JPH1073487A - Method and system for simulating color printed matter, and recording medium recording program for processing the same - Google Patents

Abstract

PROBLEM TO BE SOLVED: To faithfully reproduce a part of an optional dot percent in a color printed matter arranged in a three-dimensional space, by setting a reflection coefficient- determining means for determining a reflection coefficient through linear coupling of a plurality of reference reflection coefficients, etc. SOLUTION: An application program realizing a reflection coefficient-determining means 44, an illuminance spectrum-determining means 46 and a color data-generating means 48 is stored in a RAM 16 of a computer system for reproducing a color printed matter arranged in a three-dimensional space. The reflection coefficient-determining means 44 determines a reflection coefficient through linear coupling of a plurality of reference reflection coefficients preliminarily set for a plurality of reference colors. The illuminance spectrum-determining means 46 determines an illuminance spectrum in accordance with a predetermined numerical formula, and the color data-generating means 48 obtains tristimulus values in accordance with a predetermined numerical formula and converts the values to color data corresponding to a colorimetric system of an output device. Functions of these means are realized when the CPU 10 executes the application program.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a technique for reproducing a color print with an output device such as a display device or a printer.

[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 an object of the present invention to provide a technique capable of reproducing the image more faithfully than in the past.

[0006]

In order to solve at least a part of the above-described problems, a first invention is directed to an N-order color (N is an integer of 2 or more) arranged in a three-dimensional space. A method of reproducing the color print with an output device by performing a rendering process on the color print of (a), wherein (a) a target point on the color print is
When light of a predetermined luminance spectrum φ is irradiated, the illuminance spectrum I of the reflected light observed at a predetermined observation point is expressed by the following equation (1).
And a plurality of reference colors are set on each of N · 2 ^(N−1) sides constituting an N-dimensional color space including the target color of the target point, which is the N-order color, and Is determined by a linear combination of a first plurality of reference reflection coefficients predetermined for the plurality of reference colors, and a second reflection coefficient Ss is determined based on the plurality of reference colors. (B) determining the first and second reflection coefficients Sb and Ss determined in step (a) by a linear combination of a second plurality of reference reflection coefficients predetermined for the reference color. make use of,
Determining the illuminance spectrum I of the reflected light according to Equation 1; and (c) 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. And the following.

According to the first invention, an arbitrary halftone dot area ratio d
Illuminance spectrum I of the target color, which is the N-order color having ₁ to _N
(D _{1 -N} , θ, ρ, λ) can be obtained, and this illuminance spectrum can be converted into color data of the color system of the output device. Therefore, a portion having an arbitrary halftone dot area ratio in an Nth-order color printed matter arranged in a three-dimensional space can be reproduced more faithfully as compared with the related art.

In the first invention, it is preferable that the plurality of reference colors include at least colors at both end points of the N · 2 ^(N−1) sides.

In the first invention, it is preferable that the plurality of reference colors further include a color of a point located substantially at the center of the N · 2 ^(N−1) sides.

Further, in the first aspect of the invention, the step (a) includes the following steps: (1) n-th color (n is an integer of 2 or more and N or less)
(N−n) that form the outer edge of the n-order color space including
1) 2n virtual (n-1) -order colors are set by projecting the coordinate points of the n-th color into the next color space, respectively, and the first for the 2n virtual (n-1) -order colors is set. The first reflection coefficient Sb for the n-th color is obtained by the linear combination of the reflection coefficients, and the second reflection coefficient Ss for the n-th color is calculated for the 2n virtual (n-1) -th colors. (2) The first and second reflection coefficients Sb and Ss for the N-th color are obtained by repeating the step (1) obtained by a linear combination of the second reflection coefficients from 2 to N for n. It is preferable to include the step of determining.

Thus, the reflection coefficients Sb and Ss of the n-th color are
Can be sequentially obtained, so that the reflection coefficients Sb and Ss of the target color, which is the N-order color, can be finally obtained.

Further, the step (a) further includes the step of:
The above-mentioned N is placed on N · 2 ^(N−1) sides forming a three ^- dimensional color space.
N.2 ^(N-1) virtual primary colors are set by projecting the coordinate points of the target color of the next color, and the first plurality of reference reflection coefficients for the reference colors on each side are set. The first for the N · 2 ^(N−1) virtual primary colors by linear combination
, And a linear combination of the second plurality of reference reflection coefficients with respect to the reference color on each side, thereby obtaining a second reflection with respect to the N · 2 ^(N−1) virtual primary colors. Preferably, a step of obtaining the coefficient Ss is included.

In this way, in particular, the reflection coefficients Sb and Ss for the virtual primary color can be obtained relatively accurately.
As a result, the reflection coefficient Sb,
Ss can also be determined relatively accurately.

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

In a second aspect of the present invention, N arranged in a three-dimensional space
A system for reproducing a color printed matter by an output device by performing a rendering process on a color printed matter of the next color (N is an integer of 2 or more), wherein a target point on the color printed matter has a predetermined luminance spectrum φ. When the light is irradiated, the illuminance spectrum I of the reflected light observed at a predetermined observation point is expressed by Expression 3, and an N-dimensional color space including the target color of the target point, which is the Nth color, is defined as N · 2 A plurality of reference colors are set on each of the ^(N-1) sides, and a first reflection coefficient Sb included in Equation 3 is set to a first reflection coefficient Sb defined in advance for the plurality of reference colors. The second reflection coefficient Ss is determined by a linear combination of a plurality of reference reflection coefficients.
A reflection coefficient determining unit that determines the plurality of reference colors by a linear combination of a predetermined second plurality of reference reflection coefficients; and a first and a second determination unit that are determined by the reflection coefficient determining unit.
Illuminance spectrum determining means for determining the illuminance spectrum I of the reflected light according to Equation 3 using the reflection coefficients Sb and Ss, and a color system suitable for the output device using the illuminance spectrum I of the reflected light. Color data generating means for obtaining color data representing the target color, and according to the color data,
And an output device for outputting the target color.

The third invention is used in a computer having an output device, and performs a rendering process on a color print of an N-th color (N is an integer of 2 or more) arranged in a three-dimensional space, thereby obtaining the color image. A computer-readable recording medium on which a computer program for reproducing a printed matter by an output device is recorded, and when a target point on the color printed matter is irradiated with light having a predetermined luminance spectrum φ, a predetermined observation point The illuminance spectrum I of the reflected light observed in step (1) is expressed by equation (4), and N · 2 forming an N-dimensional color space including the target color of the target point, which is the N-order color
^(N-1) Set multiple reference colors on each of the sides of the book,
The first reflection coefficient Sb included in Equation 4 is determined by a linear combination of a first plurality of reference reflection coefficients predetermined for the plurality of reference colors, and the second reflection coefficient Ss is A second predetermined color for a plurality of reference colors
Using the reflection coefficient determination function determined by the linear combination of the plurality of reference reflection coefficients and the first and second reflection coefficients Sb and Ss determined by the reflection coefficient determination means, the illuminance spectrum I of the reflected light is calculated. An illuminance spectrum determination function determined according to Equation 4, a color data generation function for 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, and the color data And an output function of outputting the target color according to the above.

In the second and third inventions as well, similar to the first invention, an arbitrary halftone dot area portion in an Nth-order color printed matter arranged in a three-dimensional space is compared with the conventional one. It can be reproduced more faithfully.

[0018]

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

[0019]

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
(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

[0022]

(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.

[0025]

(Equation 6)

[0026]

(Equation 7)

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

The angle-dependent characteristic fb (θ) of the 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.

[0030]

(Equation 8)

Illuminance spectrum I (dC _{/ M / Y / K} , .theta., .Rho., .Lambda.) Of reflected light in a printed portion having a dot area ratio dC _{/ 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.

[0032]

(Equation 9)

Here, x (λ), y (λ), and z (λ) are color matching functions (note that in texts other than mathematical expressions, bars on the 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

[0036]

(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 Equation 8, is determined to be a constant value according to the viewing 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 is rewritten as the following equation 11.

[0040]

[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).

[0043]

(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 expression 13 similar to expression 12.

[0046]

(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).

[0049]

[Equation 14]

Here, ξ _C (d _C ) and η _C (d _C ) are weighting factors related to the cyan dot area ratio d _C , and ξ _M
(D _M ) and η _M (d _M ) are weighting factors related to the magenta dot area ratio d _M. That is, the diffuse reflection coefficient Sb at an arbitrary dot area ratio d _{C / M} of cyan and magenta
(D _{C / M} , λ) is obtained by projecting a target point (indicated by a black square) of a secondary color on four sides constituting a two-dimensional color space (color plane) shown in FIG. Diffuse reflection coefficients Sb (d _{0 / M} , λ) and Sb (d at four reference points (indicated by white squares)
_{100 / M} , λ), Sb (d _{C / 0} , λ), Sb (d _{C / 100} ,
λ). Here, for example, “d _{0 / M} ” means that the dot area ratio of cyan is 0% and the dot area ratio of magenta is d _M. In addition,
The diffuse reflection coefficient Sb at the reference point on each side is obtained according to the primary color determination method shown in FIG. 3A on each side. 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, in order to obtain the reflection coefficient of the N-order color, an N-dimensional color space (that is, each side) that forms the outer edge of the N-dimensional color space including the N-order color has The color of the reference point set by projecting each coordinate point of the next color,
This is called “virtual (N−1) -order color”.

By the way, in the above equation 14, the weighting factors ξ _C (d _C ), η _C (d _C ), ξ _M (d _M ), η
_{The reason} why _M (d _M ) is divided by 2 is that the sum of the weights applied to the four diffuse reflection coefficients included in the right side of Equation 14 is approximately 1
This is to make the value close to. As will be described later, the sum of the weighting factors （ _C (d _C ) and η _C (d _C ) for cyan is almost 1, and the weighting factor ξ _M (d
_M ) and η _M (d _M ) are also approximately 1. Equation 14 includes two sets of weighting coefficients {, η}.
, The sum of the weights becomes almost a value close to 1.
Weighting factors ξ _C (d _C ), η _C (d _C ), ξ _M (d _M ),
How to determine η _M (d _M ) will be described later.

An arbitrary halftone dot area ratio d of cyan and magenta
_Since the specular reflection coefficient Ss (d _{C / M} , λ) in _{C / M} is determined by the same equation as Equation 14, it is omitted here.
The weight coefficient for the diffuse reflection coefficient Sb and the weight coefficient for the specular reflection coefficient Ss may be determined separately. Also, for the secondary colors other than the combination of cyan and magenta, the reflection coefficient S
b and Ss can be determined.

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 the tertiary colors of cyan, magenta and yellow
Is determined according to the following equation (15).

[0055]

(Equation 15)

Here, ξ _Y (d _Y ) and η _Y (d _Y ) are weighting factors related to the yellow dot area ratio d _Y. That is, the diffuse reflection coefficient Sb (d _{C / M / Y} , λ) at an arbitrary halftone dot area ratio d _{C / M / Y} of cyan, magenta, and yellow
Represents the outer edge of the three-dimensional color space shown in FIG.
It is given by the linear combination of the diffuse reflection coefficients of the virtual secondary colors at the six reference points (indicated by black squares) that project the tertiary color target points (indicated by white triangles) on one surface.

The diffuse reflection coefficient Sb of the virtual secondary color at the reference point on each plane in FIG. 3C is obtained on each plane according to the method for determining the secondary color shown in FIG. 3B. Further, as described above, the diffuse reflection coefficient of the secondary color is given by a linear combination of the reference diffuse reflection coefficients at both ends (black circles) and midpoints (white circles) on each side of each two-dimensional color space. Therefore, the diffuse reflection coefficient Sb (d of the tertiary color
_{C / M / Y} , λ) are the respective end points (black circles) of the 12 sides constituting the three-dimensional color space (color solid) shown in FIG.
And the reference point at the midpoint (open circle).

In the above equation 15, the weight coefficient ξ _C
(D _C ), η _C (d _C ), ξ _M (d _M ), η _M (d
_M ), ξ _Y (d _Y ), and η _Y (d _Y ) are divided by 3 because the sum of the weights applied to the six diffuse reflection coefficients included in the right side of Equation 15 is set to a value close to 1. To do that.

The specular reflection coefficient Ss (d _{C / M / Y} , λ) at an arbitrary halftone dot area ratio d _{C / M / Y} is determined by the same formula as Expression 15, and will not be described here. The weight coefficient for the diffuse reflection coefficient Sb and the weight coefficient for the specular reflection coefficient Ss may be determined separately. Also,
For the tertiary colors other than the combination of cyan, magenta and yellow, the reflection coefficients Sb and Ss
Can be determined.

The diffuse reflection coefficient Sb (d _{C / M / Y / K} , λ) for the quaternary colors of cyan, magenta, yellow and sumi is determined according to the following equation (16).

[0061]

(Equation 16)

That is, the diffuse reflection coefficient Sb (d _{C / M / Y / K} , λ) at an arbitrary halftone dot area ratio d _{C / M / Y / K} of cyan, magenta, yellow and Sumi is expressed in a four-dimensional color space. Is given by a linear combination of diffuse reflection coefficients of virtual tertiary colors at eight reference points obtained by projecting target points of the quaternary color onto eight three-dimensional color spaces that form the outer edge of. By analogy with the method of determining the reflection coefficient up to the tertiary color, the reflection coefficient of the quaternary color given by Expression 16 is equivalent to 32 (=
^{4.2 (4-1)} ) It can be seen that it is given by a linear combination of the reference diffuse reflection coefficients at both end points and the midpoint of each side of the book.

By generalizing equations (14) to (16),
The diffuse reflection coefficient Sb (d _1-n , λ) for the _n-th color (n is an integer of 2 or more) having an arbitrary dot area ratio is given by the following Expression 17.

[0064]

[Equation 17]

Here, Sb (d _k = 0, λ) sets the dot area ratio of the k-th ink to 0%, and sets the dot area ratio of the other inks to the dot area ratio of the n-th color. Means the diffuse reflection coefficient when set equal to Formula 14 or Formula 1
6 corresponds to the equation in the case where n is set to 2, 3, and 4 in Equation 17 respectively. When calculating the diffuse reflection coefficient Sb (d _1−N , λ) of the N-order color, n is calculated according to a recurrence formula in which n is sequentially changed from 2 to N in Expression 17.
The diffuse reflection coefficient Sb (d _1-n , λ) of the next color may be sequentially obtained.

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 expression 18 similar to the above expression 17.

[0067]

(Equation 18)

By analogy with the method of determining the reflection coefficient up to the tertiary color, the reflection coefficient of the n-th color given by Expressions 17 and 18 is 2n (n−1) of the outer edges of the n-dimensional color space.
It can be seen that this is given by a linear combination of the reflection coefficients of the virtual (n-1) -order color at 2n reference points where the target point of the n-th color is projected on the two-dimensional color space. This is also given by a linear combination of the reference reflection coefficients at each of the end points and the midpoint of each of the n · 2 ⁽ⁿ⁻¹⁾ sides constituting the n-dimensional color space.

In the following, a method of determining a reflection coefficient for a primary color and a method of determining a reflection coefficient for secondary colors and higher colors 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 of determining the diffuse reflection coefficient Sb of the primary color by 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 each wavelength λ as described later. For example, the wavelength of visible light (about 380 nm to about 780 n
m) is divided into about 60 wavelength regions, the reference diffuse reflection coefficient values Sb (0%, λ), Sb
(50%, λ) and Sb (100%, λ) are obtained in advance. Reference diffuse reflection coefficient values Sb (0%, λ), 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
FIG. 9 is a conceptual diagram showing an advantage of a method of determining a reflection coefficient Sb (d, λ) at an arbitrary halftone dot area ratio d by interpolating 0%, λ). The dotted line at the bottom of FIG.
A reproduction value obtained by interpolating two points of 00% is shown.
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 having a dot area ratio of 50% is added, and a linear combination of values of three points of 0%, 50%, 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 in accordance with the above-mentioned equations 11 to 13 for the primary color of each ink, It is understood that the following items need to be determined 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.

FIG. 8 is an explanatory diagram showing the processing contents 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 in 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.

For extracting 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 Equation 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).

[0085]

[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 reflectance Ss (d, λ) multiplied by the incident light spectrum φ (φ). Therefore, ρ = 0
If the specular reflection component Is (d, ρ = 0, λ) is obtained under the condition (1), it means that the specular reflectance 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).

[0088]

(Equation 20)

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

[0090]

(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 of FIG. 6, the shape of the dependence fs (ρ) (also called “specular reflectance attenuation coefficient”) of the specular reflection component on the shift angle ρ 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.

[0093]

(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.

[0096]

(Equation 23)

[0097] 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.

[0099]

(Equation 24)

[0100]

(Equation 25)

As shown in Equation 25, the matrix V
org represents the value of the diffuse reflection coefficient Sb (d, λ) for each wavelength value (λmin to λmax) in the wavelength range of visible light for an arbitrary dot area ratio d. The matrix K is
Weighting factors α (d), β (d), and γ (d). The matrix Vprim has reference diffuse reflection coefficients Sb (0%, λ), Sb (50%, λ), Sb for each wavelength value (λmin to λmax).
represents the value of b (100%, λ). Here, λmin is the minimum value of the wavelength λ of visible light, and 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%) (ie, the matrix Vprim) is obtained in step S2 described above. Therefore, the only unknowns on the right side of Equation 24 are the matrix K indicating α (d), β (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 (d), β (d), and γ (d) are calculated by the least square method. A result equivalent to the approximation is obtained. Specifically, the respective values (0%,
10%... 100%), a matrix K given by the following equation 26 is obtained. As a result, 11 sets of weighting coefficients α (d), β
(D), γ (d) (d = 0%, 10%... 100%) are obtained.

[0103]

(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.

In step S5 of FIG.
Using the various results obtained in S4, an N-order color simulation was performed. FIG. 7 shows a detailed procedure of step S5. As can be seen from FIG. 7, the reflectance of the primary color to the reflectance of the Nth color (N is an integer of 2 or more) is determined in a stepwise manner.

When simulating the reflectance of the primary color, first, the weighting factors α (d), β (d), γ
(D) and reference diffuse reflection coefficient values Sb (0%, λ), Sb
Using (50%, λ) and Sb (100%, λ), the diffuse reflection coefficient Sb (d, λ) at an arbitrary halftone dot area ratio d is calculated in accordance with Equation 12 described above. 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 diffusion reference reflection coefficient and the mirror reference reflection coefficient by the procedure of steps S1 to S4 in FIG. 6 is performed for each ink constituting the higher-order 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
It is necessary to obtain reference reflection coefficients at both end points (reference color) and midpoint (quasi-reference color) of each side of the book.
Therefore, in this case, the reference reflection coefficient on each of the four sides is determined according to the procedure of FIG. For example, in FIG. 3B, the side A _M2 where cyan is 100%
When determining the reference reflection coefficients at both end points (black circles) and midpoints (white circles), a gradation is created in which cyan is 100% and magenta changes from 0% to 100% every 10%. This gradation is a secondary color because it is printed in cyan and magenta, but its reference reflection coefficient can be determined according to the procedure of FIG. It is preferable that the weighting factors α, β, and γ are also individually obtained on each of the four sides. However, the same values may be used as the weighting factors α, β, and γ between the parallel sides (sides A _C1 and A _C2 and sides A _M1 and A _{M2 in} FIG. 3B).

As shown in FIG. 3C, when it is desired to obtain the reflection coefficient of the target color which is the tertiary color, each of the 12 sides constituting the three-dimensional color space (color solid) including the target color is used. It is necessary to obtain reference reflection coefficients at both end points and the middle point. Therefore, in this case, the reference reflection coefficient on each of the 12 sides is determined according to the procedure of FIG. Further, it is preferable that the weighting coefficients α, β, and γ are also 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 Nth color. That is, when it is desired to obtain the reflection coefficient of the target color, which 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. May be determined according to the procedure shown in FIG.

E. Determination method of the reflection coefficient for the secondary color:
As described above, the diffuse reflection coefficient at an arbitrary halftone dot area ratio of the secondary color is given by Expression 14. FIG.
FIG. 4 is an explanatory diagram showing a method for determining a diffuse reflection coefficient Sb of a secondary color according to FIG. FIG. 16A shows the same contents as FIG. 3B described above. That is, an arbitrary dot area ratio d
_{C / M} diffuse reflection coefficient in _{Sb (d C / M, λ} ) has, on the four sides of the two-dimensional color space, secondary color target point of the four reference points obtained by projecting the (closed squares) ( Diffuse reflection coefficient 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). 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 changes in the weighting factors ξ and η depending on the dot area ratios d _M and d _C of each ink. As shown in FIGS. 16B and 16C, the weighting factors ξ _M (d _M ), η _M (d _M ), ξ _C (d
The values of _C ) and η _C (d _C ) depend on the dot area ratios d _M and d _C of each ink 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. Equation 14 described above is obtained from FIG.
In the corrected coordinate system of FIG. 6 (D), the expression may be such that the reflection coefficient Sb (d _{C / M} , λ) of the target point (black square) is obtained by interpolating the reflection coefficient of the reference point (white square). Easy to understand.

The reflection coefficient of the reference point (open square) in FIG. 16D can be obtained according to the above-described method of 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) and (C)) can be determined in advance according to the above-described equation (14). The reflection coefficient of the target point (black square) of the halftone dot area ratio d _{C / M} can be obtained.

Weighting factors ξ _M (d _M ), η _M (d _M ), ξ
Changes in _C (d _C ) and η _C (d _C ) are determined as follows in the same manner as in the above-described method of determining the primary color weighting factors α, β, and γ. First, the following Expressions 27 and 28 similar to Expressions 24 and 25 described above were written using a matrix.

[0117]

[Equation 27]

[0118]

[Equation 28]

As shown in Equation 28, the matrix V
_{org #} is the diffuse reflection coefficient Sb for each wavelength value (λmin to λmax) in the wavelength range of visible light for an arbitrary halftone dot area ratio d _k (subscript k means one type of ink).
(D _k , λ). The matrix K in Equations 27 and 28 represents the weighting factors ξ _k (d _k ) and η _k (d _k ). The matrix V _{prim #} has reference diffuse reflection coefficients Sb (0%, 100%) of 0% and 100% for each wavelength value (λmin to λmax).
λ) and Sb (100%, λ). For example, if the wavelength λ of visible light is divided into 60 wavelength regions, Equation 27 is equivalent to a simultaneous equation including 60 equations.

Equations 27 and 28 are respectively formed for each ink constituting the target secondary color. For example, among the four sides constituting the two-dimensional color space of FIG. 16 (A), the subscript k Equation 27 (this time in the sides (cyan axis) on A _C magenta 0% means Cyan , And on the side (magenta axis) A _M where cyan is 0%, the expressions 27 and 28 (at this time, the subscript k
Means magenta) independently. Then, on each of these sides, when a matrix K given by the following equation 29 is obtained, 11 sets of weight coefficients ξ _k (d _k ), η _k
(D _k ) (d = 0%, 10%... 100%) are obtained.

[0121]

(Equation 29)

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

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, an arbitrary halftone dot The diffuse reflection coefficient Sb of the secondary color having the 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 Expression 8, the illuminance spectrum I of the secondary color can be determined, and its color data X, Y and Z can be calculated.

FIG. 17 shows the diffuse reflection component S for the secondary color.
15 is a graph comparing the measured value of b (d, λ) · cos θ (indicated by a solid line) with the simulation result of Equation 14 (indicated by a broken line). 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) and Sb (d _{100 / M0} , λ). At this time, for each of the sides A _C1 , A _C2 , A _M1 and A _M2 ,
, Weight factors α, β, and γ are obtained independently. 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.

The weighting coefficient ξ _k used in equation (14)
Also for (d _k ) and η _k (d _k ) (k indicates the type of ink), four sides A _C1 , A _C2 , A shown in FIG.
Each of _M1 and A _M2 is determined according to the above-described equations 27 to 29. FIG. 18A shows a correction coordinate system represented by the four sets of weight coefficients determined in this way.
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. Magenta is 0
The side A _C1 (cyan axis) with constant% and the side A _M1 (magenta axis) with constant 0% cyan are perpendicular to each other. Therefore,
The shape of the square constituted by these four sides A _C1 , A _C2 , A _M1 , and 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 weight coefficient ξ shown in FIG.
_M , η _M , ξ _C , η _C are used. Here, xi] _M is side A _C2
The distance from the upper reference point (white square) to the target point (black square), and η _M is the distance from the reference point (white square) on the side A _C1 to the target point (black square). The same applies to ξ _C and η _C. The positions of the four reference points (white squares) are shown in FIG.
Since the distances are determined as shown in (A), the distances ξ _M , η _M , ， _C , and η _C shown in FIG. 18B can also be determined from the positions of these reference points. In FIGS. 18A and 18B, the position of the target point (black square) is on a line connecting the reference points of the opposing sides.

If the weighting factors ξ _M , η _M , ξ _C , and η _C used in Expression 14 are determined as shown in FIG. 18B, the reflection coefficient of the target color, which is the secondary color, can be further increased. Can be determined 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 _{C / M / Y} , λ) of the tertiary color forms the outer edge of the three-dimensional color space including the target point (white triangle) 6
It is represented by a linear combination of the reflection coefficients of the six reference points (black squares) each projecting the target point on one surface. The reflection coefficients at the six 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. The weighting factors ξ _C , η _C , ξ _M , η _M , ξ _Y , and η _Y used in Expression 15 are the same as those used in the method for determining the reflection coefficient of the secondary color. In addition,
As the weighting factors ξ _C and η _C for cyan, the weighting factors determined by the above-described formulas 27 to 29 on the side A _C (cyan axis) where magenta and yellow are both 0% can be used. Similarly, the weighting factors ξ _M and η _M for magenta use the weighting factors determined on the side A _M (magenta axis), and the weighting factors ξ _Y and η _{Y for} yellow.
Can use a weighting factor determined on the side A _Y (yellow axis).

As described above, if the weighting factors ξ _k (d _k ) and η _k (d _k ) (k represents the type of ink) are determined in advance for each target tertiary color ink, According to the equation 15, the diffuse reflection coefficient Sb of the tertiary color having an arbitrary halftone dot area ratio can be obtained. Similarly,
The specular reflection coefficient Ss can also be obtained. Therefore, by substituting these reflection coefficients Sb and Ss into the above-described Expression 8, the illuminance spectrum I of the tertiary color can be determined, and its color data X, Y and Z can be calculated.

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 Equation 16 described above. The reflection coefficient included in the right side of Expression 16 is determined according to the above-described method of determining the reflection coefficient of the tertiary color. At this time, the weighting factors ξ _k (d _k ) and η _k (d _k ) (k represents the type of ink) for each ink constituting the quaternary color also need to be obtained in advance according to FIG. This can also be obtained from the measurement results regarding the spectral spectrum of the gradation of the primary color containing only each ink, according to the above-described equations 27 to 29.

In general, the reflection coefficient for the n-th color (n is an integer of 2 or more) is determined according to the above-described equations (17) and (18). At this time, the weighting factors ξ _k (d _k ) and η _k (d _k ) (k represents the type of ink) for each ink constituting the n-th color must also be obtained in advance according to FIG. This can also be obtained from the measurement results regarding the spectral spectrum of the gradation of the primary color containing only each ink, according to the above-described equations 27 to 29.

I. Color print simulation:

Steps S6 and S7 in FIG.
The reference reflection coefficient Sb obtained by the procedures of 1 to S4,
A procedure for reproducing a printed matter by an output device using Ss and weighting factors α, β, γ, ξ, η is shown. First, in step S6, rendering processing by computer graphics is performed to generate color data for reproducing colors of a color print.

FIG. 20 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 determines the illuminance spectrum I (d, θ, ρ, λ) according to the above-described equation (8). Further, the color data generating means 48 obtains the tristimulus values X (d), Y (d), Z (d) according to the above-mentioned formula 9, and converts the tristimulus values into color data according to the color system of the output device. I do. 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 functions of these units is provided in a form recorded on a computer-readable recording medium such as a floppy disk or a CD-ROM. 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 punched 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. 21 is an explanatory view showing the three-dimensional arrangement of the printed matter 50, the light source 52, the screen (CRT screen) 54, and the observation points 56 when reproducing the color of the printed matter 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 obtains the reflection coefficients Sb (d, λ) and Ss (d, λ) according to the above-described equations (12) to (18). Then, the illuminance spectrum determining means 46 obtains the illuminance spectrum I (d, θ, ρ, λ) according to the above-described equation (8). The color data generating means 48 converts the illuminance spectrum I (d, θ, ρ, λ) thus obtained into the above-described equation (9).
To obtain a tristimulus value XYZ.

In step S7 in 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, when calculating the reflection coefficient of the target color which is the n-th color (n is an integer of 2 or more), the outer edge of the n-dimensional color space including the n-th color is formed. By projecting the coordinate points of the target color onto 2n (n-1) -dimensional color spaces, 2n reference points (virtual (n
-1) Next color) is set. Then, the reflection coefficient of the target color of the n-th color is obtained by the linear combination of the reflection coefficients of the 2n reference points (Equation 17 and Expression 18). Then, by sequentially repeating n from 2 to N, the reflection coefficient of the Nth color (N is an integer of 3 or more) is obtained. As a result, it is possible to accurately determine the reflection coefficients Sb and Ss of an arbitrary N-order target color. In addition, these reflection coefficients S
b, Ss, the color data of the Nth color (XYZ or RGB)
Data, etc.). Therefore, it is possible to accurately reproduce an Nth-color printed matter having an arbitrary halftone dot area ratio.

It should be noted that the present invention is not limited to the above Examples and Embodiments, but can be implemented in various modes without departing from the gist of the invention.
For example, the following modifications are possible.

(1) FIG. 22 shows the weight coefficient α shown in FIG.
It is the graph which simplified change of (d), (d), and (g). In FIG. 22, when the 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. 22 is close to the graph of FIG. 14 obtained in the above-described embodiment, even if the weighting coefficients of FIG. When the graph of FIG. 22 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) Expressions other than Expressions 12 and 13 may be used as expressions for determining the values of the reflection coefficients Sb and Ss at an arbitrary halftone dot ratio d of the primary color. If Equations 12 and 13 are generalized, they can be written as Equation 30 below.

[0149]

[Equation 30]

Here, a _i (d _k (i)) is a reference diffuse reflection coefficient value Sb (d _k (i) associated with the i-th reference halftone dot area ratio d _k (i) of the k-th ink. , Λ),
This is a weighting factor at the dot area ratio d _k . Also, b
_j (d _k (j)) is the j-th reference halftone dot area ratio d _k (j)
The reference specular reflection coefficient value Ss (d _k (j), λ) related to
_Is a weighting factor at the halftone dot area ratio d _{k with} respect to. m
₁ and m ₂ are integers of 2 or more. That is, the reflection coefficients Sb and Ss at an arbitrary halftone dot area ratio d _k can be generally represented as a linear combination of a plurality of reference reflection coefficient values. When m ₁ = m ₂ = 3 in Equation 30, the weighting coefficients a _i (d _k (i)) (i = 1 to 3) are replaced by the weighting coefficients α (d), β in Equation 12 described above.
(D), γ (d), and a weighting factor b _j (d _k
(J)) (j = 1 to 3) is a weighting coefficient α in Expression 13.
(D), β (d), and γ (d). It is preferable that at least one of the values of m ₁ and m ₂ is 3 or more, but both m ₁ and m ₂ may be 2.

(3) With respect to the ink of the semi-printing plate, the simultaneous equations given by Expressions 24 and 25 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 27 and 28 are also linearly dependent, and the weighting factors ξ _k and η _k are
9 may not be required. 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. 22 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 ).

(4) In the above embodiment, the reflection coefficients from the primary color to the N-th color are sequentially obtained in a stepwise manner. However, the reflection coefficient of the N-th color may be directly obtained. It is possible. For example, an expression for directly calculating the diffuse reflection coefficient Sb of the tertiary color is obtained by substituting Expression 12 into Expression 14, and further substituting Expression 14 into Expression 15. The equation obtained in this manner has a form of a linear combination of the reference reflection coefficients at both end points (black circles) and midpoints (white circles) of the 12 sides forming the outer edge of the three-dimensional color solid in FIG. ing.

In general, an expression for directly calculating the reflection coefficient of the N-th color is expressed by N which forms the outer edge of the N-dimensional color space including the N-th color.
• It is in the form of a linear combination of the reference reflection coefficients on 2 ^(N-1) sides. At this time, as the reference reflection coefficient on each side, both end points of each side (the dot area ratio of the specific ink is 0%
And the 100% point). Further, it is more preferable to use a value at a substantially center point of each side (a point where the halftone dot area ratio of the specific ink is 50%) as the reference reflection coefficient.

(5) 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.

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

FIG. 21 is an explanatory diagram showing a three-dimensional arrangement when reproducing colors of a printed material by a ray tracing method.

FIG. 22 shows simplified weighting factors α (d), β (d), and γ
The graph which shows the change of (d).

[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 determination means 46 Illuminance spectrum determination means 48 Color data generation means 50 Printed matter 52 Light source 54 Screen 56 Observation point

Claims (8)

[Claims] 1. An N-order color (N is 2) 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 illuminance spectrum I of the reflected light observed at the predetermined observation point is expressed by Expression 1, and N · 2 ^{(N -1)} A plurality of reference colors are set on each of the sides of the book, and a first reflection coefficient Sb included in Expression 1 is set to a first plurality of reference colors predetermined for the plurality of reference colors. (B) determining the second reflection coefficient Ss by a linear combination of the second plurality of reference reflection coefficients predetermined for the plurality of reference colors, and determining the second reflection coefficient Ss by a linear combination of the reflection coefficients; Determined in said step (a) A step of the first and second reflection coefficients Sb, with Ss, determines the illuminance spectrum I of the reflected light according to equation 1,
(C) using an illuminance spectrum I of the reflected light to obtain color data representing the target color in a color system suitable for the output device. (Equation 1) Here, d _1-N is a dot area ratio of N kinds of inks at the target point, λ is a wavelength of light, Sb (d _1-N , λ), Ss
(D _1−N , λ) is the first and second reflection coefficients for the N-th color, θ is the reflection angle, fb (θ) is a characteristic dependent on θ, 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 print according to claim 1, wherein the plurality of reference colors include at least colors at both end points of the N · 2 ^(N−1) sides. Simulation method. 3. The method of simulating a color print according to claim 2, wherein the plurality of reference colors further include a color of a point located substantially at the center of the N · 2 ^(N−1) sides. Simulation method of color printed matter, including. 4. The method for simulating a color print according to claim 1, wherein the step (a) includes (1) an n-th color (n is an integer of 2 or more and N or less). 2n virtual (n-1) -order colors are set by projecting coordinate points of the n-th color onto 2n (n-1) -order color spaces forming the outer edge of the n-th color space, respectively, The first reflection coefficient Sb for the n-th color is obtained by a linear combination of the first reflection coefficient for the 2n virtual (n-1) -th colors, and the second reflection coefficient Ss for the n-th color And 2
determining by linear combination of second reflection coefficients for n virtual (n-1) -order colors; and (2) repeating step (1) from 2 to N for n, thereby obtaining A method of simulating a color printed matter, including a step of calculating first and second reflection coefficients Sb and Ss. 5. The method for simulating a color printed matter according to claim 4, wherein the step (a) further comprises the step of: ^(N) 2 ^(N-1) sides constituting the N-dimensional color space. N.2 ^(N-1) virtual primary colors are set by projecting the coordinate points of the target colors of the ^N-th color, respectively, and the first plurality of reference reflections with respect to the reference colors on each side are set. A first reflection coefficient Sb for the N · 2 ^(N−1) virtual primary colors is obtained by a linear combination of coefficients, and a linearity of the second plurality of reference reflection coefficients for the reference color on each side is determined. By combining, the N · 2 ^(N−1) virtual 1
Obtaining a second reflection coefficient Ss for the next color. 6. The simulation method for a color printed matter according to claim 1, wherein the characteristics fb (θ) and fs (ρ) each have the form of Expression 2. Method. (Equation 2) Here, σ is a constant. 7. An N-order color (N is 2) 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. , The illuminance spectrum I of the reflected light observed at the predetermined observation point is expressed by Equation 3, and N forms a N-dimensional color space including the target color of the target point, which is the N-th color.
2 A plurality of reference colors are set on each of the ^(N-1) sides, and the first reflection coefficient Sb included in Equation 3 is set to a first predetermined reference color for the plurality of reference colors. A reflection coefficient determined by a linear combination of a plurality of reference reflection coefficients, and a second reflection coefficient Ss determined by a linear combination of a second plurality of reference reflection coefficients predetermined for the plurality of reference colors. Deciding means, and the first and second reflection coefficients Sb and Ss determined by the reflection coefficient deciding means, and using the illuminance spectrum I of the reflected light.
An illuminance spectrum determining unit that determines the target color in accordance with Equation 3; a color data generating unit that obtains color data representing the target color in a color system suitable for the output device using the illuminance spectrum I of the reflected light; An output device that outputs the target color according to data. (Equation 3) Here, d _1-N is the dot area ratio of the N kinds of inks 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 N-th color, θ is the reflection angle, fb (θ) is a characteristic dependent on θ, 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. 8. A computer equipped with an output device, which renders 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 having recorded thereon a computer program for reproducing in a target point on the color print, when irradiated with light of a predetermined luminance spectrum φ, is observed at a predetermined observation point The illuminance spectrum I of the reflected light is expressed by Expression 4, and N forms a N-dimensional color space including the target color of the target point, which is the N-order color.
2 A plurality of reference colors are set on each of the ^(N-1) sides, and a first reflection coefficient Sb included in Equation 4 is set to a first predetermined reference color for the plurality of reference colors. A reflection coefficient determined by a linear combination of a plurality of reference reflection coefficients, and a second reflection coefficient Ss determined by a linear combination of a second plurality of reference reflection coefficients predetermined for the plurality of reference colors. A determination function, and using the first and second reflection coefficients Sb and Ss determined by the reflection coefficient determination means, to obtain an illuminance spectrum I of the reflected light.
An illuminance spectrum determining function for determining the target color in accordance with Formula 4; a color data generating function for 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; A computer-readable recording medium on which a computer program for causing a computer to perform the output function of outputting the target color according to data is recorded. (Equation 4) Here, d _1-N is the dot area ratio of the N kinds of inks 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 N-th color, θ is the reflection angle, fb (θ) is a characteristic dependent on θ, 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.