The medial axis, a lower-dimensional descriptor that captures the extrinsic structure of a shape, plays an important role in digital geometry processing. Despite its importance, computing the medial axis transform robustly from diverse inputs, especially point clouds with defects, remains a challenging problem. In this article, we propose a new implicit method that deviates from traditional explicit medial axis computation. Our key technical insight is that the difference between the signed distance field (SDF) and the medial field (MF) of a solid shape relates to the unsigned distance field (UDF) of the shape’s medial axis. This observation allows us to formulate medial axis extraction as an implicit reconstruction problem. By employing a modified double covering strategy, we recover the medial axis as the zero level-set of the UDF. Extensive experiments demonstrate that our method achieves higher accuracy and robustness in learning compact medial axis transforms from challenging meshes and point clouds, outperforming existing approaches.

While 3D head reconstruction is widely used for modeling, existing neural reconstruction approaches rely on high-resolution multi-view images, posing notable privacy issues. Individuals are particularly sensitive to facial features, and facial image leakage can lead to many malicious activities, such as unauthorized tracking and deepfake. In contrast, geometric data is less susceptible to misuse due to its complex processing requirements, and absence of facial texture features. In this paper, we propose a novel two-stage 3D facial reconstruction method aimed at avoiding exposure to sensitive facial information while preserving detailed geometric accuracy. Our approach first uses non-sensitive rear-head images for initial geometry and then refines this geometry using processed privacy-removed gradient images. Extensive experiments show that the resulting geometry is comparable to methods using full images, while the process is resistant to DeepFake applications and facial recognition (FR) systems, thereby proving its effectiveness in privacy protection.