The properties of the same pigments in murals are affected by different concentrations and particle diameters, which cause the shape of the spectral reflectance data curve to vary, thus influencing the outcome of matching calculations. This paper proposes a spectral matching classification method of multi-state similar pigments based on feature differences. Fast principal component analysis (FPCA) was used to calculate the eigenvalue variance of pigment spectral reflectance, then applied to the original reflectance values for parameter characterization. We first projected the original spectral reflectance from the spectral space to the characteristic variance space to identify the spectral curve. Secondly, the relative distance between the eigenvalues in the eigen variance space is combined with the JS (Jensen-Shannon) divergence to express the difference between the two spectral distributions. The JS information divergence calculates the relative distance between the eigenvalues. Experimental results show that our classification method can be used to identify the spectral curves of the same pigment under different states. The value of the root means square error (RMSE) decreased by 12.0817, while the mean values of the mean absolute percentage error (MAPE) and R2 increased by 0.0965 and 0.2849, respectively. Compared with the traditional spectral matching algorithm, the recognition error was effectively reduced.

The pigment of protection and restoration are essential content of ancient mural protection. It is the precondition of murals for protection and restoration is identifying the material surface paint murals [

The matching similarity value of reflection spectrum data between unknown pigments and known pigments is the core of identifying mural pigments based on reflection spectrum information analysis [

Spectral Angel Mapping (SAM) algorithm measures the similarity between the two spectral curves by calculating the cosine angle between the spectral reflectance curves.

The smaller the Angle between two spectra, the more similar they are. As shown in

Although spectral Angle matching algorithm can obtain the similarity with the overall shape of spectral curves, it is difficult to distinguish the differences in local characteristics of spectral curves.

Spectral Similarity Fitting (SCF) [

In which,

The algorithm of Spectral Information Divergence (SID) [

The theory based on information theory measures the difference between two spectra. The larger the value of information divergence is, the more similar the spectral curves of two pigments are.

By comprehensively analyzing the above three algorithms, SAM is difficult to distinguish the local characteristics of the spectral curve. SCF is highly dependent on the correlation coefficient, and SID is too sensitive to a band with prominent spectral intensity. When matching and classifying the approximate spectral reflectance curves under different conditions of the same pigment, the traditional spectral matching algorithm has large error.

KL divergence [

KL divergence analyzes the degree of difference between two distributions of the perspective of information entropy, so it is also called relative entropy. If the two distributions are identical, then

KL divergence is asymmetric, JS divergence is improved based on KL divergence.

JS divergence range is [0, 1], the same is 1, the opposite is 0. Compared with KL, the discrimination of similarity is more accurate. At the same time, JS divergence is symmetric, namely

It is highly similar for the same pigment under the spectral reflectance data in different conditions, and the JS divergence calculated by direct distance that cannot effectively characterize the relative difference of the spectral data, which is prone to mismatch. Therefore, it introduces the spectral matching classig-1cation method of multi-state similar pigments based on feature differences. Due to the large number and dimension of pigment spectral bands, FPCA is used to process spectral reflectance data. Compared with the traditional PCA method, FPCA can quickly calculate the variance in the eigenvalues of the reflectance, improve the calculation efficiency, and save time. Using the eigenvalues variance of calculation as a parameter, and the JS divergence distance is used to measure the eigenvalues effectively. The distance is the smaller, the correlation is the greater.

Firstly, the orthogonal vector of pigment spectral reflectance is calculated by FPCA, and the linear combination of these orthogonal vectors is used to represent the original data. The Minium mean square error between the new data and the original data is obtained, which is reduced to the eigenvector problem of the overall matrix A of the original data. The definition is as follows:

The variance in the vector is used to express the relationship between the original variables, and the FPCA is introduced to represent the feature attributes of the unknown pigment. Then, it is combined with the JS divergence algorithm. The specific process is as follows:

Given a sample of

The matrix operation of the original features of the sample is mainly to subtract the mean (centralization) to make the mean of vectors

Calculation of correlation coefficient matrix

The eigenvalue

The characteristic vector information divergence formula for the known spectrum is as follows:

The characteristic vector information divergence formula for the spectrum to be measured is as follows:

After transformation JS divergence distance formula:

The variance in FPCA in feature space is more obvious to represent the change of original features. At the same time, the JS divergence is used to calculate the vector distance, which improves the problem that the original vector distance cannot better reflect the correlation between the measured data and the known data. Therefore, the combination of FPCA and JS divergence can improve the accuracy and matching accuracy of spectral similarity matching values. The flow chart of FPCAJS algorithm is shown in

Experimental equipment includes: computer program control terminal, marine optical SpectroSuite spectrophotometer, standard halogen lamp lighting source, diffuse reflection standard plate, UV/SR-VIS high hydroxyl fiber, ISP-R integrating sphere. Spectral data acquisition wavelength ranges 380–900 nm.

Using MATLAB simulation, the computer hardware environment is: Windows 1,064-bit system, I5 processor, 4 GB memory. The experimental data were collected in the range of 380–900 nm, and the spectral information on pigments in this band was less affected by noise and other factors.

Mineral pigment color blocks commonly used in ancient Chinese murals were selected to make experiments. Minium, Vermilion, Green and Cyan were selected from red, blue, and green series. The color blocks of pigments for difference are mixed by the condition of the different concentration of water glue and particle sizes. Drawn on the white plasterboard, the spectral reflectance data onto pigments were collected by spectrometer and other equipment. Each pigment has more than three groups of control samples. The pigment samples of different states are shown in

Color | Pigment | Water ratio | Glue ratio | Particle size |
---|---|---|---|---|

Red | Minium | Minium 1 |
||

Vermilion | Vermilion 1 |
|||

Blue | Cyan | Cyan |
||

Green | Green | Green 1 |

Root Mean Square Error (RMSE)

Root Mean Square Error refers to the expected value of the square of the difference between the estimated value of the parameter and the true value of the parameter. The smaller the value is, the higher the matching recognition accuracy is, and the better the recognition and classification effected are. The definition is as follows:

Mean Absolute Percentage Error (MAPE)

MAPE is a percentage value, indicating the percentage of the average deviation between the sample results and the real results. The larger the value is, the better the matching classification effect of the model is. The definition is as follows:

Coefficient of determination (R²)

The coefficient of determination is generally used for regression model, which is used to evaluate the consistency between the predicted value and the actual value. The higher the coefficient of determination, the higher the matching accuracy, the better the recognition and classification effects. The definition is as follows:

The ratio of different concentration of water and glue as well as the difference in particle size will cause the similar spectral curves of the same pigment in different conditions. Therefore, SAM, SID, SCF and FPCAJS are used for the pigments comparing and identifying. Carry out three groups of experiment comparison for the same pigment in different conditions and states.

Calculation experiment of pigment spectral data onto different water concentrations

As shown in

SAM | SCF | SID | FPCAJS | |
---|---|---|---|---|

Vermilion: Vermilion 1 | 0.9509 | 0.9734 | 0.9388 | 0.9840 |

Vermilion: Vermilion 2 | 0.9823 | 0.9651 | 0.9553 | 0.9715 |

Vermilion: Vermilion 3 | 0.9726 | 0.8716 | 0.9573 | 0.9699 |

Comparing the matching results of

SAM | SCF | SID | FPCAJS | |
---|---|---|---|---|

Green: Green 1 | 0.8841 | 0.9885 | 0.9147 | 0.9795 |

Green: Green 2 | 0.8990 | 0.9951 | 0.9427 | 0.8551 |

Green: Green 3 | 0.9040 | 0.9905 | 0.9547 | 0.8112 |

Calculation experiment of pigment spectral data onto different particle sizes

As shown in

SAM | SCF | SID | FPCAJS | |
---|---|---|---|---|

Cyan: Two Cyan | 0.8780 | 0.5933 | 0.2876 | 0.9804 |

Cyan: Three Cyan | 0.9234 | 0.8042 | 0.7163 | 0.9922 |

Cyan: Four Cyan | 0.9770 | 0.9225 | 0.9732 | 0.9202 |

Two Cyan: Three Cyan | 0.9527 | 0.9217 | 0.8962 | 0.9506 |

Two Cyan: Four Cyan | 0.8653 | 0.4845 | 0.1154 | 0.3017 |

Three Cyan: Four Cyan | 0.9084 | 0.6370 | 0.5971 | 0.9062 |

Compared with the matching results of

Calculation experiment of pigment spectral data with different glue concentration

In the drawing of mineral pigment images, the adhesive can be used as a binder to facilitate the color of the pigment to be not easy to fall off. In this experiment, granular gelatin was selected and used after foaming. As shown in

The experiments show that the concentration of glue has an impact on the pigment. Comparing the matching results of

SAM | SCF | SID | FPCAJS | |
---|---|---|---|---|

Minium: Minium 1 | 0.9802 | 0.9362 | 0.9392 | 0.9625 |

Minium: Minium 2 | 0.9774 | 0.9323 | 0.9122 | 0.9564 |

Minium: Minium 3 | 0.9791 | 0.9289 | 0.9246 | 0.9104 |

Through the above three groups of control experiments, the pigment concentration of the same pigment under different conditions was distinguished from the results, and the threshold interval was divided into the matching results, as shown in

Pigment concentration | Threshold interval |
---|---|

Vermilion 1 | 0.98–1.0 |

Vermilion 2 | 0.97–0.98 |

Vermilion 3 | 0.96–0.97 |

Green 1 | 0.90–1 |

Green 2 | 0.85–0.90 |

Green 3 | 0.80–0.85 |

Minium 2 | 0.96–1 |

Minium 2 | 0.95–0.96 |

Minium 3 | 0.91–0.95 |

Since the number of particle sizes divided by blue pigments is different, it is impossible to judge blue pigments with different particle sizes according to the threshold during matching. Therefore, the matching algorithm can only be further used to distinguish different particle sizes of blue pigments, which will be further studied in the follow-up work.

In order to further to verify the algorithm proposed to this paper, this algorithm is applied to the pigment recognition of actual temple murals. (The actual temple murals are obtained from the experimental data collection of a temple in China). The pigment reflectance data onto temple murals to be detected are compared with the spectral reflectance sample library established by this method. The pigments with obvious color and green color in temple murals are mainly studied, as shown in

Firstly, the spectral matching algorithm studied in this paper was used to match and identify the reflectance spectral data onto the color block pigments in murals. Then, the XRF (ultraviolet fluorescence) detection method was used to verify and determine that the Red 1 in murals was Minium, the Red 2 was Vermilion, and the green pigment were Green. The following is the matching recognition results of the reflection spectrum data onto mural color blocks and the samples of different concentrations of standard pigments.

Contrast

Pigment | SAM | SCF | SID | FPCAJS |
---|---|---|---|---|

Minium a | 0.7721 | 0.9869 | 0.8091 | 0.8678 |

Minium b | 0.8228 | 0.9887 | 0.5500 | 0.5642 |

Pigment | SAM | SCF | SID | FPCAJS |
---|---|---|---|---|

Green a | 0.3704 | 0.6314 | 0.8043 | 0.6058 |

Green b | 0.3746 | 0.4041 | 0.8044 | 0.8585 |

Pigment | SAM | SCF | SID | FPCAJS |
---|---|---|---|---|

Vermilion a | 0.7852 | 0.9819 | 0.9505 | 0.9881 |

Vermilion b | 0.8326 | 0.9832 | 0.9688 | 0.9889 |

Pigment | RMSE | MAPE | R² | |
---|---|---|---|---|

Vermilion | Reflectivity | 16.3036 | 0.0375 | 0.5171 |

Eigenvalues | 9.0399 | 0.0454 | 0.7152 | |

Green | Reflectivity | 6.7654 | 0.0914 | 0.7219 |

Eigenvalues | 2.3339 | 0.0466 | 0.7651 | |

Cyan | Reflectivity | 0.7892 | 0.0055 | 0.9736 |

Eigenvalues | 0.6064 | 0.0202 | 0.9843 | |

Minium | Reflectivity | 2.4761 | 0.0187 | 0.9623 |

Eigenvalues | 2.2724 | 0.1374 | 0.9952 |

Studying the spectral matching algorithms of mural pigments is of great significance in the protection and research of cultural relics. This is because traditional methods have the problem of recognition errors in the same color pigments. The enhanced spectral matching algorithm evaluated in this paper is based on different water concentrations, particle sizes, and glue concentrations. It can be applied to the recognition and classification of pigments under most conditions. According to the preprocessing of the spectral data, the projection of the data feature in the feature variance space more clearly characterizes the changes in the original features. Use the relative distance of the eigenvalues in the eigen variance space to perform spectral curve matching. The problem caused by the unobvious amplitude and few features of the same color pigments is improved. Compared with the similarity values calculated by the traditional SAM, SCF, and SID algorithms, the multi-state similar spectral matching classification calculation method based on feature differences substantially improves calculation accuracy. It has a positive effect on the identification and detection of mural pigments. In future work, a quantitative analysis of mixed colors will be considered due to mixed colors often being used in mural painting, leading to an increased number of data samples and more difficulties in analyzing the specific components of mixed pigment colors. The unknown pigment data of mixed colors will be compared with the sample database, and classifiers will be added for categorization.