Spectral characteristics of pure pigments
To construct a reliable endmember library and support subsequent modeling, we first analyzed the spectral characteristics of the 12 pure pigments. After removing noisy bands near 400 nm and 1000 nm, all spectra were standardized to 201 wavelength points. Figure 4 presents the average reflectance curves, revealing clear inter-class differences in the 400–900 nm range. Blue pigments, dominated by Azurite, exhibit a reflectance peak near 460 nm and strong absorption between 600–900 nm 22,23. Green pigments (Malachite) display a distinct absorption band around 800 nm 23. Yellow pigments (Realgar and Orpiment) show diagnostic absorption features between 470–530 nm; Cinnabar exhibits an inflection near 600 nm 22,49; and Pearl White is characterized by a nearly flat, high-reflectance profile 23. These observations are consistent with mineralogical compositions and provide a solid basis for spectral classification. Principal component analysis (PCA, n = 2; Fig. 5) further demonstrates clear class separation, with only partial overlap within blue and green pigments.
Mean spectra are shown with shaded bands indicating one standard deviation, and annotated with key diagnostic absorption features. Azurite shows a peak near 460 nm and strong absorption between 600-900 nm 22,23; Malachite displays a distinct absorption band around 800 nm 23; Realgar and Orpiment present diagnostic features at 470-530 nm; Cinnabar exhibits an inflection near 600 nm 22,49; and Pearl White maintains nearly flat high reflectance 23. These features are consistent with the mineralogical compositions of the pigments and form the basis for reliable classification. Full reflectance spectra for all 170 measurements per pigment are provided in Supplementary Fig S1.
PCA visualization of the 12 pure pigment samples (n = 2).
To evaluate the effect of preprocessing on classification, seven preprocessing strategies and six classifiers were systematically tested using both the full spectral range (201 bands) and a reduced feature set of 20 SHAP-selected wavelengths. As summarized in Table 1, the best-performing combinations achieved high accuracy, and all configurations exceeded 90% (complete results in Table S1, Supplementary Information). Derivative-based strategies (e.g., SGFD, SNVFD, MSCFD) consistently improved model stability, and the SGFD–LDA model showed the most robust performance across folds when using the full spectral range. The confusion matrix in Fig. 6 indicates near-perfect separability, suggesting that hyperspectral information alone is sufficient for reliable pigment classification.
Each cell shows classification accuracy (%) using a white-to-dark-blue gradient to indicate the level of agreement between predicted and true labels. Normalized by true class, and no off-diagonal confusion was observed under controlled conditions.
To enhance computational efficiency while retaining high accuracy, we applied feature selection to identify 20 informative wavelengths. Using SHAP, the rankings were cross-validated with feature importance (FI) and permutation importance (PI), yielding consistent results across folds. The selected wavelengths concentrate mainly in the 400–600 nm region, corresponding to known pigment absorption features 22,23, thereby supporting physical interpretability. Representative SHAP plots (Fig. 7) confirm strong class-specific discriminative power. Re-evaluation using only the 20 wavelengths maintained high accuracy, with the MSCFD–KNN model achieving the best overall performance (Table 1). This dimensionality reduction preserves predictive capability while substantially lowering computational cost and model complexity; detailed results for the 20-wavelength setting are provided in Table S1. These compact, feature-based models offer a robust foundation for subsequent tasks, including mixture regression and unknown pigment identification, highlighting the practicality of lightweight spectral approaches for cultural-heritage applications.
The 20 most influential wavelengths are primarily concentrated in the 400–600 nm range, which corresponds to diagnostically meaningful spectral regions of mineral pigments. For instance, the 460 nm peak is characteristic of azurite, while features around 470–600 nm relate to the absorption behavior of yellow and red pigments such as orpiment and cinnabar. This concentration of SHAP-selected wavelengths highlights both the statistical robustness and the physical interpretability of the feature selection process. Additional comparisons with Random Forest and permutation importance are provided in Supplementary Fig. S2.
Spectral characteristics of mixed pigments
Figure 8 shows the average reflectance curves of the 54 mixed-pigment samples. The spectra vary consistently with changing mixing ratios. For combinations such as Blue–Realgar, Blue–Cinnabar, Green–Realgar, and Green–Cinnabar, gradual shifts in reflectance profiles emerge as the dominant endmember proportion increases, reflecting a smooth transition of spectral influence across 400–1000 nm. In contrast, mixtures containing Pearl White primarily exhibit increased overall reflectance while maintaining spectral shape, confirming its role as a brightness-enhancing background pigment rather than a strong spectral modifier. These observations indicate that the behavior of mixed pigments is governed not only by relative proportion but also by intrinsic spectral strength. Deviations from linear blending, particularly in copper- and mercury-based pigments, suggest nonlinear interactions associated with scattering effects, layer thickness, or binder composition; these tendencies align with prior heritage spectroscopy reports 22,23. Consequently, regression-based models are well-suited to capture subtle compositional dependencies beyond simple linear interpolation.
Each subplot shows the gradual and systematic transition of spectral features as the relative proportions of the two pigments vary. These continuous shifts illustrate how binary mixing produces predictable spectral trends, providing a clear physical basis for quantitative unmixing analysis.
We compared three regression models—PLSR, PCR, and SVR—under seven preprocessing strategies across six pigment pairs, evaluating performance using R2, RMSE, MAE, and RPD (Table 2). Overall, PLSR consistently outperformed PCR and SVR, demonstrating superior robustness and predictive stability. The SGFD–PLSR configuration provided the best results, with average R2 = 0.98, RMSE = 0.04, and RPD = 7.20 across all groups; predicted ratios closely matched ground truth (Fig. 9), supporting its use as the backbone of the conditional regression module. Negative R2 values observed under MSC and MSCFD indicate that these corrections can distort spectral structure, likely due to nonlinear scattering behaviors of mineral pigments that depart from MSC’s linear assumptions, thereby weakening the relationship between reflectance and mixing ratio. These findings underscore the need to pair regression algorithms with preprocessing choices that balance robustness, interpretability, and computational efficiency.
Regression performance of the SGFD-PLSR model on six pigment mixture groups.
To reduce redundancy while maintaining accuracy, VIP-based wavelength selection was integrated into the SGFD–PLSR pipeline. For each pigment group, the 20 most influential wavelengths were extracted from training data and used to rebuild the regression models (Fig. 10). As summarized in Table 3, performance remained strong after dimensionality reduction: all R2 values exceeded 0.94, with an overall average of 0.975; RMSE and RPD also stayed within acceptable ranges, indicating that key diagnostic information was retained. The Blue–Cinnabar group showed slightly lower accuracy (R2 = 0.95), likely due to overlapping signatures and similar inflection points, but errors remained modest. Taken together, mixed-pigment analysis highlights both the challenges of nonlinear spectral interactions and the effectiveness of regression-based modeling. Among the evaluated options, PLSR—especially when combined with SGFD preprocessing and VIP-based feature selection—offers a reliable and computationally efficient solution for mixing-ratio estimation in practical pigment-identification workflows.
Distribution of the top 20 VIP-selected wavelengths for the six pigment mixture groups.
Evaluation of spectral unmixing methods
Assuming prior knowledge of pigment-mixture types, we first constructed local unmixing models using endmember spectra for the six predefined combinations. Three linear algorithms (FCLS, Tikhonov-FCLS, SUnSAL) and three nonlinear algorithms (GBM, PPNMM, FM) were applied to estimate abundance ratios, with performance summarized in Table 4. RMSE was used as the primary evaluation metric. Overall, the local methods yielded preliminary abundance estimates without supervised training and offered strong physical interpretability. However, quantitative accuracy was limited: the best-performing model (Tikhonov-FCLS) reached a mean RMSE of 0.179, substantially higher than the SGFD–PLSR regression model in “Spectral Characteristics of Mixed Pigments” (RMSE = 0.037). Nonlinear models (GBM, PPNMM) produced only modest gains over linear methods, consistent with predominantly weakly nonlinear or locally linear mixing. In addition, the lack of explicit spectral-variability modeling made traditional unmixing more sensitive to background interference and noise. Local unmixing remains a valuable, physically interpretable baseline, but its accuracy depends strongly on prior endmember knowledge and is insufficient for precise quantification.
To explore identification without prior knowledge, we next evaluated a global unmixing strategy. A reduced endmember library of five representative pigments (Blue 1, Green 1, Realgar, Cinnabar, Pearl White) was assembled, and Tikhonov-FCLS was applied to all 54 mixtures to infer both endmember combinations and abundances (Table 5). The global approach achieved only moderate success: approximately 74% of mixtures were assigned correct endmember sets, with substantial variation across pigment groups. For example, Blue–Realgar and Blue–Cinnabar were often correctly identified, whereas Green–Cinnabar samples were frequently misclassified as Blue–Realgar, reflecting spectral similarities between copper- and mercury-based pigments. Abundance estimates also deviated; for instance, a true 9:1 Green: Pearl White mixture was misidentified as 0.92:0.08 Green: Blue, illustrating how background reflectance and endmember confusion can distort quantitative predictions. These results highlight the limitations of global unmixing in realistic heritage scenarios: spectral similarity, nonlinear interactions, and background interference collectively reduce recognition accuracy and quantitative reliability. While global unmixing shows a degree of autonomous recognition, its precision falls short of practical requirements for Thangka pigment analysis, underscoring the need for data-driven, multi-stage frameworks that integrate classification with conditional regression under unknown conditions.
Application of the multi-stage strategy to a real Thangka
In the preceding sections, classification and regression models were systematically benchmarked on standardized laboratory-prepared samples. Multiple configurations achieved accuracies above 98% for pure-pigment classification, while the SGFD–PLSR model yielded an average R2 = 0.975 for mixture-ratio prediction (Table 3), substantially outperforming conventional spectral unmixing methods. These results establish the proposed multi-stage framework as a competitive approach that integrates pure/mixed discrimination, subclass classification, and conditional regression within a unified workflow. To assess applicability under realistic conditions, the framework was validated on a hand-painted Thangka image. For comparison, a widely used prior-free spectral matching method—Spectral Angle Mapper (SAM)—was also evaluated, enabling a fair contrast between supervised and unsupervised strategies in practical cultural-heritage scenarios (workflow in Fig. 3).
The framework was tested on a real Thangka (Baoluo Foshou) using eight annotated regions of interest (ROIs; Fig. 11) covering both pure pigments and mixtures. The classification outcomes are summarized in Table 6, with an overall accuracy of 75%. Most ROIs were correctly identified, indicating that the framework can generalize beyond laboratory samples. Misclassifications occurred in two ROIs and are discussed below. Given the small number of ROIs, this validation should be regarded as a proof of concept rather than comprehensive evidence of generalizability.
Eight regions of interest (ROIs 1-8) are marked by numbered circles in the image (with contrasting black or white outlines for visibility), and a scale bar is added for spatial reference. The expected pigments are: ROI 1 — Blue 1, ROI 2 — Pearl White, ROI 3 — Pearl White, ROI 4 — Blue 1:Pearl White = 5:5, ROI 5 — Blue 1:Realgar = 3:7, ROI 6 — Blue 1:Pearl White = 3:7, ROI 7 — Cinnabar, ROI 8 — Green 1. Model predictions and their comparison with expert annotations are summarized in Tables 6 and 7.
Pure pigments were reliably identified, whereas mixtures showed greater variability. For mixtures, the average RMSE of ratio estimation was 0.17, with one ROI exhibiting an error below 0.05. ROI 5 (Blue 1:Realgar) displayed a higher RMSE of 0.31 despite correct class assignment, likely due to uneven pigment distribution and strong scattering contrasts between blue and yellow components, which introduced local spectral nonlinearity and affected quantitative accuracy. The two misclassifications were mainly attributable to spectral similarity between closely related pigments (ROI 1: Blue 1 predicted as Blue 2; see Fig. 4) and insufficient pigment thickness that allowed canvas background interference (ROI 8: Green 1 predicted as Green 1:Pearl White).
For the SAM baseline, the overall classification accuracy also reached 75% (Table 7), correctly identifying several mixtures but without the ability to provide continuous ratio estimates. Misclassifications again appeared in ROI 1 (Blue 1 predicted as Blue 2), reflecting strong spectral similarity among azurite-based pigments, and ROI 8 (Green 1 predicted as Green 3), highlighting confusion among closely related greens when intra-class variability is not well represented in the reference library.
Both approaches achieved comparable recognition rates on this real Thangka. However, the multi-stage framework additionally provides continuous abundance estimates, shows greater robustness to spectral noise, and scales more readily to larger pigment libraries. A detailed comparative discussion and implications for conservation practice are presented in “Discussion”.
Summary of results
Overall, the results demonstrate that pure pigments exhibit highly distinctive spectral signatures, enabling near-perfect classification under controlled conditions. Mixture analyses further confirmed the effectiveness of regression-based modeling, with the SGFD-PLSR configuration consistently outperforming conventional unmixing approaches. Feature selection markedly reduced data dimensionality while maintaining predictive accuracy, supporting the development of lightweight yet interpretable models for practical use. Validation on a real Thangka painting achieved an overall accuracy of 75%, underscoring both the feasibility of the proposed framework and the challenges inherent to analyzing complex, aged artworks.
Collectively, these findings validate the potential of the proposed multi-stage recognition framework for practical pigment identification in cultural heritage applications, while also revealing critical limitations that merit further investigation. The following Discussion section elaborates on the implications of these results, addresses the observed limitations, and outlines directions for future research.
