A spectrum reconstruction method based on subspace merging and its application

Abstract

The present invention discloses a spectrum reconstruction method based on subspace merging and its application. The application includes the following steps: step S1, acquisition of object color data; step S2, optimization subspace merging: normalization of the color response values in the color response value set Tc; then taking the color response normalized value of each training sample as a subspace, setting the merging distance as k, and using the Euclidean distance as the subspace merging rule; then calculating the Euclidean distance in sequence from the first training sample as the starting point, and then performing subspace merging; substituting the initial cluster center point set L into the cost function to perform training sample subspace division to form a training sample subspace; step S3, spectrum reconstruction: spectrum reconstruction based on the sample subspace. The present invention reconstructs the object spectral reflectance through the subspace merging method on the basis of fully considering the division of sub-partitions and the screening of sample feature points, with simple calculation and high spectrum reconstruction accuracy.

Description

Technical Field

[0001] The present invention relates to the field of imaging technology, and in particular to a spectral reconstruction method based on subspace merging and its application. Background Art

[0002] Spectral reflectance is an intrinsic characteristic of the color information of an object's material and is known as the object's "fingerprint." Due to its unique ability to represent color, it is now widely used in art, remote sensing, medicine, textiles, printing, packaging, and other fields. Spectral reflectance can be directly obtained using a multispectral camera or spectrophotometer. However, these methods are limited in their application in daily life due to their cost-effectiveness, portability, and complexity. Meanwhile, digital imaging devices (such as digital cameras, smartphones, and scanners) can easily acquire the color response values (such as RGB values, HSB values, XYZ values, and Lab values) of an object's surface. Therefore, spectral reconstruction using color response values has gained widespread recognition.

[0003] Spectral reconstruction methods based on camera response values have been extensively studied, including pseudo-inverse methods (PI), compressed sensing, the Wiener method, principal component analysis (PCA), neural networks, and deep learning. The more similar the training and test samples are, the higher the spectral reconstruction accuracy. In practical applications, accurate spectral reconstruction methods improve spectral reconstruction accuracy by optimizing sample selection. Currently, existing methods primarily address underdetermination in the spectral reconstruction process by dividing the training samples into sub-partitions and filtering sample feature points. Existing methods only consider sub-partitioning or filtering sample feature points, without combining the two for optimal spectral reconstruction. Summary of the Invention

[0004] In order to make up for the defects of the prior art, the present invention proposes a spectrum reconstruction method based on subspace merging and its application on the basis of fully considering the division of sub-regions and the screening of sample feature points.

[0005] The present invention is achieved through the following technical solutions:

[0006] A spectrum reconstruction method based on subspace merging, characterized by comprising the following steps:

[0007] Step S1, acquisition of object color data: using a standard color card as a training sample set, measuring the spectral reflectance of the training sample set by a spectrophotometer to obtain the training sample spectrum set Rc; then obtaining the color response value set T corresponding to the training sample spectrum set Rc by measurement and calculation in a digital imaging device. c ;

[0008] Step S2, optimizing subspace merging: normalizing the color response values in the color response value set Tc to obtain color response normalized values; then taking the color response normalized values of each training sample as a subspace, setting the merging distance to k, and using the Euclidean distance as the subspace merging rule; then calculating the Euclidean distance starting from the first training sample, merging the subspaces to obtain an initial cluster center point set L; substituting the initial cluster center point set L into the cost function to perform training sample subspace partitioning to form a training sample subspace;

[0009] Step S3, spectrum reconstruction: spectrum reconstruction is performed based on the sample subspace.

[0010] Preferably, in step S1, the specific steps of obtaining the object color data are:

[0011] 1-1) Using a standard color card as a training sample set, measuring the spectral reflectance of the training sample set by a spectrophotometer to obtain a training sample spectrum set Rc;

[0012] 1-2) The color response value set T corresponding to the training sample spectrum set Rc is obtained by measurement and calculation using formula (1) in the digital imaging device. c :

[0013]

[0014] In formula (1), I(λ) represents the relative spectral power distribution of the ambient light source under the environment where the response value is obtained, q(λ) represents the color matching function of the color channel of the digital imaging device, r(λ) represents the spectral reflectance of the object; γ represents the noise. Since the noise γ has a small impact and is difficult to obtain, it is usually omitted.

[0015] Preferably, in step S2, the specific steps of optimizing subspace merging are:

[0016] 2-1) Since the color response value is affected by the camera filter and light source, the obtained color response value must be normalized to obtain the color response normalized value; wherein, the normalization process is performed using formula (2) and formula (3):

[0017] H=argmax(T c ) (2)

[0018] T=(T c / H)×255 (3)

[0019] In formulas (2) and (3), H represents the maximum value of the color response value, argmax represents the function for finding the maximum value; T represents the color response normalized value obtained by dividing the color response value by the maximum value and then multiplying it by 255;

[0020] 2-2) The color response normalized value of each training sample is used as a subspace, the merging distance is set to k, and the Euclidean distance is used as the subspace merging rule; then the Euclidean distance is calculated in sequence from the first training sample as the starting point, and then the subspaces are merged to obtain the initial cluster center point set L; wherein, the Euclidean distance calculation formula is shown in formula (4):

[0021]

[0022] In formula (4), T j =[r j ,g j ,b j ] represents the initial value of the j-th subspace represented; T i =[r i ,g i ,b i ] represents the normalized value of the color response of the i-th remaining training sample;

[0023] When k>s ij When T i Merge to T j In the subspace represented by T j The calculation method of the initial value is shown in formula (5):

[0024] r j =(r j +r i ) / 2

[0025] g j =(g j +g i ) / 2

[0026] b j =(b j +b i ) / 2 (5)

[0027] When k ij When T i Not with T j The subspace represented by T is merged. j The initial value remains unchanged;

[0028] After subspace merging, an initial cluster center point set L with n cluster center points is formed;

[0029] 2-3) Substitute the initial cluster center point set L into the cost function for training, divide the sample subspace, and form a training sample subspace; where the cost function is shown in formula (6):

[0030] ​

[0031] In formula (6), It represents the Euclidean distance, L a It represents the ath initial cluster center point, T w It represents the normalized value of the color response of the wth training sample, and m is the number of training samples.

[0032] Preferably, in step S3, the steps of performing spectrum reconstruction based on the sample subspace are as follows:

[0033] Step 3-1) Substitute the normalized color response value of the test sample into the cost function shown in formula (6) to determine the training sample subspace C where it is located. a ;

[0034] Step 3-2) Take the characteristics of the test sample into full consideration and calculate the normalized color response value T of the test sample. test The Euclidean distance between the normalized color response value in the training sample subspace is shown in formula (7);

[0035]

[0036] In formula (7), C ai Represents the i-th training sample subspace C a Normalized value of color response value;

[0037] Step 3-3), according to s j The size of is calculated using formula (8) to obtain the weight coefficient w of the training sample in the jth training sample subspace j Then, use formula (9) to determine the total weight coefficient W of all training samples in the training sample subspace:

[0038]

[0039]

[0040] In formula (9), ε = 0.001 is the adjustment coefficient;

[0041] Step 3-4), the conversion matrix Q is calculated using the pseudo-inverse method. The calculation formula of the conversion matrix Q is shown in formula (10); then the spectral reflectance R of the test sample is reconstructed using the conversion matrix Q test , spectral reflectance R test The calculation formula is shown in formula (11):

[0042] Q=R Train W(I Train W) -1 (10)

[0043] In formula (10), the superscript -1 is the inverse of the matrix, R Train is the spectral reflectance of the training sample in the training sample subspace, I Train is the color response normalization value of the training sample in the training sample subspace;

[0044] R test =QI Test (11)

[0045] In formula (11), I Test Normalized value for the color response of the test sample.

[0046] Application of a spectral reconstruction method based on subspace merging in printed matter quality evaluation.

[0047] A method for evaluating the quality of printed matter comprises the following steps:

[0048] (1) Obtaining printed materials: Randomly sampling printed materials obtained by the printing press to obtain printed materials to be tested, and then placing the printed materials to be tested on the printing sample table;

[0049] (2) Using the spectral reconstruction method based on subspace merging described above, the spectral reflectance of the printed matter to be tested is Calculate and obtain the spectral reflectance of the printed matter to be tested

[0050] (3) The spectral reflectance of the printed matter to be tested The spectral reflectance of the printed manuscript is compared to calculate the root mean square error (RMSE) between the two. The calculation formula of the root mean square error (RMSE) is shown in formula (12):

[0051]

[0052] In formula (12), RMSE is the root mean square error, r is the spectral reflectance of the printed manuscript, is the spectral reflectance of the printed matter to be tested, n is the wavelength dimension;

[0053] When the root mean square error (RMSE) is less than or equal to 0.05, it is a qualified product. For unqualified products, the spectral reflectance of the printed product is improved by adjusting the printing pressure of the printing press, the temperature and humidity of the printing environment, and the printing ink until the root mean square error (RMSE) is less than or equal to 0.05.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] According to the spectral reconstruction method involved in the present invention, each training sample is treated as an independent subspace, and subspace merging is performed based on Euclidean distance. The cluster center points of each subspace are obtained through continuous iterative calculation to form an initial cluster center point set L; the initial cluster center point set L is substituted into the cost function to divide the training sample subspace to form a training sample subspace; and spectral reconstruction is then performed based on the sample subspace. Therefore, the cluster center points of each subspace of the present invention are obtained through continuous iterative calculation to obtain the initial cluster center point set L, which not only combines the technology of sample feature points but also combines the technology of sub-partitioning. The cost function is then substituted into the cost function for training, and the sample subspace is divided to form a training sample subspace. The present invention reconstructs the spectral reflectance of the object through the subspace merging method, and the spectral reconstruction accuracy is high. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a flow chart of a spectrum reconstruction method based on subspace merging of the present invention;

[0057] Figure 2 is a diagram showing the relationship between the merge distance k and the color difference in the method of the present invention. DETAILED DESCRIPTION

[0058] In order to make the technical means, creative features, objectives and effects achieved by the present invention easier to understand, the following embodiments and accompanying drawings specifically illustrate a spectrum reconstruction method based on subspace merging of the present invention.

[0059] like Figure 1 As shown, the spectrum reconstruction method based on subspace merging provided by the present invention includes the following steps:

[0060] Step S1, acquisition of object color data: using a standard color card as a training sample set, measuring the spectral reflectance of the training sample set by a spectrophotometer to obtain the training sample spectrum set Rc; then obtaining the color response value set T corresponding to the training sample spectrum set Rc by measurement and calculation in a digital imaging device. c ;

[0061] The specific steps for obtaining the object color data are:

[0062] 1-1) Using a standard color card as a training sample set, measuring the spectral reflectance of the training sample set by a spectrophotometer to obtain a training sample spectrum set Rc;

[0063] 1-2) The color response value set T corresponding to the training sample spectrum set Rc is obtained by measurement and calculation using formula (1) in the digital imaging device. c :

[0064]

[0065] In formula (1), I(λ) represents the relative spectral power distribution of the ambient light source under the environment where the response value is obtained, q(λ) represents the color matching function of the color channel of the digital imaging device, r(λ) represents the spectral reflectance of the object; γ represents the noise, which is usually omitted because it has little influence and is difficult to obtain;

[0066] Step S2, optimizing subspace merging: Since the color response value acquisition is affected by the camera filter and light source, the obtained color response value must be normalized to obtain a color response normalized value; then the color response normalized value of each training sample is used as a subspace, the merging distance is set to k, and the subspace merging rule is based on the Euclidean distance; then, starting from the first training sample, the Euclidean distance is calculated in sequence, and then the subspaces are merged to obtain the initial cluster center point set L; the initial cluster center point set L is substituted into the cost function to divide the training sample subspace to form a training sample subspace;

[0067] The specific steps of optimizing subspace merging are:

[0068] 2-1) Since the color response value is affected by the camera filter and light source, the obtained color response value must be normalized to obtain the color response normalized value; wherein, the normalization process is performed using formula (2) and formula (3):

[0069] H=argmax(T c ) (2)

[0070] T=(T c / H)×255 (3)

[0071] In formulas (2) and (3), H represents the maximum value of the color response value, argmax represents the function for finding the maximum value; T represents the color response normalized value obtained by dividing the color response value by the maximum value and then multiplying it by 255;

[0072] 2-2) The color response normalized value of each training sample is used as a subspace, the merging distance is set to k, and the Euclidean distance is used as the subspace merging rule; then, starting from the first training sample, the Euclidean distance is calculated in sequence, and the subspaces are merged to obtain the initial cluster center point set L; wherein, the Euclidean distance calculation formula is shown in formula (4):

[0073]

[0074] In formula (4), T j =[r j ,g j ,bj ] represents the initial value of the j-th subspace represented; T i =[r i ,g i ,b i ] represents the normalized value of the color response of the i-th remaining training sample;

[0075] When k>s ij When T i Merge to T j In the subspace represented by T j The calculation method of the initial value is shown in formula (5):

[0076] r j =(r i +r i ) / 2

[0077] g j =(g j +g i ) / 2

[0078] b j =(b j +b i ) / 2 (5)

[0079] When k ij When T i Not with T j The subspace represented by T is merged. j The initial value remains unchanged;

[0080] After subspace merging, an initial cluster center point set L with n cluster center points is formed;

[0081] 2-3) Substitute the initial cluster center point set L into the cost function for training, divide the sample subspace, and form a training sample subspace; where the cost function is shown in formula (6):

[0082]

[0083] In formula (6), It represents the Euclidean distance, L a It represents the ath initial cluster center point, T w It represents the normalized value of the color response of the wth training sample, and m is the number of training samples;

[0084] Step S3, spectrum reconstruction: spectrum reconstruction based on sample subspace:

[0085] In step S3, the steps of performing spectrum reconstruction based on the sample subspace are as follows:

[0086] ​Step 3-1) Substitute the normalized color response value of the test sample into the cost function shown in formula (6) to determine the training sample subspace C where it is located. a ;

[0087] Step 3-2) Take the characteristics of the test sample into full consideration and calculate the normalized color response value T of the test sample. test The Euclidean distance between the normalized color response value in the training sample subspace is shown in formula (7);

[0088]

[0089] In formula (7), C ai Represents the i-th training sample subspace C a Normalized value of color response value;

[0090] Step 3-3), according to s j The size of is calculated using formula (8) to obtain the weight coefficient w of the training sample in the jth training sample subspace j Then, use formula (9) to determine the total weight coefficient W of all training samples in the training sample subspace:

[0091]

[0092]

[0093] In formula (9), ε = 0.001 is the adjustment coefficient;

[0094] Step 3-4), the conversion matrix Q is calculated using the pseudo-inverse method. The calculation formula of the conversion matrix Q is shown in formula (10); then the spectral reflectance R of the test sample is reconstructed using the conversion matrix Q test , spectral reflectance R test The calculation formula is shown in formula (11):

[0095] Q=R Train W(I Train W) -1 (10)

[0096] In formula (10), the superscript -1 is the inverse of the matrix, R Train is the spectral reflectance of the training sample in the training sample subspace, I Train is the color response normalization value of the training sample in the training sample subspace;

[0097] R test =QI Test (11)

[0098] In formula (11), I TestNormalized value for the color response of the test sample.

[0099] A method for evaluating the quality of printed matter comprises the following steps:

[0100] (1) Obtaining printed materials: Randomly sampling printed materials obtained by the printing press to obtain printed materials to be tested, and then placing the printed materials to be tested on the printing sample table;

[0101] (2) Using the spectral reconstruction method based on subspace merging described above, the spectral reflectance of the printed matter to be tested is Calculate and obtain the spectral reflectance of the printed matter to be tested

[0102] (3) The spectral reflectance of the printed matter to be tested The spectral reflectance of the printed manuscript is compared to calculate the root mean square error (RMSE) between the two. The calculation formula of the root mean square error (RMSE) is shown in formula (12):

[0103]

[0104] In formula (12), RMSE is the root mean square error, r is the spectral reflectance of the printed manuscript, is the spectral reflectance of the printed matter to be tested, n is the wavelength dimension;

[0105] When the root mean square error (RMSE) is less than or equal to 0.05, it is a qualified product. For unqualified products, the spectral reflectance of the printed product is improved by adjusting the printing pressure of the printing press, the temperature and humidity of the printing environment, and the printing ink until the root mean square error (RMSE) is less than or equal to 0.05.

[0106] Functions and Effects of the Embodiments

[0107] The Munsell color sample set was selected as the training sample, and the Munsell color sample set, ColorCherck SG color sample set, and Vrhel color sample set were used as the test samples. The CIE1964 color matching function was selected as the color matching function q(λ) of the color channel of the digital imaging device, the CIE D65 light source was used as the ambient light source under the response value environment, and the relative spectral power distribution I(λ) was used to calculate the color response value of the object. The pseudo-inverse method (PI), principal component analysis (PCA), and Proposed (the spectrum reconstruction method based on subspace merging described in this application) were used for experimental verification, and the results are shown in the figure. Figure 2As described in Table 1. The Munsell color sample set, ColorCherck SG color sample set, and Vrhel color sample set are all known data sets to those skilled in the art; the pseudo-inverse method (PI) and principal component analysis (PCA) are both existing spectral reconstruction methods in the art.

[0108] from Figure 2 It can be seen that, through verification, when the merging distance k value of the spectrum reconstruction method based on subspace merging described in this application is selected as 40, the spectrum reconstruction color difference value is the smallest. ab ) as the evaluation criteria to evaluate the advantages and disadvantages of the three spectral reconstruction methods: PI, PCA and Proposed.

[0109] Table 1 Spectral reconstruction results of different test samples under different spectral reconstruction methods

[0110]

[0111] As can be seen from Table 1, when the spectrum reconstruction method based on subspace merging claimed in this application is trained on different color sample sets, the average and maximum values of the root mean square error (RMSE) are small, the average and maximum values of the goodness of fit (GFC) are large, and the color difference (ΔE ab ) are also relatively small in terms of average and maximum values.

[0112] Comparison of root mean square error (RMSE) experimental results:

[0113] When training the Munsell color sample set, the average root mean square error (RMSE) obtained by the method of the present invention is reduced by 42.5% compared with the average root mean square error (RMSE) obtained by the PI method, and the average root mean square error (RMSE) obtained by the method of the present invention is reduced by 45.5% compared with the average root mean square error (RMSE) obtained by the PCA method;

[0114] When training the ColorChecker SG color sample set, the average root mean square error (RMSE) obtained by the method of the present invention was reduced by 27.9% compared with the average root mean square error (RMSE) obtained by the PI method, and the average root mean square error (RMSE) obtained by the method of the present invention was reduced by 27.3% compared with the average root mean square error (RMSE) obtained by the PCA method;

[0115] When training the ColorChecker SG color sample set, the average root mean square error (RMSE) obtained by the method of the present invention was reduced by 27.9% compared with the average root mean square error (RMSE) obtained by the PI method, and the average root mean square error (RMSE) obtained by the method of the present invention was reduced by 27.3% compared with the average root mean square error (RMSE) obtained by the PCA method;

[0116] When training the Vrhel color sample set, the average root mean square error (RMSE) obtained by the method of the present invention is reduced by 21.1% compared with the average root mean square error (RMSE) obtained by the PI method, and the average root mean square error (RMSE) obtained by the method of the present invention is reduced by 19.5% compared with the average root mean square error (RMSE) obtained by the PCA method;

[0117] Comparison of goodness of fit (GFC) experimental results:

[0118] When training the Munsell color sample set, the average goodness of fit (GFC) obtained by the method of the present invention is 0.4% higher than the average goodness of fit (GFC) obtained by the PI method, and the average goodness of fit (GFC) obtained by the method of the present invention is 0.4% higher than the average goodness of fit (GFC) obtained by the PCA method;

[0119] When training the ColorChecker SG color sample set, the average goodness of fit (GFC) obtained by the method of the present invention was 49.5% higher than that obtained by the PI method, and the average goodness of fit (GFC) obtained by the method of the present invention was 45.9% higher than that obtained by the PCA method.

[0120] When training the Vrhel color sample set, the average goodness of fit (GFC) obtained by the method of the present invention is 0.3% higher than the average goodness of fit (GFC) obtained by the PI method, and the average goodness of fit (GFC) obtained by the method of the present invention is 0.3% higher than the average goodness of fit (GFC) obtained by the PCA method;

[0121] Color difference (ΔE ab ) Comparison of experimental results:

[0122] When training the Munsell color sample set, the color difference (ΔE ab ) average value compared with the color difference (ΔE) obtained by PI method ab) average value was reduced by 42.0%, and the color difference (ΔE ab ) average value compared with the color difference (ΔE ab ) the average value decreased by 45.2%;

[0123] When training the ColorChecker SG color sample set, the color difference (ΔE ab ) average value compared with the color difference (ΔE) obtained by PI method ab ) average value was reduced by 34.4%, and the color difference (ΔE ab ) average value compared with the color difference (ΔE ab ) the average value decreased by 34.5%;

[0124] When training the Vrhel color sample set, the color difference (ΔE ab ) average value compared with the color difference (ΔE) obtained by PI method ab ) average value was reduced by 34.1%, and the color difference (ΔE ab ) average value compared with the color difference (ΔE ab )The average value decreased by 32.6%.

[0125] In summary, when the spectrum reconstruction method based on subspace merging claimed in this application is trained on a color sample set, the root mean square error (RMSE) is small, the goodness of fit (GFC) is good, and the color difference (ΔE ab ) is also small, therefore, the spectral reconstruction method based on subspace merging claimed in this application has high spectral reconstruction accuracy.

[0126] The above embodiments are preferred examples of the present invention and are not intended to limit the scope of protection of the present invention.

Claims

1. A spectrum reconstruction method based on subspace merging, characterized by: The following steps are involved: Step S1, acquisition of object color data: using a standard color card as a training sample set, measuring the spectral reflectance of the training sample set by a spectrophotometer to obtain the training sample spectrum set Rc; then obtaining the color response value set T corresponding to the training sample spectrum set Rc by measurement and calculation in a digital imaging device. c ; Step S2, optimizing subspace merging: normalizing the color response values in the color response value set Tc to obtain color response normalized values; then taking the color response normalized values of each training sample as a subspace, setting the merging distance to k, and using the Euclidean distance as the subspace merging rule; then calculating the Euclidean distance starting from the first training sample, merging the subspaces to obtain an initial cluster center point set L; substituting the initial cluster center point set L into the cost function to perform training sample subspace partitioning to form a training sample subspace; In step S2, the specific steps of optimizing subspace merging are: 2-1) Since the color response value is affected by the camera filter and light source, the obtained color response value must be normalized to obtain the color response normalized value; wherein, the normalization process is performed using formula (2) and formula (3): H=argmax(T c ) (2) T=(T c / H)×255 (3) In formulas (2) and (3), H represents the maximum value of the color response value, argmax represents the function for finding the maximum value; T represents the color response normalized value obtained by dividing the color response value by the maximum value and then multiplying it by 255; 2-2) The color response normalized value of each training sample is used as a subspace, the merging distance is set to k, and the Euclidean distance is used as the subspace merging rule; then, starting from the first training sample, the Euclidean distance is calculated in sequence, and the subspaces are merged to obtain the initial cluster center point set L; wherein, the Euclidean distance calculation formula is shown in formula (4): In formula (4), T j =[r j ,g j ,b j ] represents the initial value of the j-th subspace represented; T i =[r i ,g i ,b i ] represents the normalized value of the color response of the i-th remaining training sample; When k>s ij When T i Merge to T j In the subspace represented by T j The calculation method of the initial value is shown in formula (5): When k ij When T i Not with T j The subspace represented by T is merged. j The initial value remains unchanged;​ After subspace merging, an initial cluster center point set L with n cluster center points is formed; 2-3) Substitute the initial cluster center point set L into the cost function for training, divide the sample subspace, and form a training sample subspace; where the cost function is shown in formula (6): In formula (6), It represents the Euclidean distance, L a It represents the ath initial cluster center point, T w It represents the normalized value of the color response of the wth training sample, and m is the number of training samples; Step S3, spectrum reconstruction: spectrum reconstruction is performed based on the sample subspace.

2. The spectrum reconstruction method based on subspace merging according to claim 1, characterized in that: In step S1, the specific steps of obtaining the object color data are: 1-1) Using a standard color card as a training sample set, measuring the spectral reflectance of the training sample set by a spectrophotometer to obtain a training sample spectrum set Rc; 1-2) The color response value set T corresponding to the training sample spectrum set Rc is obtained by measurement and calculation using formula (1) in the digital imaging device. c : In formula (1), I(λ) represents the relative spectral power distribution of the ambient light source under the environment where the response value is obtained, q(λ) represents the color matching function of the color channel of the digital imaging device, r(λ) represents the spectral reflectance of the object; Y represents the noise. Since the noise Y has little influence and is difficult to obtain, it is usually omitted.

3. The spectrum reconstruction method based on subspace merging according to claim 1, characterized in that: In step S3, the steps of performing spectrum reconstruction based on the sample subspace are as follows: Step 3-1) Substitute the normalized color response value of the test sample into the cost function shown in formula (6) to determine the training sample subspace c where it is located. a ; Step 3-2) Take the characteristics of the test sample into full consideration and calculate the normalized color response value T of the test sample. test The Euclidean distance between the normalized color response value in the training sample subspace is shown in formula (7); In formula (7), C ai Represents the i-th training sample subspace C a Normalized value of color response value; Step 3-3), according to s j The size of is calculated using formula (8) to obtain the weight coefficient w of the training sample in the jth training sample subspace j Then, use formula (9) to determine the total weight coefficient W of the training samples in all training sample subspaces: In formula (9), ε = 0.001 is the adjustment coefficient; Step 3-4), use the pseudo-inverse method to calculate the conversion matrix Q, the calculation formula of the conversion matrix Q is shown in formula (10); Then the transformation matrix Q is used to reconstruct the spectral reflectance R of the test sample test , spectral reflectance R test The calculation formula is shown in formula (11): Q=R Train w(I Train w) —1 (10) In formula (10), the superscript -1 is the inverse of the matrix, R Train is the spectral reflectance of the test sample in the training sample subspace, I Train is the normalized value of the color response of the test sample in the training sample subspace; R test =QI Test (11) In formula (11), I Test Normalized value for the color response of the test sample.

4. An application of a spectral reconstruction method based on subspace merging in printed product quality evaluation; the spectral reconstruction method based on subspace merging is the spectral reconstruction method based on subspace merging according to any one of claims 1 to 3.

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