JPH1073489A - 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 determining means for determining a reflection coefficient of an objective color through detection of a sum of multiplication results related to reference colors. 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 of an objective color by obtaining a sum of multiplication results related to reference colors. The illuminance spectrum-determining means 46 determines an illuminance spectrum in accordance with a predetermined numerical formula. 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%) can be faithfully reproduced, but it is difficult to reproduce a color print having an arbitrary halftone dot area ratio. Further, it has not been clear how to apply the method when faithfully reproducing a color print printed with a plurality of inks.

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 it is assumed that, of the target point is an N-order color ^N · 2 ^(N-1) constituting the N-dimensional color space including the target color of each of the sides of ^the 2 ^N located at both ends point Std For each, the first reflection coefficient Sb and the second reflection coefficient S
determining s as a first reference reflection coefficient and a second reference reflection coefficient; and (b) converting a color at each intermediate point of each side of the N-dimensional color space into two reference colors at both end points of each side. Determining two weighting factors used for multiplying the two reference colors for each side of the N-dimensional color space when interpolating the two. Constructing an N-dimensional correction space with the weight coefficients determined on the sides as coordinates of each side, and the reference colors located at both end points of each side of the N-dimensional color space,
The N-dimensional correction space is assigned to the positions of both end points of the corresponding sides, and the N-dimensional correction space is divided into N (N
-1) Dividing into 2 ^N partial N-dimensional correction spaces by the dimensional space, and pairing the first reference reflection coefficient for each of the 2 ^N reference colors with a point of each reference color in the N-dimensional correction space. By multiplying each of the volumes of the partial N-dimensional correction space having an angular positional relationship and calculating the sum of the multiplication results for each of the 2 ^N reference colors, the first color of the target color is obtained.
And (d) determining the second reference reflection coefficient for each of the 2 ^N reference colors and the diagonal positional relationship with the point of each reference color in the N-dimensional correction space. (E) determining a second reflection coefficient Ss of the target color by multiplying each of the volumes of the partial N-dimensional correction space and calculating the sum of the multiplication results for each of the 2 ^N reference colors; Using the first and second reflection coefficients Sb and Ss determined in the steps (c) and (d) to determine an illuminance spectrum I of the reflected light according to Equation 1, and (f) determining the reflected light Using the illuminance spectrum I of
Obtaining color data representing the target color in a color system suitable for the output device.

Here, the "volume of the partial N-dimensional correction space" means a volume corresponding to a spatial integration value of the partial N-dimensional correction space. For example, since the “partial three-dimensional correction space” is a three-dimensional space, the “volume” means a volume in a narrow sense. Since the “partial two-dimensional correction space” is a two-dimensional plane, the “volume” means an area.

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-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.

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

[0010] The second aspect of the present invention relates to an N-channel array 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 · For each of the 2 ^N reference colors located at both end points of each of the 2 ^(N−1) sides, the first reflection coefficient Sb included in Equation 3
And a second reflection coefficient Ss as a first reference reflection coefficient and a second reference reflection coefficient, respectively, and a color at each intermediate point of each side of the N-dimensional color space, Weighting factor determining means for determining, for each side of the N-dimensional color space, two weighting factors used for multiplying the two reference colors when determining the two reference colors at both end points by interpolation; The weight coefficient determined on each side of the N-dimensional color space is set as the coordinates of each side.
While configuring a dimensional correction space, the reference colors located at both ends of each side of the N-dimensional color space are assigned to positions of both ends of corresponding sides of the N-dimensional correction space, and the N-dimensional correction space is Partitioning into 2 ^N partial N-dimensional correction spaces by N (N−1) -dimensional spaces passing through the target color,
Into ^N first reference reflection coefficients for each reference color, as well as multiplied by the volume of a portion N-dimensional correction space at the point diagonally positional relationship of each reference color in the N-dimensional correction space, respectively, 2 ^By calculating the sum of the multiplication results for each of the ^N reference colors, the first reflection coefficient Sb of the target color is obtained.
And the second reference reflection coefficient for each of the 2 ^N reference colors has a diagonal positional relationship with a point of each reference color in the N-dimensional correction space. A second reflection coefficient determining unit that determines a second reflection coefficient Ss of the target color by multiplying each of the volumes of the partial N-dimensional correction space and obtaining the sum of the multiplication results for each of the 2 ^N reference colors And the first and second reflection coefficients Sb, Sb determined by the first and second reflection coefficient determination means.
illuminance spectrum determining means for determining the illuminance spectrum I of the reflected light according to Equation 3 using s, and expressing the target color in a color system suitable for the output device using the illuminance spectrum I of the reflected light A color data generating means for obtaining color data, and an output device for outputting the target color according to the color data are provided.

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
^For each of the 2 ^N reference colors located at both end points of each of the ^(N-1) sides, the first reflection coefficient Sb and the second reflection coefficient Ss included in Expression 4 are defined as the first reflection coefficient Ss And a reference reflection coefficient determining function to determine a reference reflection coefficient as a second reference reflection coefficient and a color at each intermediate point of each side of the N-dimensional color space by interpolating two reference colors at both end points of each side. When determining, two weighting factors used for multiplying the two reference colors are determined for each side of the N-dimensional color space, and a weighting factor determination function is determined for each side of the N-dimensional color space. The N-dimensional correction space having the weighting coefficients as coordinates of each side is configured, and the reference colors located at both end points of each side of the N-dimensional color space are set at both ends of the corresponding side of the N-dimensional correction space. Assigned to a point position, and the N-dimensional correction space is Partitioning into 2 ^N partial N-dimensional correction spaces by N (N-1) -dimensional spaces passing through the target color,
The first reference reflection coefficient for each of the 2 ^N reference colors is multiplied by a volume of a partial N-dimensional correction space having a diagonal positional relationship with a point of each reference color in the N-dimensional correction space. , by determining the sum of ^the 2 ^N of the multiplication results for each reference color, the first reflection coefficient determination function for determining a first reflection coefficient Sb of the target color, said 2 ^N
The second reference reflection coefficient for each of the reference colors is multiplied by the volume of a partial N-dimensional correction space having a diagonal positional relationship with a point of each reference color in the N-dimensional correction space, and 2 ^N A second reflection coefficient determining function for determining a second reflection coefficient Ss of the target color by calculating the sum of the multiplication results for each of the reference colors; and a first and second reflection coefficient determining means. First and second reflection coefficients S
b, Ss, an illuminance spectrum determining function for determining the illuminance spectrum I of the reflected light according to Equation 4, and using the illuminance spectrum I of the reflected light, the target color in a color system suitable for the output device. Is a computer-readable recording medium that stores a computer program for causing a computer to realize a color data generation function for obtaining color data representing the following and an output function for outputting the target color according to the color data.

In the second and third inventions, as in the first invention, a portion having an arbitrary halftone dot area ratio in a color print of the Nth color arranged in a three-dimensional space is compared with the conventional one. It can be reproduced more faithfully.

[0013]

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.

[0014]

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, a printed matter, and a 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

[0017]

(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.

[0020]

(Equation 6)

[0021]

(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.

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.

[0025]

(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.

[0027]

(Equation 9)

Here, x (λ), y (λ), and z (λ) are color matching functions (note that, in sentences 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.

Equation 8 above 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

[0031]

(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.

[0035]

[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).

[0038]

(Equation 12)

Here, ξ _C (d _C ) and η _C (d _C ) are weighting factors. That is, an arbitrary dot area ratio d of cyan
Diffuse reflection coefficient Sb in _C (d _{C, λ)} has two reference area coverage _{(d C = 0%, 100} %) diffuse reflection coefficient Sb in _{(d C = 0%, λ} ), Sb (d C = 100
%, Λ). Weight coefficient ξ _C
(D _C ), η _C (d _C ) and the reference diffusion coefficient value Sb (d _C
= 0%, 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.

[0041]

(Equation 13)

The weighting coefficients in Equation 13 xi] _C, as eta _C are weighting coefficients in Equation 12 xi] _C, may be the same as the eta _C. Of course, the diffuse reflection coefficient Sb (d
_C , λ) and the specular reflection coefficient Ss (d
_C , λ) may be determined separately. Note that, for the primary colors of the inks other than cyan, the reflection coefficients Sb,
Ss can be determined.

FIG. 3B shows how to calculate the reflection coefficient for the secondary color. In FIG. 3B, ξ _C (d
_C ) and η _C (d _C ) are weighting factors related to the dot area ratio d _C of cyan, and ξ _M (d _M ) and η _M (d _M ) are related to the dot area ratio d _M of magenta. Weighting factor. These weighting factors are ξ _C , η _C , ξ _M , η _M , as shown in FIG.
A two-dimensional space (referred to as “two-dimensional correction space”) as shown in FIG. The first coordinate axis (cyan axis) A _C1 of the two-dimensional correction space is an axis having weight coefficients η _C and ξ _C as coordinates, and the second coordinate axis (magenta axis) A _M1
Is an axis having weighting coefficients η _M and ξ _M as coordinates. This 2
The origin (0, 0) of the dimension correction space corresponds to a color (paper white) in which the halftone dot area ratios of cyan and magenta are both 0%. The end point of the cyan axis A _C (η _C + ξ _C , 0) is represented by d _C =
This corresponds to a reference color of 100%, d _M = 0%. Similarly, the end point (0, η _M + ξ _M ) of the magenta axis A _M is d _C = 0
%, D _M = 100%. Origin (0,0) among the four end points constituting the contour of the two-dimensional correction space
Another end point opposite to (η _C + ξ _C , η _M + ξ _M )
Corresponds to a reference color of d _C = 100% and d _M = 100%. The coordinates of the target color of the secondary color having a dot area ratio of d _{C / M} are represented by (η _C , η _M ).

The two-dimensional correction space includes four straight lines passing through coordinate points (η _C , η _M ) corresponding to the target color and being perpendicular to either the cyan axis A _C1 or the magenta axis A _M1 . Partial two-dimensional correction space V _0/0 , V _100/0 , V _0/100 , V
_{It is divided into 100/100} (also called "subspace").
The suffix of the code indicating each subspace indicates the dot area ratio d _{C / M} of the end point which is in a diagonal positional relationship with each subspace.
For example, the subspace V _0/0 has a diagonal positional relationship with the end point of the reference color of d _C = 0% and d _M = 0%. Further, the subspace V _100/0 has a diagonal positional relationship with the end points of the reference colors of d _C = 100% and d _M = 0%.

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).

[0046]

[Equation 14]

Here, V _0/0 , V _100/0 , V _0/100 , V
_100/100 corresponds to the area of each subspace. Weight coefficient ξ
_C (d _C ), η _C (d _C ), ξ _M (d _M ), η _M (d
_M ) will be described later.

An arbitrary 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. In FIG. 3C, ξ _Y (d
_Y ) and η _Y (d _Y ) are weighting factors related to the dot area ratio d _Y of yellow.

Weighting factors ３ _C , η _C , の た め for tertiary colors
_M , η _M , ξ _Y , η _Y constitute a three-dimensional correction space as shown in FIG. This three-dimensional correction space is 3
It passes through coordinate points (η _C , η _M , η _Y ) corresponding to the target color of the next color and passes through the cyan axis A _C1 , the magenta axis A _M1, and the yellow axis A _Y1
8 planes 3 by 3 planes perpendicular to either
Dimensional correction space V _{0/0/0 to} V _100/100/100 (“Partial space”
Also called). The suffix of the code indicating each subspace indicates the dot area ratio d _{C / M / Y} of the end point which is in a diagonal positional relationship with each subspace.

The diffuse reflection coefficient Sb (d _{C / M / Y} , λ) for the tertiary colors of cyan, magenta and yellow is given by the following equation (1).
5 is determined.

[0052]

(Equation 15)

Here, V _{0/0/0 to} V _100/100/100 correspond to the area of each partial space.

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.

By generalizing equations (12) to (15),
The diffuse reflection coefficient Sb (d _1-n , λ) of an _n-th color (n is an integer of 2 or more) having an arbitrary dot area ratio is given by the following Expression 16.

[0056]

(Equation 16)

Here, Sb (refd _i = 0, λ) is
This is the diffuse reflection coefficient (reference diffuse reflection coefficient) of the reference color located at 2 ⁿ end points constituting the contour of the n-dimensional correction space.
Here, refd _i indicates the dot area ratio of the i-th (i = 1 to 2 ⁿ ) reference color. For example, in Equation 15, refd ₁ is equivalent to d _0/0/0 , and refd ₄ is d _0/0/0
It is equivalent to _100/100/100 . Also, V _i is the volume of the portion n-dimensional correction space in end point diagonally positional relationship in the position of the i-th reference color. Here, “volume” is a spatial integral value of the subspace. Therefore, when the subspace is a two-dimensional space, its “volume” is a so-called area, and when the subspace is a three-dimensional space, it is a normal volume. Χ _k (k = 1 to 2) in the second line of Expression 16
n) is equal to η _k when the dot area ratio d _k of the k-th ink in the i-th reference color is 0%, and is equal to ξ _k when it is 100%. The operator Π in the second line of Expression 16 is
means that multiplying the n values χ _k.

[0058] Equation 16, 2 ⁿ pieces of reference diffuse reflection coefficient Sb for the i-th reference color in the reference color (refd _i,
λ) is multiplied by the volume V _i of the partial n-dimensional correction space that is diagonally positioned with respect to the end point of the i-th reference color,
By calculating the sum of the multiplication results for each of the 2 ^N reference colors, the diffuse reflection coefficient Sb (d
_1-n , λ).

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 17 similar to the above expression 16.

[0060]

[Equation 17]

In the following, 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 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 according to equation (12). However, in FIG. 4, in order to indicate that an arbitrary ink is targeted, codes “d”, “ξ, η” having no subscript are used for the dot area ratio and the weighting coefficient, respectively. I have.

Reference diffuse reflection coefficient value Sb (0%, λ), S
b (100%, λ) is a diffuse reflection coefficient value experimentally determined in advance at the reference halftone dot area ratio (0%, 100%), as described later. The reference diffuse reflection coefficient value Sb (0
%, 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
(100%, λ) is obtained in advance. A method for obtaining the reference diffuse reflection coefficient values Sb (0%, λ) and Sb (100%, λ) will be described later.

The weighting factors ξ (d) and η (d) are shown in FIG.
As shown in (B), it depends on the dot area ratio d. Weight coefficient for reference diffuse reflection coefficient value Sb (0%, λ)
The value of (d) is 1 when the halftone dot area ratio d of the target print portion is 0%, and is 0 when it is 100%. Conversely, the value of the weighting coefficient η (d) with respect to the reference diffuse reflection coefficient value Sb (100%, λ) is 1 when the dot area ratio d of the target print portion is 100%, and is 0%.
It is 0 at the time of. FIG. 4C shows a one-dimensional correction space composed of these weighting factors ξ and η.

In FIG. 4B, the change in the weighting coefficient ξ is represented by 11 points (shown by black circles) in the range of 0 ≦ d ≦ 100%. Any dot area ratio d
The values of the weighting coefficients に お け る in these 11 coefficient values ξ
Is determined by interpolating. For example, the weight coefficient ξ (d) may be determined by linearly interpolating the two coefficient values に お け る at the two halftone dot rates closest to the target halftone dot rate d. of course,
The weight coefficient ξ (d) may be determined by nonlinearly interpolating the coefficient values 係数 at three or more points. This is the same for the other weighting coefficients η (d).

In order 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 according to the above-mentioned equations 11 to 13 for the primary colors of the respective inks, It is understood that the following items need to be determined in advance. (1) Reference diffuse reflection coefficient values Sb (0%, λ), Sb (1
00%, λ). (2) Reference specular reflection coefficient values Ss (0%, λ), Ss (1
00%, λ). (3) Changes in weighting factors ξ (d) and η (d) (FIG. 4
(B)). (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 Embodiment: FIGS. 5 and 6 are explanatory diagrams showing the procedure of the embodiment. In step S1 of FIG. 5, 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%, 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. 7 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. 7B 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. 7B, 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 state shown in FIG.
For each of the color patches, the spectral reflectance as shown in FIG. 7C was measured under the measurement conditions shown in FIG. 7B.
FIG. 8 is a conceptual diagram showing a measuring device of the 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 a 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. 9 is an enlarged graph showing the measured values of the spectral reflectance shown in FIG. 7C. This graph shows a plurality of measurement results having different shift angles ρ under the condition that the dot area ratio d is 50% and the incident angle θ is 8 °. 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. 5, 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. 10 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 ξ and η. In step S2, based on the spectral reflectance shown in FIG.
The diffuse reflection component shown in FIG. 10B was extracted, and the specular reflection component shown in FIG. 10C 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 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. 11 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 18, the diffuse reflection component is divided by cos θ to calculate the diffuse reflection coefficient Sb (d, λ).

[0076]

(Equation 18)

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 (λ). 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) at a shift angle ρ of 0 ° is given by the following equation (19).

[0079]

[Equation 19]

By transforming equation (19), the specular reflection component Ss
(D, λ) is given by the following equation (20).

[0081]

(Equation 20)

FIG. 12 is a graph plotting the specular reflection coefficient Ss (d, λ) estimated according to Equation 20 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. 5, 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 21 below.

[0084]

(Equation 21)

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 2.

[0087]

(Equation 22)

[0088] Here, the index n ₀ is a value in the range of from about 350 to about 400. Dependency fs given by equation 21
(Ρ) as well as the dependency fs (ρ) given by equation 22:
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.
The weighting factors ξ and η used in 2, and 13 were determined (FIG. 1).
0 (D)). In this embodiment, the weighting factors ξ and η are determined as follows from the diffuse reflection coefficient Sb (d, λ) obtained in step S2. First, Equation 12 described above is
This 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 Expressions 23 and 24.

[0090]

(Equation 23)

[0091]

(Equation 24)

As shown in Expression 24, the matrix V
org # indicates the wavelength value (λmin to λma) in the visible light wavelength range for an arbitrary halftone dot area ratio d _k of the k-th ink.
x) represents the value of the diffuse reflection coefficient Sb (d _k , λ). The matrix K represents weighting factors ξ _k and η _k . The matrix Vprim # has reference diffuse reflection coefficients Sb (0%, λ) and Sb (100%, λ) for each wavelength value (λmin to λmax).
λ). Here, λmin is the minimum value of the wavelength λ of visible light, and λmax is the maximum value. For example, the wavelength λ of visible light
Is divided into 60 wavelength regions, Equation 23 becomes 60
It is equivalent to a simultaneous equation including the above equations.

The eleven values of the dot area ratio d _k (0%, 10
%... 100%) of the diffuse reflection coefficient Sb (d _k , λ)
(That is, the matrix Vprim #) is obtained in step S2 described above. Therefore, the only unknowns on the right side of Equation 23 are the matrix K indicating ξ _k and η _k . As described above, when a system of equations (Equation 23) in which the number of unknowns is smaller than the number of equations is solved for the matrix K of unknowns, a result equivalent to that obtained by approximating the unknowns ξ _k and η _k by the least square method is obtained. Can be Specifically, for each value (0%, 10%... 100%) of the eleven dot area ratios d _k , a matrix K given by the following equation 25 is obtained.
A set of weighting factors ξ _k (d _k ), η _k (d _k ) (d _k = 0
%, 10%... 100%).

[0094]

(Equation 25)

The weight coefficient ξ shown in FIG.
The changes in (d) and η (d) are the results thus obtained.

In step S5 in FIG.
Using the various results obtained in S4, an N-order color simulation was performed. FIG. 6 shows a detailed procedure of step S5. As can be seen from FIG. 6, in this embodiment, the reflectance of an arbitrary n-th color (n is an integer of 2 or more) is selectively and directly determined.

When performing the simulation of the reflectance of the primary color, first, the weighting factors ξ (d) and η (d) and the reference diffuse reflection coefficient values Sb (0%, λ) and Sb (100%,
λ), and the diffuse reflection coefficient Sb (d, λ) at an arbitrary halftone dot area ratio d is calculated according to Equation 12 described above. Similarly, the specular reflection coefficient Ss (d, λ) is calculated according to the above-described equation (13).

FIG. 13 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. It can be seen that the solid line and the broken line agree quite well. Similarly, for the specular reflection component, it was confirmed that the measured value and the simulation result agreed relatively well.

The determination of the reference diffuse reflection coefficient and the reference specular reflection coefficient by the procedure of steps S1 to S4 in FIG. 5 is performed for each ink constituting the higher-order color. Also,
Weights ξ and η are also obtained for each ink.

As shown in FIG. 3B, when it is desired to obtain the reflection coefficient of the target color, which is the secondary color, the two end points of each of the four sides constituting the two-dimensional color space including the target color. It is necessary to obtain a reference reflection coefficient for (ie, a reference color). 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.
When determining the reference reflection coefficient at both end points (black circles) of the side A _M2 of 0%, cyan is 100% and magenta is 0%.
From 100% 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 ξ and η are also individually obtained on each of the four sides. However, parallel sides (Fig. 3
In (B), the sides A _C1 and A _C2 and the sides A _M1 and A _M2 may use the same value as the weighting coefficients ξ and η.

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 twelve 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. 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 factors ξ and η are individually obtained on each of the 12 sides. However, for sides parallel to each other, the same value may be used as the weighting coefficients ξ and η.

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-th color, the reference reflection coefficient at each of the two end points of the N · 2 ^(N−1) sides forming the N-dimensional color space including the target color May be obtained 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. 14A shows a two-dimensional color space. FIGS. 14B and 14C show changes in the weighting factors ξ and η depending on the dot percentages d _M and d _C of the respective inks. As shown in FIGS. 14B and 14C,
Weighting factors ξ _M (d _M ), η _M (d _M ), ξ _C (d _C ),
The value of η _C (d _C ) depends on the dot area ratios d _M and d _C of each ink constituting the secondary color.

FIG. 14D shows the weighting factors ξ _M (d _M ),
It shows a two-dimensional correction space composed of η _M (d _M ), ξ _C (d _C ), and η _C (d _C ). The reflection coefficient Sb (d _{C / M} , λ) of the target color (black square), which is the secondary color, is the diagonal position of the reference reflection coefficient of the four reference colors (black circles) with respect to the point of each reference color. It is given as a sum of multiplication results obtained by multiplying the area of the related partial two-dimensional correction space (Equation 14).

The reflection coefficient of the reference color (black circle) shown in FIG. 14D can be measured in advance. Therefore, the weighting factors ξ _M (d _M ), η _M (d _M ), ξ _C (d _C ), η _C (d
_C ) (FIGS. 14 (B) and 14 (C)) is calculated by the above-described equation (2).
If it is determined in accordance with 3 to 25, the reflection coefficient of the target color (black square) of an arbitrary halftone dot area ratio d _{C / M} can be determined in accordance with Expression 14 described above. 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. 15 shows a diffuse reflection component S for a 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. 15 shows a result regarding a 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 every 10% from 0% to 100%. . It can be seen that the solid line and the broken line agree quite well. Similarly, for the specular reflection component, it was confirmed that the measured value and the simulation result agreed well.

F. More Accurate Method of Determining Reflection Coefficient for Secondary Color: FIG. 16 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 _On each of _M1 and A _M2 , the weighting factors ξ, η
Independently. Therefore, the four sides A _C1 , A _C2 , A _M1 ,
For the four sets of weighting factors ξ and η for A _M2, changes as shown in FIG. 14B or FIG. 14C described above are determined.

FIG. 16 shows a correction coordinate system represented by the four sets of weighting factors determined in this way. Four sides A
The lengths of _C1 , A _C2 , A _M1 , and A _M2 are equal to the sum of the weight coefficients of each set (ξ + η). The side A _C1 (cyan axis) where magenta is constant at 0% and the side A _M1 (magenta axis) where cyan is constant at 0% are perpendicular to each other. Therefore, these four
The shape of the rectangle formed by the two sides A _C1 , A _C2 , A _M1 , and A _M2 is uniquely determined. As shown in FIG. 16A, a correction space including coordinate axes that are not parallel or perpendicular to each other is
Called "distorted correction space".

In calculating the reflection coefficient of the target color (black square) in the distorted correction space, 1
The expression in the line can be used as it is. However, the “volume V” of the partial two-dimensional correction space having a diagonal positional relationship with each reference color (black circle) is given by the area of the distorted partial two-dimensional correction space as shown in FIG. Can be Note that FIG.
The correction space in (B) is the same as that in FIG.
As can be understood from FIG. 16, in the distorted correction space, reference points (white squares) that are boundaries between the weighting factors ξ and η are virtually set on each side. The distorted two-dimensional correction space is divided into four partial two-dimensional correction spaces by two straight lines connecting reference points (white squares) on opposite sides.

If the volume V used in Equation 14 is determined as shown in FIG. 16B, the reflection coefficient of the target color, which is the secondary color, can be obtained more accurately.

G. Determination method of reflection coefficient for tertiary color or higher order color: Diffuse reflection coefficient of tertiary color at an arbitrary halftone dot area ratio is given by equation 15 above. The same applies to the specular reflection coefficient. The method of calculating the reflection coefficient for the tertiary color according to Equation 15 is almost the same as the method of calculating the reflection coefficient for the secondary color described above, and thus the details are omitted here.

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 (16) and (17). At this time, the reflection coefficient for 2 ⁿ reference colors,
Weight coefficient ξ _k (d
_k ) and η _k (d _k ) (k represents the type of ink) must be obtained in advance.

FIG. 17 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 (black square) that is the tertiary color, first, the above-described processing is performed on each of the twelve sides forming the outer edge of the three-dimensional color space including the target color. Formula 23-
25, weight factors 重 み and η are obtained independently.

FIG. 17 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 calculating the reflection coefficient of the target color (black square) in the distorted three-dimensional correction space, the expression 1
The formula in the first row of 5 can be used as it is. However,
The volume V of the partial three-dimensional correction space having a diagonal positional relationship with each reference color (black circle) is given by the volume of the distorted partial three-dimensional correction space as shown in FIG. The distorted partial three-dimensional correction space is determined as follows. That is, in the distorted three-dimensional correction space, the weighting factors ξ,
A reference point (white square) serving as a boundary of η is virtually set. The distorted three-dimensional correction space is defined by three planes each passing through reference points (white squares) on four opposing sides.
Is divided into three partial three-dimensional correction spaces.

If the volume V used in Expression 15 is determined as shown in FIG. 17, the reflection coefficient of the target color, which is the tertiary color, can be obtained more accurately.

In general, when calculating the reflection coefficient of the n-th color, n · 2 which forms the outer edge of the n-dimensional color space including the target color is used.
^{On each of the (n-1)} sides, the above-described equation (23)
The weighting factors ξ and η are obtained independently according to ２５25. Then, a distorted n-dimensional correction space having these weight coefficients ξ and η as coordinate axes is configured. When calculating the reflection coefficient of the target color in the distorted n-dimensional correction space, the above-described equation (1) is used.
The formula in the first row of No. 6 can be used as it is. However,
The volume V of the partial n-dimensional correction space having a diagonal positional relationship with each reference color is given by the volume of the distorted partial n-dimensional correction space. The distorted partial n-dimensional correction space is determined as follows. That is, in the distorted n-dimensional correction space, a reference point that is a boundary between the weighting factors ξ and η on each side is virtually set. The distorted n-dimensional correction space is divided into 2 ⁿ partial n-dimensional correction spaces by n (n-1) -dimensional spaces that respectively pass through reference points on opposing sides.

H. Simulation of color printed matter: Steps S6 and S7 in FIG. 5 are steps for reproducing the printed matter on the output device using the reference reflection coefficients Sb and Ss and the weighting coefficients ξ and η obtained by the procedures of steps S1 to S4. 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. 18 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 Equation (17). 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.

The reflection coefficient determining means 44 includes a reference reflection coefficient determining means, a weight coefficient determining means,
The function as the first and second reflection coefficient determining means is realized.

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. 19 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 shift angle ρ are, as shown in FIG.
Are defined in the minute polygon EL that exists at the position where.

In 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-mentioned equations (12) to (17). 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 of FIG. 5, 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-th color (n is an integer of 2 or more) are used.
s can be determined directly and relatively accurately from the reference reflection coefficient values for 2 ⁿ reference colors.
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 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-described 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) Regarding the ink of the semi-printing plate, the simultaneous equations given by the above-mentioned equations (23) and (24) become linearly dependent, and the weighting factors ξ _k and η _k may not be obtained from the equation (25). The simultaneous equations given by Expressions 23 and 24 become linearly dependent because the shape of the diffuse reflection component (the shape of the eleven graphs in FIG. 11 described above) for each color chart of the primary gradation becomes similar. Means that
In such a 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 . At this time, the other weight coefficient ξ _k is given by (1−d _net ).

(2) 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.

[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 flowchart showing the procedure of the embodiment.

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

FIG. 7 is an explanatory diagram showing processing contents in step S1.

FIG. 8 is a conceptual diagram showing an apparatus for measuring spectral reflectance.

FIG. 9 is a graph showing measured values of spectral reflectance.

FIG. 10 is an explanatory diagram showing a procedure for determining a diffuse reflection component and a specular reflection component from spectral reflectance and determining weighting coefficients ξ and η.

FIG. 11 is a graph plotting diffuse reflection components Sb (d, λ) · cos θ extracted under the conditions of ρ = 35 ° and θ = 8 °.

FIG. 12 shows a specular reflection component S estimated under the condition of θ = 8 °.
The graph which plotted s (d, (lambda)).

FIG. 13 is a graph comparing measured values of the diffuse reflection component Sb (d, λ) · cos θ with simulation results.

FIG. 14 is an explanatory diagram illustrating a method for determining a reflection coefficient of a secondary color.

FIG. 15 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. 16 is an explanatory diagram showing a method for more accurately determining a reflection coefficient of a secondary color.

FIG. 17 is an explanatory diagram showing a method for more accurately determining a reflection coefficient of a tertiary color.

FIG. 18 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. 19 is an explanatory diagram showing a three-dimensional arrangement when reproducing colors of a printed material by a ray tracing method.

[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 (4)

[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) For} each of the 2 ^N reference colors located at both ends of each of the sides of the book, the first reflection coefficient Sb and the second reflection coefficient Ss included in Expression 1 are defined as
And (b) determining a color at each intermediate point of each side of the N-dimensional color space by interpolating two reference colors at both end points of each side. Determining two weighting factors used for multiplying the two reference colors for each side of the N-dimensional color space; and (c) determining two weighting factors for each side of the N-dimensional color space. An N-dimensional correction space having the weighting coefficients as coordinates of each side is configured, and the reference colors located at both ends of each side of the N-dimensional color space are defined as both end points of corresponding sides of the N-dimensional correction space. , And the N
The dimensional correction space is divided into 2 ^N partial N dimensional correction spaces by N (N−1) dimensional spaces passing through the target color, and the first reference reflection coefficient for each of the 2 ^N reference colors is , By multiplying the volume of the partial N-dimensional correction space in a diagonal positional relationship with the point of each reference color in the N-dimensional correction space, and obtaining the sum of the multiplication results for each of the 2 ^N reference colors. Determining a first reflection coefficient Sb of the target color; and (d) adding a point of each reference color in the N-dimensional correction space to the second reference reflection coefficient for each of the 2 ^N reference colors. While multiplying the volume of the partial N-dimensional correction space having a diagonal positional relationship,
Determining a second reflection coefficient Ss of the target color by calculating the sum of the multiplication results for each of the ^N reference colors; and (e) determining the first reflection coefficient determined in the steps (c) and (d). Determining the illuminance spectrum I of the reflected light according to Equation 1 using the second reflection coefficient Sb and the second reflection coefficient Ss;
(F) 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. (Equation 1) 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. 2. The method for simulating a color printed matter according to claim 1, wherein the characteristics fb (θ) and fs (ρ) each have the form of Expression 2. (Equation 2) Here, σ is a constant. 3. 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.
The first reflection coefficient Sb and the second reflection coefficient Ss included in Expression 3 for each of the 2 ^N reference colors located at both end points of each of the 2 ^(N-1) sides, A reference reflection coefficient determining means for obtaining a first reference reflection coefficient and a second reference reflection coefficient; a color at each intermediate point of each side of the N-dimensional color space is interpolated between two reference colors at both end points of each side; Is used to multiply the two reference colors.
Weighting factor determining means for determining one weighting factor for each side of the N-dimensional color space; and an N-dimensional correction space having the weighting factor determined for each side of the N-dimensional color space as coordinates of each side. And assigning the reference colors located at both ends of each side of the N-dimensional color space to positions of both ends of corresponding sides of the N-dimensional correction space, and passing the target color through the N-dimensional correction space. N
Are divided into 2 ^N partial N-dimensional correction spaces by the (N-1) -dimensional space, and the first reference reflection coefficient for each of the 2 ^N reference colors is assigned to each of the reference colors in the N-dimensional correction space. And the sum of the multiplication results for each of the 2 ^N reference colors is obtained by multiplying the volume of the partial N-dimensional correction space having a diagonal positional relationship with the point A first reflection coefficient determining means for determining Sb; a second reflection coefficient for each of the 2 ^N reference colors; a diagonal positional relationship with a point of each reference color in the N-dimensional correction space; A second reflection coefficient determination for determining a second reflection coefficient Ss of the target color by multiplying the volume of a certain partial N-dimensional correction space and calculating the sum of the multiplication results for each of the 2 ^N reference colors Means, the first and second counters Illuminance spectrum determining means for determining the illuminance spectrum I of the reflected light according to Equation 3 using the first and second reflection coefficients Sb and Ss determined by the coefficient determining means; Color data generating means for obtaining color data representing the target color in a color system suitable for the output device; and an output device for outputting the target color in accordance with the color data. Simulation system for printed materials. (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. 4. 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.
The first reflection coefficient Sb and the second reflection coefficient Ss included in Expression 4 for each of the 2 ^N reference colors located at both end points of each of the 2 ^(N-1) sides, A function of determining a reference reflection coefficient determined as a first reference reflection coefficient and a second reference reflection coefficient; and interpolating a color at each intermediate point of each side of the N-dimensional color space with two reference colors at both end points of each side. Is used to multiply the two reference colors.
A weighting factor determining function of determining one weighting factor for each side of the N-dimensional color space; and an N-dimensional correction space using the weighting factor determined for each side of the N-dimensional color space as coordinates of each side. And assigning the reference colors located at both ends of each side of the N-dimensional color space to positions of both ends of corresponding sides of the N-dimensional correction space, and passing the target color through the N-dimensional correction space. N
Are divided into 2 ^N partial N-dimensional correction spaces by the (N-1) -dimensional space, and the first reference reflection coefficient for each of the 2 ^N reference colors is assigned to each of the reference colors in the N-dimensional correction space. And the sum of the multiplication results for each of the 2 ^N reference colors is obtained by multiplying the volume of the partial N-dimensional correction space having a diagonal positional relationship with the point first the reflection coefficient determination function of determining the sb, the second reference reflection coefficients for the 2 ^N pieces of each reference color, the N-dimensional correction terms for each reference color in the space diagonal positional relationship A second reflection coefficient determination for determining the second reflection coefficient Ss of the target color by multiplying each of the volumes of a certain partial N-dimensional correction space and obtaining the sum of the multiplication results for each of the 2 ^N reference colors Function and the first and second counterparts An illuminance spectrum determining function of determining the illuminance spectrum I of the reflected light according to Equation 4 using the first and second reflection coefficients Sb and Ss determined by the coefficient determining means; and an illuminance spectrum I of the reflected light. A computer for realizing a color data generation function of obtaining color data representing the target color in a color system suitable for the output device, and an output function of outputting the target color according to the color data. A computer-readable recording medium on which a program 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.