CN113095368B - A spectral color representative sample selection method and system - Google Patents

Abstract

The technical scheme of the invention is a spectral color representative sample selection method and a system. For a given total sample set, obtaining total sample collection spectral data including using spectrophotometer measurements; selecting a color matching function, and calculating to obtain color data of a total sample set; selecting a spectral representative sample by using spectral reconstruction based on principal component analysis until the spectral reconstruction error is converged, and finishing the selection of the spectral representative sample; selecting a color representative sample by using a maximum and minimum criterion, and performing a color correction test until color correction chromatic aberration is converged to finish the selection of the color representative sample; and fusing and de-duplicating the selected spectral representative sample and the color representative sample to obtain a final spectral color representative sample set. The method can provide support for constructing the portable color card which is simultaneously suitable for the modeling application of the digital camera spectrum and color characterization, and effectively improves the modeling efficiency while ensuring the application effect and robustness.

Description

A spectral color representative sample selection method and system

technical field

The invention belongs to the technical field of color imaging and information processing, and in particular relates to a method and system for selecting representative samples of spectral colors.

Background technique

With the development and progress of color imaging technology, digital cameras are more and more widely used in scientific analysis in various fields due to their advantages of fast imaging, high spatial resolution, portability and flexibility, such as color reproduction, cultural relics protection, Medical diagnosis, computer vision, remote sensing detection, and other related fields. Use digital cameras to capture digital images of the surface of the object, and then reconstruct high-precision multispectral images and chromaticity images of the surface of the object based on spectral reconstruction theory and color characterization theory. Scientific applications such as auxiliary medical diagnosis, object recognition, agricultural pest detection, and target classification provide new technical and method support for the applications in the above fields.

In the above-mentioned scientific applications of digital cameras, whether it is to carry out high-precision spectral reconstruction or color correction, it is necessary to first use a set of representative training samples to model the spectrum and color characteristics of the digital camera, and then use the constructed spectrum. and color characterization models to compute spectral and color images of object surfaces. At this stage, the spectral and color characterization modeling of digital cameras mostly uses standard color cards, and studies have shown that the spectral and color similarity between training samples and test objects directly affects the accuracy of spectral and color calculations. For different types of objects, using a standard color card as a training sample cannot guarantee the spectral and color representation of the target object, so the optimal calculation accuracy cannot be obtained.

At present, a large number of sample sets or open databases have been accumulated in cultural heritage protection, computer vision, color science, textile production, and other related application fields, providing sufficient training sample support for the specific application of digital cameras in these fields. However, these sample sets or data all contain hundreds of samples. In practical applications, if these sample sets or databases are directly used as training samples, it will bring a huge workload to the practical application and seriously reduce the spectral and spectral density. Efficiency of color characterization modeling. Studies have shown that there is a lot of information redundancy in the existing sample sets or the database itself when modeling the spectrum and color characteristics of digital cameras, and it is not necessary to use all the samples as training samples. Therefore, for the spectral and color characterization modeling application of digital cameras, how to select representative samples from the sample set or database that can be applied to the spectral and color characterization modeling of digital cameras at the same time, build a portable application color card, and ensure the application Effectively improving the efficiency of spectral and color characterization modeling at the same time of effect and robustness is a key problem currently faced in the field.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method for selecting a representative sample of spectral color in order to solve the problem described in the background art.

Aiming at the data redundancy problem of using existing sample sets or databases as training samples, the present invention proposes a spectral color representative sample selection method. Portable application color card, which can be applied to the spectral and color characterization modeling of digital cameras at the same time, and can ensure the equivalence and robustness of the portable color card to the total sample set in practical applications, effectively improving spectral reconstruction or color correction work efficiency. The technical solution of the present invention is a method for selecting a representative sample of spectral color, which specifically includes the following steps:

Step 1, for a given total sample set, use a spectrophotometer to measure and obtain the spectral data of the total sample set;

Step 2, select a color matching function, and calculate the color data of the total sample set;

Step 3: Select spectral representative samples by using the spectral reconstruction based on principal component analysis, until the spectral reconstruction error converges, and complete the selection of spectral representative samples;

Step 4, select a representative color sample using the maximum and minimum criteria, and perform a color correction test until the color correction chromatic aberration converges, and complete the selection of color representative samples;

Step 5: Perform fusion and deduplication on the selected spectral representative samples and color representative samples to obtain a spectral color representative sample set.

Further, in step 2, the CIE D50 standard illuminator recommended by the International Commission on Illumination and the color matching function under the CIE1931 standard observer condition are usually used to calculate the color data of the total sample set in the CIELab color space, and the calculation method is as formula (1) And formula (2) shows:

Among them, X, Y and Z are the sample tristimulus values, r(λ) is the spectral reflectance of the material surface, l(λ) is the relative spectral power distribution of the light source, x(λ), y(λ) and z(λ) is the color matching function, λ represents the wavelength of visible light in the range of 380nm-780nm, and k is the adjustment factor, which is calculated when the brightness value Y of the light source is adjusted to 100.

Among them, X, Y and Z are the sample tristimulus values, X _n , Y _n and _Zn are the reference white point tristimulus values, L, a and b are the color data of the sample in the CIELab color space, and L, a and When b, there are constraints as shown in formula (3), where item represents the tristimulus values X, Y and Z.

Further, in step 3, the specific method for selecting spectral representative samples by using the spectral reconstruction based on principal component analysis is as follows: First, calculate the spectral modulus value of any sample in the total sample set, and select the sample with the largest modulus value as the first sample. The sample s ₁ is selected, as shown in formula (4), where norm(·) is the function of calculating the modulus value in the present invention, ri represents the spectral vector of the _ith sample in the total sample set, and max(·) is the Maximum function, Θ is the total sample set, Ω ₁ is the sample subset containing the first spectrally representative sample.

Ω ₁ =s ₁ =max(norm(ri )), _{ri ∈Θ} , (4)

Then, the remaining spectrally representative samples are selected using principal component analysis-based spectral reconstruction. Assuming that the mth sample (m≥2) needs to be selected at present, it is necessary to traverse and combine the selected m-1 spectrum representative sample subset Ω _m-1 with all unselected samples r _m in the total sample set Θ , obtain the spectral reconstruction training sample subset Ω _m , which is expressed as follows:

Ω _m =Ω _m-1 ∪r _m , r _m ∈Θ, (5)

Perform principal component analysis on Ω _m to obtain the eigenvalues and eigenvectors of the training sample subset Ω _m , as shown in formula (6), where princomp( ) is the principal component analysis function, U is the orthogonal matrix eigenvector, S is the eigenvalue matrix, V is the score matrix, and T is the matrix transpose operator.

USV ^T =princomp(Ω _m ), (6)

The first j groups of feature quantities of PCA are selected to perform spectral reconstruction on the total sample set Θ, as shown in formula (7), where R is the spectral matrix of the total sample set, and R _rec is the reconstructed spectral matrix of the total sample set , + is the pseudo-inverse operator, and calculates the spectral root-mean-square error (RMSE) between the reconstructed total sample set and the original total sample set, as shown in Equation (8), where E‖ ·‖ is the function for calculating the spectral root mean square error RMSE in the present invention.

RMSE _m = E||R _rec -R||, (8)

Taking RMSE as the evaluation index, select the sample s _m with the smallest RMSE _m as the m-th spectral representative sample, as shown in formula (9), and add it to the spectral representative sample set subset to determine the spectral representative sample subset. Set Ω _m .

s _m =min(RMSE _m ), (9)

Finally, formulas (5) to (8) are repeated to continue to select the remaining spectral representative samples, until the spectral reconstruction error RMSE of the selected spectral representative samples for the total sample set reaches a convergence level, and the selection of spectral representative samples is completed.

Further, in step 4, the specific method for selecting color representative samples using the maximum and minimum criteria is as follows. First, calculate the color data variance of any sample in the total sample set, and select the sample with the smallest variance as the first selected sample v ₁ , as shown in formula (10), where the variance function is calculated for var(·) in the present invention, Lab _i represents the color value vector of the ith sample in the total sample set, min( ) is the minimum function, Θ represents the total sample set, and Φ ₁ is the sample subset containing the first color representative sample.

Φ ₁ =v ₁ =min(var(Lab _i )), Lab _i ∈Θ, (10)

Second, when selecting the second color representative sample v ₂ , ensure that the Euclidean distance between v ₂ and v ₁ in the CIELab color space is maximized, and obtain a sample subset Φ ₂ containing the first and second color representative samples.

Then, starting from the selection of the third representative color sample, the remaining color representative samples are selected one by one according to the maximum and minimum criteria, and the color correction test is carried out. Assuming that the qth sample (q≥3) needs to be selected currently, it is necessary to first calculate the Euclidean distance between all the remaining unselected samples and the selected q-1 samples in the CIELab color space, and obtain each remaining unselected sample. The minimum value of the Euclidean distance from the selected sample, and then select a sample with the largest Euclidean distance from these minimum values as the qth color representative sample, which is shown in formula (11), where dist( ) is in the present invention To solve the function of Euclidean distance, Φ _q-1 is the selected color representative sample subset, and Lab _q is the qth color sample to be selected.

v _q =max(min(dist(Φ _q-1 ,Lab _q ))), Lab _q ∈Θ and

After the qth color representative sample is obtained, it is added to the selected color representative sample subset Φ _q-1 to obtain a sample subset Φ _q containing q color representative samples, as shown in formula (12).

Φ _q =Φ _q-1 ∪Lab _q , (12)

Using Φ _q as a training sample, according to the method in the literature [Hong G, Luo MR, Rhodes P AA study of digital camera colorimetric characterization based on polynomial modeling [J]. Color Research & Application, 2001, 26(1): 76-84.] , perform the color correction test on the total sample set, and calculate the color correction color difference, as shown in formula (13), where C is the color matrix of the total sample set, C _rec is the color matrix after correction of the total sample set, ΔE _q is the color difference, F‖·‖ is the function for calculating the color difference in the present invention.

ΔE _q =F||C _rec ∪C||, (13)

Finally, the process of formula (11) to formula (13) is repeated, and the remaining color representative samples are continued to be selected until the selected color representative samples converge to the color correction color difference ΔE of the total sample set, and the selection of color representative samples is completed.

Further, in step 5, the fusion and deduplication of the selected spectral representative samples and the color representative samples refers to taking the union of the two selected samples to obtain the final spectral color representative sample set.

The present invention also provides a spectral color representative sample selection system, comprising the following modules:

The total sample set spectral data acquisition module is used to obtain the total sample set spectral data for a given total sample set;

The color data acquisition module of the total sample set is used to select the color matching function, and calculate the color data of the total sample set;

The spectral representative sample selection module is used to select spectral representative samples by using the spectral reconstruction based on principal component analysis, until the spectral reconstruction error converges, and the spectral representative sample selection is completed;

The color representative sample selection module is used to select the color representative sample using the maximum and minimum criteria, and perform the color correction test until the color correction chromatic aberration converges, and the color representative sample selection is completed;

The spectral color representative sample set acquisition module is used to fuse and deduplicate the selected spectral representative samples and color representative samples to obtain a spectral color representative sample set.

Further, the color data acquisition module of the total sample set adopts the CIE D50 standard illuminator recommended by the International Commission on Illumination and the color matching function under the CIE 1931 standard observer condition to calculate the color data of the total sample set in the CIELab color space. The calculation method is as follows: Formulas (1) and (2) are shown as:

Among them, X, Y and Z are the sample tristimulus values, r(λ) is the spectral reflectance of the material surface, l(λ) is the relative spectral power distribution of the light source, x(λ), y(λ) and z(λ) is the color matching function, λ represents the wavelength of visible light in the range of 380nm-780nm, and k is the adjustment factor, which is calculated when the brightness value Y of the light source is adjusted to 100;

Among them, X, Y and Z are the sample tristimulus values, X _n , Y _n and _Zn are the reference white point tristimulus values, L, a and b are the color data of the sample in the CIELab color space, and L, a and When b, there are constraints as shown in formula (3), where item represents the tristimulus values X, Y and Z;

Further, in the spectral representative sample selection module, the specific method for selecting spectral representative samples by using the spectral reconstruction based on principal component analysis is as follows;

First, calculate the spectral modulus value of any sample in the total sample set, and select the sample with the largest modulus value as the first selected sample s ₁ , as shown in formula (4), where norm(·) is the function of calculating the modulus value , ri represents the spectral vector of the _ith sample in the total sample set, max( ) is the maximum value function, Θ represents the total sample set, Ω ₁ is the sample subset containing the first spectral representative sample;

Ω ₁ =s ₁ =max(norm(ri )), _{ri ∈Θ} , (4)

Then, use the spectral reconstruction based on principal component analysis to select the remaining spectral representative samples. Assuming that the mth sample needs to be selected at present, m≥2, then the selected m-1 spectral representative sample subset Ω _m-1 , and all unselected samples rm in the total sample set Θ are traversed and combined to obtain the spectral reconstruction training sample subset Ω _m , _which is expressed as follows:

Ω _m =Ω _m-1 ∪r _m , r _m ∈Θ, (5)

Perform principal component analysis on Ω _m to obtain the eigenvalues and eigenvectors of the training sample subset Ω _m , as shown in formula (6), where princomp( ) is the principal component analysis function, U is the orthogonal matrix eigenvector, S is the eigenvalue matrix, V is the score matrix, and T is the matrix transpose operator;

USV ^T =princomp(Ω _m ), (6)

The first j groups of feature quantities of PCA are selected to perform spectral reconstruction on the total sample set Θ, as shown in formula (7), where R is the spectral matrix of the total sample set, and R _rec is the reconstructed spectral matrix of the total sample set , + is the pseudo-inverse operator, and calculates the spectral root mean square error between the reconstructed total sample set and the original total sample set, as shown in formula (8), where E‖·‖ is used to calculate the spectral root mean square function of error RMSE;

RMSE _m = E||R _rec -R||, (8)

Taking RMSE as the evaluation index, select the sample s _m with the smallest RMSE _m as the m-th spectral representative sample, as shown in formula (9), and add it to the spectral representative sample set subset to determine the spectral representative sample subset. set Ω _m ;

s _m =min(RMSE _m ), (9)

Finally, formulas (5) to (8) are repeated to continue to select the remaining spectral representative samples, until the spectral reconstruction error RMSE of the selected spectral representative samples for the total sample set reaches a convergence level, and the selection of spectral representative samples is completed.

Further, in the color representative sample selection module, the specific method for selecting color representative samples using the maximum and minimum criteria is as follows;

First, calculate the color data variance of any sample in the total sample set, and select the sample with the smallest variance as the first selected sample v ₁ , as shown in formula (10), where var(·) represents the variance function, and Lab _i represents the total The color value vector of the ith sample in the sample set, min( ) is the minimum value function, Θ represents the total sample set, and Φ ₁ is the sample subset containing the first color representative sample;

Φ ₁ =v ₁ =min(var(Lab _i )), Lab _i ∈Θ, (10)

Secondly, when selecting the second color representative sample v ₂ , ensure that the Euclidean distance between v ₂ and v ₁ in the CIELab color space is maximized, and obtain a sample subset Φ ₂ containing the first and second color representative samples;

Then, starting from the selection of the third representative color sample, the remaining color representative samples are selected one by one according to the maximum and minimum criteria, and the color correction test is performed; assuming that the qth sample needs to be selected at present, q≥3, then first in the CIELab color space , calculate the Euclidean distance between all the remaining unselected samples and the selected q-1 samples, obtain the minimum value of the Euclidean distance between each remaining unselected sample and the selected sample, and then select the one with the largest Euclidean distance from these minimum values The sample is used as the qth color to represent the sample, which is shown in formula (11), where dist( ) is the function to solve the Euclidean distance, Φ _q-1 is the selected color to represent the sample subset, and Lab _q is the qth a color sample to be selected;

v _q =max(min(dist(Φ _q-1 ,Lab _q ))), Lab _q ∈Θ and

After obtaining the qth color representative sample, add it to the selected color representative sample subset Φ _q-1 to obtain a sample subset Φ _q containing q color representative samples, as shown in formula (12);

Φ _q =Φ _q-1 ∪Lab _q , (12)

Use Φ _q as a training sample, then perform a color correction test on the total sample set, and calculate the color correction color difference, as shown in formula (13), where C is the color matrix of the total sample set, and C _rec is the corrected color of the total sample set matrix, ΔE _q is the color difference, and F‖·‖ is the function for calculating the color difference in the present invention;

ΔE _q =F||C _rec ∪C||, (13)

Finally, the process of formula (11) to formula (13) is repeated, and the remaining color representative samples are continued to be selected until the selected color representative samples converge to the color correction color difference ΔE of the total sample set, and the selection of color representative samples is completed.

The invention proposes a sample selection and fusion based on spectrum and color representative sample selection, aiming at the problem of data redundancy and serious influence on modeling work efficiency when the existing sample set or database is applied in the digital camera spectrum and color characterization modeling application. The set optimization method provides method support for the construction of a portable color card suitable for both spectral and color characterization modeling applications of digital cameras, which effectively improves the modeling efficiency of digital cameras while ensuring the application effect and robustness.

Description of drawings

FIG. 1 is a flowchart of an embodiment of the present invention.

Fig. 2 is the spectral distribution of the total sample set in the embodiment of the present invention;

Fig. 3 is the chromaticity distribution of the total sample set in the embodiment of the present invention;

FIG. 4 is the spectrum and chromaticity distribution of the selected spectrum and color representative sample in the embodiment of the present invention: (a) represents the spectral distribution of the sample, (b) represents the chromaticity distribution of the sample.

Detailed ways

The technical solutions of the present invention can be run by those skilled in the art using computer software technology. In conjunction with the accompanying drawings, a specific description of the embodiments of the present invention is provided as follows.

As shown in FIG. 1 , the embodiment provides a method for selecting representative samples of spectral colors, which can effectively solve the problem of data redundancy in practical applications in existing sample sets or databases containing a large number of samples. The portable color card for camera spectrum and color characterization modeling applications provides support, which effectively improves the modeling efficiency while ensuring the application effect and robustness. The embodiment uses a mineral pigment sample set containing 784 color samples, a Nikon D7200 digital camera, an X-rite i1-pro spectrophotometer, and a color science toolbox optprop, on the Matlab 2016a software platform, to specifically illustrate the method of the present invention. It should be noted that the present invention is not limited to the application support of the above-mentioned devices and samples, and is also applicable to any device of the same nature that can realize the functions of the above-mentioned devices.

The embodiment mainly includes the following steps:

1) For a given total sample set, use a spectrophotometer to measure and obtain the spectral data of the total sample set.

In the embodiment, the i1-pro spectrophotometer of X-rite company in the United States is used to perform spectral measurement on the total sample set containing 784 mineral pigment samples to obtain the spectral data of the total sample set. The spectral distribution of the total sample set is shown in Figure 2. .

2) Select the color matching function, and calculate the color data of the total sample set.

In the embodiment, using the CIE D50 standard illuminator recommended by the International Commission on Illumination and the color matching function under the CIE 1931 standard observer condition, according to the methods shown in formula (1) and formula (2), the constraints shown in formula (3) are used. Under the conditions, the color data of the total sample set in the CIELab color space is calculated, and the chromaticity distribution of the total sample set is shown in Figure 3.

Among them, X, Y and Z are the sample tristimulus values, r(λ) is the spectral reflectance of the material surface, l(λ) is the relative spectral power distribution of the light source, x(λ), y(λ) and z(λ) is the color matching function, λ represents the wavelength of visible light in the range of 380nm-780nm, and k is the adjustment factor, which is calculated when the brightness value Y of the light source is adjusted to 100.

Among them, X, Y and Z are the sample tristimulus values, X _n , Y _n and _Zn are the reference white point tristimulus values, L, a and b are the color data of the sample in the CIELab color space, and L, a and When b, there are constraints as shown in formula (3), where item represents the tristimulus values X, Y and Z.

3) Select spectral representative samples by using the spectral reconstruction based on principal component analysis, until the spectral reconstruction error converges, and complete the spectral representative sample selection.

In the embodiment, based on the spectral data of the total sample set obtained by the measurement in step 1), a spectral representative sample is selected by spectral reconstruction based on principal component analysis, as follows. First, the spectral modulus value of any sample in the mineral pigment sample set is calculated, and the sample with the largest modulus value is selected as the first selected sample s ₁ , as shown in formula (4), where norm(·) is calculated in the present invention The function of the modulus value, ri represents the spectral vector of the _i -th sample in the mineral pigment sample set, max( ) is the maximum value function, Θ represents the mineral pigment sample set, Ω ₁ is the sample sub-sample containing the first spectral representative sample set.

Ω ₁ =s ₁ =max(norm(ri )), _{ri ∈Θ} , (4)

Then, the remaining spectrally representative samples are selected using principal component analysis-based spectral reconstruction. Assuming that the mth sample (m≥2) needs to be selected at present, then the selected _m -1 spectra representing the sample subset Ω _m-1 need to be compared with all the unselected sample spectra rm in the mineral pigment sample set Θ Traverse the combination to obtain the spectral reconstruction training sample subset Ω _m , which is expressed as follows:

Ω _m =Ω _m-1 ∪r _m , r _m ∈Θ, (5)

Perform principal component analysis on the spectral reconstruction training sample subset Ω _m to obtain the eigenvalues and eigenvectors of the training sample subset Ω _m , as shown in equation (6), where princomp( ) is the principal component analysis function, U is the eigenvector of an orthogonal matrix, S is the eigenvalue matrix, V is the score matrix, and T is the matrix transpose operator.

USV ^T =princomp(Ω _m ), (6)

The first 10 groups of feature quantities of the principal component analysis are selected to perform spectral reconstruction on the mineral pigment sample set Θ, as shown in formula (7), where R is the spectral matrix of the mineral pigment sample set, and R _rec is the weight of the mineral pigment sample set. construct the spectral matrix, + is the pseudo-inverse operator, and calculate the spectral root mean square error (root-mean-square error, RMSE) between the reconstructed mineral pigment sample set and the original mineral pigment sample set, as shown in formula (8) , where E‖·‖ is the function of calculating the spectral root mean square error RMSE in the present invention.

RMSE _m = E||R _rec -R‖, (8)

Taking RMSE as the evaluation index, select the sample s _m with the smallest RMSE _m as the m-th spectral representative sample, as shown in formula (9), and add it to the spectral representative sample set subset to determine the spectral representative sample subset. Set Ω _m .

s _m =min(RMSE _m ), (9)

Finally, formulas (5) to (8) are repeated to continue to select the remaining spectral representative samples, until the spectral reconstruction error RMSE of the selected spectral representative samples for the mineral pigment sample set reaches a convergence level, and the selection of spectral representative samples is completed. In this embodiment, when the number of selected spectral representative samples reaches 35, the spectral reconstruction error begins to reach a convergence level, so a total of 35 spectral representative sample sets are selected.

4) Use the maximum and minimum criteria to select a representative color sample, and perform a color correction test until the color correction chromatic aberration converges, and the selection of a representative color sample is completed.

In the embodiment, based on the mineral pigment color data calculated in step 2), a color representative sample is selected using the maximum and minimum criteria, as follows. First, calculate the color data variance of any sample in the total sample set, and select the sample with the smallest variance as the first selected sample v ₁ , as shown in formula (10), where the variance function is calculated for var(·) in the present invention, Lab _i represents the color value vector of the ith sample in the mineral pigment sample set, min( ) is the minimum function, Θ represents the mineral pigment sample set, and Φ ₁ is the sample subset containing the first color representative sample.

Φ ₁ =v ₁ =min(var(Lab _i )), Lab _i ∈Θ, (10)

Second, when selecting the second color representative sample v ₂ , ensure that the Euclidean distance between v ₂ and v ₁ in the CIELab color space is maximized, and obtain a sample subset Φ ₂ containing the first and second color representative samples.

Then, starting from the selection of the third representative color sample, the remaining color representative samples are selected one by one according to the maximum and minimum criteria, and the color correction test is carried out. Assuming that the qth sample (q≥3) needs to be selected at present, it is necessary to first calculate the Euclidean distance between all the remaining unselected samples and the selected q-1 samples in the CIELab color space, and obtain each remaining unselected sample. The minimum value of the Euclidean distance between the sample and the selected sample, and then select a sample with the largest Euclidean distance from these minimum values as the qth color representative sample, which is shown in formula (11), where dist( ) is the present invention The function to solve the Euclidean distance in Φ _q-1 is the selected color representative sample subset, and Lab _q is the qth color sample to be selected.

v _q =max(min(dist(Φ _q-1 ,Lab _q ))), Lab _q ∈Θ and

After the qth color representative sample is obtained, it is added to the selected color representative sample subset Φ _q-1 to obtain a sample subset Φ _q containing q color representative samples, as shown in formula (12).

Φ _q =Φ _q-1 ∪Lab _q , (12)

Using Φ _q as a training sample, according to the method in the literature [Hong G, Luo MR, Rhodes P AA study of digital camera colorimetric characterization based on polynomial modeling [J]. Color Research & Application, 2001, 26(1): 76-84.] , perform the color correction test on the mineral pigment sample set, and calculate the color correction chromatic aberration, as shown in formula (13), where C is the color matrix of the mineral pigment sample set, C _rec is the corrected color matrix of the mineral pigment sample set, ΔE _q is the color difference, and F‖·‖ is the function for calculating the color difference in the present invention.

ΔE _q =F||C _rec ∪C||, (13)

Finally, the process of formula (11) to formula (13) is repeated, and the remaining color representative samples are continued to be selected until the selected color representative sample reaches the convergence of the color correction chromatic aberration ΔE of the mineral pigment sample set, and the selection of color representative samples is completed. In this embodiment, when the number of selected color representative samples reaches 60, the color correction chromatic aberration begins to reach a convergence level, so a total of 60 color representative sample sets are selected.

5) Fusion and deduplication are performed on the selected spectral representative samples and color representative samples to obtain a spectral color representative sample set.

In the embodiment, by taking the sum of the selected 35 spectral representative samples and the 60 color representative samples, after removing the repeated 7 samples, a total of 88 spectral color representative samples are obtained, which is compared with the original mineral pigment sample set. 784 samples, the number is greatly reduced. The spectral distribution and chromaticity distribution of the representative sample are shown in Fig. 4(a) and Fig. 4(b) respectively. From the results in the figure, it can be seen that the spectral color selected by the method of the present invention represents the sample, which has Good distribution that effectively covers the spectral and chromatic distribution of the original mineral pigment sample set.

The embodiment of the present invention also provides a spectral color representative sample selection system, including the following modules:

The total sample set spectral data acquisition module is used to obtain the total sample set spectral data for a given total sample set;

The color data acquisition module of the total sample set is used to select the color matching function, and calculate the color data of the total sample set;

The spectral representative sample selection module is used to select spectral representative samples by using the spectral reconstruction based on principal component analysis, until the spectral reconstruction error converges, and the spectral representative sample selection is completed;

The color representative sample selection module is used to select the color representative sample using the maximum and minimum criteria, and perform the color correction test until the color correction chromatic aberration converges, and the color representative sample selection is completed;

The spectral color representative sample set acquisition module is used to fuse and deduplicate the selected spectral representative samples and color representative samples to obtain a spectral color representative sample set.

Further, the color data acquisition module of the total sample set adopts the CIE D50 standard illuminator recommended by the International Commission on Illumination and the color matching function under the CIE 1931 standard observer condition to calculate the color data of the total sample set in the CIELab color space. The calculation method is as follows: Formulas (1) and (2) are shown as:

Among them, X, Y and Z are the sample tristimulus values, r(λ) is the spectral reflectance of the material surface, l(λ) is the relative spectral power distribution of the light source, x(λ), y(λ) and z(λ) is the color matching function, λ represents the wavelength of visible light in the range of 380nm-780nm, and k is the adjustment factor, which is calculated when the brightness value Y of the light source is adjusted to 100;

Among them, X, Y and Z are the sample tristimulus values, X _n , Y _n and _Zn are the reference white point tristimulus values, L, a and b are the color data of the sample in the CIELab color space, and L, a and When b, there are constraints as shown in formula (3), where item represents the tristimulus values X, Y and Z;

Further, in the spectral representative sample selection module, the specific method for selecting spectral representative samples by using the spectral reconstruction based on principal component analysis is as follows;

First, calculate the spectral modulus value of any sample in the total sample set, and select the sample with the largest modulus value as the first selected sample s ₁ , as shown in formula (4), where norm(·) is the function of calculating the modulus value , ri represents the spectral vector of the _ith sample in the total sample set, max( ) is the maximum value function, Θ represents the total sample set, Ω ₁ is the sample subset containing the first spectral representative sample;

Ω ₁ =s ₁ =max(norm(ri )), _{ri ∈Θ} , (4)

Then, use the spectral reconstruction based on principal component analysis to select the remaining spectral representative samples. Assuming that the mth sample needs to be selected at present, m≥2, then the selected m-1 spectral representative sample subset Ω _m-1 , and all unselected samples rm in the total sample set Θ are traversed and combined to obtain the spectral reconstruction training sample subset Ω _m , _which is expressed as follows:

Ω _m =Ω _m-1 ∪r _m , r _m ∈Θ, (5)

Perform principal component analysis on Ω _m to obtain the eigenvalues and eigenvectors of the training sample subset Ω _m , as shown in formula (6), where princomp( ) is the principal component analysis function, U is the orthogonal matrix eigenvector, S is the eigenvalue matrix, V is the score matrix, and T is the matrix transpose operator;

USV ^T =princomp(Ω _m ), (6)

The first j groups of feature quantities of PCA are selected to perform spectral reconstruction on the total sample set Θ, as shown in formula (7), where R is the spectral matrix of the total sample set, and R _rec is the reconstructed spectral matrix of the total sample set , + is the pseudo-inverse operator, and calculates the spectral root mean square error between the reconstructed total sample set and the original total sample set, as shown in formula (8), where E‖·‖ is used to calculate the spectral root mean square function of error RMSE;

RMSE _m = E||R _rec -R||, (8)

Taking RMSE as the evaluation index, select the sample s _m with the smallest RMSE _m as the m-th spectral representative sample, as shown in formula (9), and add it to the spectral representative sample set subset to determine the spectral representative sample subset. set Ω _m ;

s _m =min(RMSE _m ), (9)

Finally, formulas (5) to (8) are repeated to continue to select the remaining spectral representative samples, until the spectral reconstruction error RMSE of the selected spectral representative samples for the total sample set reaches a convergence level, and the selection of spectral representative samples is completed.

Further, in the color representative sample selection module, the specific method for selecting color representative samples using the maximum and minimum criteria is as follows;

First, calculate the color data variance of any sample in the total sample set, and select the sample with the smallest variance as the first selected sample v ₁ , as shown in formula (10), where var(·) represents the variance function, and Lab _i represents the total The color value vector of the ith sample in the sample set, min( ) is the minimum value function, Θ represents the total sample set, and Φ ₁ is the sample subset containing the first color representative sample;

Φ ₁ =v ₁ =min(var(Lab _i )), Lab _i ∈Θ, (10)

Secondly, when selecting the second color representative sample v ₂ , ensure that the Euclidean distance between v ₂ and v ₁ in the CIELab color space is maximized, and obtain a sample subset Φ ₂ containing the first and second color representative samples;

Then, starting from the selection of the third representative color sample, the remaining color representative samples are selected one by one according to the maximum and minimum criteria, and the color correction test is performed; assuming that the qth sample needs to be selected at present, q≥3, then first in the CIELab color space , calculate the Euclidean distance between all the remaining unselected samples and the selected q-1 samples, obtain the minimum value of the Euclidean distance between each remaining unselected sample and the selected sample, and then select the one with the largest Euclidean distance from these minimum values The sample is used as the qth color to represent the sample, which is shown in formula (11), where dist( ) is the function to solve the Euclidean distance, Φ _q-1 is the selected color to represent the sample subset, and Lab _q is the qth color samples to be selected;

v _q =max(min(dist(Φ _q-1 ,Lab _q ))), Lab _q ∈Θ and

After obtaining the qth color representative sample, add it to the selected color representative sample subset Φ _q-1 to obtain a sample subset Φ _q containing q color representative samples, as shown in formula (12);

Φ _q =Φ _q-1 ∪Lab _q , (12)

Use Φ _q as a training sample, then perform a color correction test on the total sample set, and calculate the color correction color difference, as shown in formula (13), where C is the color matrix of the total sample set, and C _rec is the corrected color of the total sample set matrix, ΔE _q is the color difference, and F‖·‖ is the function for calculating the color difference in the present invention;

ΔE _q =F||C _rec ∪C||, (13)

Finally, the process of formula (11) to formula (13) is repeated, and the remaining color representative samples are continued to be selected until the selected color representative samples converge to the color correction color difference ΔE of the total sample set, and the selection of color representative samples is completed.

The specific implementation manner of each module corresponds to each step, and will not be described in this embodiment of the present invention.

The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which the present invention pertains can make various modifications or additions to the described specific embodiments or substitute in similar manners, but will not deviate from the spirit of the present invention or go beyond the definitions of the appended claims range.

Claims (10)

1. A method of selecting a spectral color representative sample, comprising the steps of:

step 1, aiming at a given total sample set, acquiring spectrum data of the total sample set;

step 2, selecting a color matching function, and calculating to obtain color data of a total sample set;

step 3, selecting a spectral representative sample by using spectral reconstruction based on principal component analysis until spectral reconstruction errors are converged, and finishing the selection of the spectral representative sample;

step 4, selecting a color representative sample by using a maximum and minimum criterion, and performing a color correction test until color correction chromatic aberration is converged to finish the selection of the color representative sample;

and 5, fusing and de-duplicating the selected spectral representative sample and the color representative sample to obtain a spectral color representative sample set.

2. A method of selecting a spectral color representative sample according to claim 1, wherein: in step 1, total sample light spectrum data is obtained by using a spectrophotometer for measurement.

3. A method of selecting a spectral color representative sample according to claim 1, wherein: in the step 2, color data of the total sample set in a CIELab color space is calculated by adopting a CIE D50 standard illuminant recommended by the International Commission on illumination and a color matching function under the condition of a CIE 1931 standard observer, and the calculation method is shown as the following formula (1) and formula (2):

Wherein X, Y and Z are the tristimulus values of the sample, r (lambda) is the spectral reflectivity of the surface of the substance, l (lambda) is the relative spectral power distribution of the light source, x (lambda), Y (lambda) and Z (lambda) are color matching functions, lambda represents the visible light wavelength in the range of 380nm-780nm, and k is an adjustment factor calculated when the brightness value Y of the light source is adjusted to 100;

wherein X, Y and Z are the sample tristimulus values, X_n、Y_nAnd Z_nFor reference white point tristimulus values, L, a and b are color data of the sample in CIELab color space, and a constraint condition as shown in formula (3) exists when calculating L, a and b, wherein item represents tristimulus values X, Y and Z;

4. a method of selecting a spectral color representative sample according to claim 1, wherein: the specific method for selecting the spectral representative sample by using the spectral reconstruction based on the principal component analysis in the step 3 is as follows;

firstly, calculating the spectral modulus of any sample in the total sample set, and selectingSelecting the sample with the largest modulus value as the first selected sample s₁As shown in equation (4), where norm (. cndot.) is a function of the calculated modulus, r_iThe spectral vector representing the ith sample in the total sample set, max (-) is the function of solving the maximum value, theta represents the total sample set, omega₁A sample subset including a first spectral representation sample;

Ω₁＝s₁＝max(norm(r_i)),r_i∈Θ， (4)

Then, the remaining spectral representative samples are selected using principal component analysis based spectral reconstruction, and assuming that the m-th sample, m ≧ 2, is currently selected, then the selected m-1 spectra represent the subset Ω of samples_m-1And all the unselected samples r in the total sample set Θ_mTraversing combination is carried out to obtain a spectrum reconstruction training sample subset omega_mExpressed as follows:

Ω_m＝Ω_m-1∪r_m,r_m∈Θ， (5)

for omega_mPerforming principal component analysis to obtain a training sample subset omega_mThe eigenvalue and eigenvector of (a) are shown in formula (6), wherein princomp (·) is a principal component analysis function, U is an orthogonal matrix eigenvector, S is an eigenvalue matrix, V is a score matrix, and T is a matrix transposition operator;

USV^T＝princomp(Ω_m)， (6)

selecting the first j groups of characteristic quantities of the principal component analysis to carry out spectrum reconstruction on the total sample set theta, wherein R is a spectrum matrix of the total sample set theta and R is shown as a formula (7)_rec(ii) a reconstructed spectral matrix for the total sample set, + a pseudo-inverse operator, and calculating a spectral root mean square error between the reconstructed total sample set and the original total sample set, as shown in equation (8), where E | is a function used to calculate the spectral root mean square error RMSE;

RMSE_m＝E||R_rec-R||， (8)

RMSE is selected as an evaluation index_mSmallest sample s_mAnd (3) as the mth spectral representative sample, as shown in formula (9), adding the mth spectral representative sample into the spectral representative sample subset, and determining the spectral representative sample subset omega _m；

s_m＝min(RMSE_m)， (9)

And finally, repeating the formulas (5) to (8) to continuously select the rest spectrum representative samples until the spectrum representative samples reach a convergence level for the spectrum reconstruction error RMSE of the total sample set, and finishing the selection of the spectrum representative samples.

5. A method of selecting a spectral color representative sample according to claim 1, wherein: the specific method for selecting the color representative sample by using the maximum and minimum criteria in the step 4 is as follows;

firstly, the color data variance of any sample in the total sample set is calculated, and the sample with the minimum variance is selected as a first selected sample v₁As shown in equation (10), where var (·) represents a variance function, Lab_iThe color value vector of the ith sample in the total sample set is represented, min (-) is a function for solving the minimum value, theta represents the total sample set, phi₁A subset of samples containing a first color representative sample;

Φ₁＝v₁＝min(var(Lab_i)),Lab_i∈Θ， (10)

second, a second color representative sample v is selected₂When v is ensured₂And v₁Euclidean distance maximization in CIELab color space, and obtaining a sample subset phi containing first and second color representative samples₂；

Then, starting from the selection of a third representative color sample, selecting the remaining representative color samples one by one according to the maximum and minimum criteria, and performing a color correction test; assuming that the q sample is currently selected, q ≧ 3, then first in the CIELab color space Calculating Euclidean distances between all the remaining unselected samples and the selected q-1 samples, obtaining the minimum Euclidean distance value of each remaining unselected sample and the selected sample, and then selecting a sample with the maximum Euclidean distance from the minimum values as the q-th color representative sample, wherein the representation is shown as formula (11), Dist (DEG) is a function for solving the Euclidean distance, and phi is_q-1Lab for a selected color representative sample subset_qThe sample is the qth color sample to be selected;

after the qth color representative sample is obtained, it is added to the subset of selected color representative samples Φ_q-1Obtaining a sample subset phi containing q color representative samples_qAs shown in formula (12);

Φ_q＝Φ_q-1∪Lab_q， (12)

using phi_qAs a training sample, then, performing a color correction test on the total sample set, and calculating a color correction color difference, as shown in formula (13), where C is a total sample set color matrix, C is a color correction color difference matrix_recCorrecting the post-color matrix, Δ E, for the total sample set_qFor color differences, F | · |, is a function of calculating the color difference;

ΔE_q＝F||C_rec∪C||， (13)

finally, repeating the processes from (11) to (13), and continuing to select the rest color representative samples until the color correction color difference Δ E of the selected color representative sample for the total sample set reaches convergence, thereby completing the selection of the color representative sample.

6. A method of selecting a spectral color representative sample according to claim 1, wherein: and 5, performing fusion de-duplication on the selected spectral representative sample and the color representative sample, namely performing union collection on the two selected samples to obtain a final spectral color representative sample set.

7. A spectral color representative sample selection system, comprising the modules of:

a total sample spectrum data acquisition module for acquiring total sample spectrum data for a given total sample set;

the total sample set color data acquisition module is used for selecting a color matching function and calculating to obtain total sample set color data;

the spectrum representative sample selection module is used for selecting a spectrum representative sample by utilizing spectrum reconstruction based on principal component analysis until spectrum reconstruction errors are converged to finish spectrum representative sample selection;

the color representative sample selection module is used for selecting a color representative sample by utilizing a maximum and minimum criterion, and performing color correction test until color correction chromatic aberration is converged to finish color representative sample selection;

and the spectral color representative sample set acquisition module is used for fusing and de-duplicating the selected spectral representative sample and the color representative sample to obtain a spectral color representative sample set.

8. A spectral color representative sample selection system according to claim 7, wherein: the color data of the total sample set in a CIELab color space is calculated by adopting a color matching function under the conditions of a CIE D50 standard illuminant and a CIE 1931 standard observer recommended by the International Commission on illumination in the color data acquisition module of the total sample set, and the calculation method is shown as formula (1) and formula (2):

wherein X, Y and Z are the tristimulus values of the sample, r (λ) is the spectral reflectance of the material surface, l (λ) is the relative spectral power distribution of the light source, x (λ), Y (λ) and Z (λ) are color matching functions, λ represents the visible light wavelength in the range of 380nm-780nm, k is an adjustment factor, and k is calculated when the luminance value Y of the light source is adjusted to 100;

wherein X, Y and Z are sample tristimulus values, X_n、Y_nAnd Z_nFor reference white point tristimulus values, L, a and b are color data of samples in CIELab color space, and there is a constraint condition as shown in formula (3) when calculating L, a and b, where item represents tristimulus values X, Y and Z;

9. a spectral color representative sample selection system according to claim 7, wherein: the specific method for selecting the spectral representative sample by utilizing spectral reconstruction based on principal component analysis in the spectral representative sample selection module is as follows;

Firstly, calculating the spectral modulus of any sample in the total sample set, and selecting the sample with the maximum modulus as the first selected sample s₁As shown in equation (4), where norm (. cndot.) is a function of the calculated modulus, r_iThe spectral vector representing the ith sample in the total sample set, max (·) is the function of maximizing, Θ represents the total sample set, Ω₁For samples containing a first spectral representationA subset;

Ω₁＝s₁＝max(norm(r_i)),r_i∈Θ， (4)

then, the remaining spectral representative samples are selected by using spectral reconstruction based on principal component analysis, and assuming that the mth sample needs to be selected currently, and m is larger than or equal to 2, then the selected m-1 spectra represent the sample subset omega_m-1And all the unselected samples r in the total sample set Θ_mTraversing and combining to obtain a spectrum reconstruction training sample subset omega_mExpressed as follows:

Ω_m＝Ω_m-1∪r_m,r_m∈Θ， (5)

for omega_mPerforming principal component analysis to obtain a training sample subset omega_mThe eigenvalue and eigenvector of (a) are shown in formula (6), wherein princomp (·) is a principal component analysis function, U is an orthogonal matrix eigenvector, S is an eigenvalue matrix, V is a score matrix, and T is a matrix transposition operator;

USV^T＝princomp(Ω_m)， (6)

selecting the first j groups of characteristic quantities of the principal component analysis to carry out spectrum reconstruction on the total sample set theta, wherein R is a spectrum matrix of the total sample set theta and R is shown as a formula (7) _rec(iv) is the reconstructed spectral matrix of the total sample set, + is the pseudo-inverse operator, and calculates the spectral root mean square error between the reconstructed total sample set and the original total sample set, as shown in equation (8), where E | is a function used to calculate the spectral root mean square error RMSE;

RMSE_m＝E||R_rec-R||， (8)

selecting RMSE as an evaluation index_mSmallest sample s_mThe m spectrum representative sample is shown as the formula (9), and is added into the spectrum representative sample set subset to determine the spectrum representative sampleRepresentative sample subset Ω_m；

s_m＝min(RMSE_m)， (9)

And finally, repeating the formulas (5) to (8) to continuously select the rest spectrum representative samples until the spectrum reconstruction error RMSE of the selected spectrum representative sample to the total sample set reaches a convergence level, and finishing the selection of the spectrum representative sample.

10. A spectral color representative sample selection system according to claim 7, wherein: the specific method for selecting the color representative sample by using the maximum and minimum criteria in the color representative sample selection module is as follows;

firstly, the color data variance of any sample in the total sample set is calculated, and the sample with the minimum variance is selected as a first selected sample v₁As shown in equation (10), where var (. cndot.) represents the variance function, Lab_iThe color value vector of the ith sample in the total sample set is represented, min (-) is a minimum function, theta represents the total sample set, phi ₁A subset of samples containing a first color representative sample;

Φ₁＝v₁＝min(var(Lab_i)),Lab_i∈Θ， (10)

second, a second color representative sample v is selected₂While ensuring v₂And v₁Euclidean distance maximization in CIELab color space, and obtaining a sample subset phi containing first and second color representative samples₂；

Then, starting from the selection of a third representative color sample, selecting the remaining representative color samples one by one according to the maximum and minimum criteria, and performing a color correction test; assuming that the q sample needs to be selected currently, and q is larger than or equal to 3, firstly, in a CIELab color space, calculating Euclidean distances between all the remaining unselected samples and the selected q-1 samples, obtaining minimum Euclidean distances between each remaining unselected sample and the selected sample, and then selecting one sample with the maximum Euclidean distance from the minimum values as the q color representative sample, which is represented as formula (11), wherein dis ist (-) is a function for solving the Euclidean distance, phi_q-1Lab for a selected color representative sample subset_qThe sample is the q color sample to be selected;

after the qth color representative sample is obtained, it is added to the subset of selected color representative samples Φ_q-1Obtaining a sample subset phi containing q color representative samples_qAs shown in formula (12);

Φ_q＝Φ_q-1∪Lab_q， (12)

Using phi_qAs a training sample, then, performing a color correction test on the total sample set, and calculating a color correction color difference, as shown in formula (13), where C is a total sample set color matrix, C is a color correction color difference matrix_recCorrecting the post-color matrix, Δ E, for the total sample set_qFor color differences, F | · |, is a function of calculating the color difference;

ΔE_q＝F||C_rec∪C||， (13)

finally, repeating the processes from (11) to (13), and continuing to select the rest color representative samples until the color correction color difference Δ E of the selected color representative sample for the total sample set reaches convergence, thereby completing the selection of the color representative sample.

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