## 1 Introduction
GAN-based algorithms, due to their powerful image generation capabilities, have been widely applied in the practice of cultural heritage image inpainting [11; 17; 18]. Face image inpainting, as a branch of image inpainting, leverages the semantic information of the entire face image to repair damage caused by occlusion or loss or reconstructs the entire face from the extracted semantic features. Currently, deep learning-based face image inpainting methods demonstrate the best performance. Although many methods combine GANs with various prior knowledge techniques, their robustness still has room for improvement. Currently, in the field of cultural heritage with rich datasets, such as murals and paintings, image inpainting has achieved significant accomplishments [4; 13; 19; 20; 21]. However, in the field of ceramic image inpainting, related research is relatively scarce, mainly due to the lack of available data. Compared to the mural and painting fields, where datasets typically contain thousands of well-preserved images, the datasets in the ceramic field only consist of a few hundred complete images. Therefore, in the restoration of ceramic, some studies use daily ceramic with similar shapes as substitute data for archaeological ceramic [22], while other studies use traditional restoration methods that do not rely on large amounts of data. [PERSON]. [23] proposed an automated pattern completion method based on rule reasoning for the repetitive surface patterns commonly found in ancient ceramics. This method relies on known pattern sequence information rather than the data-driven strategies of deep learning, making it more suitable for completing images with low-level semantic information. However, it is challenging to effectively restore images containinghigh-level semantic information, such as facial features. In the research field of Tang Dynasty ceramics, current work mainly focuses on 3D-shape inpainting [24; 25], and image inpainting technology has not yet been applied. The Global and Local Consistency Image Completion (GLCIC) algorithm, based on convolutional neural networks, is a classic algorithm that has shown significant advantages in the field of image restoration. By combining multi-scale convolutional networks, it ensures the coordination of the overall structure and local details in the restored images, demonstrating great potential for image restoration in data-scarce situations. This study reveals that most of the facial images of Tang Dynasty female terracotta figurines exhibit moderate defects, primarily local. Consequently, during the restoration process, it is crucial to ensure the coordination and integrity between local details and the overall structure. Based on this, we reasonably infer that this method has a high probability of successfully restoring the facial images of Tang Dynasty female terracotta figurines, even when data are scarce. However, currently, there is no specifically designed algorithm for completing the facial images of Tang Dynasty female figurines; a dataset of Tang Dynasty terracotta figurines based on the GLCIC algorithm has not yet been constructed; and most importantly, the effectiveness of GLCIC in restoring the facial images of Tang Dynasty female figurines unknown. To address the aforementioned challenges, the goal of this study was to optimize the GLCIC algorithm to achieve the precise inpainting of damaged faces using the limited available data, thereby improving the accuracy and quality of the inpainting, and to provide more accurate reference samples for the restoration of Tang Dynasty female ceramic figurines, as well as to offer reference solutions for the material selection of figurines from the same era. The structure of this paper is arranged as follows. First, we will review the relevant literature and research background to lay the theoretical foundation for this study.