JP2921365B2 - Paint color reproduction method and paint color selection method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of reproducing a paint color and a method of selecting a paint color, and particularly to a method of obtaining a painted surface by applying a paint or the like or displaying a painted surface on a color CRT. The present invention relates to a method of reproducing a paint color for reproducing a paint color of a paint surface intended by a designer or the like and a method of selecting a paint color.

[0002]

2. Description of the Related Art An object surface such as a body of a vehicle is formed by a paint surface having a paint color obtained by applying a paint or the like. However, in order to obtain a paint surface of a desired paint color intended by a user, a designer, or the like. A paint or the like obtained by mixing a plurality of pigments or the like using a color sample or the like as an index is applied to the object.

Recently, for example, for an object surface having a uniform optical property, the same accuracy as that of the real object is obtained by coloring calculation based on the ray tracing method using the reflectance of the object surface such as spectral solid angle reflectance. There is a method of reproducing and displaying a three-dimensional real object by using (A. Takagi et al, Computer Grap
hics, Vol 24, No. 4, 1990 etc.). In this method, a CIE (International Commission on Illumination) standard XYZ color system colorimetric value (tristimulus value) is obtained based on the spectral solid angle reflectance of the object surface and the like, and then the color system by linear linear combination conversion. By converting to an original color specification value, performing gamma correction and converting to RGB gradation, the color of the object is reproduced and an image is displayed. According to this method, if the reflectance of the object can be specified, the color of the object can be reproduced and displayed, and the reflectance of the object corresponding to the display color is specified by the reverse processing to obtain the display color. A color component can be obtained, and a desired coating color can be obtained by applying a paint or the like obtained by mixing a plurality of pigments or the like corresponding to the amount of the color component to an object.

[0004] However, setting and blending of the mixing ratio of pigments and the like for obtaining a desired coating color requires the skill of an engineer and has extremely low productivity. Further, due to differences or variations in the types of constituent materials such as pigments, the paint color of the finished paint surface does not always reproduce the paint color intended by the user or the designer.

[0005] In order to solve this problem, a computer which determines a mixing ratio such as setting of a mixing ratio of a pigment requiring skill as a mixing of a basic color material (colorant such as a pigment) according to the Kubelka-Munk theory by computer calculation. Color matching (hereinafter referred to as CCM) has become widespread. In the CCM, a computer calculates a mixing ratio of a plurality of pigments having known reflectances so as to match the reflectance of a color sample measured by a spectrophotometer or the like. In some cases, the mixing ratio of a plurality of pigments whose tristimulus values are known is calculated by a computer so as to match the tristimulus value of the color sample. As described above, in order to reproduce the intended coating color, there is a method of determining the mixing ratio of the colorant using the CCM (Japanese Patent Application Laid-Open No. 62-149760).

[0006]

However, in the conventional method of reproducing the paint color by CCM, the blending is determined in accordance with the Kubelka-Munk theory. Can not mix. Further, it is not possible to express a paint color containing a glittering material such as metallic or mica in a constituent material.

Although the above-mentioned CCM is effective for obtaining a paint color that matches a color sample or the like, values such as reflectance and tristimulus values for specifying the paint color are intuitive. Therefore, it is difficult for a designer or the like to reflect a sensible paint color tendency, such as reddish or glossy, which is used as an expression for obtaining a desired paint color from an existing paint color.

In view of the above facts, the present invention reproduces a paint color intended by a user or a designer who does not have specialized knowledge such as color science and reflection characteristics of an object, regardless of the composition and type of the paint. It is an object of the present invention to provide a method of reproducing a paint color that can be performed and a method of selecting a paint color that allows a user, a designer, or the like to select an optimal paint color intended by the user.

[0009]

According to a first aspect of the present invention, there is provided a method for reproducing a coating color, comprising: forming one or more layers on an object to be coated; For a predetermined coating color of a coating surface formed from a constituent material, a correspondence between a characteristic value composed of the amounts of all the constituent materials constituting the coating surface and a spectral reflectance distribution of the coating surface based on the characteristic value is determined in advance. A plurality of interpolated correspondences different from the correspondence representing the correspondence between the characteristic value of the paint color and the spectral reflectance distribution in which the amount of at least one constituent material among all the constituent materials determined by the correspondence is different, When a plurality of colors are estimated based on the correspondence, and a paint color other than the predetermined paint color is reproduced, a spectral reflectance distribution of the interpolation correspondence corresponding to the paint color to be reproduced is selected, and the selected spectral reflectance is selected. Reflectance The interpolation corresponding with determined characteristic values from the relationship to determine the amount of the all the constituent materials to reproduce the paint color for.

According to a second aspect of the present invention, there is provided a method for selecting a coating color, wherein a predetermined coating color of a coating surface is formed on the object to be coated with one or more layers and each layer is formed from at least one constituent material. A plurality of correspondences between a characteristic value composed of the amounts of all the constituent materials constituting the painted surface and a spectral reflectance distribution of the painted surface based on the characteristic value are determined in advance, and the spectral reflectance of the painted surface based on the characteristic value is determined. A tristimulus value based on the distribution is obtained in advance, and the amount of at least one component material among all the component materials determined by the correspondence relationship differs from the correspondence relationship representing the correspondence between the characteristic value of the coating color and the spectral reflectance distribution.
The composed interpolation relationship, as well as a plurality estimated on the basis of a plurality of said correspondence, said tristimulus values based on the spectral reflectance distribution of the coated surface due to the characteristic values of the estimated interpolation relationship
A different interpolated tristimulus value is obtained, and for each of the tristimulus value and the interpolated tristimulus value, a coordinate value on coordinates of a predetermined color system is obtained, and a plurality of coordinate values among the obtained coordinate values represent a reference color. When the reference coordinate value is determined and the tendency of the reference color is reflected in the designated color instructed to reproduce the paint color, the coordinate value from the coordinate value representing the designated color to the reference coordinate value is calculated from the latest coordinate value. The paint color is selected by sequentially selecting.

According to a third aspect of the present invention, there is provided a method for selecting a coating color, wherein a predetermined coating color is applied to a coating surface in which one or a plurality of layers are formed on an object to be coated and each layer is formed from at least one constituent material. A plurality of correspondences between the characteristic values composed of the amounts of all the constituent materials constituting the painted surface and the spectral reflectance distribution of the painted surface based on the characteristic values are obtained in advance, and all the constituent materials determined by the correspondence are determined. Interpolation correspondence different from the correspondence representing the correspondence between the characteristic value of the coating color and the spectral reflectance distribution in which the amount of at least one constituent material is different,
Estimating a plurality based on the plurality of correspondences, based on the spectral reflectance distribution of the interpolation correspondence or the spectral reflectance distribution of the correspondence, change the light receiving angle when receiving the reflected light of the painted surface. Deflection characteristics of the painted surface representing the flip-flop relationship between the deflected angle and the brightness at the deflected angle are obtained, and the deflection characteristics of the paint color to be reproduced are selected from the obtained plural deflected characteristics. Choose a color.

According to a fourth aspect of the present invention, there is provided a method for selecting a coating color, wherein a predetermined coating color is formed on a coating surface in which one or a plurality of layers are formed on an object to be coated and each layer is formed from at least one constituent material. A plurality of correspondences between the characteristic values composed of the amounts of all the constituent materials constituting the painted surface and the spectral reflectance distribution of the painted surface based on the characteristic values are obtained in advance, and all the constituent materials determined by the correspondence are determined. Interpolation correspondence different from the correspondence representing the correspondence between the characteristic value of the coating color and the spectral reflectance distribution in which the amount of at least one constituent material is different,
A plurality is estimated based on the plurality of correspondences, the particle size distribution of the constituent material is obtained for each characteristic value of the correspondence and the characteristic value of the interpolation correspondence, and the spectral reflectance distribution or the correspondence of the interpolation correspondence is obtained. A depth index representing the depth of the paint color is obtained based on the spectral reflectance distribution and the obtained particle size distribution, and the paint color is selected by selecting a plurality of the obtained depth indices.

According to a fifth aspect of the present invention, there is provided a method of reproducing a paint color, wherein the spectral reflectance distribution and characteristics of the paint color selected by at least one of the paint color selecting methods according to the second, third and fourth aspects. The correspondence with the value is estimated based on a plurality of correspondences obtained in advance, and the amounts of all the constituent materials are determined by the characteristic values determined from the estimated correspondence to reproduce the paint color.

[0014]

According to the first aspect of the present invention, a plurality of correspondences are determined in advance for a predetermined paint color of a paint surface. The painted surface is formed of one or more layers on the object to be coated, and each layer is formed of at least one constituent material. The constituent materials include coloring materials such as pigments and glittering materials. In the plurality of correspondences, a relationship between a characteristic value composed of the amounts of all the constituent materials constituting the painted surface and a spectral reflectance distribution of the painted surface based on the characteristic value is predetermined. For example, there is a sample coated plate whose spectral reflectance, pigment, and the like are known. An interpolation correspondence representing the correspondence between the characteristic value of the paint color and the spectral reflectance distribution in which the amount of at least one constituent material among all the constituent materials determined by the correspondence is different by an interpolation method or the like based on the plurality of correspondences. Are estimated based on a plurality of correspondences determined in advance. Therefore, an interpolation correspondence between the characteristic value and the spectral reflectance distribution for a desired paint color can be obtained only from a plurality of correspondences obtained in advance. Here, when a paint color other than the predetermined paint color is reproduced, a spectral reflectance distribution having an interpolation correspondence relationship corresponding to the paint color to be reproduced is selected. If the amounts of all the constituent materials including the coloring material and the brilliant material are determined by the characteristic values determined from the interpolation correspondence relationship to the selected spectral reflectance distribution,
A desired coating color can be reproduced together with the configuration of the coating surface on a CRT or a color material mixing device.

According to a second aspect of the present invention, there is provided a method for selecting a coating color according to the first aspect, wherein a characteristic value of a predetermined coating color comprising an amount for each constituent material of the coating surface and a spectral value of the coating surface based on the characteristic value. A plurality of correspondences with the reflectance distribution are determined in advance, and tristimulus values based on the spectral reflectance distribution of the painted surface based on the characteristic values are determined in advance. The tristimulus values include values represented by a color system such as the XYZ color system, and can be represented by coordinate values on chromaticity coordinates. There is also a Munsell color system. Based on the plurality of correspondences, a plurality of interpolation correspondences described in claim 1 are estimated, and interpolated tristimulus values based on the spectral reflectance distribution of the painted surface based on the characteristic values of the estimated interpolation correspondences are obtained. The tristimulus value and the interpolated tristimulus value are represented by XYZ
A coordinate value on a coordinate of a predetermined color system such as a color system is obtained, and a plurality of the obtained coordinate values are determined as reference coordinate values representing a reference color. As the reference color, it is preferable to set a basic color used for painting or printing such as red, blue, yellow, green, magenta, cyan, white, and black. When reflecting the tendency of the reference color to the designated color designated to reproduce the paint color, the nearest coordinate value from the coordinate value representing the designated color to the reference coordinate value representing the reference color on the coordinate plane of the predetermined color system. If the paint color is selected by sequentially selecting coordinate values from, the paint color corresponding to the selected coordinate value gradually reflects the tendency of the reference color. Therefore, if the amounts of all the constituent materials including the coloring material and the glittering material are determined based on the characteristic values of the coating color corresponding to the selected coordinate values, the desired coating reflecting the tendency of the reference color is determined. Color can be reproduced.

Here, the paint color desired by a designer or the like sometimes includes a sensational flip-flop feeling such as a bright and dark sharp feeling. Therefore, in the method for selecting a paint color according to the third aspect of the present invention, the light receiving angle when receiving the reflected light of the painted surface is changed based on the spectral reflectance distribution of the interpolation correspondence or the spectral reflectance distribution of the correspondence. The bending angle
The deflection characteristic of the painted surface, which indicates the flip-flop relationship with the brightness at the deflection, is determined. Since the sense of flip-flop can be expressed by this deflection characteristic, the paint color reflecting the flip-flop feeling can be selected by selecting the deflection characteristic of the paint color to be reproduced from the determined multiple deflection characteristics. it can. Therefore, if the amounts of all the constituent materials such as coloring materials and glittering materials are determined based on the characteristic values of the paint colors corresponding to the selected bending characteristics, the sense of flip-flop feeling desired by the designer or the like can be obtained. Can reproduce the paint color that reflects the.

The paint color desired by a designer or the like also has a sensuous indication such as a deep color. Therefore, in the method for selecting a paint color according to the present invention, the particle size distribution of the constituent material is obtained for each characteristic value in the correspondence obtained in advance and the interpolation obtained from the correspondence. Then, a depth index representing the depth of the coating color is obtained based on the spectral reflectance distribution of the interpolation correspondence or the spectral reflectance distribution of the correspondence and the obtained particle size distribution. Therefore, the perceived depth corresponding to the selected depth index can be expressed as a quantity, and a paint color having a desired depth can be selected by selecting the obtained plurality of depth indexes. Therefore, if the amounts of all the constituent materials such as coloring materials and glittering materials are determined based on the characteristic values of the coating color corresponding to the selected depth index, a coating color having a desired depth desired by a designer or the like can be obtained. Can be reproduced.

Further, in the invention described in claim 5, at least one of a coating color reflecting a tendency of a reference color, a coating color having a deflection characteristic representing a flip-flop relationship, and a coating color having a desired depth. One paint color is selected, and the correspondence between the spectral reflectance distribution and the characteristic value for the selected paint color is estimated based on a plurality of correspondences obtained in advance. Therefore, even when the paint colors that the designer or the like desires to express sensuously are combined, the amounts of all the constituent materials such as the color materials and the glitter materials are determined by the characteristic values determined from the estimated correspondence. Once determined, the desired sensory paint color can be faithfully reproduced.

[0019]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, a first embodiment of the present invention will be described in detail with reference to the drawings. As shown in FIG. 1, the color reproduction device for reproducing a paint color includes a personal computer 16 and a color material mixing device 18 having an automatic weighing device. The personal computer 16 includes a keyboard 10 for inputting color data and the like, a computer body 12 for calculating relevant data for generating a desired paint color according to a program stored in advance, and a calculation result of the computer body 12. CRT that displays a certain paint color, etc.
14. The color material mixing device 18 measures a plurality of color materials such as pigments by a measuring device such as an electronic balance according to a signal output from the personal computer 16, and then prepares a paint by blending these color materials. It is a device for.

In this embodiment, in order to reproduce the paint color, the physical quantity for specifying the paint color is determined as follows.

As described in the above prior art, if the spectral reflectance of the painted surface can be specified, the tristimulus value of the color can be obtained, and the surface color can be specified. Therefore, in the present embodiment, the spectral reflectance of the document or the object surface is used to display a color image or the like and to realize color reproduction for expressing a faithful paint color on the object surface. Note that this spectral reflectance may be measured at different values depending on the light receiving direction of the measuring instrument on a sample having a complicated shape, for example, a surface of a fiber or a metallic coating. And a spectral solid angle reflectance, which is a three-dimensional reflectance obtained by changing a light receiving angle or the like to a light receiving element that receives light reflected by the sample.

The reflectivity of a sample having a flat surface is usually measured using a Gonio Spectro Photometer.
ter, hereinafter referred to as gonio. ) 24 can be measured (colorimetric), and the measured reflectance is referred to as spectral solid angle reflectance (S
pectral Reflectance Factor). This spectral solid angle reflectance is hereinafter simply referred to as reflectance R.

As shown in FIG. 2, the gonio 24 has a light source 28 and a light receiver 26 as a measuring unit. Gonio 2
4 includes an incident optical axis 32 of light traveling from the light source 28 to the measurement point Ob of the sample 30 and a reflected optical axis 34 in a regular reflection direction when the light of the incident optical axis 32 is regularly reflected at the measurement point Ob. It provides that the incident plane D ₁ plane. This gonio 24
Then, the axis connecting the light receiver 26 and the measurement point Ob is defined as the measurement optical axis 3.
As 6, the photodetector 26 as the measuring optical axis 36 is contained in the plane of incidence D ₁ is a mechanism that moves in three dimensions (not shown).

The reflectivity R is calculated based on the reflection optical axis 34 and the measurement optical axis 36.
Is a function of the angle α from the specular reflection direction of the light receiving unit (unit: deg, hereinafter referred to as the variable angle α) and the wavelength of light λ (unit: nm). Can be represented by

R (α, λ) (1) where the angle of deflection α is 0 ° when the reflection optical axis 34 and the measurement optical axis 36 coincide with each other, and the angle of deflection α is from the specular reflection direction to the light source section. The sign of the variable angle α obtained from the position of the light receiving unit 26 rotated clockwise (in the direction of the arrow indicating the variable angle α in FIG. 2) is a positive sign.

As shown in FIG. 3, the variable angle α can be determined in a rectangular coordinate system based on an incident surface or the like. That is, the normal direction ＄ N of the sample 30, the incident direction 方位 L which is the azimuth between the sample 30 and the light source 28, the light receiving direction か ら R from the sample 30 to the light receiver 26, the specular reflection direction of the light regularly reflected by the sample 30 ＄ P is determined, and a surface including the normal direction ＄ N and the specular reflection direction ＄ P is defined as an incident surface D ₁ , and a surface including the normal direction ＄ N and the light receiving direction ＄ R is defined as a light receiving surface D ₂ . Thus, the angle of the angle theta ₁ between the normal direction $ N to the incident direction $ L, the angle theta ₂ between the normal direction $ N and the light-receiving direction $ R, an incident surface D ₁ and the light-receiving surface D ₂ θ ₃ is determined. When the surface of the sample 30 has directionality (for example, a woven fabric, a brush-finished surface, or the like), the reference direction of the sample surface (painted surface) around the measurement point Ob (FIG. 3)
Is the angle θ away from the entrance surface D _{1
And 4} . Therefore, the reflectance R in the above equation (1) can be expressed by the following equation (2) as a general equation.

R (λ, θ ₁ , θ ₂ , θ ₃ , θ ₄ ) --- (2) where θ ₁ : incident angle (deg) of light source θ ₂ : light receiving angle (deg) θ ₃ : azimuth angle (deg) θ ₄ : Rotation angle (deg)

The above equation (2) has four angle parameters represented by θ ₁ , θ ₂ , θ ₃ , and θ _4. The intensity distribution of the reflected light on the general painted surface (the intensity of the reflected light is
The distribution represented by the distance from the irradiation point as a center) is always a similar shape of Spherical Symmetry with the specular reflection direction ΔP as an axis, regardless of the incident angle θ ₁ of the incident light.
It is known that

FIG. 4 is a graph showing the change in spectral solid angle reflectance in order to show the helical symmetry of reflected light on a general paint-coated surface (metallic-coated surface).
In the figure, as shown in Table 1 below, the incident angle θ ₁ is 0 °.
In this case, the variable angle characteristic when the variable angle α is changed in the positive direction is the characteristic AP, and the variable angle characteristic when the variable angle α is changed in the negative direction is the characteristic AN. Similarly, when the incident angle θ ₁ is 15 °, 30
The characteristics BP, CP, DP, EP, and FP are obtained when the deflection angle α is changed in the positive direction at the angles of 45 °, 45 °, and 60 °. And

[0030]

[Table 1]

As can be understood from FIG. 4, the characteristics are substantially symmetric regardless of the angle of incidence. When the incident angle is 7
When the angle is 5 degrees, a measurement error has occurred due to a scene phenomenon caused by the reference white plate.

Therefore, the reflectance of the paint-coated surface is opposite
As a function of the deflection angle α between the launch direction ＄ P and the receiving direction ＄ R
Then, as shown in the above equation (1), the reflectance R (α, λ)
Can be expressed as For example, the light receiving angle θ_Two Angles other than
The condition is set to a predetermined value (θ₁= 60 °, θ_Three = 0 °, θ_Four = 0
°) and the deflection angle α is 0 ° to 90 ° (in this case, α =
θ ₁−θ_Two ), The reflectance R (α, λ)
Is measured by gonio, the reflectance R (α, λ) is 0 ° <α <
It is found in the 90 ° angle range.

If the reflectance R (α, λ) is determined by the following [angle condition], the reflectance R (α, λ) can be determined in an angle range of −30 ° <α <150 °.

[Angular Condition] R (α, λ) = R (−α, λ) (−30 ° <α <0 °) = R (90 °, λ) (90 ° <α <150 °)

In the following description, the angle condition (θ
Even in cases other than ₁ = 60 °, θ ₃ = 0 °, θ ₄ = 0 °), the reflectance R (α, λ) obtained by calculating the variable angle α from the relationship between the regular reflection direction ΔP and the light receiving direction ΔR is used. .

As shown in FIGS. 5 (a) to 5 (c), the coated surface of the sample whose surface is coated may be a colored pigment for determining the color, a glittering material such as metal or pearl mica, or a clear surface. Is composed of

As shown in FIG. 5 (a), the painted surface provided with the metallic coating is composed of a clear coat layer 40, a metallic base layer 42, an intermediate coating layer 44, and an electrodeposition layer 46. The metallic base layer 42 contains a pigment 54 and aluminum 56. As shown in FIG. 5 (b), the painted surface on which the perhamica coating has been applied includes a clear coat layer 40, a mica base layer 48, a color base layer 50,
It is composed of an intermediate coating layer 44 and an electrodeposition layer 46. The mica base layer 48 contains a titanized mica pigment 58. As shown in FIG. 5C, the painted surface by the solid painting is composed of an overcoat layer 52, an intermediate coat layer 44, and an electrodeposition layer 46. The overcoat layer 52 contains the coloring pigment 60.

As shown in FIG. 6, the relationship between the deflection angle α and the brightness Y (Y is obtained from equation (25) described later) is shown.
As can be seen from the figure, the symbol MA represented as the paint color
RUN, CRISTAL CAULAL, CAMEL PEIGE, PALE GREEN, GRAPE BL
The rate of change of the reflectance R becomes slower in the order of UE. FIG. 7 shows the relationship of the reflectance R (45 degrees, λ) when the variable angle α is 45 degrees. It can be understood that the brightness at a predetermined wavelength differs depending on the type of the painted surface.

Thus, due to the difference in the configuration of the painted surface,
The characteristics of the reflectivity R (α, λ) are different, and are affected by the type and amount of the pigment and the glittering material. Therefore, in order to identify these painted surfaces, in the present embodiment, as shown in the following equation (3), the constituent materials constituting the painted surface are x ₁ , x ₂ ,
, And the characteristic value vector VX representing the painted surface is defined with the magnitude of each constituent material x _i (i = 1, 2,...) As an amount q _i (Kg).

VX = (x ₁ [q ₁ ], x ₂ [q ₂ ],...) − (3)

Since the reflectance R (α, λ) of the painted surface formed by the characteristic value vector VX is related to the characteristic value vector VX, it can be expressed by the following equation (4).

R (α, λ, VX)-(4)

In this embodiment, since the paint color is reproduced, only the constituent materials (such as pigments) that determine the color among the elements of the characteristic value vector VX are considered, and e constituent materials related to the color are considered. Assuming only the above, a characteristic value vector VX shown in the following equation (5) is considered.

VX = (x ₁ [q ₁ ], x ₂ [q ₂ ],..., X _e [q _e ]) −−− (5)

In the present embodiment, it is not possible to use, as a constituent material, a glittering material such as some special colored mica, which has such a color that the colorless pigment itself changes color by the pigment. Basically, it is not considered.

In the above description, regarding the reflectance of the painted surface, the variable angle α and the wavelength λ are assumed to be related to the characteristic value vector VX.
The reflectance R (α, λ, VX) consisting of the following continuous characteristics has been described, but it can be handled approximately as described below.

First, the deformation angle α (0 ° to 90 °) is set to the boundary value α.
_j (j = 1, 2,..., n, 0 ° = α ₁ <α ₂ <.
<Α _n = 90 °), an appropriate division is performed, such as subdivision into [n-1] equal intervals or a range in which the reflectance changes rapidly. The appropriate division is preferably set so that 19 to 91 data numbers can be obtained at intervals of 1 ° to 5 °.

Similarly, for the wavelength λ, for example, the visible wavelength is considered as a wavelength range of 380 (nm) ≦ λ ≦ 720 (nm), and this visible wavelength range is defined as a boundary wavelength λ _k (k = 1, 2,. ..M,
380 nm = λ ₁ <λ ₂ ... <Λ _m = 720 nm) and appropriately divided into [m−1] pieces. The appropriate division of the wavelength range is preferably set so that 18 to 35 data numbers can be obtained at intervals of 10 to 20 nm.

Here, a unit vector VR _j (VX) of a division angle unit defined by the following equation (6) is defined as a unit reflectance R _jk (VX) with a reflectance at α = α _j and λ = λ _k . I do.

VR _j (VX) = (R _j1 (VX), R _j2 (VX),..., R _jm (VX)) --- (6)

Assuming that interpolation is performed between the unit reflectances R _jk (VX), the reflectance R (α, λ, VX) is a discrete unit vector VR _j (VX), that is, V
R _1, VR, ···, it can be approximated from the VR _n.

That is, as shown in FIG.
In a three-dimensional coordinate system having axes of (α, λ, VX), deflection angle α, and wavelength λ, the reflectance R (α, λ, VX) is a surface such as a continuous curved surface (hereinafter, a continuous surface). .) 70. The continuous surface 70 representing the reflectance R (α, λ, VX) can be obtained by interpolation from a plurality of discrete points included on the continuous surface 70. Thereby, the continuous surface 70
The reflectance R (α, λ, VX) can be approximated from the plurality of unit vectors VR _j (VX) included above.

Therefore, the reflectance R (α,
λ, VX) can be approximated from the discrete unit vector VR _j (VX) shown in the above equation (6). In this embodiment,
The relationship between the characteristic value vector VX and the unit vector VR _j (VX) which is discrete data is defined as a specified value. This specified value can be obtained by forming an actual painted plate by the characteristic value vector VX and measuring the reflectance.

Next, the operation of this embodiment will be described. A new reflectance (hereinafter, referred to as a new reflectance R ^* (α, λ)) based on an image color assumed by a designer or the like or based on an existing reflectance R (α, λ, VX). If this new reflectance R ^* (α, λ) is determined, the color and texture of the painted surface can be visually confirmed by a color graphics device or the like (see Japanese Patent Application Laid-Open No. 1-1511). Therefore, in the present embodiment, the characteristic value vector VX ^* , which is the amount of paint or the like, is estimated from the image color assumed by the designer or the like and the desired new reflectance R ^* (α, λ) based on the existing reflectance R. Will be described.

That is, the new reflectance R ^* (α, λ) is a newly generated reflectance, and the types and amounts of pigments and glitters for realizing the reflection characteristics of the reflectance R ^* (α, λ). Is unknown. Therefore, in order to reproduce the coating color by new reflectance R ^* may be determined a characteristic value vector VX ^* corresponding to the new reflectance R ^* shown in the following equation (7).

VX ^* = (x ₁ [q ₁ ] ^* , x ₂ [q ₂ ] ^* ,..., X _e [q _e ] ^* ) −−− (7)

When a power switch (not shown) of the color reproducing apparatus including the personal computer 16 and the like is turned on, a main routine for reproducing the paint color shown in FIG. 9 is executed.

In step 100, the above-mentioned prescribed value is set. Specifically, the process proceeds to step 110 in FIG. 10, to define a characteristic value vector VX by the material x _i of the color material or the like used in the color material mixing apparatus 18. New reflectance R ^* (α, λ) is the characteristic value vector VX ^* itself for obtaining, for still unknown, whether or maximum amount q _i of each constituent material in step 110 x _i set by the random number Set.

In the next step 112, the quantity q _i of each constituent material x _i of the characteristic value vector VX is set to the boundary value q _iA (1 ≦ A ≦
By P, q _i1 <q _i2 <... <Q _iP ), it is appropriately divided into [P + 1] pieces. Thus, the constituent quantities q ₁ , q ₂ ,.
, Q _e are expanded into P quantities that increase or decrease stepwise. Therefore, there are L = P ^e combinations of the characteristic value vectors VX based on these constituent quantities q _iP as shown in the following Expression 1.

[0060]

(Equation 1)

In the next step 114, L constituent quantities q
_iPCharacteristic value vector VX for each combination_h(H =
1, 2,..., L). That is, the constituent material x
₁, X _Two , ... x_eBy sequentially changing the amount of
As shown in Equation 2 below, each of the constituent materials was changed.
Characteristic value vector VX_hAsk for.

[0062]

(Equation 2)

In the next step 116, determined characteristic values to produce a coating material prepared by mixing the color material or the like based on the amount of the constituent material of the vectors VX _h, the generated coating the coated surface of the coated plate was applied to the plate The reflectance R _h (α, λ, VX _h ) is obtained by actual measurement (see Equation 3).

[0064]

(Equation 3)

The reflectance R _h (α, λ,
VX _h ) is to obtain a plurality (nm) of unit reflectivities R _jk when the deflection angle α and the wavelength λ are appropriately divided as described above.

When the specified value setting process in step 100 is completed, the process proceeds to step 200, where a new reflectance R ^* (α, λ) desired by a designer or the like is read. A new characteristic value vector VX ^* (x ₁ ^* , x ₂ ^* ,... X) for this arbitrary new reflectance R ^* (α, λ)
_e ^* ), that is, the amount of constituent materials such as coloring materials
It is calculated at 00. In step 300, a known value is obtained from the reflectance and the characteristic value vector using a method using the inverse estimation method by interpolation that has already been proposed by the present applicant (Japanese Patent Application No. 5-196082).

In this case, the characteristic value vector VX = (x ₁ , x ₂ ,...) Capable of determining the amount of e constituent materials
_xe ) is input, and nm reflectance data of the reflectance R (α, λ, VX) is output. This output nm data is converted into a reflectance vector VR represented by the following equation (8).
Is determined.

VR = (R ₁₁ (VX), R ₁₂ (VX),..., R _nm (VX)) (8)

If the conversion for obtaining the output of the reflectance vector VR from the input of the characteristic value vector VX is a function f, it can be expressed by the following equation (9). The inverse problem can be handled as shown in equation (10) below.

F: VX → VR --- (9) f ^-1 VR → VX --- (10)

The details of step 300 will be briefly described with reference to the flowchart of FIG.
In 10, the reflectance R (the output value Oi in FIG. 12) for a predetermined number (in the present embodiment, for example, 5 ³ ) of the characteristic value vectors VX (the input value Si as the sample point in FIG. 12) is determined (FIG. 1)). That is, this relationship is determined by measuring the reflectance of a painted plate with a known amount of constituent material. This step 310 corresponds to step 100 described above.
Is the same processing as the setting of the specified value. In step 312, an interpolation point SIi (i: i: i) for the discrete input value Si is obtained from the correspondence between the input value Si and the output value Oi using an interpolation method.
..) And the estimated output value OIi corresponding to the interpolation point SIi are calculated (see FIG. 12 (2)). In the next step 314, the output value Oi closest to the output value to be obtained (that is, the data of the reflectance of the paint color to be reproduced, the data indicated by the symbol * in (3) of FIG. 12) corresponding to the desired color. Alternatively, the estimated output value OIi is selected to obtain the input value Si or the interpolation point SIi (that is, the characteristic value vector VX) corresponding to the selected value (Oi or OIi) (FIG. 1).
2 (3)).

It should be noted here that all combinations of the characteristic value vectors VX (VX ₁ ,.
VX _L ), there is no solution of the characteristic value vector VX for the reflectance vector VR ^* that is out of the range of the reflectance vector VR formed with respect to the reflectance vector VR ^*.
Cannot be generated. Deviating from the value range of the reflectance vector VR means that, for example, as shown in FIG.
When i, m = 8, the unit vector VR _j (VX) becomes
VX _1, ···, refers to the case where out of the area Area where VR _j (VX) may take the change in the VX _L. In this case, the points A ₁ , A ₂ , A ₃ , A ₄ , and A ₅ are included in the area Area, but the points A ₆ , A ₇ , and A ₈ are not included in the area Area.

Thus, the new reflectance R^*(Α,
λ) to obtain the characteristic value vector VX ^*Is found,
In step 400, the characteristic value vector VX^*Formulation by
x₁[q ₁]^*, X_Two[q_Two]^*, ..., x_e[Q_e]^*The table
Output to the color material mixing device 18,
, The desired reflectance R^*(Α,
λ) to produce a coated object such as a coated plate.

Next, a second embodiment will be described. In the first embodiment, the case where each of the amounts of the constituent materials is appropriately divided is described as the setting process of the specified value. However, when there are a large number of constituent materials, the combination becomes enormous and is not practical. . Therefore, in the second embodiment, a case will be described in which the specified value is easily determined regardless of the number of types of constituent materials. Since the second embodiment has the same configuration as that of the first embodiment, the same portions are denoted by the same reference numerals, and detailed description will be omitted.

For example, an existing paint color A can be represented by a characteristic value vector VX shown in the following equation.

VX = (x ₁ [q ₁ ], x ₂ [q ₂ ],..., X ₅ [q ₅ ]) where x ₁ : holy metallic coarse texture (brilliant material) q ₁ : 41. 19 (g) x _2: 〃 subdivision (〃) q _2: 4.40 (〃) x _3: huntingtin click black (pigment) q _3: 11.70 (〃) x _4: Blue black (〃) q ₄ : 6.69 (〃) x ₅ : Slen blue (〃) q ₅ : 14.54 (〃)

Here, the amounts q ₁ , q ₂ of the brilliant materials of the constituent materials x ₁ , x ₂ are kept constant, and the amounts q ₃ , q ₄ , q ₅ of the constituent materials x ₃ , x ₄ , x ₅ are set as follows. To create the actual painted board. Next, as shown in the following [State A], the amounts are changed in six steps in 10 g increments so that each amount does not exceed a fixed value (for example, 50 g). This gives 6 ³ =
216 coated plate states are obtained. Therefore, the reflectance R (α, λ, VX) for the 216 characteristic value vectors VX
Can be sought.

[0078]

(Equation 4)

By the way, the number (type) of constituent materials x _i ,
When x _{i + 1} ,... x _p increases, a large number of painted plates for obtaining sample data (unit reflectance) must be generated, which is not practical. For example, assuming that there are nine color materials and each of them is divided into six (0, 10, 20,..., 50 (g)), a huge number of samples of 6 ⁹ ≒ 1.0 × 10 ^{7 in} total ( It is impossible to put it to practical use.

Therefore, in this embodiment, the color expression is simplified as described below. FIG. 15 shows xy color coordinates of CIE. The points in the figure are the outermost parts when plotted at positions corresponding to colors that can be represented by existing color materials in the xy color coordinates.

When a power switch (not shown) of the color reproducing apparatus constituted by the personal computer 16 and the like is turned on, the main routine shown in FIG.
Then, the specified value is set. Specifically, the process proceeds to step 120 in FIG. 14, as well as define the characteristic value vector VX by the material x _i used in the colorant mixing apparatus 18, x
A primary color is set from colors that can be represented by existing color materials in the y-color coordinates. In the present embodiment, points G (green), Y (yellow), R (red), M (magenta), B (blue), and C ( C), and a point K corresponding to white is determined, and a color corresponding to these points is set as a primary color.

In the next step 122, a triangular area of three points including the point K among the above-mentioned primary colors for generating a sample painted plate is set as a target color area. In this case, the target color area is a triangle {KGY, {KYR, {KRM,}
KMB, $ KBC, and $ KCG. An arbitrary color can be reproduced using data (amount) of three vertices of a triangle including a point at a position corresponding to the color. That is, by changing the amount of each of the three vertices of the triangle, the colors at all positions included in the triangle can be represented.

In the next step 124, one of the set triangles is selected. For example, in order to reproduce the paint color located at the point C1 in FIG. 15, the points K, Y, and G are used as the primary colors, and the change in the amount of the constituent material is processed within ΔKGY. In the next step 126, the amount of the constituent material of each primary color of the selected triangle is appropriately divided into, for example, six stages as shown in the following [State B]. Accordingly, for △ KGY in this case, 6 ³ = 216 combinations are assumed, and a sample coated plate is generated for each.
In the next step 128, the reflectance of the generated sample painted plate is measured, and the process proceeds to step 130.

[0084]

(Equation 5)

In the next step 130, step 1
It is determined whether or not the above processing has been completed for all of the triangular regions set in 22 and the processing is performed until the above processing has been completed for all of the triangles. By doing so, it is possible to generate a small number of sample painted plates for color reproduction for all of the color regions that can be represented by the color material,
The specified value can be easily determined regardless of the number of types of constituent materials.

Next, a third embodiment will be described. The first fruit
In the embodiment and the second embodiment, the inverse estimation method by interpolation is used.
Unknown characteristic value vector VX^*Seeking.
In the third embodiment, the reflectance factor shown in the above equation (10) is used.
Unknown characteristic value vector VX from vector VR^*Reverse
Problem (f^-1), That is, the reflectance R^*(Α, λ) (R ₁₁
^*, R₁₂ ^*, ..., R_nm ^*Characteristic value vector for
VX^*It is well known that a neural network (Ne
ural Network) method. That is,
Reflectivity R^*R as an input layer for inputting^*of
It has neurons according to the number and outputs the amount of constituent materials
Value vector VX as an output layer for ^*According to the number of
Each neuron has a synapse.
Neural networks connected by
Learning by the learning process, the desired reflectance R^*Unknown from
Characteristic value vector VX^*Is obtained.

In the neural network method of the third embodiment (hereinafter referred to as the NNW method), the structure of the neural network is extended to continuous N layers, and the reflectance R
Three examples of estimating the characteristic value vector VX ^* for ^* (α, λ) will be described. The third embodiment is different from the first embodiment.
Since the configuration is the same as that of the embodiment and the second embodiment, the same portions are denoted by the same reference numerals, and detailed description will be omitted. Since the first, second and third NNW methods have substantially the same configuration, different portions will be sequentially described. Further, in the following description, a neural network method based on supervised learning will be described, but it may be based on unsupervised learning.

As shown in FIG.
Computer 16 includes a neural network device 72
I have. The neural network device 72 is a network
And a teacher 74. Network
74 has a reflectance R^*Is input and the estimation
Characteristic value vector VX^*Is output.
You. Input reflectance R^*Signal TC and output corresponding to
Characteristic value vector VX ^*The output signal OC corresponding to
The input to the section 76, the teacher section 76
The modified signal SC is output to the network 74.
ing.

In the first NNW method, the network 74
, The reflectance vector VR ^* constituting the reflectance R ^* is input, and the estimated characteristic value vector VX ^* is output. The known characteristic value vector VX corresponding to the input reflectance vector VR ^* is input to the teacher unit 76 as the teacher signal TC, and the output signal OC corresponding to the output characteristic value vector VX ^* is also input to the teacher unit 76. . Teacher 76
Is the corrected signal SC obtained from the difference between these input signals.
Is output to the network 74.

As shown in FIG. 17, the configuration of the network 74 used in the present embodiment has a feed-forward (FF) type in which each layer receives an input only from the immediately preceding layer in order to simplify the description. I do. The network 74 is composed of N layers, and the input layer 78 has neurons 8 in the number (in this embodiment, nm) of the reflectance vectors VR as input signals.
4 (hereinafter, referred to as a unit 84). The first to nm-th units 84 in the input layer 78 are connected in parallel to all the units 84 in the first layer of the intermediate layer 80 as the next layer. This intermediate layer 80
Has N-2 layers, and each of the units 84 existing in each layer is connected in parallel to all the units 84 in the next layer. Further, the output layer 82 is continuous after the final layer of the intermediate layer 80,
All the units 84 existing in the final layer of the intermediate layer 80 are connected in parallel to each unit 84 of the output layer 82. The output layer 82 includes units 84 corresponding to the number (e in the present embodiment) of the constituent materials of the characteristic value vector that is the output signal.
Exists. In the following units 84, the order of the last unit 84 existing in the input layer 78, the intermediate layer 80, and the output layer 82 is denoted as S _Z (1 ≦ Z ≦ N). That is, the last unit of the input layer 78 is S ₁
(= Nm), and the last unit of the output layer 82 is the S _N (= e). The above connection may be disconnected at the time of learning described below.

As shown in FIG. 18, the network 74
And the adjacent S layer (1 ≦ S ≦ N−1) and [S + 1]
Referring to the layers, outputs from all units in the S layer are input to the u-th unit in the [S + 1] layer. Therefore, the input in _{S + 1} (u) to the u-th unit 84 in the [S + 1] layer is represented by the following equation (11).

[0092]

(Equation 6)

Where w _s (u, v) is the coupling coefficient between the v-th unit in the S layer and the u-th unit in the [S + 1] layer, and t _{S + 1} (u) is the offset value. Unit output value out
_{S + 1} (u) is determined by the following equation (12): out _{S + 1} (u) = sigmoid (μ ₀ , in _{S + 1} (u)) --- (12) where sigmoid () Is a sigmoid function shown in the following equation (13).

[0094]

(Equation 7)

Accordingly, the output of the v-th unit in the S layer can be similarly described as follows. out _S (v) = sigmoid (μ ₀ , in _S (v))

Next, the error δ _S (S = 1, 2,..., N) of each unit in each layer in the above network 74
Is defined as follows.

First, v in the N-th layer which is the output layer 82
The error δ _Nv of the th unit (v = 1, 2,...,
S _N ) is represented by the following equation (14).

[0098]

(Equation 8)

Next, the error δ _Su (u = 1, 2,..., S _Z ) of the u-th unit in the S-th layer is expressed by the following equation (15).

[0100]

(Equation 9)

Where δ _{(S + 1) v is} the error of the v-th unit in the [S + 1] layer.

Using the above equations, the correction values of the coupling coefficient and the offset value in the equation (11) can be expressed by the following equation (16).

Δw _S (u, v) = α _S · δ _{(S + 1) v} · out _S (v) Δt _{S + 1} (u) = β _S · δ _{(S + 1) v} −−− (16 ) Where α _S and β _{S are} constants

As an example of the above neural network learning method, an error back propagation method (back propagation method,
Back Propagation method, hereinafter referred to as BP method. ).
The BP method converges the network 74 by converging the correction values Δw _s (u, v) and Δt _{s + 1} (u) of the coupling coefficient and the offset value shown in the above equation (16). Is a method of stabilizing

In the BP method, like the well-known delta rule,
The minimum value of the error may not be determined. In order to solve this, there are a moment method and a modified moment method. As another method, there is also a constant changing method in which the initial value of the modified value is set large and the modified value is reduced as the error becomes smaller.

The coupling coefficient correction method in the BP method includes a successive correction method for correcting the coupling coefficient for one input,
There is a batch correction method in which a correction amount is accumulated and corrected collectively after all input is completed.

Next, the operation of the present embodiment using the first NNW method will be described. When a power switch (not shown) of the color reproduction device including the personal computer 16 and the like is turned on, a main routine for reproducing the paint color shown in FIG. 19 is executed. Set. Accordingly, a combination of L = P ^e combinations of the characteristic value vector VX and the reflectance R (α, λ, VX) is obtained as shown in the above equation (2).

For example, a combination (5 ³ = 125) of five types of tristimulus values each having coordinate values distributed on xy chromaticity coordinates.
With respect to the reflectance R of the (set), learning is performed as follows using the relationship between the known reflectance vector VR and the characteristic value vector VX.

At the next step 102, the network 7
4 learning is done. That is, as an input of the network 74, data of nm reflectances R ₁₁ (VX), R ₁₂ (VX),..., R _nm (VX) for the characteristic value vector VX
: VR is given. At the same time, the teacher unit 76 provides the elements (quantities) x ₁ [q ₁ ], x ₂ [q ₂ ],..., X _e [of the _e characteristic value vectors VX for obtaining the reflectance vector VR. q _e ] is output as a teacher signal, and the teacher unit 76 outputs the correction signal SC while monitoring the characteristic value vector VX and the output of the network as follows. Such a process learns the network 74 using the BP method described above for the L group. In this learning, the characteristic value vector VX which is the target value and the output value of the network (the characteristic value vector composed of the amount of the constituent material) VX 'are used to determine whether the mean square error ε shown in the following equation (17) converges. The process is repeated until the values become smaller, and the coupling coefficient w _S (u, v) and offset t _{S + 1} (u) at this time are obtained.

[0110]

(Equation 10)

In this manner, the learning of the network 74
Is completed, the process proceeds to step 200, where designers and the like
Desired new reflectance R^*(Α, λ) is read and the next
In step 302, the above coupling coefficient and offset
Using desired values of reflectance data R₁₁ ^*, R₁₂ ^*, ...
・, R_nm ^*Output x of network 74 for₁[q₁]
^*, X_Two[q_Two]^*, ..., x_e[Q_e]^*Get. this
Thus, the new reflectance R^*(Α, λ)
Sex value vector VX^*Is found, and in step 400
And the characteristic value vector VX^*Formula x₁[q₁]^*, X
_Two[q_Two]^*, ..., x _e[Q_e]^*Signal that represents
The paint is output to the combining device 18 and the paint is
If generated, the desired reflectance R^*(Α, λ) painted plate, etc.
Can be produced.

Next, the second NNW method of the third embodiment will be described. The first NNW method is effective for a linear problem in which the convergence of the solution is easily obtained, but the solution may not converge in a complicated problem such as a nonlinear problem. The second N
The NW method is also effective for complex problems such as non-linear problems.

In the second NNW method, the input to the network 74 is a characteristic value vector VX constituting a known reflectance R, and the teacher signal TC is a reflectance vector VR corresponding to the known reflectance R. The network 74 is L
Converge using the set of known relationships (stabilize the system). Thus, a network 74 that outputs the reflectance vector VR when the characteristic value vector VX is given can be configured. This converged network 74 corresponds to a function f for solving the problem corresponding to the above equation (9). Therefore, in the second NNW method, in order to obtain a characteristic value vector VX ^* corresponding to a desired reflectance R ^* , as described below, an inverse function for obtaining a solution to the inverse problem corresponding to equation (10) Find f- ¹ .

In the second NNW method, since a square matrix is used (details will be described later), a network 74 having the same number of units in each layer is used. In the present embodiment, an example in which the number of units in each layer is p (order is p) will be described. Further, regarding the input and output of the network 74, the element of the characteristic value vector VX which is the input and the reflectance vector V which is the output
In some cases, the number of elements in the input layer 78 may exceed the number of elements in the input characteristic value vector VX. By inputting, as an input signal, a small value that does not affect the above, it is possible to cope with this.

First, the v-th unit in the S layer and [S +
1] Consider the u-th unit in the layer (see FIG. 18). [S + 1] Input of the u-th unit in in _{S + 1}
(U), assuming that the output is out _{S + 1} (u), [S + 1]
Since the unit in the u-th layer has inputs from all units in the S-layer, the relationship between the input and output in the u-th unit in the [S + 1] layer can be expressed by the following equation (18).

[0116] In this embodiment, the order S _z of the last unit of each layer in FIG. 18 are all p, 1 ≦ v ≦
p, 1 ≦ u ≦ p. Also, since only one input signal corresponding to each unit is input to the input layer 78, in ₁
(V) = out ₁ (v).

[0117]

[Equation 11]

Here, a matrix IN _{S + 1} and a matrix OUT _S are determined as follows, and IN _{S + 1} = [in _{S + 1} (1), in _{S + 1} (2),.
_{S + 1} (p)] OUT _S = [out _S (1), out _S (2),.
·, Out _S (p)] A square matrix A whose elements are coupling coefficients w _S (u, v)
_{When S} is defined, the above equation (18) becomes the following equation (1)
9).

IN _{S + 1} = A _S · OUT _S --- (19)

For this matrix OUT _S , the above equation (1)
Using the sigmoid function as in the case of 2), the following expression (2)
0) is defined. Therefore, the inverse function of the sigmoid function represented by the following equation (20) is represented by equation (21), and [S + 1]
The relationship between the input and output in the layer can be expressed by the following equation (22).

OUT _S = sigmoid (μ ₀ , IN _S ) = g (IN _S ) (20)

[0122]

(Equation 12)

Then, the following equation (23) can be derived using the above equations (19) and (22).

OUT ₁ = IN ₁ , OUT _S = A _S ⁻¹ · IN _{S + 1} = A _S ⁻¹ · g ⁻¹ (OUT _{S + 1} ) OUT ₁ = A ₁ ⁻¹ · g ⁻¹ (OUT ₂ ) = A ₁ ⁻¹ g ⁻¹ (A ₂ ⁻¹ g ⁻¹ (... A _N−1 ⁻¹ g ⁻¹ (OUT _N )...)) −−− (23) where S = 1 2, ..., N-1

As understood from the above equation (23),
When the output signal of the output layer is obtained, the input signal to the input layer can be obtained. Therefore, the equation (23) becomes the inverse function f ^-1.
And can be expressed by the following equation (24).

F ^-1 (OUT) = A ₁ ^-1 g ^-1 (A ₂ ^-1 g ^-1 (... A _N-1 ^-1 g ^-1 (OUT _N )) ...) (24) Since the inverse function f ^-1 can be obtained in this manner,
An operation can be performed to obtain the characteristic value vector VX ^* corresponding to the desired reflectance R ^* using the coupling coefficient of the converged network 74.

Next, the operation of the present embodiment using the second NNW method will be described. When the main routine for reproducing the paint color is executed (see FIG. 19), a specified value is set (step 100), and a learning process of the network 74 is performed (step 102). In the learning process of the network 74 by the second NNW method, a learning process routine shown in FIG. 42 is executed.

In step 102A of FIG. 42, the convergence processing (system stability) of the network 74 is performed using the specified value as described above. In the next step 104A, the derivative is determined using the coupling coefficient of the stable system. That is, the square matrix _AS and the function g are obtained. In the next step 106A, the obtained square matrix A _S and function g
Then, the square inverse matrix A _s ^-1 and the inverse function g ^-1 are derived from, and in the next step 108A, the obtained square inverse matrix A _s ^-1 and the inverse function g ^-1 are stored.

In this way, the learning of the network 74
Upon completion of the process, the process proceeds to a step 200 in FIG.
New reflectance R desired by Zainer etc.^*(Α, λ) reads
Taken and in the next step 302 the stored square
Inverse matrix A_S ^-1And the inverse function g^-1The desired reflectance data using
R₁₁ ^*, R₁₂ ^*, ..., R_nm ^*Network for
Output x₁[q₁]^*, X_Two[q_Two]^*, ..., x_e
[Q_e]^*Get. Thus, the new reflectance R
^*Characteristic value vector VX for obtaining (α, λ)^*Sought
And the characteristic value vector VX^*Formula x₁[q₁]^*, X
_Two[q_Two]^*, ..., x _e[Q_e]^*Signal that represents
Output to the combining device 18 (step 400), and the color material mixing device
If the paint is generated at 18, the desired reflectance R
^*(Α, λ) can produce painted objects such as painted boards.
Wear.

Next, the third NNW method of the third embodiment will be described. In the third NNW method, similarly to the second NNW method, an input to the network 74 is a characteristic value vector VX constituting a known reflectance R, and the teacher signal TC is a known reflectance R
As described above, the network 74 is made to converge (stabilize the system) using the known L sets of relationships as the reflectance vector VR corresponding to the above. Thereby, the characteristic value vector VX
Is given, a network 74 that outputs the reflectance vector VR can be configured.

Next, the operation of the present embodiment using the third NNW method will be described. When the main routine for reproducing the paint color is executed (see FIG. 19), a specified value is set (step 100), and a learning process of the network 74 is performed (step 102). In the learning process of the network 74 according to the third NNW method, a learning process routine shown in FIG. 43 is executed.

In step 102B of FIG. 43, convergence processing (system stability) of the network 74 is performed using the specified value (sample) as described above. In the next step 104B, while the value of the characteristic value vector VX is close to the sample used in the above step 102B,
By dividing each amount of the constituent material by a predetermined number of boundary values, a predetermined number of interpolation characteristic value vectors VVX are set at equal intervals. In the next step 106B, using the above-mentioned stable system, the interpolation characteristic value vector VVX set in step 104B is input, and the output interpolation reflectance vector V
Find VR. In the next step 108B, the correspondence between the characteristic value vector VX and the reflectance vector VR and the correspondence between the interpolation characteristic value vector VVX and the interpolation reflectance vector VVR obtained in step 106B are stored.

As described above, the learning of the network 74 is performed.
Upon completion of the process, the process proceeds to a step 200 in FIG.
New reflectance R desired by Zainer etc.^*(Α, λ) reads
Taken. In the next step 302, the new read
Reflectivity R^*Reflectance data R corresponding to (α, λ)₁₁ ^*,
R₁₂ ^*, ..., R_nm ^*Matches or is closest to
Vector VR or interpolation reflectance vector VVR is selected.
And a characteristic value vector VX corresponding to the selected vector.
Or output the interpolation characteristic value vector VVX x₁[q ₁]^*,
x_Two[q_Two]^*, ..., x_e[Q_e]^*And like this
And the new reflectance R^*Characteristic value for obtaining (α, λ)
Vector VX^*Is obtained, and the characteristic value vector VX^*by
Formula x₁[q₁]^*, X_Two[q_Two]^*, ..., x_e[Q_e]^*
Is output to the color material mixing device 18 (step 40).
0), if paint is generated in the color material mixing device 18,
Desired reflectance R^*Generate painted objects such as painted boards by (α, λ)
can do.

The first and third embodiments show two methods for obtaining the unknown characteristic value vector VX ^* . The first method of the first embodiment can obtain a highly accurate solution, but requires a large amount of calculation in advance. The second method of the third embodiment is lower in accuracy than the first method, but requires less computation and is faster. Both may be used properly depending on the application.

Next, a fourth embodiment will be described. In the above embodiment, when the reflectance R (α, λ) is determined, the characteristic value vector VX that realizes this is obtained. By the way, from the designer's point of view, the numerical reflectivity is a familiar one, and it is not appropriate to control this as it is from the viewpoint of operability. Therefore, in the present embodiment, the paint color is reproduced based on the feeling of a user such as a designer (hereinafter, referred to as design feeling). The fourth
In this embodiment, the same components as those in the above embodiment are denoted by the same reference numerals, and detailed description will be omitted.

In this embodiment, a case where a person in charge such as a color designer or a paint maker selects a paint color based on the Munsell color system and the CIE chromaticity coordinates, which is usually easy to use and understand.

The above characteristic value vectors VX ₁ , VX ₂ ,.
..., the reflectance with respect to _{VX L R (α, λ,} VX 1), R
_{(Α, λ, VX 2)} , ···, R (α, λ, VX L) is determined. Once this reflectivity R is determined, the following equation (2)
5) and (26), the tristimulus value (X, Y, Z) and chromaticity (x, y) can be calculated.

[0138]

(Equation 13)

This Y indicates the brightness of the light I (λ). The values of x and y obtained from the following equation (26) are used as chromaticity coordinates. As is well known, x is the horizontal axis and y is the vertical axis. The color can be specified by plotting on a chromaticity diagram of the coordinate system orthogonal to the axis (all colors are included inside the oblique bell shape).

X = X / (X + Y + Z) y = Y / (X + Y + Z) (26)

The correspondence between the chromaticity coordinates (x, y) and the Munsell color system can be obtained from a table or the like of JISZ8721 (color display method based on three attributes).
When y) and brightness Y are determined, the three attributes H (hue), lightness (V), and saturation (C) of the color corresponding to the Munsell are determined.
Can be requested.

Therefore, if the data of the sample coated plate obtained in the above embodiment is plotted in the diagram of the Munsell color system shown in FIG. 21 or the corresponding position on the CIE chromaticity coordinates shown in FIG. All the points have information on the reflectance R (α, λ). In addition,
A diagram in which the Munsell color system and the CIE chromaticity coordinate system shown in FIG. 23 correspond may be used.

Next, the operation of the present embodiment will be described. When proceeding to step 200 of the above-mentioned flowchart, a paint color selection routine shown in FIG. 20 is executed. Step 2 in FIG.
In 10, the designer determines whether the color system indicating the paint color is the Munsell color system by determining the command signal specified by the keyboard 10. If the determination is affirmative, the data of the Munsell color system stored in advance is read in step 214, the diagram of the Munsell color system is displayed on the CRT 14, and the process proceeds to step 216.
On the other hand, in the case of a negative determination, in step 212, the data of the CIE XYZ color system stored in advance is read and the xy chromaticity coordinates of the CIE XYZ color system are displayed.

In the next step 216, a desired paint color is specified by selecting a designer or the like from the Munsell color system diagram or the plot points 86 plotted on the CIE chromaticity coordinates. In the next step 218, the reflectance R ^* (α, λ) is obtained based on the selected plot point 86, and the reflectance R ^* (α, λ) is output. Therefore,
The characteristic value vector V corresponding to the reflectance R ^* (α, λ)
X is determined, and a desired desired paint color can be obtained from the characteristic value vector VX.

When the designer selects the plot point 86 and selects a point between the plot points, as described in the above embodiment, the plot point 86 corresponds to the plot point selected by interpolation or the like. A characteristic value vector can be obtained. Specifically, from the relationship of the above equation 3, R (α, λ, V
X), the chromaticity (x, y) is calculated by the formulas (25) and (26), and the Munsell color system diagram or CIE is calculated.
What is necessary is just to plot on a chromaticity coordinate (refer FIG. 24).

Next, a fifth embodiment will be described. The fifth embodiment is intended to accurately reproduce an ambiguous paint color instruction by words such as "give red" in a designer or the like. Since the fifth embodiment has the same configuration as that of the above-described embodiment, the same reference numerals are given to the same portions, and detailed description will be omitted. In this embodiment, in step 216 of the fourth embodiment, C
It is assumed that a plurality of plot points 86 that can be selected from the IE chromaticity coordinates have been obtained (see FIG. 24).

Next, the operation of this embodiment will be described. FIG.
In step 216 of FIG. 25, when a plot point 86 on the CIE chromaticity coordinates which is expected to be a desired paint color is selected and designated by the designer or the like, the process proceeds to step 220 in FIG. The plot point 86 selected by the designer or the like is defined as xy
Plot points #P chromaticity coordinates (x _p, y _p) will be described as was.

In step 220, the designer or the like sets several main reference colors indicating hue on the xy chromaticity coordinates. In this embodiment, as shown in FIG. 28, a plot point #R representing red, a plot point #B representing blue, and a plot point #G representing green used as so-called three primary colors are set as reference colors.

FIG. 26 shows the color characteristics of the main paint colors used for coating the vehicle. Each point in the figure represents the chromaticity of each coating color. Therefore, since the approximate area of the area of the color to be controlled can be predicted, the outermost plot point may be selected so that the predetermined reference color includes the approximate area.

FIG. 27 shows a color area 87 that can be reproduced by color printing. This color area 87 includes reference colors R,
The area is surrounded by G, B, C, M, Y, and BK. These reference colors are plotted as colors according to the tristimulus values shown in Table 2 below. The colors shown in Table 2 may be stored in advance as reference colors. Normally, the CRT 14 has a monitor gamut (color reproduction range) 88 slightly larger than the color area 87. However, considering that the control result is output not only on the CRT but also on a color hard copy or the like and is evaluated, this range is considered. It is desirable.

[0151]

[Table 2]

[0152] In the next step 222, the read plot points selected by the designer or the like #P (x _p, y p) as the initial presentation color, reflecting the color against plotted points #P In the next step 224 Read the instructions for the color to make it work. The indication of the color is, for example, plot point #P
A command corresponding to the designer's word, such as [give redness], is input from the keyboard 10 for the paint color.

The expression “give red” means that the chromaticity of the coordinate value on the xy chromaticity coordinates with respect to the paint color changes from the plot point #P to the plot point #R of the reference color (red). Is fine. Therefore, in the next step 226, a line segment 90 connecting the plot point #P and the plot point #R is obtained. At the same time, the plot points around the line segment 90 are read in order from the plot point #P as trend points #P _R1 , #P _R2 ,. Step 228
Then, among the read trend points, the trend point closest to the currently designated plot point (in this case, plot point #P) and existing in the color direction (direction toward plot point #R) is selected. I do. In the next step 230, it is determined whether or not the degree of tint is desired according to an instruction from a designer or the like. When the degree of tint reaches a desired coordinate position, the process proceeds to step 232.

Therefore, plot points around this line segment 90 are repeatedly selected in order from plot point #P to plot point #R until the tint is reflected. This allows
For example, in [Add red], as shown in FIG.
# P → # P _R1 → # P _R2 → ... and plot point #P
Will be reddish in this order.

In the next step 232, it is determined whether or not all of the desired colors have been imparted. That is, it is determined whether or not the above processing has been completed for the other colors, blue and green. In this case, there are a case where the above-mentioned single color is imparted and a case where a plurality of colors are imparted. When the colors are given to the plurality of colors, the line segment 90 may be obtained in step 226 using the plot point at the time when the color of the predetermined color is determined as the presentation color.

When the reflection of the tint is finished for the plot point #P for the first presentation color (original color) in this way, the color coordinate value of the determined plot point is stored in step 234, and this routine is executed. finish.

Therefore, by outputting the reflectance R ^* (α, λ) obtained based on the selected plot point 86 (step 218 in FIG. 20), the reflectance R ^* (α,
The characteristic value vector VX corresponding to (λ) is determined, and a paint color in which a desired desired tint is reflected can be obtained from the characteristic value vector VX. Therefore, a desired coating color can be generated in an easy-to-understand manner in accordance with the feeling of the designer.

Here, when expressing a painted surface, a material may be used for the one used in association with the painted color.
There are many words indicating the material of the painted surface, and typical ones are roughly classified into four types as shown in the following [Material state]. These material conditions are important factors in determining the quality of the painted surface.

[Material state] Basic material: mica, metallic, solid Diffuse reflection: flip-flop (a term indicating the difference between bright and dark) Specular reflection: gloss, gloss, etc .: depth , Depth, transparency

Therefore, in the following embodiment, the paint color affected by the material is reproduced based on the sense of design. The following embodiment has the same configuration as the above embodiment,
The same portions are denoted by the same reference numerals, and detailed description will be omitted.

In the sixth embodiment, mica feeling, metallic feeling,
It reproduces the paint color influenced by the basic material, which is intuitively expressed as a solid feeling. In this embodiment, a metallic material x _met and a mica material x _mic are further added to the characteristic value vector VX = (x ₁ , x ₂ ,..., X _e ) for determining the coating color used in the above embodiment. The following equation (2
A new characteristic value vector VeX shown in 7) is defined.

VeX = (x ₁ [q ₁ ], x ₂ [q ₂ ],..., X _e [q _e ], x _met [q _met ], x _mic [q _mic ]) −−− (27 )

In this embodiment, the paint color affected by the basic material is reproduced. For the sake of simplicity, it is assumed that the constituent materials and amounts for reproducing the paint color have already been determined. Component materials x ₁ , x that determine the paint color
_2, in a state of fixing the amount q _i of · · · x _e, to derive the desired coating surface configuration and the like can be varying amounts q _mic amount q _{the met} mica material x _mic metallic material x _{the met.}

The power switch (not shown) of the color reproducing device is turned off.
The main routine for reproducing the paint color (Fig. 9
Is performed, a specified value is set (step 1).
00). Specifically, the process proceeds to step 140 in FIG.
Constituent material x such as color material used in color material mixing device 18_iTo
Using the characteristic value vector VX
_metAnd mica material x_micCharacteristic value vector VeX
Is determined.

In the next step 142, the metallic quantity q _{met is changed} to the boundary value q _metB (1 ≦ B ≦
P), the mica quantity q _{mic is changed} to the boundary value q _micC (1 ≦ C ≦ P)
And [P + 1] pieces are appropriately divided. As a result, the metallic material x _met and the mica material x _mic are developed into P quantities that gradually increase or decrease.

The metallic quantity q _met and the mica quantity q
The sum of _mic is set to a constant amount as in the following equation (28).

Q _metB + q _micC = ρ (constant) --- (28) ρ = q _met1 > q _met2 >> ... q _metp = 0

Therefore, there are P ² combinations of the characteristic value vectors VeX based on these quantities q _met and q _mic .

In the next step 144, P^TwoEach of
Characteristic value vector VeX_h(H = 1, 2,..., P^Two)
Ask for. That is, the metallic material x_metAnd mica wood
Fee x _micCharacteristic value vector when each amount of
Le VeX_hAsk for.

[0170] In the next step 146, determined characteristic values to produce a coating material prepared by mixing the color material or the like based on the amount of the constituent material of the vector VEX _h, the generated coating the coated surface of the coated plate was applied to the plate The reflectance R _h (α, λ, VeX _h ) is obtained by actual measurement. Therefore, as shown in Table 3 below, P ²
Samples can be generated.

[0171]

[Table 3]

In Table 3 above, the above formulation (small number)
It can be said that the higher the metallic feeling, the lower the composition (the larger the number), the stronger the mica feeling.

[0173] Further, as described in the first embodiment, by interpolation from the relationship of the p ² samples, by obtaining a more detailed relationship, feeling and finer metallic
Mica feeling can be selected.

Thus, the process of setting the specified value is completed.
Then, the new reflectance R desired by the designer or the like^*(Α,
λ) is read (step 200 in FIG. 9) and the new reflection
Rate R ^*New characteristic value vector VeX for (α, λ)^*
(X₁ ^*, X_Two ^*, ... x _e ^*, X_met, X_mic),
That is, the amount of constituent materials such as metallic and mica is calculated.
(Step 300 in FIG. 9). As a result, the characteristic value
Vectre VX^*Signal indicating (mixing) to color material mixing device 18
The output (step 400 in FIG. 9) is sent to the color material mixing device 18.
Paint is formed at the desired reflectance R^*(Α, λ)
A coated object such as a coated plate can be produced.

The above-described specific division of the amounts of the metallic material x _met and the mica material x _mic will be described with reference to the existing constituent material of the coating color A in the second embodiment. In addition, the quantity q = q ₁ + q ₂ +... + Q _{e of} the metallic glittering material X _met , the mica glittering material X _mic and all the constituent materials that determine the color.
, Q is constant. This quantity q is 32.93 g as follows.

[0176]

On the other hand, the quantities q _met and q _mic are appropriately divided. Here, the values are changed by 0, 10,..., 50 (g), respectively. As a result, as shown in the following [State C], a total of 6 ² = 36 samples can be generated.

[0178]

In the above description, the paint color based on the basic material is reproduced by reflecting the metallic feeling and the mica feeling. However, the paint color affected by the basic material that expresses each of the mica feeling, the metallic feeling, and the solid feeling sensuously. Can also be reproduced. That is, the above-mentioned sense is considered including a solid feeling.

In this case, as shown in FIG. 30, the amounts q of all the constituent materials for determining the coating color, the amounts of metallic q _met ,
It may be considered in a three-dimensional space of a coordinate system having the mica amount _qmic as an axis.

Next, the following equation is used instead of the above equation (28). _{q = q 1 + q 2 +} ··· + q e q + q metB + q micC = ρ ( _{constant) q ≧ 0, q metB ≧} 0, q micC ≧ 0

The quantities q, q _met , and q _mic correspond to a solid feeling, a metallic feeling, and a mica feeling, respectively.
, A point A (ρ, 0, 0) and a point B (0, ρ,
0) and a triangle having a point C (0, 0, ρ) as a vertex (FIG. 3).
1) By moving the upper point P (x, y, z), it is possible to control a solid feeling, a metallic feeling, and a mica feeling while relating them to each other. In this case, it is sufficient to generate a sample for each point in which the triangle is appropriately divided and points are present at appropriate positions on the triangle.

[0183] In the sixth embodiment, it has been to generate a sample in a setting process of the prescribed value, after obtaining the amounts of each of the constituent materials for determining the paint color, metallic amount q _{me t,} mica amount q _mic may be determined. In this case, the above triangle (see FIG. 31) may be displayed on the CRT 14 so that desired position coordinates can be input.

Next, a seventh embodiment will be described. The seventh embodiment reproduces a paint color affected by diffuse reflection which is intuitively expressed as a flip-flop feeling. The flip-flop feeling is sometimes expressed as a sharp feeling of light and dark, and is considered to mainly depend on the changing angle characteristic (reflectance or change in brightness Y due to changing angle).
Therefore, in this embodiment, the metallic material x, which is a glitter material, is used.
Characteristic value vector VeX including _met and mica material x _mic
(See equation (27)).

Next, the operation of this embodiment will be described. When a power switch (not shown) of the color reproducing apparatus is turned on, FIG.
The main routine for reproducing the paint color shown in (1) is executed, and after setting a specified value (step 100), a new reflectance R ^* (α, λ) desired by a designer or the like is read (step 200). This new reflectance R ^* (α,
A new characteristic value vector VX ^* (amount of constituent material) for λ) is calculated (step 300). Next step 3
In step 04, a characteristic value vector VeX reflecting the flip-flop feeling is obtained, and a signal representing this characteristic value vector VeX is output to the color material mixing device 18 (step 40).
0), the paint is generated by the blending based on the characteristic value vector in the color material mixing device 18, and a painted object such as a painted plate with a desired reflectance (paint color) reflecting the flip-flop feeling can be generated.

In the above-mentioned step 304, the free operation shown in FIG.
A flip-flop processing routine is executed. Painted surface anti
The firing rate R (α, λ) is expressed by the unit vector VR₁(VeX),
VR _Two(VeX), ..., VR_n(VeX)
It is approximated from discrete points for each wavelength. Therefore, FIG.
In step 322 of FIG. 5, the unit vector VR_jRead
In the next step 324, as shown in FIG.
In addition, these unit vectors VR_jContinuous points by interpolation
Connected curve LR₁(VeX, λ), LR_Two(VeX₁,
λ), LR_n(VeX, λ) is obtained. like this
If the characteristic of the predetermined wavelength range is obtained, the following equation (29)
Brighter Y_jIs obtained, so in step 326
Then, the brightness for each variable angle α is obtained.

[0187]

[Equation 14]

At the next Step 328, Step 326 is executed.
The deflection characteristic obtained from the brightness Y _j obtained by
Draw on top. That is, since the brightness Y _j represents the brightness for each angle of change, the points on which the points are plotted are connected by a free curve by interpolation or the like on a coordinate plane where the horizontal axis is the angle of change α and the vertical axis is the brightness Y _j. , The brightness in the variable angle direction, that is, the variable angle characteristic can be drawn.

FIG. 34 shows characteristic curves of different deflection characteristics.
showed that. As can be understood from the figure, the characteristic curve has a greater difference in brightness and darkness than the characteristic curve, so that the flip-prop feeling increases.

In the next step 330, among the constituent materials of the characteristic value vector VeX, the reflectance R (α, λ) obtained by slightly changing the amount of a predetermined or appropriate constituent material is obtained. In the next step 332, it is determined whether or not the above processing has been completed a predetermined number of times (for example, five times), and the above processing is repeatedly executed. Thereby, a plurality of deflection characteristics are drawn.
In the next step 334, the user such as a designer selects a characteristic curve having a desired flip-flop degree with reference to the drawn characteristic curve, and ends this routine. Therefore, since the characteristic value vector VeX corresponding to this characteristic curve is easily determined, a paint color having a desired flip-flop feeling can be created from the characteristic value vector VeX.

As described above, it is not easy to assume a substantial flip-flop feeling even with the variable-angle characteristic curve drawn on the CRT 14 in order to obtain a desired flip-flop paint color. Therefore, after selecting the deflection characteristic curve,
A visual judgment can be given by displaying the paint color of the selected flip-flop degree as a kamaboko-shaped shading diagram and giving a gradation judgment by displaying the shading diagram.

In the above description, the case where a desired flip-flop feeling curve is selected from the variable-angle characteristic curves drawn on the CRT 14 to form a paint color that provides a desired flip-flop feeling has been described. However, the present invention is not limited to this, and a plurality of painted plates having different flip-flop degrees may be formed in advance as samples and selected. In addition, designers, etc., respond to sensory expressions such as [colors with more flip-flops], after the paint color is determined, obtain multiple deflection characteristic curves as described above and sequentially flip-flop. What is necessary is just to select the characteristic value vector with a large degree.

Next, an eighth embodiment will be described. In the eighth embodiment, a paint color influenced by specular reflection expressed intuitively as glossiness and glossiness is reproduced.

The glossiness and glossiness mainly depend on the surface finish (such as polishing), but also on the thickness (amount) of the surface clear coat. Clear coat material x
As _ce, this amount as q _ce, may execute a defined value setting routine of FIG. 29 in place of the metallic material x _{the met} mica material x _mic in the sixth embodiment the clear coat material x _ce. In this case, the amount _{q ce q ce1 <q ce2 <} ·
_{··· Divides} into p pieces of <q _cep to determine the reflectance. Therefore, P samples can be generated as in Table 3 above.

When the amount of the clear coat material _xce is changed, only the amount of the clear coat material is changed while the amounts of the coloring material and the glittering material are kept constant. Usually 0 ~ MAX
(Maximum value, for example, 100 g) is preferably divided into 30 to 50 to generate a sample. Further, according to the same interpolation method as in the first and third embodiments, it is possible to obtain a finer glossiness than the relationship between the p samples.

Next, a ninth embodiment will be described. In the ninth embodiment, the paint color affected by the other material states expressed intuitively is reproduced. The sensations felt by designers and the like according to the above other material states mainly include a sense of depth and a sense of depth. The sense of depth and the sense of depth are substantially the same. Also, these sensations, as explained below,
There is a relationship between the reflectance characteristics and the deflection characteristics. If the relationship between these senses and the reflectance is known, a characteristic value vector is determined, and a paint color having a sense of depth and a sense of depth can be reproduced. A process for quantitatively treating the sense of depth will be described in detail.

[0197] The sense of depth is a sensational expression when a person sees and feels the surface of an object. The sense of depth is as follows: a sense of depth A in which the object surface feels as if it were three-dimensionally geometrically; a sense of depth B in which the object surface feels as if it is virtually three-dimensional depth; It can be broadly divided into a deep feeling C that is associated with a sense of quality, such as giving a sense and a strict feeling. These geometric depth A, virtual depth B,
Further, the sense of depth C that gives a sense of quality mainly relates to the hue and the sense of material. The texture here is mainly due to the glitter material. In extreme cases, the chrome-plated surface does not feel deep. It is expected that this is because the chromium plating layer does not transmit information such as the internal structure and effect because of only specular reflection.

Therefore, the sense of depth is considered to be caused by the propagation of reflected light due to the structure inside the object surface when viewed. The reflection form of the reflected light is roughly classified into specular reflection and diffuse reflection as is well known.

The specular reflection substantially follows the Fresnel reflection regardless of the type of the painted surface. FIG. 36 shows a reflectance curve 62 of metallic A4245 (gold) as an experimental example.
A, the reflectance curve 62B of the solid 3E5 (red) and the ideal reflectance curve 62C obtained by calculation based on the Fresnel equation shown in the following equation (30) are shown. Therefore, it is understood that only the diffuse reflection is involved, not the specular reflection, as the physical quantity for expressing the sense of depth. This diffuse reflection can be obtained by the measurement using the gonio 24 described above.

[0200]

(Equation 15)

Where f: the refractive index of Fresnel (intermediate value between s-wave and p-wave) n ₁ : refractive index of air ≒ 1.00 n ₂ : refractive index of medium (1.567 in this embodiment) θ ₁ : incident angle θ ₂ : reflection angle n ₁ / n ₂ = sin θ ₁ / sin θ ₂ (Snell's law)

Next, with respect to the sense of depth, a sense of depth B and a sense of depth C will be described. First, consider the case where the paint color is constant. Even the painted surface of the same hue may have a different sense of depth. Since the difference in the sense of depth is considered to correspond to the difference in brightness due to the change in angle, it can be represented by the difference in the change in angle characteristic (see FIG. 33).

Therefore, the following experiment was conducted to determine the condition of a sense of depth for a coated plate having a constant coating color. As an object to be tested, a painted plate that gives a sense of depth was prepared.
As shown in FIG. 7 (b), the painted plate is formed in a semicircular shape so that the deflection characteristics of the painted plate can be uniquely measured, and a plurality of positions a, b, and a on the painted surface of the semicircular painted plate are formed. The reflectance of c and d is measured. The position a is the position of the highlight of the painted plate, and the positions b, c, d are positions separated from the position a by a predetermined angle in a predetermined direction. Based on the measured reflectivity, the brightness Y _j is calculated using the above equation (29) to determine the deflection characteristic (see FIG. 37 (a)). As a result of this experiment, the change in lightness and darkness becomes sharp near the positions a and b near the highlight (the portion where the shading changes from highlight a to b → c). When visually observing the areas at positions a and b as masks, a result was obtained in which the sense of depth was not felt at positions c and d where the change in brightness was relatively flat. Thus, it is assumed that a sense of depth is felt in the vicinity of the highlight (the part where the density changes from highlight a to b → c).

FIG. 38 shows a characteristic 64 representing the relationship between the deflection angle and the brightness when the above-described experiment was performed on a plurality of painted plates.
A, 64B, 64C and 64D are shown. As can be understood from FIG. 38, the deformation characteristics of the deformation angle α ≧ 5 ° are relatively small, and the slower the change, the easier it is to feel the depth (characteristics 64A and 64B in FIG. 38), and the highlight. (Position a) shines brilliantly, the change in brightness when going from position a → position b →... Is small, and it is required that those with high reflectivity as a whole do not feel a sense of depth (FIG. 38). Characteristics 64C, 6
4D). Therefore, the depth conditions (i) and (ii) shown below are
The paint color is defined as a condition for the depth of the painted plate.

(I) The brightness Y in the region where α ≧ 5 ° excluding the highlight portion is not large. (Ii) The brightness change in the region where the brightness Y is not large is slow.

From these conditions (i) and (ii), it is expected that the sense of "depth" is similar to the sense of darkness. However, it does not mean that the entire painted surface is uniformly dark, but is accompanied by a slow change in brightness. This is similar to seeing the sun appearing as a sunbeam from a dark forest bush, for example, through a layer of trees. In this case, the sun can be considered as the highlight, and the shade of the trees in the forest can be compared with the brightness of the paint.

Next, let us consider a case where the paint color is changed while the amount of the glittering material or the like for determining the material is kept constant. In general, as described above, a dark color is more likely to give a sense of depth to a bright color and a dark color. Therefore, if a paint composed of coloring materials such as colored pigments having the same amount is prepared, and the reflectance at a deflected angle (for example, α = 40 °) excluding the specular reflection of the coated plate to which the paint is applied, the paint color is obtained. Is associated with the reflectance. For example, the reflectance R _{0 of} colors such as indigo, dark blue, and black is low,
The reflectance R ₀ of colors such as white and yellow is high. Therefore, it is understood that the condition of the depth feeling regarding the color is the following depth condition (iii).

(Iii) The reflectance of the diffuse reflection portion is low

[0209] In this manner, the depth condition for specifying the sense of depth is determined. The depth condition (i), define values F ₁ using (ii), in order to quantify the (iii), the following equation (31).

[0210]

(Equation 16)

Here, wavelength: 380 ≦ λ ≦ 720 Deflection: 5 ° ≦ α ≦ 90 ° m ₁ : Positive constant f ₁ (x): Decreasing function in a broad sense (when f ₁ (x ₁ <x ₂ , f ₁ (x ₁ )
≧ f ₁ (x ₂ ), hereinafter referred to as decreasing function)

This value F ₁ is determined by the reflectance R (α, λ, Ve
X) becomes larger as it becomes smaller, which corresponds to an increase in the sense of depth.

Next, in the above equation (29), the curve that is smoothly continued by spline interpolation or the like with the brightness Y ₁ , Y ₂ ,... Therefore, in the present embodiment, a function Y (α) is defined as a function representing the brightness Y with respect to the variable angle α. This function Y (α)
Is obtained by differentiating dY (α) / dα from the function Y
It represents the slope of (α).

For the variable angle α, from 5 ° to 90 °,
N angles α₁, Α_Two , ..., α _n(5 ° ≦ α₁<Α
_Two <... <α_n= 90 °) (for example, 1
86 pieces of 5 °, 6 °, ... 89 °, 90 ° in increments of °
Choose). For each selected angle αi, the following equation (32)
To find the differential value. That is, the deflection angle α and the brightness Y
The measurement point (α)_i, Y_i)
At the measurement point by approximation processing such as spline interpolation.
To a smooth curve, such as minimizing the square error with
If the function Y (α) is obtained, the angle α can be freely determined._iAsk for
be able to. This smooth curve can be differentiated and the differential value a
_i= DY (α) / dα.

[0215]

[Equation 17]

[0216] obtained differential values a _1, a _2, · · ·, using a _n, the following equation (33), distributed alpha _A ² by (34)
An average value mu _A and.

[0219]

(Equation 18)

Here, the gradual change in the brightness Y means that the variance σ _A ² is small and the absolute value | μ _A | of the average value is small. Therefore, the following quantity shown in Expression (35) is defined.

F ₂ = m ₂ f ₂ (σ _A ) + m ₃ f ₂ (| μ _A |) −35 (35) where m ₂ and m _{3 are} positive constants f ₂ (x) and f ₃ ( x): decreasing function

Thus, the greater the value F ₁ , the greater the depth condition
(iii) will be satisfied and the sense of depth will increase. In this way, the virtual depth B and the depth C as sensitivity can be quantified.

Next, the sense of depth A will be described. The fact that a person feels a geometric three-dimensional depth is equivalent to recognizing a perspective.

FIG. 39 (a) shows an image with a correct perspective, and FIG. 39 (b) shows an image without a perspective.

By the way, the depth can be felt to some extent without an accurate perspective as shown in FIG. For example, when you look at the stars in the night sky, you feel the depth of the universe. Large moons appear closer than small stars. In other cases, shining stars may appear closer, and bluish stars may appear farther than reddish light.

In the case of paint, it is considered that the glittering material corresponds to the above-mentioned star. Empirically, in the case of a star, the more stars with different sizes, colors, and glitters, the more the depth is felt. Therefore, the more the glittering material in the paint has various particle diameters, colors, and reflection characteristics, the more the sense of depth is felt.

For example, when comparing two paints having a particle size distribution as shown in FIGS. 40A and 40B, it can be said that FIG. 40B has a sense of depth.

Therefore, the number of glittering materials having a particle diameter of ξ (nm) among the glittering materials xi is defined as aξ. For example, the range of particles includes the following <Example>. <Example> Micro-titanium yellow: 0.03 μm Silver-plated glass flake: 10 to 40 μm Aluminum solid flake red iron oxide: 10 to 40 μm Small particle size pearl: 15 μm or less Thus, there are various glittering materials and their particle diameters. However, it may be considered in the range of approximately 0 to 50 μm. The particle size distribution is
It can be easily obtained by image analysis technology.

Next, the variance σ _r ² of the particle size distribution is determined as in the above equation (33), and it is assumed that the greater the value of the variance σ _r ² , the greater the sense of depth. Furthermore, the dispersion σ _r
² , the dispersions σ _C ² and σ _R ² are also determined for the color variation and the reflection characteristic variation, and as shown in the following equation (36), appropriate positive real numbers m ₄ , m ₅ , m define a value F ₃ denoted by the weights _6.

F ₃ = m ₄ f ₄ (σ _r ² ) + m ₅ f ₅ (σ _C ² ) + m ₆ f ₆ (σ _R ² ) --- (36)

With this value F ₃ , the sense of depth A can be quantified. As a result, the value F ₃ and the values F ₁ , F
If the depth index F is determined as shown in the following equation (37) using ₂ , the depth sensation A, the depth sensation B and the depth sensation C can be quantified.

F = F ₁ + F ₂ + F ₃ (37) where f ₄ (x), f ₅ (x), and f ₆ (x): increasing function in a broad sense (x ₁
<X ₂ If _{f i (x 1) ≦ f} i (x 2) (i = 4,5,6)) and there is a deep enough depth index F is large is.

Here, for example, f ₁ (x), f ₂ (x),.
Equation (38) below is defined as follows. f ₁ (x) = f ₂ (x) = f ₃ (x) = 1 / x f ₄ (x) = f ₅ (x) = f ₆ (x) = x (38)

As a result, the depth index F is given by the following equation (39).

[0233]

[Equation 19]

The variance σ _C ² is obtained by calculating the coating color of the glittering material by the coordinate value ¢ (L ₁ ^* , a ₁ ^* ,
b ₁ ^* ), ¢ (L ₂ ^* , a ₂ ^* , b ₂ ^* ),..., the reference paint color (white) is represented by coordinate values ¢ _W (L _W ^* , a _W ^* , b
_W ^* ), and the paint colors ¢ ₁ , ¢ ₂ ,... Deviate from white ξ ₁ = | ¢ _W − ¢ ₁ |, ξ ₂ = | ¢ _W − ¢ ₂ |,.
Defined by Hereinafter, the deviation ξ is represented as a paint color ξ. The number of brilliant materials having the paint color ξ _i is a _i , and the variance σ _C ² is obtained in the same manner as in the equation (33).

In this embodiment, L _w ^* = 100, a
_w ^* = b _w ^* = using a 0 of white as the basis for the paint color ¢ _W. Further, the color of the glittering material alone can be determined by measuring the surface composed only of the glittering material by spectral colorimetry.

For the variance σ _R ² , the brightness Y calculated by using the above equation (29) from the reflectance of the coating surface made of the glittering material i at the deflection angle α = 40 ° is calculated as the brightness ξi
And At this time, values representing the positions of the permutations obtained by rearranging the brightness ξ ₁ , ξ ₂ ,... In ascending order are values n ₁ , n ₂ ,.
··· (n ₁ ≤n ₂ ≤ ...) Assuming that the number of glittering materials having the brightness of the value n _i is α _i , the variance σ _R ² can be obtained in the same manner as in Expression (33).

Next, the operation of this embodiment will be described. In addition,
Let R (α, λ, VeX _i ) be the reflectance of the painted surface with respect to the characteristic value vector VeX with a constant paint color or material,
The following describes the depth index F _i for this characteristic value vector VeX. Further, in order to simplify the following description, the correspondence between the reflectance and the depth index obtained by changing the amount of the brilliant material while keeping the colored pigment and the like constant is obtained.

In step 160 of FIG. 41, the constituent materials x _i including the coloring material and the glittering material used in the coloring material mixing device 18 are used.
The characteristic value vector VeX is determined by

In the next step 162, the metallic amount and the mica amount are defined as boundary values [P + 1], as in the above embodiment.
Divide each one appropriately. As a result, the luster such as the metallic material and the mica material increases or decreases step by step.
And the characteristic value vector V based on these quantities
There are P combinations of eX.

In the next step 164, P characteristic value vectors VeX _h (h = 1, 2,..., P) are obtained. That is, determine the respective characteristic value vector VEX _h when changing the amount of luminous material in order. Next step 166
In obtains the depth index F described above corresponds to the characteristic value vector VEX _h of each rearranges in the next step 168 from a minimum depth index F in order. Accordingly, the characteristic value vector of the coating color with a plurality of color depth for paint color of the same hue determined by the characteristic value vector VEX _h is obtained.

[0241] In the next step 170, determined characteristic values to produce a coating material prepared by mixing the color material or the like based on the amount of the constituent material of the vector VEX _h, the generated coating the coated surface of the coated plate was applied to the plate The reflectance R _h (α, λ, VeX _h ) is obtained by actual measurement. Accordingly, as shown in Table 4 below, P samples can be generated, and the reflectance obtained by changing the glittering material when the colored pigment is constant can be made to correspond to the depth index. However, the depth index in Table 4 is F ₁ ≦ F ₂ ≦ ·
Is a ·· ≦ F _P.

[0242]

[Table 4]

As described above, in the above embodiment,
The color and material of the coating color can be virtually generated and selected on a CRT before manufacturing a real object (objects to be coated in various shapes by applying a paint or the like). In addition, the characteristic value vector is derived only when a desired paint color is generated (selected), and the actual product may be manufactured based on the derived characteristic value vector. Can be.

In the above description, a case was described in which painted plates having different depths in the same hue were formed. However, the present invention is not limited to this, and the present invention is applicable even when selecting a painted color. It is. In this case, after the paint color is determined, the depth index F is obtained as described above, and only the paint colors including the sense of depth are displayed in ascending order of the depth index F, whereby the paint including the displayed sense of depth is displayed. From the colors, a desired color and a paint color including a sense of depth can be selected. In addition, designers and the like respond to sensible expressions such as [more deep colors] by determining the depth index F as described above after the paint color is determined, and sequentially increasing the depth index F. What is necessary is just to select a value vector.

If a finer depth index is required to reproduce a delicate sense of depth, the correspondence may be increased by the interpolation described in the first and third embodiments.

A color copying apparatus such as a color copying machine such as a color copying machine of a thermal transfer system, an inkjet system, an electrophotographic system, and a silver halide photographic system which outputs a color copied image by using color data such as an RGB color system as an input value is connected. Alternatively, the paint color may be reproduced as a color image.

[0247]

As described above, according to the first aspect of the present invention, it is possible to obtain the characteristic value of the painted surface which is a painted color composed of a plurality of constituent materials including a coloring material and a glittering material. There is an effect that a desired color can be accurately reproduced as a paint color even on a paint surface containing a glittering material such as metal or pearl mica which does not follow the Kubelka-Munk theory.

According to the second aspect of the present invention, since the colors in the course of the designated color to the reference color can be sequentially selected, the designer or the like is instructed of the paint color to which a tint such as more reddish is imparted. However, there is an effect that a paint color matching the sense of a designer or the like can be easily selected. In addition, since it is possible to obtain the characteristic value of the paint surface of the paint color selected as the paint color that matches the feeling of the designer or the like, it is possible to accurately reproduce the desired paint color imparted with color. There is.

According to the third aspect of the present invention, since it is possible to determine and select the bending characteristic of the painted surface, which represents the relationship between the bending and the brightness in the bending, which can express a sense of flip-flop, designers and the like can select the bending characteristics. There is an effect that a paint color in which a desired light and dark sharpness is reflected can be selected. In addition, since it is possible to determine the characteristic value of the painted surface of the paint color selected as the paint color that matches the flip-flop feeling of the designer or the like, it is possible to accurately reproduce the paint color according to the desired flip-flop feeling. effective.

According to the fourth aspect of the present invention, the depth index representing the depth of the coating color is obtained based on the particle size distribution of the constituent material for each characteristic value. There is an effect that a paint color having a desired depth expressed intuitively as a depth can be selected. Further, since the painted surface can be formed based on the characteristic value of the painted color with respect to the depth index, there is an effect that a painted color having a sensible depth desired by a designer or the like can be reproduced.

According to the fifth aspect of the present invention, the correspondence relation to the paint color reflecting the tendency of the reference color, the paint color having a flip-flop feeling, or the paint color having a desired depth is selectively estimated. Because it is possible, even if the sensory paint color desired by the designer etc. is combined,
There is an effect that the desired sensory color can be faithfully reproduced in the paint color.

[Brief description of the drawings]

FIG. 1 is a schematic configuration diagram of a color reproduction device including a personal computer of the present embodiment for reproducing a paint color.

FIG. 2 is a conceptual diagram for explaining a configuration of a gonio.

FIG. 3 is a diagram showing a rectangular coordinate system for explaining a deflection angle α used in the present embodiment.

FIG. 4 is a characteristic diagram showing a deflection characteristic of a spectral solid angle reflectance of a painted surface.

FIG. 5 is an image diagram showing a configuration of a painted surface, and FIG.
Is a metallic painted surface, (b) is a Pahamica painted surface,
(C) shows a solid painted surface.

FIG. 6 is a characteristic diagram showing reflectance characteristics of a plurality of paint colors when the variable angle α is 45 degrees.

FIG. 7 is a characteristic diagram showing a relationship between a variable angle α and brightness Y for a plurality of paint colors.

FIG. 8 is an image diagram showing a reflectance characteristic with respect to a paint color in a three-dimensional coordinate system having a reflectance, a deflection angle, and a wavelength as axes.

FIG. 9 is a flowchart showing a flow of a control main routine for reproducing a paint color according to the first embodiment.

FIG. 10 is a flowchart showing details of step 100 in FIG. 9 in the first embodiment.

FIG. 11 is a color reproduction process of the first embodiment (step 300).
It is a flowchart which shows the flow of.

FIG. 12 is an explanatory diagram showing, as an image, the flow of the paint color reproduction process of FIG.

FIG. 13 is an explanatory diagram for explaining a correspondence between a characteristic value vector VX and a reflectance vector VR.

FIG. 14 is a flowchart showing details of step 100 in FIG. 9 in the second embodiment.

FIG. 15 shows xy of CIE including primary colors determined in the second embodiment.
It is a chromaticity diagram.

FIG. 16 is a schematic configuration diagram of a neural network device of a second embodiment.

FIG. 17 is an image diagram showing a network configuration of the neural network device.

FIG. 18 is an image diagram showing adjacent layers in a network.

FIG. 19 is a flowchart showing the flow of a control main routine for reproducing a paint color according to the third embodiment.

FIG. 20 is a flowchart showing the flow of a paint color selection routine according to a fourth embodiment.

FIG. 21 is a diagram showing a Munsell color system.

FIG. 22 is a diagram showing chromaticity coordinates of CIE.

FIG. 23 is a diagram showing the correspondence between the Munsell color system and the chromaticity coordinates of CIE.

FIG. 24 is an explanatory diagram for explaining that points other than plot points are obtained by interpolation.

FIG. 25 is a flowchart showing a flow of a process of imparting a tint to a designated paint color in the fifth embodiment.

FIG. 26 is a distribution diagram of a plurality of actual paint colors in which these colors are plotted on a chromaticity coordinate plane.

FIG. 27 is a diagram showing a color area that can be formed on a monitor and with a paint on a chromaticity coordinate plane.

FIG. 28 is an explanatory diagram (chromaticity coordinate diagram) for explaining a process of imparting a tint to a designated paint color.

FIG. 29 is a flowchart showing a flow of a process for obtaining a paint color reflecting a metallic mica feeling according to the sixth embodiment.

FIG. 30 is an image diagram showing a three-dimensional space of a coordinate system having axes of amounts of constituent materials, metallic amount, and mica amount which determine a coating color.

FIG. 31 is a diagram showing a changeable region of each amount in FIG. 30;

FIG. 32 is a flowchart showing a main routine for obtaining a paint color having a flip-flop feeling according to the seventh embodiment.

FIG. 33 is a diagram related to reflectance for explaining a process for obtaining the reflectance.

FIG. 34 is a diagram showing a deflection characteristic.

FIG. 35 is a flowchart showing the flow of processing for obtaining a paint color having a flip-flop feeling according to the seventh embodiment.

FIG. 36 is a diagram showing spectral reflectance characteristics for explaining specular reflectance.

FIG. 37 (a) is a diagram showing a deflection characteristic, and FIG. 37 (b) is an image diagram showing a shape of a paint surface to be measured.

FIG. 38 is a diagram showing a deflection characteristic.

39A and 39B are image diagrams showing a perspective of an image, wherein FIG. 39A shows an image without a perspective, and FIG. 39B shows an image with a perspective.

FIG. 40 is a characteristic curve showing a particle size distribution of a glittering material.

FIG. 41 is a flowchart showing the flow of a process for obtaining a paint color having a sense of depth in the ninth embodiment.

FIG. 42 is a flowchart showing the flow of a process (step 102 in FIG. 19) of the second NNW method in the third embodiment.

FIG. 43 is a flowchart showing the flow of a process (step 102 in FIG. 19) of the third NNW method in the third embodiment.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 10 Keyboard 12 Computer main body 14 CRT 16 Personal computer 18 Color material mixing apparatus

Claims (5)

(57) [Claims] 1. A predetermined coating color of a coating surface which is formed of one or more layers on an object to be coated and each layer is formed of at least one constituent material, for each of the constituent materials constituting the coating surface. A plurality of correspondences between the characteristic values of the quantities and the spectral reflectance distributions of the painted surfaces based on the characteristic values are obtained in advance, and the amount of at least one of the constituent materials among all the constituent materials determined by the correspondence is different in the paint color. A plurality of interpolation correspondences different from the correspondence representing the correspondence between the characteristic value and the spectral reflectance distribution are estimated based on the plurality of correspondences, and when a paint color other than the predetermined paint color is reproduced, reproduction is performed. Selecting the spectral reflectance distribution of the interpolation correspondence corresponding to the paint color to be applied, and determining the amounts of all the constituent materials by the characteristic value determined from the interpolation correspondence with respect to the selected spectral reflectance distribution. A method for reproducing paint colors that reproduces paint colors. 2. A predetermined coating color of a coating surface, which is formed of one or a plurality of layers on an object to be coated and each layer is formed of at least one constituent material, for every constituent material constituting the coating surface A plurality of correspondences between a characteristic value consisting of an amount and a spectral reflectance distribution of a painted surface based on the characteristic value, and a tristimulus value based on a spectral reflectance distribution of the painted surface based on the characteristic value are determined in advance; An interpolation correspondence relationship different from the correspondence relationship representing the correspondence between the characteristic value of the paint color and the spectral reflectance distribution in which the amount of at least one of the constituent materials among all the constituent materials determined by is different, based on a plurality of the correspondence relationships. while several estimates, calculated the tristimulus values and different interpolation tristimulus values based on the spectral reflectance distribution of the coated surface due to the characteristic values of the estimated interpolation relationship, the tristimulus values and interpolated tristimulus values In each case, the coordinate values on the coordinates of the predetermined color system are determined, and among the obtained coordinate values, a plurality of coordinate values are determined as reference coordinate values representing the reference color, and the designated color is designated to reproduce the paint color. A paint color selection method for selecting a paint color by sequentially selecting coordinate values from the coordinate value representing the designated color to the reference coordinate value from the nearest coordinate value when reflecting the tendency of the reference color. 3. A predetermined coating color of a coating surface formed of one or a plurality of layers on an object to be coated and each layer formed of at least one constituent material, for each of all the constituent materials constituting the coating surface. A plurality of correspondences between the characteristic values of the quantities and the spectral reflectance distributions of the painted surfaces based on the characteristic values are obtained in advance, and the amount of at least one of the constituent materials among all the constituent materials determined by the correspondence is different in the paint color. A plurality of interpolation correspondences different from the correspondence representing the correspondence between the characteristic value and the spectral reflectance distribution are estimated based on the plurality of correspondences, and the spectral reflectance distribution of the interpolation correspondence or the spectrum of the correspondence is estimated. Based on the reflectance distribution, the deflection angle of the painted surface, which represents the flip-flop relationship between the deflection angle obtained by changing the light reception angle when receiving the reflected light from the painted surface and the brightness at the deflection angle, is determined. A method of selecting a paint color by selecting a paint color to be reproduced from a plurality of bend characteristics. 4. With respect to a predetermined coating color of a coating surface which is formed of one or more layers on an object to be coated and each layer is formed of at least one constituent material, each of all the constituent materials constituting the coating surface is used. A plurality of correspondences between the characteristic values of the quantities and the spectral reflectance distributions of the painted surfaces based on the characteristic values are obtained in advance, and the amount of at least one of the constituent materials among all the constituent materials determined by the correspondence is different in the paint color. A plurality of interpolation correspondences different from the correspondence representing the correspondence between the characteristic values and the spectral reflectance distributions are estimated based on the plurality of correspondences, and for each of the characteristic values of the correspondence and the characteristic values of the interpolation correspondence. Along with obtaining the particle size distribution of the constituent materials, a depth index representing the depth of the coating color is obtained based on the spectral reflectance distribution of the interpolation correspondence or the spectral reflectance distribution of the correspondence and the obtained particle size distribution. A method for selecting a paint color by selecting a paint color by selecting a plurality of depth indices. 5. A plurality of correspondence relations between a spectral reflectance distribution and characteristic values for a paint color selected by at least one of the paint color selection methods according to claim 2, 3, and 4, which are determined in advance. A paint color reproduction method in which a paint color is reproduced by estimating based on the relationship and determining the amounts of all the constituent materials based on characteristic values determined from the estimated correspondence.