CN113095368B - Spectral color representative sample selection method and system - Google Patents

Spectral color representative sample selection method and system Download PDF

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CN113095368B
CN113095368B CN202110281047.XA CN202110281047A CN113095368B CN 113095368 B CN113095368 B CN 113095368B CN 202110281047 A CN202110281047 A CN 202110281047A CN 113095368 B CN113095368 B CN 113095368B
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梁金星
辛磊
刘安平
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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

Spectral color representative sample selection method and system
Technical Field
The invention belongs to the technical field of color imaging and information processing, and particularly relates to a spectral color representative sample selection method and system.
Background
With the development and progress of color imaging technology, digital cameras are increasingly widely used for scientific analysis in various fields, such as color reproduction, cultural relic preservation, medical diagnosis, computer vision, remote sensing and other related fields, due to the advantages of rapid imaging, high spatial resolution, portability, flexibility and the like. The digital image of the surface of the object is shot and obtained by using a digital camera, then the high-precision multispectral image and the chrominance image of the surface of the object are reconstructed based on a spectral reconstruction theory and a color characterization correction theory, high-fidelity color copying, pigment in-situ nondestructive analysis, auxiliary medical diagnosis, object identification, agricultural pest detection, target classification and other scientific applications can be developed, and new technical and method supports are provided for the applications in all the fields.
In the above scientific application of the digital camera, no matter high-precision spectral reconstruction or color correction is performed, a set of representative training samples is required to be adopted to perform spectral and color characterization modeling on the digital camera, and then the spectral and color images of the object surface are calculated by using the constructed spectral and color characterization model. At the present stage, the spectral and color characterization modeling of the digital camera mostly adopts a standard color chart, and researches show that the spectral and color similarity between a training sample and a test object directly influences the accuracy of spectral and color calculation. For different types of objects, the standard color chart is used as a training sample, so that the spectrum and color representativeness of the standard color chart on a target object cannot be guaranteed, and the optimal calculation accuracy cannot be obtained.
At present, a large number of sample sets or open databases are accumulated in the fields of cultural heritage protection, computer vision, color science, textile production and other related application, and sufficient training sample support is provided for the specific application of a digital camera in the fields. However, these sample sets or data all contain hundreds of samples, and in practical applications, if these sample sets or databases are directly used as training samples, huge workload will be brought to practical applications, and efficiency of spectral and color characterization modeling will be seriously reduced. Research shows that when the modeling is oriented to the spectral and color characterization of the digital camera, a great deal of information redundancy exists in the existing sample sets or databases, and all samples are not necessarily adopted as training samples. Therefore, for the application of the spectral and color characterization modeling of the digital camera, how to select a representative sample which can be simultaneously suitable for the spectral and color characterization modeling of the digital camera from a sample set or a database and construct a portable application color chart is a key problem in the field at present, so that the spectral and color characterization modeling efficiency is effectively improved while the application effect and the robustness are ensured.
Disclosure of Invention
The invention aims to solve the problems in the background art and provides a spectral color representative sample selection method.
Aiming at the problem of data redundancy existing when the existing sample set or database is used as a training sample, the invention provides a spectral color representative sample selection method, which can select a small number of representative samples from hundreds of total sample sets to construct a portable application color card, can be simultaneously suitable for the spectral and color characterization modeling of a digital camera, can ensure the equivalence and robustness of the portable color card on the total sample set in practical application, and effectively improve the working efficiency of spectral reconstruction or color correction. The technical scheme of the invention is a spectral color representative sample selection method, which specifically comprises the following steps:
step 1, aiming at a given total sample set, measuring by using a spectrophotometer to obtain total sample collection spectrum data;
step 2, selecting a color matching function, and calculating to obtain color data of a total sample set;
3, 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;
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.
Further, in step 2, color data of the total sample set in the CIELab color space is calculated by using color matching functions under the conditions of CIE D50 standard illuminant and CIE 1931 standard observer, which are recommended by the international commission on illumination, and the calculation method is shown as formula (1) and formula (2):
Figure BDA0002978406650000021
wherein X, Y and Z are the tristimulus values of the sample, r (λ) is the spectral reflectance of the surface of the substance, 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 wavelength of visible light in the range of 380nm-780nm, and k is an adjustment factor calculated when the luminance value Y of the light source is adjusted to 100.
Figure BDA0002978406650000031
Wherein X, Y and Z are the sample tristimulus values, Xn、YnAnd ZnFor reference to white point tristimulus values, L, a and b are the color data of the sample in CIELab color space, and a constraint condition as shown in equation (3) exists in calculating L, a and b, where item represents tristimulus values X, Y and Z.
Figure BDA0002978406650000032
Further, in step 3, a specific method for selecting the spectral representative sample by using the spectral reconstruction based on the principal component analysis 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 formula (4), where norm (. cndot.) is a function of the calculated modulus of the present invention, riThe 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 subset of samples containing a first spectral representation sample is identified.
Ω1＝s1＝max(norm(ri)),ri∈Θ， (4)
The remaining spectrally representative samples are then selected using principal component analysis-based spectral reconstruction. Assuming that the mth sample (m ≧ 2) needs to be selected currently, then the need will have already beenThe selected m-1 spectra represent the sample subset omegam-1And all the unselected samples r in the total sample set thetamTraversing combination is carried out to obtain a spectrum reconstruction training sample subset omegamExpressed as follows:
Ωm＝Ωm-1∪rm,rm∈Θ， (5)
for omegamPerforming principal component analysis to obtain a training sample subset omegamThe eigenvalue and eigenvector of (a) are shown in formula (6), where 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 transpose operator.
USVT＝princomp(Ωm)， (6)
Selecting the first j groups of characteristic quantities of principal component analysis to carry out spectrum reconstruction on the total sample set theta as shown in a formula (7), wherein R is a spectrum matrix of the total sample set theta, and R isrecIs 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 a function of the calculated spectral root mean square error RMSE in the present invention.
Figure BDA0002978406650000041
RMSEm＝E||Rrec-R||， (8)
Selecting RMSE as an evaluation indexmSmallest sample smAnd (4) as the mth spectrum representative sample, as shown in the formula (9), adding the mth spectrum representative sample into the spectrum representative sample subset, and determining the spectrum representative sample subset omegam。
sm＝min(RMSEm)， (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.
Further, in step 4, a specific method for selecting the color representative sample by using the maximum and minimum criteria 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 v 1In which a variance function, Lab, is calculated for var (-) in the present invention, as shown in equation (10)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, phi1A subset of samples containing a first color representative sample.
Φ1＝v1＝min(var(Labi)),Labi∈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 with the selection of the third representative color sample, the remaining color representative samples are selected one by one according to the maximum-minimum criterion and subjected to a color correction test. Assuming that the q sample (q ≧ 3) needs to be selected currently, it is necessary to first calculate the euclidean distances between all remaining unselected samples and the selected q-1 samples in the CIELab color space, obtain the minimum euclidean distance between each remaining unselected sample and the selected sample, and then select one sample with the largest euclidean distance from these minimum values as the q color representative sample, as shown in formula (11), where dist (·) is a function for solving the euclidean distance in the present invention, and Φ (phi) ·q-1Lab for a selected color representative sample subset qIs the qth color sample to be selected.
vq＝max(min(dist(Φq-1,Labq))),LabqEpsilon theta and
Figure BDA0002978406650000042
after the qth color representative sample is obtained, it is added to the subset of selected color representative samples Φq-1Obtaining a sample subset Φ containing q color representative samplesqAs shown in formula (12).
Φq＝Φq-1∪Labq， (12)
By using phiqAs training samples, according to the literature [ Hong G, Luo M R, Rhodes P A.A student of digital camera chromatography based on a polymeric model [ J ]].Color Research&Application,2001,26(1):76-84 ], performing a color correction test on the total sample set, and calculating a color correction color difference as shown in equation (13), wherein C is a color matrix of the total sample set, and C isrecCorrecting the post-color matrix, Δ E, for the total sample setqFor the color difference, F | is a function of the calculation of the color difference in the present invention.
ΔEq＝F||Crec∪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.
Further, in step 5, the selected spectral representative sample and color representative sample are fused and de-duplicated, which means that a union set of the selected two samples is taken to obtain a final spectral color representative sample set.
The invention also provides a spectral color representative sample selection system, which comprises the following modules:
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 the selection of the color representative sample;
and the spectral color representative sample set acquisition module is used for carrying out fusion de-duplication on the selected spectral representative sample and the color representative sample to obtain a spectral color representative sample set.
Further, the color data of the total sample set in the CIELab color space is calculated by using 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):
Figure BDA0002978406650000051
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;
Figure BDA0002978406650000061
wherein X, Y and Z are sample tristimulus values, Xn、YnAnd ZnFor 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;
Figure BDA0002978406650000062
further, a specific method for selecting the spectral representative sample by using the 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, riThe 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(ri)),ri∈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 omegam-1And all the unselected samples r in the total sample set ΘmTraversing and combining to obtain a spectrum reconstruction training sample subset omegamExpressed as follows:
Ωm＝Ωm-1∪rm,rm∈Θ， (5)
to omegamPerforming principal component analysis to obtain a training sample subset omegamThe 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;
USVT＝princomp(Ωm)， (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;
Figure BDA0002978406650000071
RMSEm＝E||Rrec-R||， (8)
RMSE is selected as an evaluation indexmSmallest sample smAnd (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；
sm＝min(RMSEm)， (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.
Further, a 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 (·) represents a variance function, LabiThe 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(Labi)),Labi∈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 is selected currently, and q is equal to or more than 3, first, in CIELab color space, calculation is performed Obtaining 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 a q-th color representative sample, wherein the q-th color representative sample is represented as formula (11), dist (·) is a function for solving the Euclidean distances, and phi isq-1Lab for a selected color representative sample subsetqThe sample is the q color sample to be selected;
vq＝max(min(dist(Φq-1,Labq))),Labqe to theta and
Figure BDA0002978406650000072
after the qth color representative sample is obtained, it is added to the subset of selected color representative samples Φq-1Obtaining a sample subset phi containing q color representative samplesqAs shown in formula (12);
Φq＝Φq-1∪Labq， (12)
using phiqAs 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 matrixrecCorrecting the post-color matrix, Δ E, for the total sample setqFor color differences, F | is a function of the calculation of the color differences in the present invention;
ΔEq＝F||Crec∪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.
The invention provides a sample set optimization method based on spectrum and color representative sample selection and fusion, which aims at solving the problems of data redundancy and serious influence on the modeling working efficiency when the existing sample set or database is applied to the digital camera spectrum and color characteristic modeling, provides method support for constructing a portable color card which is simultaneously suitable for the digital camera spectrum and color characteristic modeling application, and effectively improves the digital camera modeling efficiency while ensuring the application effect and robustness.
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FIG. 1 is a flow chart of an embodiment of the present invention.
FIG. 2 is a graph of the spectral distribution of the total sample set in an embodiment of the present invention;
FIG. 3 is a chromaticity distribution of a total sample set in an embodiment of the present invention;
FIG. 4 is a spectrum and chromaticity distribution of a selected spectral and color representative sample in an embodiment of the present invention: (a) a spectral distribution representative of the sample, and (b) a chromatic distribution representative of the sample.
Detailed Description
The technical solution of the present invention can be implemented by a person skilled in the art using computer software technology. The following provides a detailed description of embodiments of the invention, taken in conjunction with the accompanying drawings.
As shown in fig. 1, the embodiment provides a spectral color representative sample selection method, which can effectively solve the problem of data redundancy in practical application of the existing sample set or database containing a large number of samples, construct a portable color chart suitable for modeling application of digital camera spectrum and color characterization at the same time, provide support, and effectively improve modeling efficiency while ensuring application effect and robustness. Example the method of the invention is specifically illustrated on a Matlab 2016a software platform using a mineral pigment sample set comprising 784 color samples, a nikon D7200 digital camera, an X-rite i1-pro spectrophotometer, and a color science kit, optprop. It should be noted that the present invention is not limited to the application support of the above-described devices and samples, but is equally applicable to any device of equivalent nature that can perform the functions of the above-described devices.
The embodiment mainly comprises the following steps:
1) for a given total sample set, total sample collection spectral data is obtained using spectrophotometer measurements.
In the examples, a total sample set containing 784 mineral pigment samples was subjected to spectroscopic measurement using an i1-pro spectrophotometer by X-rite, usa, and the total sample set spectrum data was obtained, and the spectral distribution of the total sample set was as shown in fig. 2.
2) And selecting a color matching function, and calculating to obtain the color data of the total sample set.
In the examples, color data of the total sample set in the CIELab color space is calculated according to the methods shown in formula (1) and formula (2) and under the constraint conditions shown in formula (3) by using the CIE D50 standard illuminant and the color matching function under the CIE 1931 standard observer conditions recommended by the commission internationale de l' eclairage, and the chromaticity distribution of the total sample set is shown in fig. 3.
Figure BDA0002978406650000091
Wherein X, Y and Z are the tristimulus values of the sample, r (λ) is the spectral reflectance of the surface of the substance, 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 wavelength of visible light in the range of 380nm-780nm, and k is an adjustment factor calculated when the luminance value Y of the light source is adjusted to 100.
Figure BDA0002978406650000092
Wherein X, Y and Z are sample tristimulus values, X n、YnAnd ZnFor reference to white point tristimulus values, L, a and b are the color data of the sample in CIELab color space, and a constraint condition as shown in equation (3) exists in calculating L, a and b, where item represents tristimulus values X, Y and Z.
Figure BDA0002978406650000093
3) And selecting the 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.
In the examples, the total sample set spectral data obtained by the measurement in step 1) is used as the basisSpectral representative samples are selected using principal component analysis-based spectral reconstruction, as follows. Firstly, calculating the spectral modulus of any sample in the mineral pigment sample set, and selecting the sample with the maximum modulus as the first selected sample s1As shown in formula (4), where norm (. cndot.) is a function of the calculated modulus of the present invention, riThe spectral vector representing the ith sample in the mineral pigment sample set, max (. cndot.) is the function of the maximum value, and Θ represents the mineral pigment sample set, Ω1A subset of samples containing a first spectral representation sample.
Ω1＝s1＝max(norm(ri)),ri∈Θ， (4)
The remaining spectrally representative samples are then selected using principal component analysis-based spectral reconstruction. Assuming that the mth sample (m ≧ 2) needs to be selected currently, then the selected m-1 spectra need to be represented as the sample subset Ω m-1And all the spectra r of the non-selected samples in the set of mineral pigment samples ΘmTraversing combination is carried out to obtain a spectrum reconstruction training sample subset omegamExpressed as follows:
Ωm＝Ωm-1∪rm,rm∈Θ， (5)
training sample subset omega for spectrum reconstructionmPerforming principal component analysis to obtain a training sample subset omegamThe eigenvalue and eigenvector of (a) are shown in formula (6), where 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 transpose operator.
USVT＝princomp(Ωm)， (6)
Selecting the first 10 groups of characteristic quantities of the principal component analysis to carry out spectral reconstruction on the mineral pigment sample set theta, wherein R is a mineral pigment sample set spectral matrix and R is shown as a formula (7)recIs a reconstructed spectral matrix of the mineral pigment sample set, + is a pseudo-inverse operator, and calculates a spectral Root Mean Square Error (RMSE) between the reconstructed mineral pigment sample set and the original mineral pigment sample set,as shown in equation (8), where E | is a function of the calculated spectral root mean square error RMSE in the present invention.
Figure BDA0002978406650000101
RMSEm＝E||Rrec-R‖， (8)
RMSE is selected as an evaluation indexmSmallest sample smAnd (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。
sm＝min(RMSEm)， (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 mineral pigment sample set, and finishing the selection of the spectrum representative samples. In this embodiment, when the number of the selected spectral representative samples reaches 35, the spectral reconstruction error starts to reach the convergence level, so that 35 sets of spectral representative samples are selected in total.
4) And 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.
In the examples, a representative sample of the color was selected using the maximum and minimum criteria based on the color data of the mineral pigment calculated in step 2), 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 the variance function, Lab, is calculated for var (-) in the present inventioniA vector of color values representing the ith sample in the set of mineral pigment samples, min (-) is a function of the minimum, Θ represents the set of mineral pigment samples, Φ1A subset of samples containing a first color representative sample.
Φ1＝v1＝min(var(Labi)),Labi∈Θ， (10)
Second, a second color representative sample v is selected2While ensuring v2And v1Euclidean distance maximization in CIELab color space, resulting in a subset of samples Φ comprising first and second color representative samples2。
Then, starting with the selection of the third representative color sample, the remaining color representative samples are selected one by one according to the maximum-minimum criterion and subjected to a color correction test. Assuming that the q sample (q ≧ 3) needs to be selected currently, it is necessary to first calculate the euclidean distances between all the remaining unselected samples and the selected q-1 samples in the CIELab color space, obtain the minimum euclidean distance between each remaining unselected sample and the selected sample, and then select one sample with the largest euclidean distance from these minimum euclidean distances as the q color representative sample, as shown in formula (11), where dist (·) is a function for solving the euclidean distance in the present invention, and Φ (Φ) is a function for solving the euclidean distancesq-1Lab for a selected color representative sample subsetqIs the qth color sample to be selected.
vq＝max(min(dist(Φq-1,Labq))),LabqEpsilon theta and
Figure BDA0002978406650000111
after the qth color representative sample is obtained, it is added to the subset of selected color representative samples Φq-1Obtaining a sample subset phi containing q color representative samplesqAs shown in formula (12).
Φq＝Φq-1∪Labq， (12)
Using phiqAs training samples, according to the literature [ Hong G, Luo M R, Rhodes P A.A student of digital camera chromatography based on a polymeric model [ J ] ].Color Research&Application,2001,26(1):76-84 ] method of performing a color correction test on a sample set of mineral pigments and calculating a color correction color difference, as shown in equation (13), wherein C is the mineral colorSample set color matrix of material, CrecCorrected color matrix, Δ E, for a sample set of mineral pigmentsqFor the color difference, F | is a function of the calculation of the color difference in the present invention.
ΔEq＝F||Crec∪C||， (13)
Finally, repeating the processes from (11) to (13), and continuing to select the rest color representative samples until the color correction chromatic aberration delta E of the selected color representative sample for the mineral pigment sample set converges, thereby completing the selection of the color representative sample. In the present embodiment, when the number of the selected color representative samples reaches 60, the color correction chromatic aberration starts to reach the convergence level, and thus 60 color representative sample sets are selected in total.
5) And fusing and de-duplicating the selected spectral representative sample and the color representative sample to obtain a spectral color representative sample set.
In the example, by taking and collecting the selected 35 spectral color representative samples and 60 color representative samples, and removing 7 samples which are repeated, 88 spectral color representative samples are obtained, and the number is greatly reduced compared with the original 784 samples of the mineral pigment sample set. The spectral distribution and the chromaticity distribution of the representative sample are respectively shown in fig. 4(a) and 4(b), and the results in the graphs show that the spectral color representative sample selected by the method has good distribution in spectral and chromaticity space regions, and can effectively cover the spectral and chromaticity distribution of the original mineral pigment sample set.
The embodiment of the invention also provides a system for selecting the representative sample of the spectral color, which comprises the following modules:
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.
Further, the color data of the total sample set in the 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):
Figure BDA0002978406650000121
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;
Figure BDA0002978406650000131
wherein X, Y and Z are sample tristimulus values, Xn、YnAnd ZnFor 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;
Figure BDA0002978406650000132
further, a specific method for selecting the spectral representative sample by using the 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, riThe 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(ri)),ri∈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 omegam-1And all the unselected samples r in the total sample set ΘmTraversing and combining to obtain a spectrum reconstruction training sample subset omegamExpressed as follows:
Ωm＝Ωm-1∪rm,rm∈Θ， (5)
to omegamPerforming principal component analysis to obtain a training sample subset omegamThe 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;
USVT＝princomp(Ωm)， (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;
Figure BDA0002978406650000141
RMSEm＝E||Rrec-R||， (8)
RMSE is selected as an evaluation indexmSmallest sample smAnd (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；
sm＝min(RMSEm)， (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.
Further, a 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 (·) represents a variance function, LabiThe 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(Labi)),Labi∈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 the third representative color sample, the remaining representative color samples are selected one by one according to the maximum and minimum criteria, and color processing is performedPerforming correction test; assuming that the q sample needs to be selected currently, and q is greater than or equal to 3, firstly, in a CIELab color space, calculating Euclidean distances between all 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, wherein Dist (DEG) is a function for solving the Euclidean distance, and phi is phi, and is expressed as formula (11) q-1Lab for a selected color representative sample subsetqThe sample is the qth color sample to be selected;
vq＝max(min(dist(Φq-1,Labq))),Labqepsilon theta and
Figure BDA0002978406650000142
after the qth color representative sample is obtained, it is added to the subset of selected color representative samples Φq-1Obtaining a sample subset Φ containing q color representative samplesqAs shown in formula (12);
Φq＝Φq-1∪Labq， (12)
by using phiqAs 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 matrixrecCorrecting the post-color matrix, Δ E, for the total sample setqFor color differences, F | is a function of the calculation of the color differences in the present invention;
ΔEq＝F||Crec∪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.
The specific implementation manner and the steps of each module correspond, and the embodiment of the invention is not described.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.

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):
Figure FDA0002978406640000011
Figure FDA0002978406640000012
Figure FDA0002978406640000013
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;
Figure FDA0002978406640000021
Figure FDA0002978406640000022
wherein X, Y and Z are the sample tristimulus values, Xn、YnAnd ZnFor 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;
Figure FDA0002978406640000023
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, riThe 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(ri)),ri∈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 samplesm-1And all the unselected samples r in the total sample set ΘmTraversing combination is carried out to obtain a spectrum reconstruction training sample subset omegamExpressed as follows:
Ωm＝Ωm-1∪rm,rm∈Θ， (5)
for omegamPerforming principal component analysis to obtain a training sample subset omegamThe 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;
USVT＝princomp(Ωm)， (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;
Figure FDA0002978406640000031
RMSEm＝E||Rrec-R||， (8)
RMSE is selected as an evaluation indexmSmallest sample smAnd (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；
sm＝min(RMSEm)， (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, LabiThe 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(Labi)),Labi∈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 isq-1Lab for a selected color representative sample subsetqThe sample is the qth color sample to be selected;
Figure FDA0002978406640000032
after the qth color representative sample is obtained, it is added to the subset of selected color representative samples Φq-1Obtaining a sample subset phi containing q color representative samplesqAs shown in formula (12);
Φq＝Φq-1∪Labq， (12)
using phiqAs 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 matrixrecCorrecting the post-color matrix, Δ E, for the total sample setqFor color differences, F | · |, is a function of calculating the color difference;
ΔEq＝F||Crec∪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):
Figure FDA0002978406640000041
Figure FDA0002978406640000042
Figure FDA0002978406640000043
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;
Figure FDA0002978406640000051
Figure FDA0002978406640000052
wherein X, Y and Z are sample tristimulus values, Xn、YnAnd ZnFor 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;
Figure FDA0002978406640000053
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, riThe 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(ri)),ri∈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 omegam-1And all the unselected samples r in the total sample set ΘmTraversing and combining to obtain a spectrum reconstruction training sample subset omegamExpressed as follows:
Ωm＝Ωm-1∪rm,rm∈Θ， (5)
for omegamPerforming principal component analysis to obtain a training sample subset omegamThe 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;
USVT＝princomp(Ωm)， (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;
Figure FDA0002978406640000061
RMSEm＝E||Rrec-R||， (8)
selecting RMSE as an evaluation indexmSmallest sample smThe 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 Ωm；
sm＝min(RMSEm)， (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, LabiThe 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(Labi)),Labi∈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, phiq-1Lab for a selected color representative sample subsetqThe sample is the q color sample to be selected;
Figure FDA0002978406640000062
after the qth color representative sample is obtained, it is added to the subset of selected color representative samples Φq-1Obtaining a sample subset phi containing q color representative samplesqAs shown in formula (12);
Φq＝Φq-1∪Labq， (12)
Using phiqAs 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 matrixrecCorrecting the post-color matrix, Δ E, for the total sample setqFor color differences, F | · |, is a function of calculating the color difference;
ΔEq＝F||Crec∪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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