Coating color value accuracy verification method based on Hilbert space

Abstract

The invention discloses a Hilbert space-based coating color value accuracy verification method, which belongs to the technical field of inspection and detection, and comprises the following steps: firstly, determining Lab color value data of a group of qualified coating samples, and taking the Lab color value data as a reference vector set; then establishing a Hilbert subspace, and mapping Lab color value data in the reference vector set into vectors in the Hilbert subspace; and finally, measuring the Lab color value of the to-be-measured coating sample, mapping the Lab color value to the Hilbert subspace, calculating the shortest distance between the mapping point of the to-be-measured coating sample and the reference vector in the Hilbert subspace, if the shortest distance is within a set color difference threshold, determining that the coating color value is accurate and qualified, otherwise, determining that the coating color value is unqualified. According to the method, the multi-dimensional characteristics of the coating color value can be comprehensively considered, the high-precision verification of the coating color value is realized by utilizing the completeness of the Hilbert space, the accuracy of an evaluation result is ensured, and the method is suitable for various coatings with different types and color values.

Description

Technical Field

[0001] The present invention relates to the field of inspection and testing, and in particular to the color value verification of composite coatings in industrial manufacturing. Specifically, it relates to a method for verifying the accuracy of coating color values based on Hilbert space. Background Art

[0002] During the product manufacturing process, various coatings are usually applied to the product surface to achieve various different functions. The color value consistency of the coating is a key indicator for product quality control. In the prior art, the invention patent with the publication date of January 9, 2024, and the publication number of CN117372334 A discloses a method for detecting color difference of textiles based on image data. The technical solution is as follows: First, a standard library is established, and known and accurate color samples are recorded as the standard templates for textile colors, and through professional color measurement instruments. The present invention uses an imaging device to obtain the image of the textile to be detected, converts it into the CIELAB color space, and forms a difference between the actual color value obtained through detection and the color value of the standard textile sample in the CIELAB color space. Then, ΔE is calculated through the CIELAB formula, and then ΔE is compared with the set color difference threshold to determine whether the color of the textile is qualified, and at the same time, the detection data is displayed and recorded. Traditional color value verification methods rely on color difference calculations in the Lab color space, but these methods may not fully consider the multi-dimensional characteristics and complexity of coating color values. Therefore, a more accurate and reliable method is needed to evaluate the accuracy of coating color values. Summary of the Invention

[0003] The present invention aims to solve the problem of insufficient accuracy in detecting coating color values in the prior art, and proposes a method for verifying the accuracy of coating color values based on Hilbert space. This method uses the concepts of vectors and inner products in Hilbert space to mathematically model the Lab color space of the coating, and represents the color value as a point in a high-dimensional space, which can more accurately evaluate the accuracy and consistency of the coating color value.

[0004] In order to achieve the above invention purpose, the technical solution of the present invention is as follows:

[0005] A method for verifying the accuracy of coating color values based on Hilbert space, comprising:

[0006] First, determine the Lab color value data of a set of qualified coating samples, and use it as a reference vector set; then establish a Hilbert subspace, and map the Lab color value data in the reference vector set one by one into vectors in the Hilbert space; finally, measure the Lab color value of the coating sample to be tested, and map it into the above Hilbert subspace. Evaluate the accuracy of the color value by calculating the shortest distance between the mapped point of the coating sample to be tested and the reference vector in the Hilbert subspace. If the measured vector is within the set color difference threshold, it is considered that the coating color value is accurate and qualified, otherwise it is unqualified.

[0007] Further, the number of qualified coating samples is not less than 20.

[0008] Further, the qualified coating samples cover the expected color value range and coating types, and all samples are kept consistent during the preparation and processing.

[0009] Further, when determining the Lab color value data of the qualified coating samples, color value sampling is carried out in a standardized environment with the same light, temperature, and humidity conditions.

[0010] Further, when determining the Lab color value data of the qualified coating samples, each sample is measured independently multiple times, and the specific time, operator, and instrument settings of each measurement are recorded.

[0011] Further, map the Lab color value data in the reference vector set one by one into vectors in the Hilbert space, that is, v = (L, a, b); where L is the brightness, a is the chromaticity component from green to red, and b is the chromaticity component from blue to yellow.

[0012] Further, when performing the mapping of the reference vector set, range normalization is performed on the Lab color value data:

[0013] For the brightness L, its value range is between 0 and 100, and no transformation is required; for the chromaticity component a and the chromaticity component b, they are transformed into the range of 0 to 255 according to the following formula:

[0014] a' = a + 128, b' = b + 128; a' and b' respectively represent the transformed values.

[0015] Further, if it is necessary to scale the Lab color value data to a specific range, a scale factor is used to adjust the values of each dimension L, a, b in the Lab color value data.

[0016] Further, the shortest distance between the mapping points of the coating sample to be measured and the reference vector in the Hilbert subspace, that is, the color difference, is defined as the norm difference between two color vectors; the norm is defined as the square root of the inner product of the vectors, and the inner product is a function defined on the vector pair in the Hilbert space, and the expression is: <v, w> = Lv·Lw + av·aw + bv·bw; in the formula, v and w respectively represent three-dimensional vectors in the Hilbert space, Lv, av, bv are the components of the vector v; Lw, aw, bw are the components of the vector w respectively.

[0017] Further, the shortest distance between the mapping points of the coating sample to be measured and the reference vector in the Hilbert subspace, that is, the color difference ΔE i , is calculated according to the following formula:

[0018]

[0019] In the formula, v sample represents the color value vector of the coating sample to be measured, and v standard represents the reference color value vector; L i , a i , b i respectively represent the components of the color value vector of the coating sample to be measured, and L base , b base , a base represent the components of the reference color value vector

[0020] In summary, the present invention has the following advantages:

[0021] The method of the present invention utilizes the mathematical framework of the Hilbert space to provide a new method for verifying the color value of the coating. This method can comprehensively consider the multi-dimensional characteristics of the coating color value, and utilize the completeness of the Hilbert space to achieve high-precision verification of the coating color value, ensuring the accuracy of the evaluation result, thereby ensuring the consistency of the product color value and the satisfaction of the quality standard, and is applicable to various types and color values of coatings. Specific embodiments

[0022] In order to illustrate the present invention more clearly, the following further describes the present invention in conjunction with preferred embodiments. Those skilled in the art should understand that the content specifically described below is illustrative rather than restrictive, and should not be used to limit the protection scope of the present invention.

[0023] The present invention provides a method for verifying the accuracy of the coating color value based on the Hilbert space. This method utilizes the concepts of vectors and inner products in the Hilbert space to mathematically model the Lab color space of the coating, and represents the color value as a point in a high-dimensional space. This method provides a new perspective and mathematical tool for more accurately evaluating the accuracy and consistency of the coating color value.

[0024] When implementing the present invention, first, determine the Lab color value data of a set of qualified coating samples and use it as a reference vector set; then, comprehensively consider the differences in brightness, chromaticity, and saturation of the color values, define a new color difference metric standard using the concepts of inner product and norm in Hilbert space, establish a Hilbert subspace containing the reference vector set through this metric, and calculate its orthogonal complement space to determine the acceptable deviation of the color values; finally, actually measure the color values of the coating samples to be tested, map them to the above-mentioned Hilbert subspace, and evaluate the accuracy of the color values by calculating the shortest distance between the mapping points and the subspace. If the measured vector is within the defined color difference threshold, it is considered that the coating color value is accurate and qualified, otherwise it is unqualified.

[0025] Specifically, the present invention includes the following implementation steps:

[0026] Step 1: Collect and prepare data

[0027] This step specifically includes sample selection, environmental condition control, measurement instrument calibration, sampling procedures, and data collation, etc.

[0028] Regarding sample selection, a sufficient number (≥20) of coating samples need to be selected to ensure the representativeness and reliability of the statistical results, and the samples should cover the expected color value range and coating types; at the same time, it is necessary to ensure that all samples are consistent during the preparation and processing to reduce the influence of operating variables on the color value measurement.

[0029] Regarding environmental condition control, color value sampling should be carried out as much as possible in a standardized environment, controlling conditions such as light (light source type and intensity), temperature, and humidity to reduce the influence of external factors on the color values. If possible, use a constant temperature and humidity laboratory environment for sampling.

[0030] Regarding the calibration of the measurement instrument, an accurate color measurement device should be used when measuring Lab color values; and the instrument should be calibrated before use to ensure the accuracy and repeatability of the measurement; if multiple instruments are used, it is necessary to ensure the consistency of the measurement results between them.

[0031] Regarding the sampling procedure, it mainly includes: detailed recording of the Lab color values of each sample, including three parameters of L (brightness), a (red - green chromaticity), and b (yellow - blue chromaticity); multiple independent measurements of each sample to obtain reliable color value data; recording the specific time, operator, and instrument settings for each measurement for subsequent data review and analysis.

[0032] Regarding data collation, it mainly includes: encoding and collating all measurement data to construct a database containing all sample color value information; conducting a preliminary analysis of the data to exclude any outliers or obvious incorrect data; ensuring the consistency of the data format for subsequent mathematical processing and analysis.

[0033] Step 2: Vector Mapping

[0034] After collecting the Lab color value data of the coating, the next step is to convert these color values into vectors in Hilbert space. The whole process includes the following steps:

[0035] 1) Vector Representation

[0036] For each coating sample, there is a Lab color value, denoted as (L, a, b). This color value will be converted into a three-dimensional vector v in Hilbert space. The representation of the three-dimensional vector v is v = (L, a, b), where L is the brightness, a is the chromaticity component from green to red, and b is the chromaticity component from blue to yellow.

[0037] 2) Coordinate Transformation

[0038] a. Range Normalization: L is between 0 and 100 and does not need to be transformed. The values of a and b are usually between -128 and +127, but in Hilbert space, it is better that the values of all dimensions are non-negative. Therefore, the ranges of a and b need to be shifted to 0 to 255. The specific transformation formula is:

[0039] (a' = a + 128);

[0040] (b' = b + 128);

[0041] In this way, the values of (a') and (b') will be in the range of 0 to 255, which is more consistent with the range of L.

[0042] b. Scaling Factor Adjustment: If it is necessary to scale the values to a specific range, for example, to maintain numerical stability when calculating the inner product in Hilbert space, a scaling factor can be used to adjust the values of each dimension. Assuming that all values are desired to be between 0 and 1, then the transformation formula is:

[0043] (L” = L / 100);

[0044] (a” = a' / 255);

[0045] (b” = b' / 255);

[0046] Here, (L”, a”, b”) will be the normalized values, suitable for vector representation in Hilbert space.

[0047] 3) Inner Product Calculation Formula

[0048] In Hilbert space, the inner product calculation formula for two vectors v and w is:

[0049] <v, w> = Lv · Lw + av · aw + bv · bw;

[0050] This inner product will be used to define a measure of color value difference in subsequent steps. In the formula, Lv, av, and bv are the components of vector v; Lw, aw, and bw are the components of vector w respectively.

[0051] 4) Vector mapping verification

[0052] For a set of known Lab color values, map them to vectors in Hilbert space, and calculate their inner product and norm to ensure that there is no error in the mapping process. Compare the mapped vectors with the original Lab color values to ensure that they are numerically consistent, that is, the mapping is invertible.

[0053] 5) Completeness test

[0054] Although Hilbert space R 3 is known to be complete, it is still necessary to confirm that this property is maintained during the mapping and transformation processes to ensure that the limit points of all vectors still exist within this space.

[0055] 6) Data structure preparation

[0056] To facilitate subsequent distance measurement and color value consistency judgment, it is necessary to organize the mapped vector data in an easy-to-operate data structure, such as an array or a matrix. This data structure will support fast inner product and norm calculations, as well as subsequent mathematical analysis.

[0057] Step Three: Color difference detection

[0058] Inner product and norm are two basic concepts in Hilbert space, providing a way to measure the similarity and magnitude between vectors. In the verification of coating color values, these concepts are used to define the differences between color values.

[0059] Specifically, the inner product can be used to measure the similarity between two color values. If two color values are exactly the same, then their inner product is equal to the square of the norm. In Hilbert space R 3 , the inner product is a function defined on vector pairs, which satisfies the following conditions: positive definiteness, linearity, and symmetry. For coating color value vectors v and w, the inner product is defined as <v, w> = L1L2 + a1a2 + b1*b2, where L1, a1, b1 are the components of vector v, and L1, a1, b1 are the components of vector w.

[0060] The norm is a direct result of the inner product and is defined as the "length" of a vector. For the coating color value vector v, the norm is defined as This is equal to the square root of the inner product of the vector.

[0061] After defining the inner product and norm, the consistency of color values can be evaluated by calculating the distance between the color value vectors of the coatings. Specifically, for two coating color value vectors v and w, the distance between them is defined as d(v, w) = ||v - w||, which is the norm of the difference vector between v and w. This distance metric reflects the actual color difference between the two color values in the Lab color space. The color difference ΔE can be understood as the norm difference between a sample color value vector v sample and the reference color value vector v standard in the Hilbert space, that is, the "distance" between the two vectors. Therefore, the calculation of the color difference ΔE i can be represented by the norm in the Hilbert space:

[0062]

[0063] where v sample represents the color value vector of the coating sample to be measured, and v standard represents the reference color value vector; L i , a i , b i respectively represent the components of the color value vector of the coating sample to be measured, and L base , b base , a base represent the components of the reference color value vector.

[0064] Step 4. Determination of the color difference threshold

[0065] Furthermore, to ensure the accuracy of the inspection of the coating color values, the color difference threshold must be determined according to specific applications and quality requirements. This threshold defines the maximum acceptable difference between color values and is a key indicator for evaluating whether the coating color values meet the standards.

[0066] This solution gives the following examples of color difference thresholds:

[0067] a) Ideal match: If the norm difference ||v1 - v2|| between two color vectors v1 and v2 falls within the interval [0, 0.25], then their color match is considered ideal. The mathematical expression is: ||v1 - v2|| ≤ 0.25.

[0068] b) Acceptable match: If the norm difference is in the interval (0.25, 0.5], then the match is considered minor and acceptable, that is: 0.25 < ||v1 - v2|| ≤ 0.5.

[0069] c) Acceptable in some applications: When the norm difference is in the interval (0.5, 1.0], the match may be accepted in some applications, that is: 0.5 < ||v1 - v2|| ≤ 1.0.

[0070] d) Acceptable in specific applications: If the norm difference falls within the interval (1.0, 2.0], the match is acceptable in specific applications, expressed as: 1.0 < ||v1 - v2|| ≤ 2.0.

[0071] e) There is a gap: When the norm difference is within the interval (2.0, 4.0], although the match may be acceptable in specific applications, there is an obvious gap. At this time: 2.0 < ||v1 - v2|| ≤ 4.0.

[0072] f) Unacceptable: If the norm difference is greater than 4.0, the match is considered unacceptable in most applications, that is: ||v1 - v2|| > 4.0.

[0073] Step Five: Distance Measurement and Result Judgment

[0074] During the inspection process of the coating color value, the norm difference between each coating color value vector and the predetermined standard color value vector will be calculated, that is, ||v sample -v standard ||. This norm difference will be compared with the set color difference threshold. If the norm difference is less than or equal to the set color difference threshold, it is considered that the coating color value is within the acceptable range and meets the quality standard; if the norm difference is greater than the set color difference threshold, the coating color value is unqualified and further adjustment or correction is required.

[0075] Example 1

[0076] To verify the effectiveness of the coating color value inspection method based on Hilbert space, this experiment will be verified and tested based on the data measured in the X-type coating color uniformity test to ensure that the experimental design can reflect the mapping and calculation accuracy of the inspection method.

[0077] The specific operation steps are as follows:

[0078] Step One: Test Implementation

[0079] A) Prepare 20 standard test plates of A-type X-type coatings with the same thickness (25 μm), and measure the L*, a*, and b* values of the coatings on each test plate. Remove the abnormal measurement values, and the results are shown in Table 1 below:

[0080] Table 1 Lab color value data of standard test plates of A-type X-type coatings

[0081]

[0082] B) Convert the Lab color value into a vector in Hilbert space

[0083] Among them, the L* value remains unchanged because it is already a positive number.

[0084] Adjust the a* and b* values for each sample to ensure they are positive:

[0085] a adjusted = a* + 128, b adjusted = b* + 128.

[0086] C) Calculate the color difference ΔE between samples

[0087] Using the color of the standard A-type X-type coating as the reference (L*: 70, a*: -2, b*: -1), calculate the color difference ΔE for each coating sample to be measured:

[0088]

[0089] where L i 、a adjusted,i 、b adjusted,i correspond to the vector components of the coating sample to be measured, and L base 、b base 、a base correspond to the components of the reference color value vector.

[0090] Finally, obtain the color difference results of the coating samples to be measured as shown in Table 2 below.

[0091] Table 2 Color difference data of coating samples to be measured

[0092]

[0093] Step 2. Data analysis

[0094] Color difference range analysis:

[0095] Based on the ΔE values obtained above, the color difference range of all samples is between 2.13 and 2.31. This indicates that the color differences of all samples are within a small range, and no extreme color deviations occur.

[0096] Color difference standard comparison:

[0097] According to the color difference ΔE standard given in the color value threshold above, the color difference ΔE of each of the above samples is between 2.0 and 4.0, which belongs to the category of "there is a difference; acceptable in specific applications".

[0098] Average color difference and standard deviation:

[0099]

[0100] The average color difference is 2.22, and the standard deviation is approximately 0.054.

[0101] Step 3. Result evaluation

[0102] In summary, the ΔE values of all the coating samples to be measured are relatively close, and the colors are generally consistent.

[0103] Example 2

[0104] To verify the effectiveness of the coating color value verification method based on the Hilbert space, this experiment will verify and test based on the data measured in the color uniformity test of the B-type Y-type coating to ensure that the experimental design can reflect the mapping and calculation accuracy of the verification method. The B-type Y-type coating refers to a functional composite coating containing a base layer and a functional layer, such as an electromagnetic coating, an infrared coating, etc.

[0105] The specific operation steps are as follows:

[0106] Step 1: Test implementation

[0107] A) Prepare 20 standard test plates of the B-type Y-type composite coating with the same thickness (25 μm), and measure the L*, a*, and b* values of the coating on each test plate. Remove the abnormal measurement values, and the results are shown in Table 3 below.

[0108] Table 3 Lab color value data of the standard test plates of the B-type Y-type composite coating

[0109]

[0110] B) Convert the Lab color values into vectors in the Hilbert space

[0111] Adjust the a* and b* values of each sample to ensure that they are positive:

[0112] Among them, the L* value remains unchanged because it is already a positive number.

[0113] a adjusted = a* + 128, b adjusted = b* + 128.

[0114] C) Calculate the color difference between samples

[0115] Taking the color of the standard B-type Y-type coating as the reference (L*: 70, a*: -2, b*: -1), calculate the color difference ΔE for each sample one by one:

[0116]

[0117] In the formula, L i 、a adjusted,i 、b adjusted,i correspond to the vector components of the coating sample to be measured, and L base 、b base 、a base correspond to the components of the reference color value vector.

[0118] Finally, the color difference results of the coating samples to be measured as shown in Table 4 below are obtained.

[0119] Table 4 Color difference data of the coating samples to be measured

[0120]

[0121] Step 2: Data analysis

[0122] Analysis of the color difference range:

[0123] For the ΔE values obtained above, the color difference range of all samples is between 2.14 and 2.29. This indicates that the color differences of all samples are within a small range, and no extreme color deviations occur.

[0124] Comparison with the color difference standard:

[0125] According to the color difference ΔE standard given in the color value threshold above, the color difference ΔE of each of the above samples is between 2.0 and 4.0, which belongs to the category of "having a gap; acceptable in specific applications".

[0126] Substituting the above data into the average color difference formula and the standard deviation formula, we can obtain: the average color difference is 2.229, and the standard deviation is approximately 0.04543.

[0127] Step 3: Result evaluation

[0128] In summary, the color difference ΔE values of all samples are relatively close, and the colors are consistent as a whole.

[0129] Through verification and testing, as well as possible variations and optimizations, this method has demonstrated its applicability and effectiveness.

[0130] The above is only a preferred embodiment of the present invention, and does not impose any form of limitation on the present invention. Any simple modification or equivalent change made to the above embodiments based on the technical essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for verifying the accuracy of coating color values based on Hilbert space, characterized in that Including: First, determine the Lab color value data of a set of qualified coating samples and use it as the reference vector set. Then, establish a Hilbert subspace, map the Lab color value data in the reference vector set one by one into vectors in the Hilbert space. Finally, measure the Lab color value of the coating sample to be tested and map it into the above Hilbert subspace. Evaluate the accuracy of the color value by calculating the shortest distance between the mapped point of the coating sample to be tested and the reference vectors in the Hilbert subspace. If the measured vector is within the set color difference threshold, it is considered that the coating color value is accurate and qualified; otherwise, it is regarded as unqualified.

2. The method for verifying the accuracy of the coating color value based on the Hilbert space according to claim 1, wherein, The number of qualified coating samples is not less than 20.

3. The method for verifying the color value accuracy of a coating based on a Hilbert space according to claim 1, characterized in that, The qualified coating samples cover the expected color value range and coating types, and all samples are consistent during the preparation and processing.

4. The method for verifying the accuracy of coating color value based on Hilbert space according to claim 3, characterized in that, When determining the Lab color value data of the qualified coating samples, color value sampling is carried out in a standardized environment with the same light, temperature, and humidity conditions.

5. The method for verifying the color value accuracy of a coating based on a Hilbert space according to claim 4, characterized in that When determining the Lab color value data of the qualified coating samples, each sample is measured independently multiple times, and the specific time, operator, and instrument settings of each measurement are recorded.

6. A method for verifying the accuracy of coating color values based on Hilbert space according to any one of claims 1 to 5, characterized in that, Map the Lab color value data in the reference vector set one by one into vectors in the Hilbert space, that is, v = (L, a, b); where L is the luminance, a is the chromaticity component from green to red, and b is the chromaticity component from blue to yellow.

7. The method for verifying the accuracy of coating color value based on Hilbert space according to claim 6, characterized in that When performing the mapping of the reference vector set, perform range normalization on the Lab color value data: For the luminance L, whose value range is between 0 and 100, no transformation is required; for the chromaticity component a and the chromaticity component b, transform them into the range of 0 to 255 according to the following formula: a' = a + 128, b' = b + 128; a' and b' respectively represent the transformed values.

8. The method for verifying the color value accuracy of a coating based on a Hilbert space according to claim 7, wherein If it is necessary to scale the Lab color value data to a specific range, use a scaling factor to adjust the values of each dimension L, a, b in the Lab color value data.

9. The method for verifying the accuracy of coating color value based on Hilbert space according to claim 1, characterized in that, Define the shortest distance between the mapped point of the coating sample to be tested and the reference vectors in the Hilbert subspace, that is, the color difference, as the norm difference between two color vectors; the norm is defined as the square root of the inner product of the vectors.

10. The method for verifying the color value accuracy of a coating based on a Hilbert space according to claim 9, characterized in that The shortest distance between the mapping points of the coating sample to be measured and the reference vector in the Hilbert subspace, i.e., the color difference ΔE i , is calculated according to the following formula: Where, v sample represents the color value vector of the coating sample to be measured, and v standard represents the reference color value vector; L i , a i , b i respectively represent the components of the color value vector of the coating sample to be measured, and L base , b base , a base represent the components of the reference color value vector.

Images