflection coefficient of the target color (black square), which is a secondary color, first, four sides A _C1 , A _C2 , and A _C that form the outer edge of the two-dimensional color space including the target color _For the reference points (white squares) where the target color is projected on _M1 and A _M2 , the reflection coefficient Sb (d _{C / 0} ,
λ), Sb (d _{C / 100} , λ), Sb (d _{0 / M} , λ), S
b (d _{100 / M0} , λ) is obtained. At this time, each side A _C1 ,
The weighting factors α, β, and γ are obtained independently for each of A _C2 , A _M1 , and A _{M2 in} accordance with the above-described equations 24 to 26. Therefore, for the four sets of weighting factors α, β, and γ for the four sides A _C1 , A _C2 , A _M1 , and A _M2 , changes as shown in FIG. 14 described above are determined.

Further, Expressions 14 and 27 (or Expressions 14 and 27)
The weighting factors ξ _M , η _M , ξ _C , and η _C used in 28) are also applied to the four sides A _C1 , A _C2 , and A _C shown in FIG.
Each of _M1 and A _M2 is determined according to the above-mentioned equations 29 to 31. FIG. 18A shows four sets of weighting factors (ξ _M1 , η _M1 ), (ξ _M2 , η _M2 ), (ξ
_C1 , η _C1 ) and (補正_C2 , η _C2 ) are shown as corrected coordinate systems. The length of the four sides A _C1 , A _C2 , A _M1 , and A _M2 is equal to the sum (重 み + η) of the weight coefficients of each set. Also, a side A _C1 (cyan axis) where magenta is constant at 0%, and a side where cyan is 0%
The sides A _M1 (magenta axis) with a constant% are perpendicular to each other. Therefore, these four sides A _C1 , A _C2 , A _M1 , A _M2
Is uniquely determined.

When calculating the reflection coefficient of the target point (black square) in the corrected coordinate system as shown in FIG. 18A, the above-described equations (14) and (27) (or equations (14) and (28)) are used in FIG. The weighting factors ξ _M , η _M , ξ _C , and η _C are used. Here, xi] _M is the distance of the reference point on the side A _C2 from (open squares) to a target point (closed square), eta _M is the target point from the reference point on the sides A _C1 (open squares) (closed squares ). The same applies to ξ _C and η _C. Since the positions of the four reference points (white squares) are determined as shown in FIG. 18A, the distances ξ _M , η _M , ξ _C ,
η _C can also be determined from the positions of these reference points. In addition,
In FIGS. 18A and 18B, the position of the target point (black square) is on a line connecting reference points on opposite sides.

The equations (14) and (27) are obtained as shown in FIG.
(Or the weighting factors ， _M , η used in Equations 14 and 28)
_M, if xi] _C, to determine the eta _C, the reflection coefficient of the target color is a secondary color can be determined more accurately.

G. Determination method of reflection coefficient for tertiary color:
The diffuse reflection coefficient of the tertiary color at an arbitrary halftone dot area ratio is given by Expression 15 described above. FIG. 19 is an explanatory diagram showing a method for determining the reflection coefficient of the tertiary color according to Expression 15. The diffuse reflection coefficient Sb (d of the target color (white triangle) of the tertiary color
When calculating _{C / M / Y} , λ), first, a virtual secondary color that is a plane including the target point and is perpendicular to the axis of one ink (eg, cyan) constituting the tertiary color Plane PTP is 1
Then, four reference points (indicated by black squares) are set by projecting target points on four sides of the virtual secondary color plane PTP. The reflection coefficient of the target point is represented by a linear combination of the reflection coefficients of these four reference points. FIG.
FIG. 4 is an explanatory diagram showing a relationship between a target point (white triangle) and a reference point (black square) on the virtual secondary color plane PTP. Virtual 2
The relationship between the target color (white triangle) and the reference color (black square) on the next color plane PTP is the relationship between the target color (black square) and the reference color (white square) of the secondary color shown in FIG. It is easy to understand that the relationship is the same.

The reflection coefficients at the four reference points (black squares) in FIG. 19 are respectively determined by the method for determining the reflection coefficient of the secondary color described with reference to FIG. 16 or FIG. That is, in the example of FIG. 19, the following four virtual secondary color planes are used when calculating the reflection coefficients at the four reference points.

(1) White (W) / Cyan (C) / Blue (BL) / Magenta (M) plane (WC-BL-M)
(Plane) (2) White (W) / Cyan (C) / Green (G)
/ Yellow (Y) plane (WCGY plane) (3) Yellow (Y) / Green (G) / Black (B
K) / Red (R) plane (YG-BK-R plane) (4) Magenta (M) / Blue (BL) / Black (B
K) / Red (R) plane (M-BL-BK-R plane)

The names of colors other than white used in the above (1) to (4) are coordinate points where the density of each color is 100% (vertices indicated by black circles in FIG. 19).
Means

In the example shown in FIG. 19, a virtual secondary color plane PTP having a constant cyan halftone dot area ratio is used. However, in general, the halftone dot area ratio of any ink constituting the tertiary color is constant. And 3 using a virtual secondary color plane including the target color.
It is possible to obtain the reflection coefficient of the target color which is the next color.

FIG. 21 is an explanatory diagram showing a correction coordinate system for a tertiary color. Weighting factor ξ used in FIG.
_M , η _M , ξ _Y and η _Y can be used as they are when determining the reflection coefficient of the reference point (black square), which is a virtual secondary color. That is, the weighting factors ξ _M and η _M depending on the magenta halftone dot area ratio are the values used in determining the reflection coefficient of the reference point (black square) on the WC-BL-M plane. The weighting factors ξ _Y and η _{Y that} are used and depend on the halftone dot area ratio of yellow were used in determining the reflection coefficient of the reference point (black square) on the WCGY plane. The value is used as is.

As described above, if the diffuse reflection coefficients Sb with respect to the four reference points are determined, the diffuse reflection coefficient S3 of the tertiary color having an arbitrary halftone dot area ratio can be obtained according to the above-described equation (15).
b can be obtained. Similarly, the specular reflection coefficient S
s can also be determined. Therefore, these reflection coefficients S
By substituting b and Ss into Equation 8 above, 3
The illuminance spectrum I of the next color can be determined.
, The color data X, Y, Z can be calculated.

FIG. 22 is an explanatory diagram showing a method for more accurately determining the reflection coefficient of the tertiary color. When it is desired to more accurately determine the reflection coefficient of the target color (white triangle) that is the tertiary color, first, the above-described processing is performed on each of the 12 sides forming the outer edge of the three-dimensional color space including the target color. Formula 29-
In accordance with 31, the weight coefficients ξ and η are independently obtained.

FIG. 22 shows a correction coordinate system represented by the twelve sets of weighting factors thus determined. The length of the twelve sides is equal to the sum of the weighting coefficients of each set (の + η).
The side A _C1 (magenta axis) where magenta is constant at 0%, the side A _M1 (magenta axis) where cyan is constant at 0%, and the side A _Y1 where yellow is constant at 0% are perpendicular to each other. Therefore, the shape of the distorted three-dimensional correction space composed of these 12 sides is uniquely determined.

In the distorted three-dimensional correction space shown in FIG. 22, the reflection coefficient of the target color (white triangle) also has four reference points Re.
It can be determined according to Equation 15 based on the reflection coefficients of f1 to Ref4 (black squares). Four reference points Re
The reflection coefficients of f1 to Ref4 (black squares) are determined on the virtual secondary color plane including each reference point according to the method described with reference to FIG. However, each virtual secondary color plane (for example, the YG-BK-R plane) is not strictly speaking a plane but a twisted curved surface. In the present embodiment, the calculation is simplified assuming that each virtual secondary color surface is not a curved surface but a plane as described below.

FIG. 23 shows a correction coordinate system on the YG-BK-R plane which is the upper surface of the three-dimensional correction space of FIG. The weighting factors η _C3 , ξ _C3 ,
The values of η _C4 , ξ _C4 , η _M3 , ξ _M3 , η _M4 , and ξ _M4 are calculated from the halftone dot area ratio of the reference point (white square) of the virtual primary color on each side as in FIG. It is determined. The YG-BK-R plane has these weighting factors η _C3 , ξ _C3 , η _C4 , ξ _C4 ,
It is assumed to be a rectangle having four sides defined by η _M3 , ξ _M3 , η _M4 , ξ _M4 . Weighting factors ηa, ξa, ηb, ξ used in determining the reflection coefficient of the reference point Ref1.
The value of b corresponds to the distance between the reference point Ref1 and the reference points (white squares) of the four virtual primary colors.

FIG. 24 is an explanatory diagram showing a correction coordinate system on a virtual secondary color plane including the target color of the tertiary color. The four sides of the corrected coordinate system correspond to four reference points Ref1 to Re shown in FIG.
f4. The values of the weighting factors ηa and ξa on the side including the first reference point Ref1 are the same as the weighting factors ηa and ξa used in FIG. Also, the weighting factors ηa ′ to ηa ″ ′ and ξa ′ to に お け る
a ′ ″ is the same as the weighting factor used in the virtual secondary color plane including the respective reference points. By using these weighting factors ηa to ηa ′ ″ and ξa to ξa ″ ′, weighting factors η ₁ , ξ ₁ , The values of η ₂ and ξ ₂ depend on the reference point R
This corresponds to the distance between ef1 and the reference points (white squares) of the four virtual primary colors. These weighting factors η ₁ , ξ ₁ , η
_2, in the case of using the xi] _2, instead of the equations 27 and 28 described above, the following formula 32 and 33 are used.

[0162]

(Equation 32)

[0163]

[Equation 33]

Therefore, the reflection coefficient of the target color, which is the tertiary color, can be determined using Expressions 15 and 32 (or Expressions 15 and 33).

FIG. 25 shows the spectral reflectance I /
6 is a graph showing a simulation result of φ. Here, cyan, magenta, and yellow are mixed in equal amounts by 1
For one type of gray color, the actual measured value of the spectral reflectance is indicated by a solid line, and the simulation result (interpolated value) is indicated by a broken line. The estimated value of the spectral reflectance by simulation is slightly lower than the actually measured value, but it is almost a good result.

In addition, cyan, magenta, and yellow are
1331 kinds of colors are generated by independently changing every 10% from 0% to 100%, and the color difference ΔE (defined by the Lab color system) between the actually measured color and the estimated color is generated for the 1331 colors. Color difference) was calculated. The average value of the color difference ΔE is 1.241, and the maximum value of the color difference ΔE is 3.6.
55. These results also indicate that the tertiary color simulation described above gives good results.

H. Method of Determining Reflection Coefficients for Quaternary Colors and Higher Colors: The above-described method of determining reflection coefficients for tertiary colors can be easily extended to quaternary and higher order colors. The reflection coefficient for the quaternary color can be determined according to Equations 16 and 32 (or Equations 16 and 33) described above.

In general, the reflection coefficient for the n-th order color (n is an integer of 2 or more) is calculated by the above-described formulas (17) and (18) and formula (3).
2 (or Equations 17 and 18 and Equation 33). At this time, as in the description with reference to FIGS. 23 and 24, the values of the weighting coefficients η and 求 め る used to determine the reflection coefficient of the n-th color are the reflection coefficients of the reference color that is the (n−1) -th color What was used when asking for can be used.

I. Simulation of color printed matter: Steps S6 and S7 in FIG. 6 use the reference reflection coefficients Sb and Ss obtained by the procedures of steps S1 to S4 and the weighting coefficients α, β, γ, ξ, and η to output the output device. Indicates a procedure for reproducing a printed matter. First, in step S6,
A rendering process using computer graphics is performed to generate color data for reproducing colors of a color print.

FIG. 26 is a block diagram showing a third embodiment according to the present invention.
FIG. 2 is a block diagram showing a computer system for reproducing a color print arranged in a three-dimensional space. This computer system includes a CPU 10 and a bus line 12. A ROM 14 and an R
AM 16, and a keyboard 30 and a mouse 32 via input / output interfaces 40 and 41.
, A digitizer 34, a color CRT 36, a magnetic disk 38, and a full-color printer 42.

In the RAM 16, the reflection coefficient determining means 44
And an application program for realizing the illuminance spectrum determining means 46 and the color data generating means 48. The reflection coefficient determination means 44 calculates
Further, the reflection coefficients Sb and Ss are determined in accordance with Expression (18). The illuminance spectrum determining means 46 calculates the above-described equation (10).
, The illuminance spectrum I (d, θ, ρ, λ) is determined. Further, the color data generating means 48 calculates the above-mentioned equation 9
, The tristimulus values X (d), Y (d), and Z (d) are obtained, and are converted into color data corresponding to the color system of the output device. The function of each of these units is realized by the CPU 10 executing an application program stored in the RAM 16. The computer system also stores an application program for reproducing a color print placed in a three-dimensional space by performing a so-called rendering process.

A computer program for realizing the function of each of these means is a flexible disk or a CD-RO.
It is provided in a form recorded on a computer-readable recording medium such as M. The computer reads the computer program from the recording medium and transfers it to an internal storage device or an external storage device. Alternatively, a computer program may be supplied to a computer via a communication path. When implementing the functions of the computer program, the computer program stored in the internal storage device is executed by the microprocessor of the computer. Further, a computer may read a computer program recorded on a recording medium and directly execute the computer program.

In this specification, a computer is
The concept includes a hardware device and an operation system, and means a hardware device that operates under the control of the operation system. In the case where an operation system is unnecessary and a hardware device is operated by an application program alone, the hardware device itself corresponds to a computer. The hardware device includes at least a microprocessor such as a CPU and means for reading a computer program recorded on a recording medium. The computer program includes a program code that causes such a computer to realize the functions of the above-described units. Some of the functions described above may be realized by an operation system instead of the application program.

The "recording medium" in the present invention includes a flexible disk, a CD-ROM, a magneto-optical disk, an IC card, a ROM cartridge, a punch card, a printed matter on which a code such as a bar code is printed, and an internal storage of a computer. Device (RAM, ROM, etc.)
And various computer-readable media such as an external storage device.

FIG. 27 is an explanatory diagram showing the three-dimensional arrangement of the printed matter 50, the light source 52, the screen (CRT screen) 54, and the observation point 56 when the color of the printed matter is reproduced by the ray tracing method. Ray tracing method is 3
This is a well-known rendering technique in the field of three-dimensional computer graphics, and each pixel P on the screen 54 is
In this method, the color data (RGB data) of each pixel PX on the screen 54 is obtained by reversing the line of sight RL passing through the X and the observation point 56 from the observation point 56 to the light source 52. The printed matter 50 is divided into a plurality of minute polygons EL in advance. This minute polygon EL corresponds to a target point in the present invention. Each of the minute polygons EL is a plane, but the whole printed matter 50 can be modeled to be three-dimensionally curved. The incident angle θ and the deviation angle ρ are, as shown in FIG.
Are defined in the minute polygon EL that exists at the position where.

When performing ray tracing, first,
The reflection coefficient determining means 44 calculates the reflection coefficients Sb (d, λ) and Ss (d, λ) according to the above-described equations (12) to (18).
Ask for. Then, the illuminance spectrum determining means 46 calculates the illuminance spectrum I (d, θ,
ρ, λ). The color data generating means 48 integrates the illuminance spectrum I (d, θ, ρ, λ) thus obtained in accordance with the above-described equation 9 to obtain the tristimulus value X.
Find YZ.

In step S7 of FIG. 6, the color data generating means 48 converts the tristimulus values XYZ thus obtained into RGB data and assigns them to pixels on the color CRT 36. Specifically, the RGB data is stored at the pixel position of the frame memory. A color print is displayed on the color CRT 36 according to the RGB data in the frame memory. Note that the conversion from the XYZ color system to the RGB color system depends on the characteristics of the output device. Therefore, by using a conversion formula corresponding to the output device, a faithful conversion can be made within the color expression range of the output device. Color reproduction can be performed.

As described above, in this embodiment, the reflection coefficients Sb, Sb of the target color, which is the N-order color (N is an integer of 3 or more).
Since s is determined by the linear combination of the reflection coefficients of the four reference colors that are the (N−1) -order colors, the reflection of the target color of the N-th color is smaller than when five or more reference colors are used. Coefficient S
b and Ss can be determined with a small amount of calculation. Further, from these reflection coefficients Sb and Ss, the color data (XYZ, RGB data, etc.) of the N-order color can be obtained. Therefore, it is possible to accurately reproduce the N-th color printed matter having an arbitrary halftone dot area ratio with a relatively small amount of calculation.

J. Modifications regarding simulation of printed matter: With respect to the above-described simulation, the following modifications are possible.

(1) FIG. 28 shows the weight coefficient α shown in FIG.
It is the graph which simplified change of (d), (d), and (g). In FIG. 28, when the halftone dot area ratio is in the range of 0% to 50%, the value of the first weighting coefficient α (d) decreases linearly from 1.0 to 0, while the second weighting coefficient α (d) decreases. Coefficient β (d)
Increases linearly from 0 to 1.0. Also,
When the halftone dot area ratio is in the range of 50% to 100%, the value of the second weighting coefficient β (d) decreases linearly from 1.0 to 0, while the third weighting coefficient γ (d ) Is from 0 to 1.
It increases linearly to zero. In other words, when the dot area ratio is in the range of 0% to 50%, the value of the reflection coefficient (Equation 12) at an arbitrary dot area ratio d is equal to the first and second reference reflection coefficients Sb (0%, λ) and Sb (50%, λ) by linear interpolation. Also, the dot area ratio is 50% or more.
In the range of 100%, the value of the reflection coefficient at an arbitrary halftone dot area ratio d is equal to the second and third reference reflection coefficients Sb (50%,
λ) and Sb (100%, λ) by linear interpolation.

Since the graph of FIG. 28 is close to the graph of FIG. 14 obtained in the above-described embodiment, even if the weighting coefficients of FIG. 28 are used, a simulation of a printed matter can be performed with considerable accuracy. When the graph of FIG. 28 is used, step S4 of FIG. 6 can be omitted. In this case, the halftone dot area ratio d _k itself is used as the weighting coefficient η _k (d _k ) used when obtaining the reflection coefficient of the secondary color or higher color, and ξ _k (d _k ) Can be (1-d _k ).

(2) With respect to the ink of the semi-printing plate, the simultaneous equations given by Expressions 24 and 25 described above become linearly dependent, and the weighting factors α, β, and γ may not be obtained from Expression 26 in some cases. Similarly, the simultaneous equations given by Equations 29 and 30 are also linearly dependent, and the weighting factors ξ _k and η _k are
In some cases, it cannot be obtained from 1. The simultaneous equations given by Expressions 24 and 25 become linearly dependent because the shape of the diffuse reflection component (the shape of the eleven graphs in FIG. 12 described above) for each color chart of the primary gradation becomes similar. Means that In such a case, the weighting factors α,
As β and γ, those shown in FIG. 28 can be used.
In this case, the real halftone dot area ratio d _net calculated according to the well-known Murray-Davis formula can be used as the weighting coefficient η _k used for obtaining the reflection coefficient of the higher-order color. At this time, the other weighting coefficient ξ _k is (1-
d _net ).

(3) In the above embodiment, the weighting factors ξ _k and η _k are calculated for each ink. However, the weighting factors ξ _k and η _k obtained for one type of ink are diverted to other inks. You may make it. The same applies to the primary color weighting factors α, β, γ.

K. Application to conversion of color expression data: In the above-described simulation, the method used to determine the reflection coefficients Ss and Sb is a method of directly converting the dot area ratio of CMYK into tristimulus values of the XYZ color system. Can be used as

When the three stimulus values of the XYZ color system are directly obtained from the dot area ratio of the CMYK component,
And an expression obtained by replacing the reflection coefficient Sb in Expressions 14 to 17 with tristimulus values. For example, tristimulus values (X (d _C ), Y (d _C ), Z (d
As an expression for calculating _C )), the following Expression 34 is used instead of Expression 12 described above.

[0186]

(Equation 34)

That is, an arbitrary halftone dot area ratio d _{C of} cyan
Are represented by a linear combination of the tristimulus values at three reference halftone dot area ratios (d _C = 0%, 50%, 100%). Note that the weighting factors α _C , β
_C and γ _C may use the same value common to the three stimulus values, or may use different values for each of the three stimulus values.

When calculating tristimulus values for a target color of a quaternary color composed of four inks of cyan, magenta, yellow, and black, the following equation 35 is used instead of the above-mentioned equation 16. Is done.

[0189]

(Equation 35)

The four sets of tristimulus values included in the right side of Expression 35 are tristimulus values at four reference points where the target color is projected onto four sides of the virtual secondary color plane including the target color. is there.
This virtual secondary color plane is obtained by fixing the dot area ratios of cyan and black to values equal to the dot area ratios d _c and d _K of the target color. That is, the tristimulus values of the XYZ color system for the target color of the quaternary color are obtained by fixing the halftone dot area ratio of one of the two specific inks to 0% or 100%. Given by selecting four reference colors and determining a linear combination of tristimulus values for these four reference colors.

In general, a tristimulus value (X (d (d)) for a target color of an n-th color (n is an integer of 2 or more) having an arbitrary density.
₍₁ → _n ), Y (d ₁ → _n ), Z (d ₁ → _n )), the following equation 36 is used instead of equation 17 described above.

[0192]

[Equation 36]

Here, for example, X (d _i = 0), X (d _i
= 100) means that the halftone dot area ratio of the i-th ink is 0% and 1
It means the X stimulus value when each is set to 00% and the dot area ratio of the other inks is set equal to the dot area ratio of the target color. Also, X (d _j = 0), X (d _j = 10
0) indicates that the dot area ratio of the j-th ink is 0% or 100%.
, Respectively, and the X stimulus values when the dot percentages of the other inks are set equal to the dot percentages of the target color. That is, the tristimulus value of the XYZ color system for the target color of the n-th color is obtained by fixing the halftone dot area ratio of one of the two specific inks to 0% or 100%. Given by selecting four reference colors and determining a linear combination of tristimulus values for these four reference colors.

If n is set to 2, 3, and 4 in the above equation (36), equations corresponding to the above equations (14) to (16) are obtained.

When the tristimulus values of the XYZ color system are determined from the halftone dot area ratios of the CMYK components, these equations 34 to 3 are used.
6, the processing may be performed in accordance with the procedure shown in FIG. At this time, the “reflection coefficients Sb, Ss” in the flowchart of FIG. 7 are read as “XYZ colorimetric tristimulus values”, and step S20 is omitted.

In general, XY for the target color, which is the Nth color
When it is desired to obtain the tristimulus values of the Z color system, three end points and the midpoint of each of the N · 2 ^(N−1) sides constituting the N-dimensional color space including the target color are set in advance. Measure the stimulus value in advance. Also, weighting factors α, for the virtual primary colors on each side,
β and γ are obtained in advance according to the same procedure as in step S4 of FIG. Then, by executing the processing of FIG.
The tristimulus values for the target color, which is the Nth color, can be obtained.

FIG. 29 is a graph showing a comparison between a color value obtained by actually measuring a color patch printed with CMYK ink and a color value obtained by the above-described conversion method. However, FIG. 29 shows the tristimulus values of the XYZ color system as L *
a * b * The value converted to the color value of the color system is used, and L *
It is a perspective view of a three-dimensional color space of a * b * color system. The black points in the figure are measured values, and the white points are conversion results. The line segment connecting the black point and the white point indicates that they are values for the same target color. In the target color in which the measured value (black point) matches the conversion result (white point), only the black point is visible. As can be seen from this figure, the measured value and the conversion result for the same target color are relatively well matched, and it can be understood that the color conversion can be performed with considerably high accuracy.

The halftone dot area ratio of CMYK is represented by 3 in the XYZ color system.
The above-described technique of converting into a stimulus value generally involves the following processing with respect to a specific target color that is an N-order color reproduced by N (N is an integer of 3 or more) primary colors included in an arbitrary first color system. It is applicable when converting the first color expression data representing the densities of the N primary colors into the second color expression data related to the target color. An arbitrary color system other than the CMYK color system can be selected as the first color system. Further, as the second color expression data, it is possible to select the reflection coefficients Ss and Sb and a color specification value of a second color system different from the first color system. Here, the “color specification value” means a value for representing a color in a specific color system. As a color system,
For example, a CMYK color system used for printing, a device-dependent color system that depends on an output device (a display device such as a CRT or a printer), and a device-independent color system that does not depend on an output device. There is.
CIE-X is used for the device independent color system.
YZ color system, CIE-RGB color system, CIE-L * a *
b * color system and the like are included.

The term “color expression data” has a broad meaning that includes the color values of such a color system and the reflection coefficients Ss and Sb. The reason why the color values and the reflection coefficients Ss and Sb are called “color expression data” is that the color values are also the reflection coefficients Ss.
This is because both s and Sb are data that can be used to reproduce the target color, which is the Nth color.

According to such a method of converting color expression data, the second color expression data for an arbitrary target color, which is the N-th color, is converted into four basic reference colors on a virtual secondary color plane including the target color. (This algorithm is called a “virtual secondary color conversion algorithm”). Therefore, there is an advantage that the second color expression data of the target color can be obtained based on relatively few data. In particular, as for the higher-order target colors equal to or higher than the tertiary color, as shown in FIG. 7, the conversion of the color expression data is performed by applying the virtual secondary color conversion algorithm hierarchically. Even if the degree N of the color is increased, the conversion can be easily performed in the same procedure. This advantage is particularly effective when the conversion is realized by an application program. In addition, since a hierarchical conversion procedure is adopted, based on less data than in the conventional method of dividing the color space into many rectangular parallelepipeds,
Relatively accurate conversion can be performed.

[Brief description of the drawings]

FIG. 1 is an explanatory diagram showing a state in which incident light is reflected by ink applied on printing paper.

FIG. 2 is an explanatory diagram showing a relationship between a light source, a printed matter, and a visual system (observer).

FIG. 3 is an explanatory diagram showing a method of calculating a reflection coefficient for colors from a primary color to a tertiary color.

FIG. 4 is an explanatory diagram showing a method of determining a diffuse reflection coefficient Sb (d, λ) for a primary color.

FIG. 5 is a conceptual diagram illustrating an advantage of a method of determining a reflection coefficient for a primary color by interpolating three reference reflection coefficient values.

FIG. 6 is a flowchart showing the procedure of the embodiment.

FIG. 7 is a flowchart showing the procedure of the embodiment.

FIG. 8 is an explanatory diagram showing processing contents in step S1.

FIG. 9 is a conceptual diagram showing an apparatus for measuring spectral reflectance.

FIG. 10 is a graph showing measured values of spectral reflectance.

FIG. 11 is an explanatory diagram showing a procedure for determining a diffuse reflection component and a specular reflection component from spectral reflectance and determining weighting factors α, β, and γ.

FIG. 12 is a graph plotting diffuse reflection components Sb (d, λ) · cos θ extracted under the conditions of ρ = 35 ° and θ = 8 °.

FIG. 13 shows a specular reflection component S estimated under the condition of θ = 8 °.
The graph which plotted s (d, (lambda)).

FIG. 14 shows the weighting factors α (d), β obtained in the embodiment.
7D is a graph showing changes in γ (d).

FIG. 15 is a graph comparing a measured value of a diffuse reflection component Sb (d, λ) · cos θ with a simulation result.

FIG. 16 is an explanatory diagram illustrating a method for determining a reflection coefficient of a secondary color.

FIG. 17 shows a diffuse reflection component Sb (d, λ) related to a secondary color.
A graph comparing the actually measured value of the cos θ (solid line) with the simulation result (dashed line) by the equation (14).

FIG. 18 is an explanatory diagram showing a method for more accurately determining a reflection coefficient of a secondary color.

FIG. 19 is an explanatory diagram showing a method for determining a reflection coefficient of a tertiary color.

FIG. 20 is an explanatory diagram showing a relationship between a target point (white triangle) and a reference point (black square) on a virtual secondary color plane PTP.

FIG. 21 is an explanatory diagram showing a correction coordinate system for a tertiary color.

FIG. 22 is an explanatory diagram showing a method for more accurately determining a reflection coefficient of a tertiary color.

FIG. 23 is an explanatory diagram showing a correction coordinate system on a YG-BK-R plane.

FIG. 24 is an explanatory diagram showing a correction coordinate system on a virtual secondary color plane including a target color of a tertiary color.

FIG. 25 is a graph showing a simulation result of the reflectance I / φ for the tertiary color.

FIG. 26 is a block diagram showing a computer system which reproduces colors of a printed matter arranged in a three-dimensional space by applying an embodiment of the present invention.

FIG. 27 is an explanatory diagram showing a three-dimensional arrangement when colors of a printed matter are reproduced by a ray tracing method.

FIG. 28 shows simplified weighting factors α (d), β (d), γ
The graph which shows the change of (d).

FIG. 29 is a graph showing a comparison between a color value obtained by actually measuring a color patch printed with CMYK ink and a color value obtained according to the conversion method of the embodiment.

[Explanation of symbols]

 Reference Signs List 10 CPU 12 Bus line 14 ROM 16 RAM 20 Measurement sample 22 Light source 24 Spectrophotometer 30 Keyboard 32 Mouse 34 Digitizer 36 Color CRT 38 Magnetic disk 40, 41 Input / output interface Face 42 Full-color printer 44 Reflection coefficient determining means 46 Illuminance spectrum determining means 48 Color data generating means 50 Printed matter 52 Light source 54 Screen 56 Observation point

Claims (11)

[Claims] 1. An N-order color (N is 3) arranged in a three-dimensional space.
A method of reproducing the color print by an output device by performing a rendering process on the color print of the above (integer), wherein (a) irradiating a target point on the color print with light having a predetermined luminance spectrum φ. In this case, the step of defining the illuminance spectrum I of the reflected light observed at the predetermined observation point by Expression 1; and (b) in the N-dimensional color space including the target color of the target point, which is the N-order color, ΔN (N−N−N) is obtained when the dot area ratio of (N−2) types of ink among the N types of inks constituting the Nth color is fixed to a value equal to the dot area ratio of the target color. 1) selecting one of the 2/2 virtual secondary color planes; and (c) projecting the coordinate points of the target color onto four sides of the selected virtual secondary color plane. By doing so, 4
(D) determining a first reflection coefficient Sb and a second reflection coefficient Ss included in Equation 1 for each of the four basic reference colors;
(E) the first and second reflection coefficients S for the target color
determining the values of b and Ss by a linear combination of the values of the first and second reflection coefficients Sb and Ss in the four reference colors, respectively; (f) first and second values for the target color Determining an illuminance spectrum I of the reflected light according to Equation 1 using the reflection coefficients Sb and Ss; (g)
Obtaining color data representing the target color in a color system suitable for the output device using the illuminance spectrum I of the reflected light. (Equation 1) Here, d ₁ → _N is the dot area ratio of N kinds of target colors at the target point, λ is the wavelength of light, Sb (d ₁ → _N , λ), Ss
(D ₁ → _N , λ) is the first and second reflection coefficients for the Nth color, θ is the reflection angle, fb (θ) is a characteristic dependent on θ, and ρ is the deviation between the light reflection direction and the observation direction. Angle, fs (ρ) is ρ
Ie (λ) is an illuminance spectrum of ambient light observed at the observation point. 2. The method for simulating a color printed matter according to claim 1, wherein, when N is 4 or more, the step (d) includes:
(1) a step of repeating the first process while sequentially changing a parameter n (n is an integer equal to or less than (N-1) equal to or greater than 3) from (N-1) to 3, wherein the first process is Each of the four basic reference colors is regarded as a virtual n-th reference color, and (n-2) of the n kinds of inks constituting the virtual n-th reference color in an n-dimensional color space including each virtual n-th reference color. ) Of the (n (n-1) / 2) virtual secondary color planes obtained when the dot area ratio of each type of ink is fixed to a value equal to the dot area ratio of the virtual n-th reference color. And projecting the coordinate points of the virtual n-th reference color on the four sides of the selected virtual secondary color plane, so that four virtual (n-
1) a process of setting a next reference color; the step (1) is a step of setting a plurality of virtual secondary reference colors by repeating the first process; and the step (d) is further performed. (2) repeating a second process while sequentially changing a parameter m (m is an integer of 3 or more and N or less) from 3 to N, wherein the second process includes the step of: The first and second reflection coefficients for each virtual m-th reference color are obtained by a linear combination of the first and second reflection coefficients Sb and Ss for four virtual (m-1) -th reference colors set by projection. The step (2) is a step of determining the first and second reflection coefficients Sb and Ss for the four basic reference colors by repeating the second processing. How to simulate color prints Law. 3. The method for simulating a color printed matter according to claim 1, wherein the characteristic fb (θ),
fs (ρ) is a method of simulating a color print, each having the form of Equation 2. (Equation 2) Here, σ is a constant. 4. An N-order color (N is 3) arranged in a three-dimensional space.
A system that reproduces the color print with an output device by performing a rendering process on the color print of the above (integer), and irradiates a target point on the color print with light having a predetermined luminance spectrum φ. Means for defining the illuminance spectrum I of the reflected light observed at a predetermined observation point by Expression 3, and configuring the N-order color in an N-dimensional color space including the target color of the target point, which is the N-order color. ｛N (N) obtained when the dot area ratio of the (N-2) type ink among the N types of ink is fixed to a value equal to the dot area ratio of the target color.
Means for selecting one of -1) / 2} virtual secondary color planes; and projecting coordinate points of the target color on four sides of the selected virtual secondary color plane. Means for setting four basic reference colors on the four sides, and a first reflection coefficient Sb and a second reflection coefficient Ss included in Expression 3 are respectively determined for the four basic reference colors. Basic reference color determination means; and the first and second reflection coefficients Sb, S for the target color
means for determining the value of s by a linear combination of the values of the first and second reflection coefficients Sb, Ss in the four reference colors, respectively; and the first and second reflection coefficients Sb, Ss for the target color Means for determining the illuminance spectrum I of the reflected light according to Equation 3, and means for obtaining color data representing the target color in a color system suitable for an output device using the illuminance spectrum I of the reflected light. And an output device for outputting the target color in accordance with the color data. (Equation 3) Here, d ₁ → _N is the dot area ratio of N kinds of target colors at the target point, λ is the wavelength of light, Sb (d ₁ → _N , λ), Ss
(D ₁ → _N , λ) is the first and second reflection coefficients for the Nth color, θ is the reflection angle, fb (θ) is a characteristic dependent on θ, and ρ is the deviation between the light reflection direction and the observation direction. Angle, fs (ρ) is ρ
Ie (λ) is an illuminance spectrum of ambient light observed at the observation point. 5. A computer equipped with an output device, which performs rendering processing on a color print of Nth color (N is an integer of 2 or more) arranged in a three-dimensional space, thereby outputting the color print. A computer-readable recording medium on which a computer program for reproducing in a device is recorded.When a target point on the color print is irradiated with light having a predetermined luminance spectrum φ, the target point is observed at a predetermined observation point. And the function of defining the illuminance spectrum I of the reflected light by Equation 4 in the N-dimensional color space including the target color of the target point which is the N-order color. −２N (N) obtained when the dot area ratio of the N-2) types of inks is fixed to a value equal to the dot area ratio of the target color.
-1) / 2 function of selecting one of the virtual secondary color planes, and projecting the coordinate points of the target color onto four sides of the selected virtual secondary color plane A function of setting four basic reference colors on the four sides, and a first reflection coefficient Sb and a second reflection coefficient Ss included in Equation 4 are determined for the four basic reference colors, respectively. A basic reference color determination function, and the first and second reflection coefficients Sb, S for the target color
a function of determining a value of s by a linear combination of the values of the first and second reflection coefficients Sb and Ss in the four reference colors, respectively, and a first and second reflection coefficient Sb and Ss of the target color And a function of determining the illuminance spectrum I of the reflected light according to Equation 4, and using the illuminance spectrum I of the reflected light to obtain color data representing the target color in a color system suitable for the output device. A computer-readable recording medium storing a computer program for causing a computer to realize a function and a function of outputting the target color to the output device according to the color data. (Equation 4) Here, d ₁ → _N is the dot area ratio of N kinds of target colors at the target point, λ is the wavelength of light, Sb (d ₁ → _N , λ), Ss
(D ₁ → _N , λ) is the first and second reflection coefficients for the Nth color, θ is the reflection angle, fb (θ) is a characteristic dependent on θ, and ρ is the deviation between the light reflection direction and the observation direction. Angle, fs (ρ) is ρ
Ie (λ) is an illuminance spectrum of ambient light observed at the observation point. 6. N types (N is 3) included in the first color system
The first color expression data representing the densities of the N types of primary colors is converted to the second color expression data related to the target colors for a specific target color that is an N-order color reproduced by the above primary colors (A) N including the target color
In the three-dimensional color space, (N-
2) selecting one of {N (N-1) / 2} virtual secondary color planes obtained when the densities of the primary colors are fixed to values equal to the densities of the target colors; (B) setting four basic reference colors on the four sides by projecting coordinate points of the target color on the four sides of the selected virtual secondary color plane; Determining the value of the second color expression data for each of the four basic reference colors; and (d) determining the value of the second color expression data for the target color.
Determining each of the values of the color expression data by a linear combination of the values of the second color expression data in the four reference colors. 7. The method for converting color expression data according to claim 6, wherein, when said N is 4 or more, said step (c) comprises:
(1) a step of repeating the first process while sequentially changing a parameter n (n is an integer equal to or less than (N-1) equal to or greater than 3) from (N-1) to 3, wherein the first process is Each of the four basic reference colors is regarded as a virtual n-th reference color, and in the n-dimensional color space including each virtual n-th reference color, (n-2) of the n types of primary colors constituting the virtual n-th reference color One) is selected from {n (n-1) / 2} virtual secondary color planes obtained when the density of the primary colors is fixed to a value equal to the density of the virtual n-th reference color. Setting four virtual (n-1) secondary reference colors on the four sides by projecting coordinate points of the virtual n-th reference color on four sides of the selected virtual secondary color plane In the step (1), a plurality of virtual secondary references are performed by repeating the first processing. The step (c) further includes: (2) repeating the second process while sequentially changing the parameter m (m is an integer of 3 or more and N or less) from 3 to N, The second processing is performed by linearly combining the second color expression data with four virtual (m-1) -th reference colors set by the projection of each virtual m-th reference color, thereby forming each virtual m-th reference color. And the step (2) is a step of obtaining the second color expression data for the four basic reference colors by repeating the second processing. , Color expression data conversion method. 8. The method for converting color expression data according to claim 6, wherein the target color is a color of a specific target point existing on a color print reproduced with the N primary colors. The second color expression data, when the target point on the color printed matter arranged in a three-dimensional space is irradiated with light of a predetermined luminance spectrum, the reflected light observed at a predetermined observation point A reflection coefficient component included in the illuminance spectrum,
How to convert color expression data. 9. The color expression data conversion method according to claim 6, wherein the second color expression data is a colorimetry of a second color system different from the first color system. How to convert color expression data, which is a value. 10. A specific target color, which is an N-order color reproduced by N (N is an integer of 3 or more) primary colors included in a first color system, represents the densities of the N primary colors. An apparatus for converting first color expression data into second color expression data related to the target color, wherein (N−N−N) among the N primary colors in an N-dimensional color space including the target color. 2) ΔN (N−N) obtained when the densities of the primary colors are fixed to values equal to the densities of the target colors.
1) means for selecting one of the 2/2 virtual secondary color planes, and projecting coordinate points of the target color on four sides of the selected virtual secondary color plane, Basic reference color setting means for setting four basic reference colors on the four sides; means for determining the value of the second color expression data for each of the four basic reference colors; Means for respectively determining the value of the second color expression data for each of the four reference colors by linear combination of the values of the second color expression data in the four reference colors. . 11. A specific target color, which is an N-order color reproduced by N (N is an integer of 3 or more) primary colors included in the first color system, represents the densities of the N primary colors. A computer-readable recording medium recording a computer program for converting first color expression data into second color expression data related to the target color, wherein the computer program is a computer-readable recording medium.と き に N (N−) obtained when the densities of the (N−2) primary colors of the N primary colors are fixed to values equal to the densities of the target colors.
1) a function of selecting one from / 2｝ virtual secondary color planes, and projecting coordinate points of the target color on four sides of the selected virtual secondary color plane, A basic reference color setting function for setting four basic reference colors on the four sides; a function for determining the value of the second color expression data for each of the four basic reference colors; And a function of determining the value of the second color expression data for each of the four reference colors by a linear combination of the values of the second color expression data in the four reference colors. A readable recording medium.