## 3 Materials and Methods
### Facial Deficiency Evaluation  
In this study, we conducted a preliminary analysis of the collected facial images of Tang Dynasty terracotta figurines and found that 55% of the samples had varying degrees of damage. To systematically evaluate the extent of this damage, we employed the Fuzzy Analytic Hierarchy Process (FAHP) to determine the importance of facial features of the figurines, followed by identifying the importance of image visual features. Finally, we derived the overall facial damage extent based on the weights and damage degrees of both aspects. The FAHP method expands upon [PERSON]'s Analytic Hierarchy Process (AHP) by incorporating the fuzzy set theory [60]. The fuzzy set theory, proposed by [61], introduces the concept of degrees to extend classical Boolean logic and set theory, allowing for conditions to be more flexible and capable of handling imprecision and uncertainty. Compared to traditional AHP, FAHP is more suitable for dealing with uncertainty and fuzzy information in decision-making [62; 63]. Currently, FAHP has been widely applied in heritage field assessments [64]. The FAHP process in this study includes the following steps: (1) Define the top-level goal; (2) establish a hierarchical structure for the goal; (3) construct fuzzy judgment matrices and fuzzy weight vectors; (4) rank all alternatives and select the best one. We invited five experts in cultural heritage from Liaoning Museum and the Art College of Northeastern University to perform subjective evaluations and scoring. The study used the fuzzy linguistic variable set mentioned by [65] to score, ultimately determining the relative weights of multiple criteria and evaluating the reliability of these weights through consistency testing. The human face is defined by its parts (such as eyes, nose, and mouth) and the spatial relationships between these parts and their subparts. Therefore, listing these parts is important. This study referred to the hierarchical framework in [66] and made appropriate adjustments based on the facial images of the figurines. The first top-level goal of the study \begin{table}
\begin{tabular}{c c} \hline \hline
**Software/Support Platform** & **Version** \\ \hline Pycharm & PyCharm Community Edition 2021.3.2 \\ Python & 3.7 \\ Windows & 11 \\ GPU & NVIDIA GeForce RTX 4060 Ti \\ CPU & Intel(R) Core (TM) i5-14400F \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Software and support platforms required for the experiment. Figure 4: (a) Tricolor hand-in-hand standing female figurine; (b) painted terracotta standing female figurine; (c) tricolor horse-riding figurine; (d) tricolor hand-in-hand standing female figurine (Source: the Palace Museum). was to assess the importance of the facial features of the figurines, evaluating four aspects: eyes, eyebrows, nose, and mouth. Table 2 defines the 23 sub-criteria used to describe these four basic aspects. The second top-level goal of this study was to evaluate the importance of the visual features of Tang Dynasty female terracotta figurine facial images. The study evaluated these features from three aspects: color, texture, and shape. Table 3 defines the 11 sub-criteria used to describe these three basic aspects. The most common visual features of images include color, texture, and shape. Most image annotation and retrieval systems are built based on these features. Color features are described and quantified through parameters in specific color spaces (such as RGB, CMYK, HSV, etc.). In this study, we referred to the HSV color space and categorized color features into the following: hue (type of color), saturation (purity of color), and value (brightness of color) [67]. Texture features are the quantitative characteristics of the surface feel represented by visual patterns that are uniformly distributed in the image.