In the field of 3D geometric modeling, a hole refers to the incompleteness on the surface of a 3D model, often arising during data acquisition, processing, or transformation. The presence of such holes can significantly impact the geometric integrity and visual quality of the model. In the domain of cultural heritage preservation, traditional hole-filling techniques focus on the repair of geometric surfaces, neglecting the restoration of texture information, which is crucial for recovering the authenticity and material characteristics of artifacts. This paper proposes a diffusion model method that combines geometric and texture repair, particularly suitable for the restoration of facial models of cultural relics. Due to the absence of ground truth for facial models of cultural relics, this study uses similar incomplete Asian facial models for evaluation. Given the scarcity of publicly available Asian facial datasets, this paper constructs an Asian facial dataset comprising approximately 20000 Asian facial images, corresponding 3D models and textures, as well as high-fidelity facial images rendered from the models. Experiments are first conducted on the constructed dataset to validate the effectiveness of the proposed method. The results show that compared to existing benchmark methods, our method achieves significant improvements in facial imageinpainting and simultaneously repairs the geometric surfaces and texture information of the facial 3D models. Subsequently, the proposed repair technique is applied to facial models of cultural relics, and experiments confirm its excellent performance in both geometric and texture repair of the relic facial models. These findings provide an effective technical means for the digital restoration of facial models of cultural relics, contributing to the enhancement of the quality of cultural heritage preservation and digital exhibition.

Isometric 3D shape partial matching has attracted a great amount of interest, with a plethora of applications ranging from shape recognition to texture mapping. In this paper, we propose a novel isometric 3D shape partial matching algorithm using the geodesic disk Laplace spectrum (GD-DNA). It transforms the partial matching problem into the geodesic disk matching problem. Firstly, the largest enclosed geodesic disk extracted from the partial shape is matched with geodesic disks from the full shape by the Laplace spectrum of the geodesic disk. Secondly, Generalized Multi-Dimensional Scaling algorithm (GMDS) and Euclidean embedding are conducted to establish final point correspondences between the partial and the full shape using the matched geodesic disk pair. The proposed GD-DNA is discriminative for matching geodesic disks, and it can well solve the anchor point selection problem in challenging partial shape matching tasks. Experimental results on the Shape Retrieval Contest 2016 (SHREC’16) benchmark validate the proposed method, and comparisons with isometric partial matching algorithms in the literature show that our method has a higher precision.