基于自适应非凸高阶法向滤波与Mumford-Shah间断函数的${\ell }_p$-${\ell }_1$混合保特征网格去噪模型

A Feature-Preserving Mesh Denoising Model Based on Adaptive Non-Convex High-Order Normal Filtering and Mumford-Shah Discontinuity Function with ${\ell }_p$-${\ell }_1$ Hybrid Regularization

摘要: 近几年来，随着激光扫描，结构光扫描，摄影测量等3D数字化技术逐渐普及到成为刚需，人们可以轻松地从这些设备当中获取到三角网格模型。但是，我们从中获取到的三角网格模型往往会因为激光、结构光扫描仪的测量精度的限制或者是深度相机的深度值漂移值等设备带来的物理误差，或是物体表面反光，环境光变化等环境干扰引入各类噪声的干扰。这些噪声会降低网格模型的质量，还会给网格分割、参数化、可视化、重构等网格处理应用带来一定的误差。因此，如何从含噪的三角网格模型中还原出高质量的网格模型是我们要解决的重要问题。网格去噪的核心难点在于在去噪保真的同时也要尽可能保证网格的特征。

Abstract: In recent years, 3D digitization technologies such as laser scanning, structured light scanning, and photogrammetry have evolved from niche applications into indispensable tools, enabling convenient acquisition of triangular mesh models. However, the raw meshes obtained from these devices are inevitably corrupted by various types of noise. This noise arises from either hardware-induced physical errors—such as the limited measurement precision of laser and structured light scanners, or depth value drift in depth cameras—or environmental interferences including object surface reflectance and ambient illumination variations. The presence of noise degrades the quality of mesh models and introduces significant errors into subsequent mesh processing tasks, including segmentation, parameterization, visualization, and surface reconstruction. Therefore, reconstructing high-quality meshes from noisy triangular mesh data has become a critical research problem. The core challenge in mesh denoising lies in achieving a balance between effective noise removal and faithful preservation of intrinsic geometric features.