A method for measuring the color of a textile based on RBF

Abstract

The application discloses a kind of textile color measurement methods based on RBF, it is related to mechanical fault diagnosis technical field.Select textile sample, light source and so on instrument and color imaging system, and the relevant data of textile sample imaging system is collected to construct data set, construct RBF neural network, using GA algorithm, the chroma characteristic model is obtained by training set to RBF neural network training, test set is input into the model and is evaluated.This application uses GA algorithm to train neural network without prior knowledge and is not sensitive to initial parameters, will not fall into local minimum point, overcomes the influence of local extreme value on RBF neural network, and the determination of RBF neural network hidden layer node center has randomness, using the global search ability of GA algorithm, the hidden node center value is optimized, make up the defect that RBF neural network adjustable parameter is single, with good prediction accuracy, provide effective method for textile color measurement.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of textile color measurement method based on RBF, belong to color science and image technology research field. BACKGROUND

[0002] Textile industry is the traditional pillar industry and important civilian industry of China's national economy.The traditional process level such as dyeing, color matching, color matching has important significance for textile production, and accurate color measurement and color difference detection are particularly important for textile design and production.Many enterprises rely on artificial visual method, instrument color measurement method.The imaging system is used as color measurement device, and the image collected can reflect the color of textile to a certain extent, with the characteristics of large field of view and multiple sampling, which is the development trend of future color measurement.

[0003] However, as a color measurement device, the imaging system is influenced by many factors in the imaging process, and it is difficult to achieve the effect consistent with the actual observation of the human eye, while the colorimetric characterization model can realize accurate color prediction and control of digital image device.The colorimetric characterization model of color imaging system establishes the conversion relationship between device-dependent color space and device-independent color space, and can realize the color consistency from color information collection to color information output.It is very important for image high-fidelity display, colorimetric measurement, color reproduction, color management and color appearance prediction of different devices.Common colorimetric characterization methods include lookup table method, polynomial method and BP neural network method.The adjustment of BP neural network weight and threshold value adopts negative gradient descent method, and its convergence speed is slow and easy to fall into local minimum point.

[0004] Therefore, how to carry out textile color measurement research based on imaging system, provide a kind of color feature information that can be better extracted by imaging system, and the effectiveness and feasibility of textile color measurement method by color difference formula comparison algorithm are the problems that the skilled in the art need to solve. SUMMARY

[0005] Therefore, the present application provides a kind of textile color measurement method based on RBF, the purpose of the present application is to train neural network using GA algorithm without prior knowledge and not sensitive to initial parameters, and will not fall into local minimum point, which overcomes the influence of local extremum on RBF neural network.And the determination of RBF neural network hidden layer node center has randomness, so the global search ability of GA algorithm is used to optimize the hidden node center value, make up for the single defect of adjustable parameter of RBF neural network, with good prediction accuracy, which provides an effective method for textile color measurement.

[0006] In order to achieve the above purpose, the present application adopts the following technical solutions:

[0007] A method for textile color measurement based on RBF, characterized in that it comprises the following steps:

[0008] S1, selecting a textile experimental sample, a light source, a measurement environment, a colorimetric measuring instrument and a color imaging system to be characterized;

[0009] S2, collecting color imaging system device-dependent spatial RGB values and device-independent CIE1931 XYZ tristimulus values of the textile experimental sample, and constructing a data set;

[0010] S3, constructing an RBF neural network including an input layer, a hidden layer and an output layer, setting the number of neurons of the input layer, the hidden layer and the output layer, and setting the radial basis function, and establishing an RBF neural network model;

[0011] S4, training the RBF neural network model based on the training set, optimizing the hidden layer node centers of the RBF neural network with a GA algorithm, selecting the optimal center point, completing parameter optimization, and constructing a textile imaging system colorimetric characterization model based on the RBF neural network;

[0012] S5, inputting the test set into the colorimetric characterization model to obtain the XYZ stimulus values predicted by the model.

[0013] Optionally, step S1 specifically comprises:

[0014] S11, selecting a test sample, including silk fabric, blended fabric, cotton fabric, wool fabric and various textile samples;

[0015] S12, selecting a light source, including D65 light source, D55 light source and various actual light sources, which should be consistent with the actual application environment;

[0016] S13, selecting a measurement environment, the imaging system colorimetric characterization environment should be consistent with the actual application environment;

[0017] S14, selecting a colorimetric measuring instrument, including a spectral photometer and a colorimeter;

[0018] S15, selecting a color imaging system to be measured, including various types of commercial digital cameras, video cameras, mobile phones and cameras.

[0019] Optionally, step S2 specifically comprises:

[0020] S21, vertically aligning the sample to be measured with the colorimetric measuring instrument, and measuring the CIE1931 XYZ tristimulus values;

[0021] S22, adjusting the color imaging system to manual mode, setting the ISO and system F number, vertically shooting the sample to be measured, and collecting the device-dependent spatial RGB values;

[0022] S23, taking the RGB three-channel response value as an input space, taking the CIE1931 XYZ three-stimulus value as an output space, taking the RGB value of each test sample as an attribute value, and taking the CIE1931 XYZ three-stimulus value as a label value, realizing data set construction.

[0023] The data set is divided into a training set and a test set, and specifically:

[0024] A total of 128 textile samples were used in the experiment, including red, blue and neutral (black, white and gray), green, purple and yellow textile samples.

[0025] In order to ensure the balance of sample allocation and the stability of the algorithm, 5 textile samples were extracted from each of the 8 colors as the training set, and the rest were the test set. Finally, 104 samples were selected as the training set, and 24 as the test set for evaluating the model.

[0026] Optionally, step S3 specifically includes:

[0027] S31, the number of neurons in the input layer, hidden layer and output layer is 3, 15 and 3 respectively;

[0028] S32, the neuron setting range is 10-60, and the optimal hidden layer neuron number is determined according to the minimum color difference standard;

[0029] S33, the hidden layer is a radial basis layer, and a Gaussian function is used as a radial basis function, and the output layer is set to a linear layer.

[0030] Optionally, step S4 specifically includes:

[0031] S41, encode the hidden layer node center value length to form a chromosome by GA algorithm, and initialize the parameters;

[0032] S42, determine the appropriate initialization parameters by training and adjusting, and select the error absolute value of the predicted three-stimulus value and the measured three-stimulus value as the fitness function;

[0033] S43, perform genetic operations such as selection, crossover and mutation, and calculate the individual fitness value;

[0034] S44, determine the iteration termination precision ε=0.001; if the individual fitness value is less than or equal to ε, the training is ended, and the optimal individual is output, otherwise return to step S43;

[0035] S45, assign the optimal individual to the RBF neural network, wherein the optimal individual is the optimal hidden layer node center value;

[0036] S46, after determining the centers of each hidden layer node, taking the minimum value as the width of the corresponding radial basis function according to the distance between the centers;

[0037] S47, using pseudo-inverse method to determine the weight of linear layer, each individual in the population contains a hidden layer node center of RBF neural network, using the training set to train the RBF neural network according to the fitness function, and taking the absolute value of the difference between the predicted three-stimulus value obtained by training and the actual measured three-stimulus value as the individual fitness value, evaluating the performance of the network through the fitness value, the smaller the individual fitness value, the better the individual.

[0038] After training, the final population P is 40, the crossover probability is 0.5, the mutation probability is 0.5, and the iteration number is 100.

[0039] Optionally, it further includes a model accuracy evaluation step, which specifically includes:

[0040] According to the XYZ stimulus value predicted by the model in step S5 and the XYZ three-stimulus value actually measured by the test set, the LAB color difference is calculated;

[0041] The color difference results of the test samples are averaged to obtain the average color difference, and the colorimetric characterization accuracy is evaluated.

[0042] According to the above technical solution, compared with the prior art, the textile sample, the light source and the color imaging system are selected, the related data of the textile sample imaging system are collected to construct a data set, which is divided into a training set and a test set, an RBF neural network is constructed, a GA algorithm is used, the RBF neural network is trained by the training set to obtain a colorimetric characterization model, and the test set is input into the model for evaluation. The GA algorithm is used to train the neural network without prior knowledge and is not sensitive to the initial parameters, and will not fall into a local minimum point, which overcomes the influence of local extreme value on the RBF neural network, and the determination of the hidden layer node center of the RBF neural network has randomness, the global search ability of the GA algorithm is used to optimize the hidden node center value, which makes up for the single defect of adjustable parameters of the RBF neural network, has good prediction accuracy, and provides an effective method for textile color measurement. BRIEF DESCRIPTION OF DRAWINGS

[0043] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the following embodiment or prior art description will be briefly introduced. Obviously, the drawings in the following description are only embodiments of the present application, and those skilled in the art can obtain other drawings according to the provided drawings without creating any creative labor.

[0044] Figure 1A flow chart of colorimetric characterization of a textile imaging system based on an RBF neural network in an embodiment of the present application.

[0045] Figure 2 A structure diagram of an RBF neural network in colorimetric characterization of a textile imaging system based on an RBF neural network in an embodiment of the present application.

[0046] Figure 3 A construction diagram of an experiment of colorimetric characterization of a textile imaging system based on an RBF neural network in an embodiment of the present application.

[0047] Figure 4 A distribution diagram of sample data RGB values in colorimetric characterization of a textile imaging system based on an RBF neural network in an embodiment of the present application.

[0048] Figure 5 A distribution diagram of sample data XYZ tristimulus values in colorimetric characterization of a textile imaging system based on an RBF neural network in an embodiment of the present application.

[0049] Figure 6 A flow chart of colorimetric characterization based on an RBF neural network in an embodiment of the present application.

[0050] Figure 7 A diagram of average color difference of test samples in colorimetric characterization of a color imaging system based on an RBF neural network in an embodiment of the present application. DETAILED DESCRIPTION

[0051] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0052] The embodiments of the present application disclose a textile color measurement method based on an RBF, as shown in Figure 1 A flow chart of colorimetric characterization of a textile imaging system based on an RBF neural network in an embodiment of the present application, specifically comprising the following steps:

[0053] S1, selecting a textile experiment sample, a light source, a measurement environment, a colorimetric measurement instrument and a color imaging system needing colorimetric characterization;

[0054] S2, collecting color imaging system device related spatial RGB values and device independent spatial CIE1931 XYZ tristimulus values of the textile experiment sample, and constructing a data set;

[0055] S3, constructing an RBF neural network including an input layer, a hidden layer and an output layer, setting the number of neurons of the input layer, the hidden layer and the output layer and a radial basis function, and establishing an RBF neural network model;

[0056] S4, training the RBF neural network model based on a training set, optimizing the hidden layer node center of the RBF neural network by using a GA algorithm, selecting an optimal center point, completing parameter optimization, and constructing a colorimetric characterization model of a textile imaging system based on the RBF neural network;

[0057] S5, inputting a test set into the colorimetric characterization model to obtain XYZ stimulus values predicted by the model.

[0058] Step S1 further includes steps of

[0059] S11, selecting a silk fabric color sample card as a test sample, and the silk fabric color sample card is as shown in (c); Figure 3

[0060] S12, selecting a standard color matching light box of model QTC-600-7, and testing under a D65 light source, as shown in (b); Figure 3

[0061] S13, placing the light box in a dark room for experiment;

[0062] S14, selecting a CS2000 spectral radiometer to measure CIE1931 XYZ three stimulus values, as shown in (b) of FIG. 3;

[0063] S15, selecting a Cannon EOS 600D commercial digital camera to perform colorimetric characterization, as shown in (a); Figure 3

[0064] Step S2 further includes steps of

[0065] S21, applying the spectral radiometer to vertically align the silk fabric color sample card, measuring CIE1931 XYZ three stimulus values of different fabric color samples, and the spectral radiometer is 75 cm away from the fabric color sample card, and the field of view is set to 1°.

[0066] S22, adjusting the Cannon EOS 600D commercial digital camera to manual mode, setting the ISO sensitivity to 400, the system F number to 10, vertically shooting the silk fabric color sample card, obtaining a RAW format digital image, and extracting three channel response RGB values of the RAW format image fabric color sample shot by the Cannon EOS 600D commercial digital camera.

[0067] ​​​S23, taking the three-channel response RGB value of the Cannon EOS 600D commercial digital camera as an input space, taking the CIE1931 XYZ three-stimulus value as an output space, taking the RGB value of each color sample of the silk color sample card as an attribute value, and taking the CIE1931 XYZ three-stimulus value of the color sample card as a label value, to realize the construction of the data set.

[0068] The data set is divided into a training set and a test set, specifically:

[0069] A total of 128 textile color samples are used in the experiment, including red, blue and neutral (black, white and gray), green, purple and yellow textile color samples, as shown in Figure 4 、 5

[0070] In order to ensure the balance of sample allocation and the stability of the algorithm, 5 textile samples are extracted from each of the 8 colors as a training set, and the rest are used as a test set. Finally, 104 samples are selected as a training set, and 24 are selected as a test set for evaluating the model.

[0071] Step S3 further comprises the steps of:

[0072] S31, the number of neurons in the input layer, hidden layer and output layer is 3, 15 and 3 respectively;

[0073] S32, the neuron setting range is 10-60, and the optimal hidden layer neuron number is determined according to the minimum color difference standard;

[0074] S33, the network hidden layer is a radial basis layer, a Gaussian function is used as a radial basis function, and the output layer is set to a linear layer; the Gaussian radial basis function is shown in formula (1), the approximation model is shown in formula (2), and the implementation is shown in Figure 2

[0075]

[0076] In the formula, the input vector is P, the center of the hidden layer basis function is C, and the width of the basis function around the center point is sigma.

[0077] a 2 = Wa 1 +b (2)

[0078] In the formula, the weight between the hidden layer and the output layer is represented as W; and the threshold value of the output layer node is represented as b.

[0079] Step S4 further comprises the steps of:

[0080] ​​S41, encode the center C of the hidden layer node by GA algorithm to form a chromosome, initialize parameters, set the center vector C to be a real number in the interval [10, -10], the dimension of the input vector [R, G, B] is 3, the number of hidden layer nodes is h, the population size is P, then the length of a center vector chromosome is 3xh, and the center vector is a Px(3xh) matrix;

[0081] S42, determine the appropriate initialization parameters by training set training adjustment, select the sum of the absolute value of the error between the predicted tristimulus value and the measured tristimulus value as the fitness function f, as shown in formula (3);

[0082]

[0083] In the formula, n represents the dimension of the output variable, m represents the number of input variables, and r ij represents the predicted tristimulus value, represents the actual measured tristimulus value.

[0084] S43, perform genetic operations such as selection, crossover, and mutation, and calculate individual fitness values;

[0085] S44, determine the iteration termination precision ε=0.001; if the individual fitness value is less than or equal to ε, the training is ended, and the optimal individual is output, otherwise return to step S43;

[0086] Where the running parameters are the parameters determined by the GA algorithm initialization, the appropriate initialization parameters are determined by training set training adjustment, the population P is 40, the crossover probability is 0.5, the mutation probability is 0.5, and the iteration number is 100 times;

[0087] S45, assign the optimal individual to the RBF neural network, where the optimal individual is the optimal hidden layer node center value;

[0088] S46, after determining each hidden layer node center, take the minimum value as the width of the corresponding radial basis function according to the distance between each center, as shown in formula (4).

[0089] σ j = λ min (||c j -c i ||)j=1,2,…,n (4)

[0090] In the formula, λ is the overlap coefficient, and n is the number of hidden layer nodes;

[0091] S47, determine the linear layer weight by using the pseudo-inverse method, and evaluate the performance of the network by the fitness value, where the smaller the individual fitness value, the better the individual.

[0092] When the input is xp When the j-th hidden layer node is in the specified position, the output of the j-th hidden layer node is shown in Equation (5).

[0093]

[0094] In the formula, h is the number of training samples.

[0095] The hidden layer output matrix is ​​shown in equation (6):

[0096]

[0097] If the current weights of the RBF network are W = (w1, w2, ..., w m If the network output vector is Y = ΦW, then the network output vector is Y = ΦW. Let the network output vector Y be equal to the expected value D of the network output vector, then W can be expressed as the pseudo-inverse Φ. + Find: W = Φ + D. That is, Φ + =(Φ T Φ) -1 Φ T ;

[0098] like Figure 6 As shown, it is a flowchart of the RGB neural network chromaticity feature optimization based on the GA algorithm in an embodiment of the present invention.

[0099] The Genetic Algorithm (GA) finds the optimal individual by calculating the fitness value of each individual in the population. Based on this, it obtains the hidden layer node centers of the RBF neural network, and then calculates the linear layer weights and basis function widths. These parameters are assigned to the RBF neural network to obtain the individual's fitness value. During the optimization process, as the number of iterations increases, the error decreases, and the iteration termination precision ε = 0.001 is determined. If the individual's fitness value is less than or equal to ε, training ends; otherwise, it returns to recalculation. When the iteration termination condition is met, the output of the last generation corresponds to the optimal individual, i.e., the optimal center point.

[0100] The RBF-based textile color measurement method proposed in this invention also includes a model accuracy evaluation step, which specifically includes:

[0101] The LAB color difference is calculated based on the XYZ stimulus values ​​predicted by the model in step S5 and the actual XYZ tristimulus values ​​measured in the test set.

[0102] Calculate the average value of the color difference results of the test samples to obtain the average color difference and evaluate the accuracy of colorimetric characterization.

[0103] The formula for calculating LAB color difference is as follows:

[0104]

[0105]

[0106]

[0107] (X,Y,Z) are the tristimulus values ​​of the color sample; (X0,Y0,Z0) are the tristimulus values ​​of white light reflected from a CIE standard illuminator onto a totally diffuse reflector and reflected to the observer's eye, where Y0 = 100; L * a represents the lightness coordinates; * b * Here are the chromaticity coordinates.

[0108]

[0109] L is obtained from formulas (7)(8)(9) * a * b * The value;

[0110] The average color difference is calculated by averaging the color difference results of each test sample. This average color difference is then used to evaluate the colorimetric characterization results, using ΔE. ab As an evaluation criterion, it is shown in formula (11);

[0111]

[0112] When ΔE ab A value ≤3 indicates that the model's prediction accuracy is relatively high.

[0113] The average color difference ΔE of the test samples was obtained through 10 cycles. ab like Figure 7 As shown in the figure, the average color difference of the textile imaging system's colorimetric characterization is mostly distributed below 3 LAB, indicating good prediction accuracy. Simultaneously, using the SG color chart as a training sample for colorimetric characterization to measure textile colors, the color measurement results using the SG color chart show an average color difference 5 LAB higher than those using textiles as the training sample. Therefore, using textiles as the training sample results in higher prediction accuracy for color measurement.

[0114] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0115] The foregoing description of the disclosed embodiments enables a person skilled in the art to make or use the application. Modifications of these embodiments will occur to persons of skill in the art, and, while certain modifications are discussed, it is desired to be protected in accordance with the spirit and scope of the application. Therefore, the application is not limited to the specific embodiments shown and described, but only by the scope of the appended claims, unless otherwise specified.

Claims

1. A method of textile color measurement based on RBF characterized in that, The method comprises the following steps: S1, selecting a textile experimental sample, a light source, a measurement environment, a colorimetric measuring instrument, and a color imaging system to be colorimetrically characterized; S2, collecting color imaging system device-related spatial RGB values and device-independent spatial CIE1931 XYZ tristimulus values of the textile experimental sample, and constructing a data set; S3, constructing an RBF neural network including an input layer, a hidden layer, and an output layer, setting the number of neurons of the input layer, the hidden layer, and the output layer and a radial basis function, establishing an RBF neural network model, and specifically comprising: S31, the number of neurons of the input layer, the hidden layer, and the output layer is 3, 15, and 3 respectively; S32, the neuron setting range is 10-60, and the optimal hidden layer neuron number is determined according to the minimum color difference as the standard; S33, the hidden layer is a radial basis layer, a Gaussian function is used as the radial basis function, and the output layer is set as a linear layer, comprising: The radial basis function is shown in formula (1), wherein, the input vector is P, the center of the hidden layer basis function is C, and the width of the basis function around the center point is σ; The approximation model is shown in formula (2), a 2 = Wa 1 +b(2) wherein, the weight value between the hidden layer and the output layer is represented as W; and the threshold value of the output layer node is represented as b; S4, training the RBF neural network model based on the training set, optimizing the hidden layer node center of the RBF neural network by using a GA algorithm, selecting the optimal center point, completing parameter optimization, constructing a textile imaging system colorimetric characterization model based on the RBF neural network, and specifically comprising: S41, encoding the length of the hidden layer node center value into a chromosome by using the GA algorithm, and initializing parameters; wherein, the center vector C is initialized as a real number in the interval [10, -10], the number of dimensions of the input vector [R, G, B] is 3, the number of hidden layer nodes is h, the population size is P, the length of a center vector chromosome is 3×h, and the center vector is a matrix with a size of P×(3×h); S42, determining appropriate initialization parameters by training and adjusting the training set, selecting the sum of the absolute values of the prediction tristimulus values and the measured tristimulus values as the fitness function f, as shown in formula (3); where n represents the dimension of the output variable, m represents the number of input variables, r ij represents the predicted tristimulus values, represents the actual measured tristimulus values; S43, performing genetic operations such as selection, crossover, and mutation, and calculating individual fitness values; S44, determining the iteration termination accuracy ε=0.001; if the individual fitness value is less than or equal to ε, the training is ended, the optimal individual is output, otherwise, returning to step S43; S45, assigning the optimal individual to the RBF neural network, wherein the optimal individual is the optimal hidden layer node center value; S46, after determining each hidden layer node center, taking the minimum value as the width of the corresponding radial basis function according to the distance between the centers, as shown in formula (4): σ j = λ min (||c j -c i ||) j = 1,2,...,n (4) wherein, λ is an overlap coefficient, and n is the number of hidden layer nodes; S47, determining the weight value of the linear layer by using a pseudo-inverse method, and evaluating the performance of the network by the fitness value, wherein the smaller the individual fitness value, the better the individual; S5, inputting the test set into the colorimetric characterization model to obtain the XYZ stimulus values predicted by the model.

2. A method of textile color measurement based on RBF according to claim 1, characterized in that, The step S1 specifically comprises: S11, selecting test samples, including silk fabric, blended fabric, cotton type fabric, wool type fabric and various textile samples; S12, selecting light source, including D65 light source, D55 light source and various actual light sources, the light source should be consistent with the actual application environment; S13, selecting measurement environment, the imaging system colorimetric characterization environment should be consistent with the actual application environment; S14, selecting colorimetric measuring instrument, including spectral photometer and colorimeter; S15, selecting the color imaging system to be measured, including various types of commercial digital cameras, video cameras, mobile phones and cameras.

3. A method of textile color measurement based on RBF according to claim 1, characterized in that, The step S2 specifically comprises: S21, applying the colorimetric measuring instrument to vertically align the sample to be measured, measuring the CIE1931 XYZ three stimulus values; S22, adjusting the color imaging system to manual mode, setting the ISO and system F number, vertically shooting the sample to be measured, and collecting the device related spatial RGB values; S23, taking the RGB three channel response values as the input space, the CIE1931 XYZ three stimulus values as the output space, the RGB values of each test sample as the attribute values, and the CIE1931 XYZ three stimulus values as the label values, to realize the data set construction.

4. A method of textile color measurement based on RBF according to claim 1, characterized in that, Further comprising a model precision evaluation step, the model precision evaluation step specifically comprises: According to the XYZ stimulus values predicted by the model in step S5 and the XYZ three stimulus values actually measured by the test set, calculating the LAB color difference; Calculating the average value of the test sample color difference result to obtain the average color difference, and evaluating the colorimetric characterization precision.

5. A method of textile color measurement based on RBF according to claim 4, characterized in that, The LAB color difference is calculated by the following formula: (X, Y, Z) are the model predicted XYZ tristimulus values; (X0, Y0, Z0) are the test set actually measured XYZ tristimulus values, where Y0= 100; L * is the lightness coordinate; a * , b * is the chroma coordinate; Wherein, or The values of L * , a * , b * are obtained from equations (7) (8) (9) respectively. The average color difference is obtained by averaging the color difference of each test sample, and the colorimetric characterization result is evaluated by using ΔE ab As an evaluation standard, as shown in formula (11);

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