Ink color matching prediction method based on NPE-Transformer model and KM theory

Abstract

An ink color matching prediction method based on the combination of NPE-Transformer model and K-M theory, which relates to the field of intelligent ink color matching technology, includes the following steps: S1 constructs an NPE-Transformer model; S2 constructs a mixed loss function; S3 performs standardization processing on the input spectral reflectance data; S4 generates an adaptive position code related to the wavelength; S5 adds the spectral reflectance data to the generated adaptive position code, and then inputs it into multiple encoder modules of the NPE-Transformer model; S6 generates a CMYK concentration prediction value that conforms to the physical laws in practical applications after multi-layer decoding processing by a decoder module. It can better understand and utilize the complex patterns and physical properties in spectral data, so as to more accurately predict the CMYK (cyan, magenta, yellow, and black) formula under complex spectral data conditions, and further improve the accuracy of color matching prediction.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent ink color matching, and in particular to an ink color matching prediction method based on the combination of an NPE-Transformer model and a KM theory. Background Art

[0002] Color matching in the traditional printing industry mainly relies on manual experience and intuition, which is time-consuming and difficult to meet the needs of the modern printing industry for high-precision colors and efficient production. With the advancement of computer color matching technology, researchers have proposed a variety of color matching methods, such as Stearns-Noechel, Kubelka-Munk, tristimulus color matching, mask equation, spectral color matching, and neural network color matching theory. For example, the Kubelka-Munk color matching model is based on physical optics theory, suitable for multi-layer media and its parameters have physical meaning, but its linear assumption limits the ability to handle complex nonlinear light reflections and requires a large amount of experimental data. In contrast, the neural network model has strong nonlinear fitting and adaptive learning capabilities, and is suitable for a variety of scenarios, but its training is complex, data requirements are high, and it lacks interpretability. Summary of the invention

[0003] In view of the shortcomings of the prior art, the purpose of the present invention is to provide an ink color matching prediction method based on the combination of NPE-Transformer model and KM theory.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] An ink color matching prediction method based on the combination of NPE-Transformer model and KM theory includes the following steps:

[0006] S1 builds an NPE-Transformer model that takes spectral reflectance data as input and outputs CMYK color density predictions, which includes several encoder modules and decoder modules, wherein the encoder module uses a multi-head self-attention mechanism to allow the NPE-Transformer model to dynamically allocate weights between different wavelengths, and the decoder module uses a masked multi-head self-attention mechanism to adaptively process the current wavelength to capture the relevance of sequence information in the output, and extracts relevant information from the encoder through the multi-head self-attention mechanism, so that the decoder can generate CMYK color density predictions that are context-sensitive to the current input data;

[0007] S2 constructs a hybrid loss function based on KM theory and mean absolute error, and introduces the hybrid loss function into the NPE-Transformer model constructed in step S1;

[0008] S3 performs standardization on the input spectral reflectance data;

[0009] S4 generates wavelength-dependent adaptive position coding through an adaptive nonlinear position coding module;

[0010] S5 adds the spectral reflectance data to the generated adaptive position code and inputs it into multiple encoder modules of the NPE-Transformer model;

[0011] After S6 is processed by the decoder module with multiple layers of decoding, the decoder output enters the linear layer and the softmax function, and finally generates a CMYK concentration prediction value that conforms to the physical laws in practical applications.

[0012] In S3, it is ensured that the spectral reflectance data covers the reflectance values ​​in the wavelength range of 400-700 nm, and sampling is performed every 10 nm.

[0013] In S4, the wavelength input is mapped into a 31-dimensional encoding vector through a multi-layer perceptron, giving each wavelength a unique representation.

[0014] The encoder module includes a feedforward neural network and a multi-head self-attention mechanism, and residual connections and normalization are added between the feedforward neural network and the multi-head self-attention mechanism.

[0015] The hybrid loss function includes a standard error to capture the data loss and the physical consistency loss based on the KM single constant theory, the standard error And the weighted summation of the physical consistency loss based on the KM single constant theory constitutes the final comprehensive error , is the reflectivity error.

[0016] The standard error :

[0017] ,

[0018] in is the CMYK value predicted by the model, For the true CMYK value.

[0019] The physical consistency loss based on the KM single constant theory is:

[0020] 1. Use the CMYK color values ​​predicted by the NPE-Transformer model to calculate the absorption coefficient of the KM single constant theory ,

[0021] ,

[0022] in , , , is the predicted CMYK color value, , , , The corresponding absorption coefficients of the four CMYK inks;

[0023] 2. Calculate the reflectance predicted by the model through the KM single constant theoretical formula and compare it with the actual spectral reflectance R true For comparison, the reflectivity error is measured using the mean square error. ,

[0024] .

[0025] A non-transitory computer-readable storage medium, wherein the non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, the above-mentioned ink color matching prediction method based on the combination of NPE-Transformer model and KM theory is implemented.

[0026] An electronic device includes a processor, a memory and a computer program, wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the above-mentioned ink color matching prediction method based on the combination of NPE-Transformer model and KM theory.

[0027] Beneficial effects of the present invention: A Transformer (NPE-Transformer) model combining KM (Kubelka-Munk) single constant theory and adaptive nonlinear position encoding is used for ink color matching prediction. By effectively integrating the physical information (such as absorption coefficient and scattering coefficient) in the KM single constant theory into the Transformer model, and combining adaptive nonlinear position encoding to automatically capture the wavelength position characteristics in the spectral data, the model can not only rely on data-driven, but also follow physical principles. This improvement enables the model to better understand and utilize the complex patterns and physical properties in the spectral data, thereby more accurately predicting the CMYK (cyan, magenta, yellow, and black) formula under complex spectral data conditions, further improving the accuracy of color matching prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a structural diagram of the NPE-Transformer model of the present invention.

[0029] Figure 2 It is a schematic diagram of the MAE changes of each model during the training process. DETAILED DESCRIPTION

[0030] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0031] It should be noted that all directional indications in the embodiments of the present invention (such as up, down, left, right, front, back, etc.) are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0032] In color matching tasks, the physical continuity of spectral reflectance data and the complex nonlinear relationship between wavelength directly affect the accuracy of prediction. However, traditional convolutional neural networks (CNN) and recurrent neural networks (RNN) have their limitations in processing sequence dependencies and cannot fully adapt to the physical characteristics of spectral reflectance data. Although the Transformer model performs well in sequence data processing, the sine and cosine position encoding it relies on is mainly used for discrete sequences, so it is still insufficient in capturing the continuity information of spectral reflectance data. To this end, the present invention proposes a wavelength-based adaptive nonlinear position encoding method, combined with the NPE-Transformer (Nonlinear Position Encoding Transformer) model, to deeply explore the complex relationship between wavelength and reflectance in spectral reflectance data, significantly improving the accuracy and physical consistency of color matching prediction.

[0033] The present invention provides an ink color matching prediction method based on the combination of NPE-Transformer model and KM theory, which comprises the following steps:

[0034] S1 builds an NPE-Transformer model that takes spectral reflectance data as input and outputs CMYK color density predictions, which includes several encoder modules and decoder modules, wherein the encoder module uses a multi-head self-attention mechanism to allow the NPE-Transformer model to dynamically allocate weights between different wavelengths, and the decoder module uses a masked multi-head self-attention mechanism to adaptively process the current wavelength to capture the relevance of sequence information in the output, and extracts relevant information from the encoder through the multi-head self-attention mechanism, so that the decoder can generate CMYK color density predictions that are context-sensitive to the current input data;

[0035] S2 constructs a hybrid loss function based on KM theory and mean absolute error, and introduces the hybrid loss function into the NPE-Transformer model constructed in step S1;

[0036] S3 performs standardization on the input spectral reflectance data;

[0037] S4 generates wavelength-dependent adaptive position coding through an adaptive nonlinear position coding module;

[0038] S5 adds the spectral reflectance data to the generated adaptive position code and inputs it into multiple encoder modules of the NPE-Transformer model;

[0039] After S6 is processed by the decoder module with multiple layers of decoding, the decoder output enters the linear layer and the softmax function, and finally generates a CMYK concentration prediction value that conforms to the physical laws in practical applications.

[0040] like Figure 1As shown in the figure, in the model process, the input spectral reflectance data is first standardized to ensure that the data covers the reflectance values ​​in the wavelength range of 400-700nm, and sampling is performed every 10nm to ensure the consistency of the input data. Next, the wavelength-related position encoding is generated through an adaptive nonlinear position encoding module (MLP). This encoding is different from the traditional sine and cosine encoding. Instead, the wavelength input is mapped to a 31-dimensional encoding vector through a multi-layer perceptron (MLP), giving each wavelength a unique representation. These encoding vectors can be adjusted dynamically to better reflect the complex nonlinear relationship between wavelength and spectral reflectance. Subsequently, the spectral reflectance data is added to the generated adaptive position encoding and input into multiple encoder modules of the NPE-Transformer. A multi-head self-attention mechanism is used inside each encoder module, allowing the model to dynamically allocate weights between different wavelengths and flexibly capture long-range dependencies and complex patterns in spectral reflectance data. To ensure the stability and training efficiency of the model, the encoder module adds residual connections and layer normalization (LayerNorm) between the self-attention and feedforward neural network (FFN) layers, which helps to keep the gradient stable and prevent the gradient from disappearing or exploding.

[0041] In the decoder module, the model first uses a masked multi-head self-attention mechanism to adaptively process the current wavelength to capture the relevance of the sequence information in the output. Then, the multi-head self-attention mechanism extracts relevant information from the encoder, enabling the decoder to generate CMYK color density predictions that are context-sensitive to the current input data. After multiple layers of decoding processing, the decoder output enters the linear layer and softmax function, and the final generated CMYK concentration prediction value conforms to the physical laws in practical applications, ensuring the physical consistency and operability of the color formula.

[0042] In addition, in order to further optimize the prediction accuracy and physical consistency of the model, this paper introduces a hybrid loss function based on Kubelka-Munk (KM) theory and mean absolute error (MAE). KM theory provides constraints on the physical relationship between spectral reflectance and color concentration, and embeds the KM constant into the loss function to ensure that the CMYK color concentration values ​​output by the model conform to physical laws. At the same time, MAE is used to measure the error between the model prediction and the actual concentration, thereby improving the accuracy of the model. This hybrid loss function achieves the dual effects of physical constraints and error minimization during the training process, which helps to accelerate the convergence of the model and improve the rationality and reliability of the prediction.

[0043] In summary, NPE-Transformer achieves high-precision spectral data processing capabilities through adaptive position encoding, dynamic weight allocation, multi-layer residual connections and layer normalization. At the same time, the hybrid loss function based on KM theory further enhances the physical consistency and accuracy of the model, providing an effective solution for color matching tasks.

[0044] KM Single Constant Theory

[0045] Kubelka-MunK (KM) theory is a commonly used mathematical model in dye color matching and printing industry, which is used to describe the absorption and scattering characteristics of light in opaque and semi-transparent media. The theory matches colors by analyzing the absorption and scattering behavior of light in the medium. KM theory has two forms: single constant and double constant, which are respectively applicable to different types of materials and optical conditions.

[0046] In the single constant theory, it is assumed that the scattering coefficient S of the medium remains constant or can be ignored, and the absorption behavior of the material is mainly considered, that is, the absorption of light by the material. Therefore, this theory is suitable for media with weak scattering effects, and the color performance is mainly determined by the absorption coefficient K. The KM double constant theory considers both the absorption coefficient K and the scattering coefficient S at the same time, and more comprehensively describes the propagation process of light in the medium. It is suitable for materials that have both obvious absorption characteristics and strong scattering effects. Since paper is used as the experimental substrate in this article, it is a highly scattering medium, and its scattering coefficient is significantly higher than that of ink. The absorption behavior of ink on light during the printing process is dominant, and its scattering effect is weak. Therefore, the scattering coefficient of the ink can be ignored, and the KM single constant theory is used for analysis, and the color matching prediction is made through the absorption coefficient of the ink and the absorption coefficient and scattering coefficient of the paper.

[0047] According to this theory, the absorption coefficient of the dyed sample is and scattering coefficient It is determined by the characteristics of the substrate itself and the superposition effect of different dyes. Since the absorption coefficient is proportional to the ink concentration, the absorption coefficient can be simplified as:

[0048]

[0049] in For the The concentration of ink in For the The absorption coefficient corresponding to the ink. Represents the color of the ink. and are the absorption coefficient and scattering coefficient of the paper itself respectively. The relationship is established as follows:

[0050]

[0051] Therefore, the spectral reflectance and The relationship between the values:

[0052]

[0053] This formula shows that the spectral reflectance and absorption coefficient and scattering coefficient Based on this relationship, the spectral reflectance of the sample can be predicted according to the absorption and scattering properties of paper and ink.

[0054] Combination of NPE-Transformer model and KM single constant theory

[0055] In the process of ink color matching, in addition to relying on data, it is also necessary to consider clear physical laws, such as the KM single constant theory. In the NPE-Transformer model, the custom loss function is combined with the KM constant theory, so that the model can optimize the physical consistency with the KM single constant theory when predicting CMYK values.

[0056] Its loss function consists of two parts:

[0057] Standard error , used to capture the error-driven data:

[0058]

[0059] in is the CMYK value predicted by the model, For the true CMYK value.

[0060] (2) Physical consistency loss based on KM single constant theory, mainly measures the difference between the spectral reflectance predicted by KM single constant theory and the spectral reflectance of real data. Physical model prediction: CMYK color values ​​predicted by the model , , , , the KM single constant theory is used to calculate the predicted spectral reflectance. First, the CMYK color values ​​predicted by the model are used to calculate the absorption coefficient of the KM single constant theory :

[0061]

[0062] Then, the reflectance predicted by the model was calculated using the KM single constant theoretical formula and compared with the actual spectral reflectance. R true The reflectivity error is measured by the mean square error. :

[0063]

[0064] In order to integrate data-driven and physical law-driven, we perform a weighted summation of data loss and physical loss to form the final comprehensive error, that is, :

[0065] .

[0066] Dataset preparation

[0067] To verify the effectiveness of the model, the data set adopts the "ISO 12642-2" standard to ensure the accuracy of color management and representation in the four-color (CMYK) printing process. The experiment uses Silian brand ink and white paper substrate to produce five types of samples, totaling 1553 color blocks, to comprehensively evaluate the color performance. Among them, the single-color sample covers the four colors of CMYK, and the dot area rate changes at intervals of 5% to ensure sufficient coverage of the monochrome channel. The two-color sample contains a variety of overprint combinations (such as CM, CY, MY, etc.), and the dot area rate changes at intervals of 10% to evaluate the two-color overprinting effect. The three-color sample is overprinted with different three-color combinations, with an interval of 15%, and the multi-color overprinting performance is further analyzed. The four-color sample shows a complete CMYK combination, which is mainly used to evaluate the complex four-color overprinting effect. Among them, the dot area rates of cyan, magenta, and yellow change at intervals of 20%, and black changes at intervals of 50%, which fully reflects the color interaction effect of four-color overprinting. As shown in Table 1:

[0068] Table 1 Sample color block combination

[0069]

[0070] Test Method

[0071] The data of sample color blocks of different proportions were collected by using X-rite Ci64 spectrophotometer. The measurement conditions were D65 standard light source, 10° measurement angle, and specular reflection. To ensure the consistency of the measurement environment, four pieces of white paper of the same material were placed under the sample. First, the spectral reflectance of the blank paper was measured as a benchmark, and then the sample color blocks were measured. Each color sample was measured three times and the average value was taken to improve the accuracy of the data. The measurement point was selected in the middle area with uniform ink layer and clean surface to reduce errors. The spectral value measurement range is 400 nm to 700 nm, with an interval of 10 nm, and the spectral value and CMYK dot area rate corresponding to the color block are recorded.

[0072] Experimental environment and parameter settings

[0073] To ensure the reliability of the results, all experiments were conducted on the same platform. The specific configuration is as follows: CPU is 8-core Intel(R) Core(TM) i5-8265U CPU @ 1.60GHz, memory is 16 GB, hard disk is 1TB, operating system is Windows 10, deep learning framework Pytorch 2.3.1, Python version 3.11.7.

[0074] The experiment used spectral reflectance with a wavelength range of 400-700 nm (every 10 nm interval) as input data, and CMYK dot area ratio as prediction output. The dataset contains 1556 sets of samples, 80% of which are used for training and 20% for testing. The experiment was repeated 5 times, and the average error was taken as the final evaluation. All models used the same optimizer (Adam) and batch size (Batch Size), and adopted an adaptive learning rate descent strategy. In addition, the early stopping method was introduced in the training process.

[10] , by setting the patience parameter to control the maximum number of iterations allowed when the validation loss does not improve, ensuring that the training process and results are comparable.

[0075] Several typical prediction neural network models were selected for verification in the experiment, such as CNN, RNN, DNN, SVR, BP, GA-BP, LSTM and Transformer. The performance of each model was evaluated by testing and verification on the same data set, and the model with the best effect was selected as the backbone network for the study. The experimental results are shown in Table 2. The evaluation indicators are (Mean Absolute Error), which is used to measure the average difference between the predicted value and the actual value. The calculation formula is as follows:

[0076]

[0077] in is the actual CMYK value, is the CMYK predicted value, is the number of samples.

[0078] Table 2 MAE evaluation results of each prediction model

[0079]

[0080] The results show that Transformer performs better than other models in the color matching prediction task. Therefore, we select the Transformer network as the backbone model for this study.

[0081] This experiment uses the Bayesian optimization method to approximate the prediction of validation loss through a proxy model (such as Gaussian process regression) to effectively guide the selection of the best hyperparameters for the Transformer model. The core idea of ​​Bayesian optimization is to use Bayes' theorem to update the uncertainty estimate of the objective function (validation loss). In each round of experiments, Bayesian optimization constructs a proxy model (such as a Gaussian process) to represent the probability distribution of the objective function based on the observed hyperparameter combinations and their corresponding validation loss results. Through this proxy model, Bayesian optimization can calculate the expected performance and uncertainty of the objective function under given hyperparameters, and use the acquisition function to intelligently select the next set of optimal hyperparameter combinations, thereby efficiently exploring the optimal solution with the minimum number of experiments.

[0082] When optimizing the Transformer model, the key hyperparameters that need to be adjusted include the model embedding dimension D_model, the number of multi-head attention heads N_head, the encoder and decoder Num_layers, and the hidden layer dimension Dim_feedforward of the feedforward neural network. In each experiment, Bayesian optimization tries 50 different hyperparameter combinations, each group is trained for 20 epochs, and the validation loss of each experiment is recorded. With the iterative update of Bayes' theorem, the optimization strategy gradually converges to the hyperparameter combination with the lowest validation loss. Finally, the optimal hyperparameter combination obtained by the experiment is shown in Table 3, which provides effective support for further optimization of the model.

[0083] Table 3 Optimal hyperparameter combinations of models

[0084]

[0085] In order to verify the effectiveness of the color matching prediction based on NPE-Transformer and KM single constant theory proposed in this paper, experiments were conducted on Transformer, NPE-Transformer, and multiple models fused with Transformer and KM theory. In the experiment, the mean absolute error (MAE) of each model was recorded and the relationship between the training cycle and MAE was plotted. The specific results are shown in Table 4:

[0086] Table 4 MAE comparison of models in color matching prediction

[0087]

[0088] Figure 2 The changing trend of MAE of each model in different training cycles is shown. As the number of training times increases, the NPE-Transformer model based on KM theory performs best in terms of convergence speed and error stability.

[0089] These results show that the model combining NPE-Transformer with KM single constant theory performs best, verifying the effectiveness of the method of the present invention in the color matching prediction task.

[0090] This model combines the physical information in KM theory and the self-attention mechanism of the Transformer network, so that it can not only rely on spectral reflectance data to drive, but also follow the physical laws to predict ink formulas. Experimental results show that compared with traditional Transformer models and other neural networks, the combination of NPE-Transformer and KM theory significantly improves the accuracy of CMYK color matching prediction, and the mean absolute error (MAE) is reduced to 5.26, which verifies the effectiveness and superiority of this method under complex spectral data. In future work, we can further study how to generalize this model on different paper substrates and ink types to improve its application potential in the actual printing industry.

[0091] The present invention also provides a non-transitory computer-readable storage medium, characterized in that: the non-transitory computer-readable storage medium is used to store computer instructions, and when the computer instructions are executed by a processor, the above-mentioned ink color matching prediction method based on the combination of the NPE-Transformer model and the KM theory is implemented.

[0092] The present invention also provides an electronic device, characterized in that it includes a processor, a memory and a computer program, wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the above-mentioned ink color matching prediction method based on the combination of the NPE-Transformer model and the KM theory.

[0093] The embodiments should not be regarded as limiting the present invention, but any improvements made based on the spirit of the present invention should be within the protection scope of the present invention.

Claims

1. An ink color matching prediction method based on the combination of NPE-Transformer model and KM theory, characterized by: It includes the following steps: S1 builds an NPE-Transformer model that takes spectral reflectance data as input and outputs CMYK color density predictions, which includes several encoder modules and decoder modules, wherein the encoder module uses a multi-head self-attention mechanism to allow the NPE-Transformer model to dynamically allocate weights between different wavelengths, and the decoder module uses a masked multi-head self-attention mechanism to adaptively process the current wavelength to capture the relevance of sequence information in the output, and extracts relevant information from the encoder through the multi-head self-attention mechanism, so that the decoder can generate CMYK color density predictions that are context-sensitive to the current input data; S2 constructs a hybrid loss function based on KM theory and mean absolute error, and introduces the hybrid loss function into the NPE-Transformer model constructed in step S1; S3 performs standardization on the input spectral reflectance data; S4 generates wavelength-dependent adaptive position coding through an adaptive nonlinear position coding module; S5 adds the spectral reflectance data to the generated adaptive position code and inputs it into multiple encoder modules of the NPE-Transformer model; After S6 is processed by the decoder module with multiple layers of decoding, the decoder output enters the linear layer and the softmax function, and finally generates a CMYK concentration prediction value that conforms to the physical laws in practical applications.

2. The ink color matching prediction method based on the combination of NPE-Transformer model and KM theory according to claim 1 is characterized in that: In S3, it is ensured that the spectral reflectance data covers the reflectance values ​​in the wavelength range of 400-700 nm, and sampling is performed every 10 nm.

3. The ink color matching prediction method based on the combination of NPE-Transformer model and KM theory according to claim 1 is characterized in that: In S4, the wavelength input is mapped into a 31-dimensional encoding vector through a multi-layer perceptron, giving each wavelength a unique representation.

4. The ink color matching prediction method based on the combination of NPE-Transformer model and KM theory according to claim 1 is characterized in that: The encoder module includes a feedforward neural network and a multi-head self-attention mechanism, and residual connections and normalization are added between the feedforward neural network and the multi-head self-attention mechanism.

5. The ink color matching prediction method based on the combination of NPE-Transformer model and KM theory according to claim 1 is characterized in that: The hybrid loss function includes a standard error to capture the data loss and the physical consistency loss based on the KM single constant theory, the standard error And the weighted summation of the physical consistency loss based on the KM single constant theory constitutes the final comprehensive error , is the reflectivity error.

6. The ink color matching prediction method based on the combination of NPE-Transformer model and KM theory according to claim 5 is characterized in that: The standard error : ， in is the CMYK value predicted by the model, For the true CMYK value.

7. The ink color matching prediction method based on the combination of NPE-Transformer model and KM theory according to claim 6 is characterized in that: The physical consistency loss based on the KM single constant theory is:

1. Use the CMYK color values ​​predicted by the NPE-Transformer model to calculate the absorption coefficient of the KM single constant theory , ， in , , , is the predicted CMYK color value, , , , The corresponding absorption coefficients of the four CMYK inks; 2. Calculate the reflectance predicted by the model through the KM single constant theoretical formula and compare it with the actual spectral reflectance R true For comparison, the reflectivity error is measured using the mean square error. , 。 8. A non-transitory computer-readable storage medium, characterized in that: The non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by the processor, the ink color matching prediction method based on the combination of the NPE-Transformer model and the KM theory as described in any one of claims 1 to 7 is implemented.

9. An electronic device, characterized in that: It includes a processor, a memory and a computer program, wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the ink color matching prediction method based on the combination of the NPE-Transformer model and the KM theory as described in any one of claims 1 to 7.

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