Color formulation method and system based on ostwald full-color gamut color mixing model

Abstract

A color formulation method and system based on an Ostwald full-color gamut color mixing model, relating to the technical fields of color matching and color model construction and color design and application development in the textile field. The method uses actually obtained red, yellow, green, blue, highest-lightness gray and lowest-lightness gray to construct an Ostwald's color solid that can be applied to actual industrial design, and surpasses the traditional 24 hues, thus allowing flexible application in different color design scenarios; in addition, in the Ostwald's color solid gridded model in the method, the grid point position corresponding to each color is directly associated with the mixing concentration ratio of black, white and pure color pigments required for formulating the color, such that a designer can directly acquire the proportion of each color pigment from the model during color formulation to obtain target colors, thereby greatly improving the design efficiency.

Description

Color matching method and system based on Ostwald full color gamut color mixing model TECHNICAL FIELD

[0001] The present application relates to a color matching method and system based on Ostwald full color gamut color mixing model, belonging to the field of color matching theory, color model construction and color design method and application development technology in the field of textiles. BACKGROUND

[0002] Ostwald color solid, also known as Ostwald's color solid, is a three-dimensional biconical color solid composed of 24 isochromatic faces, 8 equal white faces and 8 equal black faces, and is characterized by hue, whiteness and blackness.

[0003] Ostwald color solid is based on standard four primary colors to construct a hue ring containing 24 hues, and is based on standard white and black to construct an eight-level gray axis from standard white to standard black. The pure and turbid changes and light and dark changes of various hues are processed with the same step to construct 24 isochromatic faces. Therefore, Ostwald color solid explains the quantitative relationship between color and mixing ratio with a color distribution rule. However, when used in industrial design, Ostwald color solid has the following problems:

[0004] First, the color values of the red, yellow, green, blue, black and white primary colors produced by industrial production are not the standard colors defined by color optics. The color values of the four primary colors are actually not uniformly distributed on the hue ring. Black and white are actually high-lightness gray close to white and low-lightness gray close to black. Therefore, when designers perform color matching, if the actual six primary colors are used as the basis and the mixing concentrations of each color are calculated according to the color distribution rule of the standard Ostwald color solid, the ideal color matching effect cannot be obtained, resulting in a large color matching error.

[0005] Second, the existing Ostwald color solid only provides color cards. Even if the color distribution rule is disclosed, designers cannot directly obtain the mixing ratio of each color when performing color matching. In combination with the error caused by the actual color values of the six primary colors, the amount of each color can only be adjusted manually by referring to the color card, resulting in very low color matching efficiency. Therefore, the existing Ostwald color solid cannot be applied to efficient and accurate industrial color design.

[0006] SUMMARY

[0007] In order to provide an Ostwald color solid that can be applied to actual industrial color design, reduce color difference and improve color matching efficiency, the present application provides a color matching method and system based on Ostwald full color gamut color mixing model, which comprises:

[0008] The first object of the present application is to provide a color matching method, comprising:

[0009] Step one: based on actual color measurement, obtain color values of six primary colors of Ostwald color solid, and construct an Ostwald full color gamut gridding color mixing model;

[0010] Step two: obtain a target color from the Ostwald full color gamut gridding color mixing model, and obtain the mixing concentration values of the six primary colors required for matching the color according to the grid point coordinates of the target color in the model;

[0011] Step three: mix the six primary colors based on the mixing concentration obtained in step two to obtain a target color material;

[0012] The construction process of the Ostwald full color gamut gridding color mixing model comprises:

[0013] Step 1: taking the color values of red, yellow, green and blue color materials as the basis, a hue ring of Ostwald color solid is constructed, comprising:

[0014] Four color mixing intervals are constructed, and binary coupling color mixing is performed based on the color values of the two end points of the color mixing interval to obtain the color value C(ξ) of each hue on the hue ring of Ostwald color solid, which is expressed as:

[0015] The color mixing concentration of each hue on the hue ring of Ostwald color solid is:

[0016] Wherein, ξ represents the grid point serial number of each hue on the hue ring of Ostwald color solid, ε m ≥ 2; δ = 1, 2, 3, 4 respectively represent the serial numbers of the four color mixing intervals; [r α (δ), g α (δ), b α (δ)] and [r β (δ), g β (ξ), b β (δ)] respectively represent the color values of the two end points of the δth color mixing interval; and Respectively represent the mixing concentration of the color mixing interval end color C α (δ) and C β (δ) corresponding to the ξth grid point, and the increasing gradient of the mixing concentration is 1 / ε m ;

[0017] The grid point coordinate value of each hue on the hue ring of Ostwald color solid is:

[0018] Wherein, θ ξ , ρξ and z ξ respectively represent the polar angle, polar radius and height of the grid point;

[0019] Step 2: taking the color value of white and black as the color value of the highest lightness node and the lowest lightness node, a gray axis of the Ostwald color solid is constructed, and the polar coordinates of the 8 nodes on the gray axis are:

[0020] The color value corresponding to the 8 nodes on the gray axis and the mixing concentration are obtained in a geometric progression, an arithmetic progression or a non-linear progression;

[0021] The concentration value matrix of the 8 nodes on the gray axis is:

[0022] The color value matrix of the 8 nodes on the gray axis is:

[0023] Wherein, η = 1 corresponds to the gray axis constructed in a common ratio coefficient, η = 2 corresponds to the gray axis constructed in an arithmetic coefficient, and η = 3 corresponds to the gray axis constructed in a non-linear progression;

[0024] Step 3: taking a certain hue color value C ξ =(r ξ ,g ξ ,b ξ ), the highest lightness node color value C W =(r W ,g W ,b W ) and the color value C K =(r K ,g K ,b K ) of the lowest lightness node to construct each isochromatic plane of the Ostwald color solid, and the three primary color mixing concentrations of the color block on each isochromatic plane are:

[0025] The color value of the color block corresponding to the grid point P(τ,δ,ξ) is:

[0026] Wherein, δ = 1, 2,..., 7, 8 is the equal blackness serial number, τ = 1, 2,..., 7, 8 is the equal whiteness serial number, γ = 1, 2,..., 7, 8 is the equal purity serial number, Ω ξ , Ω W , Ω K respectively represent the weight of the three primary color pigments.

[0027] ​Optionally, step 2 adopts the method of equal-ratio increment of lightness to construct the gray axis, and the mixture concentration value matrix of eight nodes of the gray axis is:

[0028] wherein,

[0029] The color value of each color node of the gray axis is:

[0030] wherein, C W =[r W ,g W ,b W ] and C K =[r K ,g K ,b K ] represent the color values of the highest lightness node and the lowest lightness node respectively.

[0031] Optionally, step 2 adopts the method of equal-difference increment of lightness to construct the Ostwald gray axis, and the mixture concentration value matrix of eight nodes of the gray axis is:

[0032] The color value of each color node of the gray axis is:

[0033] wherein, C W =[r W ,g W ,b W ] and C K =[r K ,g K ,b K ] represent the color values of the highest lightness node and the lowest lightness node respectively.

[0034] Optionally, step 2 adopts the method of non-linear increment of lightness to construct the gray axis, and the mixture concentration value matrix of eight nodes of the gray axis is:

[0035] The color value of each color node of the gray axis is:

[0036] wherein, C W =[r W ,g W ,b W ] and C K =[r K ,g K ,b K ] represent the color values of the highest lightness node and the lowest lightness node respectively.

[0037] Optionally, when ξ = 1, 2,..., 23, 24, the equal white surface of the Ostwald color solid is respectively:

[0038] The color matrix of the equal white surface when τ = 1 is:

[0039] The color matrix of the equal white surface when τ = 2 is:

[0040] The color matrix of the equal white surface when τ = 3 is:

[0041] The color matrix of the equal white surface when τ = 4 is:

[0042] The color matrix of the equal white surface when τ = 5 is:

[0043] The color matrix of the equal white surface when τ = 6 is:

[0044] The color matrix of the equal white surface when τ = 7 is:

[0045] The color matrix of the equal white surface when τ = 8 is:

[0046] Optionally, when ξ = 1, 2,..., 23, 24, the equal black surface of the Ostwald color solid is respectively: The color matrix of the equal black surface when δ = 1 is:

[0047] The color matrix of the equal black surface when δ = 2 is:

[0048] The color matrix of the equal black surface when δ = 3 is:

[0049] The color matrix of the equal black surface when δ = 4 is:

[0050] The color matrix of the equal black surface when δ = 5 is:

[0051] The color matrix of the equal black surface when δ = 6 is:

[0052] The color matrix of the equal black surface when δ = 7 is:

[0053] The color matrix of the equal black surface when δ = 8 is:

[0054] Optionally, when ξ = 1, 2,..., 23, 24, the isopurity surfaces of the Ostwald color solid are respectively: the color matrix of the isopurity surface when γ = 1 is:

[0055] The color matrix of the isopurity surface when γ = 2 is:

[0056] The color matrix of the isopurity surface when γ = 3 is:

[0057] The color matrix of the isopurity surface when γ = 4 is:

[0058] The color matrix of the isopurity surface when γ = 5 is:

[0059] The color matrix of the isopurity surface when γ = 6 is:

[0060] The color matrix of the isopurity surface when γ = 7 is:

[0061] The color matrix of the isopurity surface when γ = 8 is:

[0062] A second object of the present application is to provide a color matching system for implementing the color matching method according to any one of the preceding items, the system comprising: a color measurement device, an Ostwald full color gamut gridding color mixing model construction module, and a visualization module.

[0063] The color measurement device is configured to obtain the color values of the Ostwald six primary colors in the actual colorant.

[0064] The Ostwald full color gamut gridding color mixing model construction module comprises:

[0065] A colorant color value acquisition module configured to obtain the color values of the actual colorant from the color measurement device;

[0066] A hue ring construction module configured to construct an equatorial hue ring based on the actually obtained Ostwald six primary colors, and to give the color values, position coordinate values, and mixing concentrations of each hue;

[0067] A gray axis construction module configured to construct a gray axis based on the actually obtained black and white as the lowest and highest lightness nodes, respectively, and to give the color values, position coordinate values, and mixing concentrations of black and white of each lightness node;

[0068] An isohue surface spectrum construction module configured to construct 4εm isochromatic face chromaticity;

[0069] The visualization module is configured to display a model chromaticity and output the mixture concentration and color value corresponding to the six primary colors based on the grid point coordinate value of the target color.

[0070] Optionally, the Ostwald full-color gamut gridding mixture model construction module further comprises:

[0071] The isochromatic face chromaticity construction module is configured to construct a conical surface formed by all grid points with equal white content on each hue face as an isochromatic face of the Ostwald color solid based on the 4ε m isochromatic face chromaticity.

[0072] The isochromatic face chromaticity construction module is configured to construct a conical surface formed by all grid points with equal white content on each hue face as an isochromatic face of the Ostwald color solid based on the 4ε m isochromatic face chromaticity.

[0073] The isochromatic face chromaticity construction module is configured to construct a conical surface formed by all grid points with equal white content on each hue face as an isochromatic face of the Ostwald color solid based on the 4ε m isochromatic face chromaticity.

[0074] A third object of the present application is to provide a computer-readable storage medium, the storage medium having a computer program stored thereon, when the computer program is executed by a processor, the method as claimed in any one of the above is implemented.

[0075] The present application has the following advantages:

[0076] 1. The obtained red, yellow, green and blue are used as the primary colors of the four color pigments, the position of the grid point is defined by the mixing concentration of the four primary color pigments, the color value of each grid point is obtained by the binary coupling mixture equation, and a hue circle matching the classical Ostwald color solid is constructed, solving the problem of uneven distribution of the hue circle based on the actual color obtained, and the number of hues of the hue circle can be arbitrarily set, breaking through the traditional 24 hues, so it can be flexibly applied to different industrial design scenes with different color matching requirements.

[0077] 2. The highest brightness gray and the lowest brightness gray obtained by actual dyeing are used as the south and north poles of the gray axis, the common ratio coefficient of eight times of equal ratio increment or equal ratio decrement is obtained, and the brightness color value of the eight levels on the gray axis is obtained, so as to construct the actual gray axis, solving the problem of mismatching between the theoretically constructed gray axis and the actual brightness distribution of the gray axis.

[0078] 3. The highest lightness gray and the lowest lightness gray obtained by actual dyeing are used as the south and north poles of the gray scale axis, a non-linear increasing function of lightness value is designed between the color values of the south and north poles, and 8 levels of lightness color values on the gray scale axis are designed to construct an actual gray scale axis, thereby solving the problem of mismatch between the theoretically constructed gray scale axis and the actual lightness distribution of the gray scale axis.

[0079] 4. The highest lightness gray and the lowest lightness gray obtained by actual dyeing are used as the south and north poles of the gray scale axis, an arithmetic increasing function of lightness value is designed between the color values of the south and north poles, and 8 levels of lightness color values on the gray scale axis are designed to construct an actual gray scale axis, thereby solving the problem of mismatch between the theoretically constructed gray scale axis and the actual lightness distribution of the gray scale axis.

[0080] 5. In an embodiment, the Ostwald color solid is divided into 24 levels of hue, 8 levels of lightness, and 8 levels of purity, thereby obtaining an Ostwald color solid composed of 8 white lightness planes, 8 black lightness planes, and 24 hue planes, and obtaining the spatial coordinates of each grid point and the corresponding mixing concentration, color value and other parameters. The mixing concentration of the primary color pigments corresponding to the grid point and the color value corresponding to the grid point can be obtained through the grid point coordinate value.

[0081] 6. In an embodiment, the mixing concentration value matrix and the color spectrum matrix of the 24 hue planes, 8 black lightness planes and 8 white lightness planes are given respectively with the grid point coordinates as the independent variable.

[0082] 7. In an embodiment, based on the actual obtained color values of the six primary color pigments, the color values of 36 color blocks on the 24 hue planes are obtained by the constructed mathematical model with hue as the reference; the color values of 169, 145, 121, 97, 73, 49, 25 and 1 color blocks on the 8 black lightness planes are obtained by the constructed mathematical model with the mixing concentration of the black color pigment as the reference; and the color values of 169, 145, 121, 97, 73, 49, 25 and 1 color blocks on the 8 white lightness planes are obtained by the constructed mathematical model with the mixing concentration of the white color pigment as the reference.

[0083] In the Ostwald full-color domain gridding color mixing model constructed by the present application, the grid point position corresponding to each color is directly related to the mixing concentration ratio of the black, white and pure color pigments required to mix the color, so that the designer can directly obtain the proportion of each pigment from the model to obtain the target color, thereby greatly improving the design efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0084] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly introduced. Obviously, the drawings in the following description only constitute some embodiments of the present application, and for those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0085] Fig. 1 is a flow chart of constructing the Ostwald full color gamut gridding color mixing model of the present application.

[0086] Fig. 2 is a color mixing concentration contrast curve diagram of three gray axes construction modes in the first embodiment of the present application.

[0087] Fig. 3 is a flow chart of the second embodiment of the present application. DETAILED DESCRIPTION

[0088] In order to make the objects, technical solutions and advantages of the present application more clear, the embodiments of the present application will be further described in detail.

[0089] Embodiment one:

[0090] This embodiment takes 24 hue rings as an example to further describe the specific derivation and construction process of the Ostwald full color gamut gridding color mixing model of the present application, mainly including the following contents:

[0091] (I) Digital construction of Ostwald hue ring

[0092] 1. Obtaining four primary colors of hue ring

[0093] There are four primary colors of red, yellow, green and blue in the Ostwald model, and their color values are respectively C 2R =(r 2R ,g 2R ,b 2R ), C 2Y =(r 2Y ,g 2Y ,b 2Y ), C 2SG =(r 2SG ,g 2SG ,b 2SG ), and C 2UB =(r 2UB ,g 2UB ,b 2UB ). In practical operation, the color values of red, yellow, green and blue dyes obtained based on actual dyeing and measurement can be used as the color values of the four primary colors of the Ostwald model, and the weights of the four primary colors of dyes are equally taken as Ω 2R , Ω 2Y , Ω 2SG , and Ω 2UB .

[0094] 2、Four primary colors two two coupling color mixing mode construction

[0095] With Ostwald color solid four primary colors red, yellow, green, blue (marked as 2R, 2Y, 2SG, 2UB) as the benchmark, respectively, (2R~2Y), (2Y~2SG), (2SG~2UB), (2UB~2R) and other four color mixing intervals. Take δ = 1, 2, 3, 4, set C α (δ) and C β (δ) respectively represent the color value of the two end points of the four color mixing intervals, Ω α (δ) and Ω β (δ) represent the weight of its color material, then:

[0096] The color values of the above four color mixing interval end points C α (δ) and C β (δ) are used as the benchmark for binary coupling color mixing. Let the increasing gradient of the mixing concentration be 1 / ε m (ε m ≥ 2) and ε = 1, 2,..., ε m -1, ε m , then (ε α +1) grid points are obtained in the color mixing interval of C β (δ)-C m (δ), and the mixing concentration corresponding to each grid point is set as The weight of the corresponding mixed sample is Ω α～β (ε), the corresponding color value is C α-β (ε), then:

[0097] 3、Ostwald color ring color spectrum construction

[0098] In order to obtain the Ostwald color ring color spectrum, four independent color mixing intervals (2R~2Y), (2Y~2SG), (2SG~2UB), (2UB~2R) with four primary colors as nodes can be combined into a continuous circulating color mixing process. Let ξ be the grid point number of the (2R~2Y~2SG~2UB~2R) continuous circulating color mixing process, and:

[0099] From equation (6), we have:

[0100] Substitute equation (7) into equations (3), (4), and (5), and set ξ = 1, 2,..., (2ε m -1), 2ε m , 2εm +1,...,(3ε m -1),3ε m ,(3ε m +1),...,(4ε m -1),4ε m , then based on the change of grid point sequence number ξ, the continuous cycle color mixing process of (2R~2Y~2SG~2UB~2R) can be realized.

[0101] Let the color mixing concentration value corresponding to each grid point sequence number be The mixed sample weight corresponding to each grid point sequence number is Ω(ξ), and the color value corresponding to the grid point sequence number is C(ξ), then:

[0102] At this time, the corresponding relationship of the grid point sequence number ξ, the mixed sample color mixing concentration , the mixed sample weight Ω(ξ), and the mixed sample color value C(ξ) is obtained. When ξ=1, 2,...,(2ε m -1),2ε m ,2ε m +1,...,(3ε m -1),3ε m ,(3ε m +1),...,(4ε m -1),4ε m , the color value corresponding to each grid point is obtained, and thus the color mixing color spectrum matrix is obtained as follows:

[0103] As can be seen from equation (11), through the change of grid point ξ=1, 2,...,(2ε m -1),2ε m ,2ε m +1,...,(3ε m -1),3ε m ,(3ε m +1),...,(4ε m -1),4ε m , the color C(ξ)=[r(ξ), g(ξ), b(ξ)] of each grid point realizes the continuous cycle color mixing of (2R~2Y~2SG~2UB~2R) in turn.

[0104] 4. Position coordinates of each hue in the hue circle

[0105] Based on equation (11), the color is divided into 4ε m hue levels, and the color mixing color spectrum composed of all hues is Mapping to the hue circle of Ostwald color solid, we get 4ε m grid points P ξ (θ ξ ,ρ ξ )=[θ ξ ,ρ ξ ,z ξ ], each grid point corresponds to polar angle coordinate θ ξ , polar radius coordinate ρ ξ , and height coordinate z ξ in polar coordinate system. The coordinate values of each grid point on the hue circle are as follows:

[0106] When ξ=1,2,...,(2ε m -1),2ε m ,2ε m +1,...,(3ε m -1),3ε m ,(3ε m +1),...,(4ε m -1),4ε m , the coordinate values of each grid point are combined into the grid point coordinate matrix as follows:

[0107] or

[0108] 5、Ostwald color solid 24-hue circle corresponding polar coordinate values and color values

[0109] Based on equations (11)-(14), when ε m =6, the hue angle of Ostwald color solid 24-hue circle is θ ξ =(ξ-1)×15°. The position coordinates and color values of each hue are shown in Table 1.

[0110] Table 1. Ostwald color solid 24-hue circle corresponding polar coordinates and color values

[0111] (II) Digital construction of Ostwald gray axis

[0112] 1、The composition of gray axis and the position coordinates of each node

[0113] Ostwald gray axis is divided into 8 levels of lightness. The gray with the highest lightness is denoted as color white O a , and the gray with the lowest lightness is denoted as color black O p . In color white O a and color black O pInserting 6 gray levels of gray between them, 8 nodes with different lightness from low to high on the Ostwald gray axis are obtained: O p ,O n ,O l ,O i ,O g ,O e ,O c ,O a Then the polar coordinate values of the 8 nodes on the gray axis are:

[0114] 2. Obtaining the mixing concentration of each node of the Ostwald gray axis

[0115] This embodiment constructs the gray axis of the Ostwald color solid in three ways: the first way is to obtain the lightness values (color values) of the eight nodes of the gray axis in equal ratio increment of lightness, and to construct the gray axis in this way; the second way is to obtain the lightness values (color values) of the eight nodes of the gray axis in equal difference increment of lightness, and to construct the gray axis in this way; the third way is to obtain the lightness values (color values) of the eight nodes of the gray axis in non-linear increment of lightness, and to construct the gray axis in this way.

[0116] (1) Ostwald gray axis constructed by equal ratio increment of lightness

[0117] ① Obtaining the common ratio coefficient of the gray axis with equal ratio increment of lightness

[0118] Suppose that the lightness values of the eight nodes of the Ostwald defined gray axis are in equal ratio progression, and the color values of the highest lightness node and the lowest lightness node of the Ostwald color system gray axis are C W =[r W ,g W ,b W ] and C K =[r K ,g K ,b K ], respectively, and the fiber weight is Ω W ,Ω K . The fiber weights corresponding to the nodes a, c, e, g, i, l, n, and p of the gray axis are Set Ω W ,Ω K to obtain by mixing Then the mixing concentrations corresponding to the eight nodes of the gray axis are The corresponding color values are Then:

[0119] Let the common ratio coefficient λ1 of the color value of the eight nodes of the Osterwald gray scale axis be:

[0120] Then:

[0121] If r W = g W = b W ; r K = g K = b K , then Then:

[0122] 2. Obtaining the mixing concentration values of the nodes of the lightness equi-ratio-increasing gray scale axis

[0123] Let τ take 1 and 2 respectively, and according to formula (19), the common ratio coefficient λ1 is:

[0124] From formula (22), we can obtain:

[0125] Based on formula (23), we can obtain

[0126] Let τ take 1 and 2 respectively, and the common ratio coefficient λ1 can also be written as:

[0127] From formula (25), we can obtain:

[0128] Then we can obtain

[0129] The concentration value matrix of the eight nodes of the gray scale axis can be written as:

[0130] 3. Obtaining the color values of the nodes of the lightness equi-ratio-increasing gray scale axis

[0131] Based on formula (20), the common ratio coefficient λ1 can be obtained from the actually obtained highest lightness C W and the lowest lightness C K . Let:

[0132] Then from the color value C W = [r W , g W , b W ] of the highest lightness of the gray scale axis and the color value C​​K = [r K ,g K ,b K ] The color values of the remaining nodes on the gray axis are obtained as follows:

[0133] It can also be written as:

[0134] Based on the color values of the 8 nodes of the gray axis The color spectrum matrix of the gray axis can be obtained That is:

[0135] If the highest lightness color value C W = [r W ,g K ,b K ] and the lowest lightness color value C K = [r K ,g W ,b K ] of the gray axis are known, the mixed color of the 8 nodes of the gray axis can be obtained by mixing the color values in the concentration value matrix Then:

[0136] From equation (33), based on the highest lightness C W = [r W ,g W ,b K ] and the lowest lightness C K = [r K ,g W ,b K ] of the colorant and the mixed concentration of the 8 nodes on the gray axis, the color values corresponding to the 8 nodes on the gray axis can be obtained. If C τ = [247, 247, 247], C τ = [11, 11, 11], τ = 1, 2, …, 7, 8 are substituted into equations (22), (24), (27), we can obtain:

[0137] Then equation (35) can be written as:

[0138] (2) Ostwald gray axis constructed by increasing lightness in equal difference

[0139] ① Obtaining the equal difference coefficient of the lightness-increasing-equal-difference gray axis

[0140] ​Similarly, for formula (16)-(18), assuming the color values of the eight nodes of the Ostwald model gray axis increase by an arithmetic coefficient λ2, then:

[0141] From formula (37), we have:

[0142] If r W = g W = b W , r K = g K = b K , then C W , C K can be written as:

[0143] Then formula (38) can be written as:

[0144] ②Obtaining the mixing concentration values of each node of the gray axis with equal difference in lightness

[0145] Let τ take 1 and 2 respectively, according to formula (37)-(40), the arithmetic coefficient λ2 can be written as:

[0146] From formula (41), we have as:

[0147] Let τ take 1 and 2 respectively, according to formula (37)-(40), the arithmetic coefficient λ2 can also be written as:

[0148] From formula (43), we have as:

[0149] Then the concentration value matrix of the eight nodes of the gray axis can be written as:

[0150] ③Obtaining the color values of each node of the gray axis with equal difference in lightness

[0151] Based on formula (38)-(40), the color values of the remaining nodes on the gray axis can be obtained as follows:

[0152] Based on the color values of the eight nodes of the gray axis , the color spectrum matrix of the gray axis can be obtained as:

[0153] (3) Construction of Ostwald gray axis with nonlinear increase in lightness

[0154] ① Construction of a non-linear coupled color mixing mode between the highest brightness white and the lowest brightness black

[0155] To achieve a non-linear increase in brightness along the Ostwald grayscale axis, this patent employs a non-linear coupling mixing process between the highest brightness white pigment and the lowest brightness black pigment. Specifically, while maintaining a constant total weight, the white pigment concentration increases non-linearly, while the black pigment concentration decreases non-linearly. This results in a non-linear change in brightness values ​​across the eight nodes of the grayscale axis from lowest to highest brightness. Let the weight of the highest brightness white pigment be Ω. w The weight of the lowest brightness black pigment is Ω. k The above fiber weights are discretized as follows:

[0156] Based on the highest brightness white pigment Ω w With the lowest brightness black pigment Ω k The nonlinear coupled color mixing mode is constructed as follows:

[0157] When τ = 1, 2, ..., 7, 8, The weights of the mixed samples corresponding to each node on the grayscale axis.

[0158] ② Obtaining the mixing concentration values ​​of each node on the grayscale axis

[0159] Based on equation (49), when τ = 1, 2, ..., 7, 8, the mixing concentration corresponding to each node of the grayscale axis can be obtained. for:

[0160] Based on equation (50), when τ = 1, 2, ..., 7, 8, let... The concentration values ​​of white and black fibers in the mixed sample corresponding to each node of the grayscale axis can be obtained as follows:

[0161] Figure 2 shows a comparison of the color mixing density matrix equations based on three grayscale axis construction methods: proportional, arithmetic, and non-linear increases in brightness. Blue, green, and red correspond to the grayscale axis fiber mixing concentrations under the proportional, arithmetic, and non-linear increase methods, respectively. Curves comparing the three construction methods The values ​​show that as the brightness value τ increases, the proportion of the decrease in the black fiber mixing concentration in the nonlinear mode gradually increases, which is significantly less than the black fiber mixing concentration in the equal ratio and equal arithmetic modes. In practical applications, this can improve the color recognition of mixed color blocks.

[0162] ③Obtaining color values of each node on the non-linearly increasing lightness gray axis

[0163] Assuming that the lightness values of the eight nodes on the gray axis defined by Ostwald are increased in a non-linear manner, the color values of the highest lightness and the lowest lightness on the gray axis of the Ostwald color system are C W =[r W ,g W ,b W ] and C K =[r K ,g K ,b K ], respectively, and the fiber weight is Ω W ,Ω K . The fiber weights corresponding to the nodes a, c, e, g, i, l, n, and p on the gray axis are Ω O , and the color values corresponding to the eight nodes on the gray axis are Let Ω W ,Ω K be mixed at a mixing concentration to obtain , and the color value thereof is Then:

[0164] The color values of the eight nodes on the Ostwald gray axis are :

[0165] The digital color matrix of the color values of the eight nodes on the gray axis is :

[0166] (4) Digital gray axis constructed based on the coordinate values of each node, the mixing concentration, and the color value

[0167] Based on the foregoing derivation, the construction of the Ostwald gray axis can be divided into three modes. Let η = 1 correspond to the gray axis constructed in a geometric progression, η = 2 correspond to the gray axis constructed in an arithmetic progression, and η = 3 correspond to the gray axis constructed in a non-linear manner.

[0168] Let the mixing weight matrix of the eight nodes on the gray axis obtained by the three construction modes be Then:

[0169] Let the concentration value matrix of the eight nodes on the gray axis obtained by the three construction modes be Then:

[0170] Let the color value matrix of the eight nodes on the gray axis obtained by the three construction modes be Then:

[0171] Based on formula (14) (48) (49), the position coordinates, mixing concentrations and color values corresponding to each node of the gray axis can be obtained, as shown in Table 2. Thus, the digitalized gray axis is constructed.

[0172] Table 2 Color values and position coordinates of each node of the gray axis

[0173] (Three) Digital construction of Ostwald color solid

[0174] Ostwald color solid is a three-dimensional biconic color solid, mainly including a series of isochromatic phase planes, isogreyscale planes and isowhiteness planes. The main task of constructing Ostwald color solid is to construct its 24 isochromatic phase planes, 8 isowhiteness planes, 8 isoblackness planes and 8 isopurity planes. Among them, the construction of isochromatic phase plane is the key.

[0175] In constructing the isochromatic phase plane, a color phase in 24 color phases is mixed with white and black to obtain the color phase plane. There are two mixing methods. One mixing method is to combine a certain proportion of black on the gray axis with another eight different proportions of white, eliminate combinations with mixing concentration proportion greater than 100%, leave combinations with mixing concentration proportion less than or equal to 100%, and fill the part with mixing concentration proportion less than 100% with the color phase in the remaining proportion, thereby obtaining eight isoblackness lines on the isochromatic phase plane and further obtaining an isochromatic phase plane containing 36 color blocks. The other mixing method is to combine a certain proportion of white on the gray axis with another eight different proportions of black, eliminate combinations with mixing concentration proportion greater than 100%, leave combinations with mixing concentration proportion less than or equal to 100%, and fill the part with mixing concentration proportion less than 100% with the color phase in the remaining proportion, thereby obtaining eight isowhiteness lines on the isochromatic phase plane and further obtaining an isochromatic phase plane containing 36 color blocks.

[0176] The construction of isowhiteness plane is to regard the conical surface formed by all grid points with equal white content on each color phase plane as an isowhiteness plane, thereby obtaining eight isowhiteness planes.

[0177] The construction of isoblackness plane is to regard the conical surface formed by all grid points with equal black content on each color phase plane as an isoblackness plane, thereby obtaining eight isoblackness planes.

[0178] The construction of isopurity plane is to regard the cylindrical surface formed by all grid points with equal (white + black) content, i.e. equal color content, on each color phase plane as an isopurity plane, thereby obtaining eight isopurity planes.

[0179] 1. Base color combination design of each isochromatic phase plane

[0180] According to the equal hue, equal whiteness, equal blackness, and equal purity, the Ostwald color solid is grid-divided, and the hue serial number of each grid point is ξ = 1, 2,..., 23, 24; the equal blackness serial number is δ = 1, 2,..., 7, 8; the equal whiteness serial number is τ = 1, 2,..., 7, 8; and the equal purity serial number is γ = 1, 2,..., 7, 8. The color block in the Ostwald color solid is formed by mixing a corresponding certain hue (denoted by C ξ , a highest brightness white (denoted by C W ), and a lowest brightness black (denoted by C K ). The base color combination of each equal hue plane is shown in Table 3.

[0181] Table 3 Base color combination of Ostwald color solid equal hue plane

[0182] 2. Construction of a ternary base color grid-mixed color mode based on an equal hue plane

[0183] On the ξth equal hue plane of the Ostwald color solid, let the color values of the three base colors be C ξ = (r ξ , g ξ , b ξ ), C W = (r W , g W , b W ), and C K = (r K , g K , b K ), and the weights be Ω ξ , Ω W , and Ω K . When the equal hue plane θ ξ = (ξ-1) × 15° (ξ = 1, 2,..., 23, 24), let Ω(τ, δ, ξ) = Ω ξ = Ω W = Ω K = Ω, and according to the mixing rule of each color block on the Ostwald equal hue plane, the coupled mixing mode corresponding to each grid point is constructed as follows:

[0184] The ternary base color mixed color concentration η in the mixed color sample Ω (τ, δ, ξ) can be obtained by the following formula:

[0185] or written as:

[0186] The color value corresponding to the grid point P(τ, δ, ξ) can be obtained For:

[0187] 3. Grid Osterberg color cube based on digital color mixing construction

[0188] Let Where (τ, δ, ξ) is the grid point number, according to the construction method of Osterberg color cube, eliminate the color blocks with mixing concentration ratio greater than 100% in the Osterberg color cube constructed under the three modes of equal ratio, equal difference and non-linear when η = 1, 2, 3, the remaining 680 color blocks can be expressed as follows:

[0189] Equation (64) is the mass matrix of the 680 color mixing color blocks of the Osterberg color cube.

[0190] Equation (65) is the color mixing concentration matrix of the 680 color mixing color blocks of the Osterberg color cube.

[0191] Equation (66) is the color matrix of the 680 color mixing color blocks of the Osterberg color cube.

[0192] 4. Construction of Osterberg color cube isochromatic surface and its color spectrum matrix

[0193] In the Osterberg model, mixing one color with white and black in 24 hues can obtain isochromatic surfaces, a total of 24 isochromatic surfaces, each containing 36 color blocks.

[0194] Let ξ = 1, 2,..., 23, 24, when η = 1, 2, 3, the color matrix of the 24 isochromatic surfaces defined by the grid point number is as follows:

[0195] 5. Construction of Osterberg color cube isochromatic surface and its color spectrum matrix

[0196] In the Osterberg model, the conical surface formed by all grid points with equal white content on each hue surface is regarded as the isochromatic surface, and 8 isochromatic surfaces can be obtained, each containing 169, 145, 121, 97, 73, 49, 25, 1 color blocks. Let ξ = 1, 2,..., 23, 24, the color matrix of the 8 isochromatic surfaces is as follows.

[0197] The color matrix of the isochromatic surface when τ = 1 is:

[0198] The color matrix of the equal whiteness surface when τ = 2 is:

[0199] The color matrix of the equal whiteness surface when τ = 3 is:

[0200] The color matrix of the equal whiteness surface when τ = 4 is:

[0201] The color matrix of the equal whiteness surface when τ = 5 is:

[0202] The color matrix of the equal whiteness surface when τ = 6 is:

[0203] The color matrix of the equal whiteness surface when τ = 7 is:

[0204] The color matrix of the equal whiteness surface when τ = 8 is:

[0205] 6. Ostwald color solid equal blackness surface and construction of its color spectrum matrix

[0206] In the Ostwald model, the conical surface formed by all grid points with equal black content on each hue surface is regarded as an equal blackness surface, and eight equal blackness surfaces can be obtained, each of which contains 1, 25, 49, 73, 97, 121, 145, and 169 color blocks, respectively. Let ξ = 1, 2,..., 23, 24, then the color matrix of the eight equal blackness surfaces is as follows.

[0207] The color matrix of the equal blackness surface when δ = 1 is:

[0208] The color matrix of the equal blackness surface when δ = 2 is:

[0209] The color matrix of the equal blackness surface when δ = 3 is:

[0210] The color matrix of the equal blackness surface when δ = 4 is:

[0211] The color matrix of the equal blackness surface when δ = 5 is:

[0212] The color matrix of the equal blackness surface when δ = 6 is:

[0213] The color matrix of the equal blackness surface when δ = 7 is:

[0214] The color matrix of the equal brightness surface of δ = 8 is:

[0215] 7. Ostwald color solid equal purity surface and construction of its color matrix

[0216] The construction of the equal purity surface is to take all the grid points on the hue surface (white + black) content equal, that is, the color content equal cylindrical surface as the equal purity surface, thus 8 equal purity surfaces can be obtained. Take the (white + black) content minimum (0%) as the first equal purity surface, at this time γ = 1, and so on, set τ , δ = 1 1,2 ,..., 8; ξ = 1 1,2 ,..., 23,24 The color matrix of the 8 equal purity surfaces is as follows.

[0217] The color matrix of the equal purity surface of γ = 1 is:

[0218] The color matrix of the equal purity surface of γ = 2 is:

[0219] The color matrix of the equal purity surface of γ = 3 is:

[0220] The color matrix of the equal purity surface of γ = 4 is:

[0221] The color matrix of the equal purity surface of γ = 5 is:

[0222] The color matrix of the equal purity surface of γ = 6 is:

[0223] The color matrix of the equal purity surface of γ = 7 is:

[0224] The color matrix of the equal purity surface of γ = 8 is:

[0225] Example two:

[0226] The color values of the six primary colors obtained by dyeing and color measurement are: red (235, 12, 23), yellow (235, 225, 32), green (23, 224, 36), blue (28, 32, 238), black (11, 11, 11), and white (247, 247, 247). The 24-hue chromaticity of the Ostwald color solid is designed by means of the Ostwald color solid chromaticity matrix model and algorithm constructed independently. The eight-grade gray axis chromaticity with increasing lightness is designed. The second Y hue plane, the seventh white lightness plane, the second black lightness plane, and the third purity plane chromaticity are designed. The specific process is shown in FIG. 3, and specifically includes the following steps.

[0227] (1) Design of hue ring chromaticity of Ostwald model

[0228] The color values of the four primary colors of red, yellow, green, and blue in the Ostwald model are C 2R =(235, 12, 23), C 2Y =(235, 225, 32), C 2SG =(23, 224, 36), and C 2UB =(28, 32, 238). The color values of the 24 hues can be obtained as shown in Table 4.

[0229] Table 4 Color values of 24 hues of Ostwald color system

[0230] (2) Design of lightness-increasing gray axis chromaticity of Ostwald model

[0231] The color values of the highest lightness gray Oa and the lowest lightness gray Op on the gray axis of the Ostwald model are C W =(247, 247, 247) and C K =(11, 11, 11), respectively. According to the lightness-increasing gray axis model algorithm, the common ratio coefficient λ1 of the color values of the 8 nodes on the gray axis can be obtained.

[0232] The position coordinates and color values of the 8 nodes on the gray axis are shown in Table 5.

[0233] Table 5 Color values and position coordinates of 8 nodes on the gray axis

[0234] The white-black mixed concentrations of the remaining 7 nodes on the gray axis can also be obtained as shown in Table 6.

[0235] Table 6 White-black mixed color ratio of 8 nodes on the gray axis

[0236] (3) Design of Ostwald model isochromatic surface chromatogram

[0237] Taking 2Y yellow isochromatic surface as an example, at this time, ξ = 2, the known C 2Y =(235,225,32), based on the mixing concentration formula (67) of each color block on the isochromatic surface, the color values of each color block on the 2Y isochromatic surface are shown in Table 7, and the color values of each color block on the other 23 isochromatic surfaces can be obtained in the same way.

[0238] Table 7 Color values of each color block on the 2Y yellow isochromatic surface

[0239] (4) Design of Ostwald model isochromatic surface chromatogram

[0240] Taking the 7th isochromatic surface as an example, at this time, τ = 7, based on the mixing concentration of each color block on the isochromatic surface, the color values of each color block are shown in Table 8, and the color values of each color block on the other seven isochromatic surfaces can be obtained in the same way.

[0241] Table 8 Color values of each color block on the 7th isochromatic surface

[0242] (5) Design of Ostwald model isochromatic surface chromatogram

[0243] Taking the 2nd isochromatic surface as an example, at this time, δ = 2, based on the mixing concentration of each color block on the isochromatic surface, the color values of each color block are shown in Table 9, and the color values of each color block on the other seven isochromatic surfaces can be obtained in the same way.

[0244] Table 9 Color values of each color block on the 7th isochromatic surface

[0245] (6) Design of Ostwald model isochromatic surface chromatogram

[0246] Taking the 3rd isochromatic surface as an example, at this time, γ = 3, based on the mixing concentration of each color block on the isochromatic surface, the color values of each color block are shown in Table 10, and the color values of each color block on the other seven isochromatic surfaces can be obtained in the same way.

[0247] Table 10 Color values of each color block on the 3rd isochromatic surface

[0248] Some steps in the embodiments of the present application can be realized by software, and the corresponding software programs can be stored in a readable storage medium, such as an optical disc or a hard disk.

[0249] The above merely describes preferred embodiments of the present application and is not used to limit the present application, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A color formulation method characterized by, The method comprises: Step 1: obtaining color values of six basic colors of the Ostwald color solid based on actual color measurement, and constructing an Ostwald full-color-domain grid color mixing model; Step 2: obtaining a target color from the Ostwald full-color-domain grid color mixing model, and obtaining mixing concentration values of six basic colors required for mixing the colors according to grid point coordinates of the target color in the model; Step 3: mixing the six basic colors based on the mixing concentration obtained in step 2 to obtain a target color material; The construction process of the Ostwald full-color-domain grid color mixing model comprises: Step 1: taking color values of red, yellow, green and blue color materials as a reference to construct a hue ring of the Ostwald color solid, comprising: Four mixed color intervals are constructed, and binary coupling mixed colors are performed based on the color values of the two end points of the mixed color intervals to obtain the color values C(ξ) of each hue on the Ostwald color solid hue circle, which are expressed as: The mixing concentration of each hue on the Oswald color solid color wheel is as follows: wherein, ξ represents the grid point serial number of each hue on the Ostwald color solid, ε m ≥ 2; δ = 1, 2, 3, 4 respectively represent the serial number of four mixed color intervals; [r α (δ), g α (δ), b α (δ)] respectively represent the color values of the two end points of the δth mixed color interval; β (δ), g β (ξ), b β (δ)] respectively represent the color values of the two end points of the δth mixed color interval; and respectively represent the color C of the mixed color interval corresponding to the ξth grid point α (δ) and C β (δ) of the mixed concentration, the incremental gradient of the mixed concentration is 1 / ε m ; The grid point coordinate values of each hue on the Ostwald color solid hue circle are: where θ ξ , p ξ , and z ξ represent the polar angle, polar radius, and height of the grid point, respectively; Step 2: Construct the gray axis of the Ostwald solid color, with the color value of white and black as the color value of the highest lightness node and the lowest lightness node, and the polar coordinates of the 8 nodes on the gray axis are: Color values and mixing concentrations of eight nodes on the gray axis are obtained by equal ratio increment or equal difference increment or non-linear increment; The concentration value matrix of the 8 nodes of the gray scale axis is: The color value matrix of the 8 nodes of the gray scale axis is: Wherein, η = 1 corresponds to a gray axis constructed by equal ratio increment, η = 2 corresponds to a gray axis constructed by equal difference increment, and η = 3 corresponds to a gray axis constructed by non-linear increment; Step 3: Constructing the isochromatic planes of the Ostwald solid by the hue color value C ξ = (r ξ , g ξ , b ξ ), the highest lightness node color value C W = (r W , g W , b W ), and the lowest lightness node color value C K = (r K , g K , b K ). The trichromatic color mixing concentration of the color block on each isochromatic plane is: Color value of the color block corresponding to the grid point P(τ, δ, ξ) For: wherein δ = 1, 2,..., 7, 8 is the equal darkness index, τ = 1, 2,..., 7, 8 is the equal whiteness index, γ = 1, 2,..., 7, 8 is the equal purity index, Ω ξ ,Ω W ,Ω K respectively represent the weight of the colorant of the three primary colors.

2. The color formulation method of claim 1, wherein The step 2 adopts the method of constructing the gray axis with equal ratio increment of brightness, and the matrix of the mixture concentration values of eight nodes of the gray axis is: wherein, The color values of the color nodes of the gray scale axis are: where C W = [r W ,g W ,b W ] and C K = [r K ,g K ,b K ] represent the color values of the highest and lowest intensity nodes, respectively.

3. The color formulation method of claim 1, wherein The step 2 adopts the equal difference increment of the lightness to construct the Ostwald gray scale axis, and the mixture concentration value matrix of eight nodes of the gray scale axis is: The color values of the color nodes of the gray scale axis are: where C W = [r W ,g W ,b W ] and C K = [r K ,g K ,b K ] represent the color values of the highest and lowest intensity nodes, respectively.

4. The color formulation method of claim 1, wherein The step 2 adopts the method of non-linear increase of lightness to construct the gray axis, and the matrix of the mixture concentration value of eight nodes of the gray axis is: The color values of the color nodes of the gray scale axis are: where C W = [r W , g W , b W ] and C K = [r K , g K , b K ] represent the color values of the highest and lowest intensity nodes, respectively.

5. The color formulation method of claim 1, wherein When ξ = 1, 2,..., 23, 24, the equal whiteness planes of the Ostwald color solid are respectively: The color matrix of the equal whiteness surface when τ = 1 is: The color matrix of the equal whiteness surface when τ = 2 is: The color matrix of the equal whiteness surface when τ = 3 is: The color matrix of the equal whiteness surface when τ = 4 is: The color matrix of the equal whiteness surface when τ = 5 is: The color matrix of the equal whiteness surface when τ = 6 is: The color matrix of the equal whiteness surface when τ = 7 is: The color matrix of the equal whiteness surface when τ = 8 is:

6. The color formulation method of claim 1, wherein When ξ = 1, 2,..., 23, 24, the equal blackness planes of the Ostwald color solid are respectively: The color matrix of the isodensity surface when δ = 1 is: The color matrix of the isodensity surface when δ = 2 is: The color matrix of the isodensity surface when δ = 3 is: The color matrix of the isodensity surface when δ = 4 is: The color matrix of the isodensity surface when δ = 5 is: The color matrix of the isodensity surface when δ = 6 is: The color matrix of the isodensity surface when δ = 7 is: The color matrix of the isodensity surface when δ = 8 is:

7. The color formulation method of claim 1, wherein When ξ = 1, 2,..., 23, 24, the equal purity planes of the Ostwald color solid are respectively: The color matrix of the equihue surface when γ = 1 is: The color matrix of the equihue surface when γ = 2 is: The color matrix of the equihue surface when γ = 3 is: The color matrix of the equi-purity surface when γ = 4 is: The color matrix of the equi-purity surface when γ = 5 is: The color matrix of the equihue surface when γ = 6 is: The color matrix of the equihue surface when γ = 7 is: The color matrix of the equi-purity surface when γ = 8 is:

8. A color formulation system characterized by, The system for implementing the color mixing method according to any one of claims 1-7 comprises a color measurement device, an Ostwald full-color-domain grid color mixing model construction module and a visualization module; The color measurement device is used to obtain color values of six basic colors of the Ostwald color solid in actual color materials; The Ostwald full-color-domain grid color mixing model construction module comprises: A color value acquisition module configured to obtain color values of actual color materials from the color measurement device; A hue ring construction module configured to construct an equatorial hue ring based on the actual obtained Ostwald six basic colors, and give color values, position coordinate values and mixing concentrations of each hue; A gray axis construction module configured to construct a gray axis based on the actual obtained black and white as the lowest and highest lightness nodes, and give color values, position coordinate values and mixing concentrations of black and white of each lightness node; An isochromatic-hemigraphic color spectrum construction module configured to construct a 4ε isochromatic-hemigraphic color spectrum of an Ostwald color solid. m An isochromatic-hemigraphic color spectrum construction module configured to construct a 4ε isochromatic-hemigraphic color spectrum of an Ostwald color solid. The visualization module is configured to display a model color spectrum, and output mixing concentrations and color values of the six basic colors based on grid point coordinate values of the target color.

9. The color formulation system of claim 8, wherein, The Ostwald full-color-domain grid color mixing model construction module further comprises: The isometric surface color spectrum module is configured to construct an isometric surface of the austenitic color based on the four ε m color spectrum, and a conical surface formed by all grid points with equal white content in each color spectrum as an isometric surface of the austenitic color. The isochromatic surface color spectrum construction module is configured to construct a conical surface composed of all grid points with equal black content in each color phase surface as an isochromatic surface of the austenitic color solid based on the 4ε m m The equal purity surface color spectrum construction module is configured to construct a cylindrical surface composed of all grid points with equal color content in each color phase surface as the equal purity surface of the austenatized color solid based on the 4ε m color phase surface.

10. A computer-readable storage medium, characterized in that, The storage medium has a computer program stored thereon, and when the computer program is executed by the processor, the method according to any one of claims 1 to 7 is implemented.

Images