Normal filtering is a fundamental step of feature-preserving mesh denoising. Methods based on convolutional neural networks (CNNs) have recently made their debut for normal filtering. However, they require complicated voxelization and/or projection operations for regularization, and afford an overall denoising accuracy with few powers of preserving surface features. We devise a novel normal filtering neural network algorithm, which we call as NormalF-Net. NormalF-Net consists of two cascaded subnetworks with a comprehensive loss function. The first subnetwork learns mapping from non-local patch-group normal matrices (NPNMs) to their ground-truth low-rank counterparts for denoising, and the second subnetwork learns mapping from the recovered NPNMs to the ground-truth normals for normal refinement. Different from existing learning-based methods, NormalF-Net, which bridges the connection between CNNs and geometry domain knowledge of non-local similarity, can not only preserve surface features when removing different levels and types of noise, but be free of voxelization/projection. NormalF-Net has been validated on different datasets of meshes with multi-scale features yet corrupted by noise of different distributions. Experimental results consistently demonstrate clear improvements of our method over the state-of-the-arts in both noise-robustness and feature awareness.

普通滤波是保留特征的网格去噪的基本步骤。基于卷积神经网络（CNN）的方法最近首次在常规过滤中亮相。然而，它们需要复杂的体素化和/或投影操作以进行正则化，并以很少的保留表面特征的能力提供总体去噪精度。我们设计了一种新颖的常规过滤神经网络算法，称为NormalF-Net。NormalF-Net由两个具有全面损耗功能的级联子网组成。第一个子网学习从非本地补丁组法线矩阵（NPNM）映射到它们的地面真实低秩对应进行降噪，第二个子网学习从恢复的NPNM到地面真实法线进行映射以进行常规细化。与现有的基于学习的方法不同，具有非局部相似性的几何域知识，不仅可以在移除不同级别和类型的噪声时保留表面特征，而且还可以避免体素化/投影。NormalF-Net已在具有多尺度特征的网格的不同数据集上得到验证，这些数据却因不同分布的噪声而损坏。实验结果始终证明，我们的方法在噪声鲁棒性和特征感知方面都比最新技术有了明显的改进。