The normals of feature points, i.e., the intersection points of multiple smooth surfaces, are ambiguous and undefined. This paper presents a unified definition for point cloud normals of feature and non-feature points, which allows feature points to possess multiple normals. This definition facilitates several succeeding operations, such as feature points extraction and point cloud filtering. We also develop a feature preserving normal estimation method which outputs multiple normals per feature point. The core of the method is a pair consistency voting scheme. All neighbor point pairs vote for the local tangent plane. Each vote takes the fitting residuals of the pair of points and their preliminary normal consistency into consideration. Thus the pairs from the same subspace and relatively far off features dominate the voting. An adaptive strategy is designed to overcome sampling anisotropy. In addition, we introduce an error measure compatible with traditional normal estimators, and present the first benchmark for normal estimation, composed of 152 synthesized data with various features and sampling densities, and 288 real scans with different noise levels. Comprehensive and quantitative experiments show that our method generates faithful feature preserving normals and outperforms previous cutting edge normal estimation methods, including the latest deep learning based method.

Point cloud processing is rapidly expanding the applicable scenarios in the industry. The surface normal is a fundamental feature for various point cloud processing tasks. Recently, deep supervised normal estimators outperform traditional normal estimation methods by adapting to dataset statistics. However, existing normal estimation methods mainly adopt hand-crafted features or complicated networks borrowed from other tasks and make less effort to design network models specifically for the problem. Instead of regressing the normal vector directly, we propose a simple deep network to estimate the normal vector based on a latent tangent space representation learned in the network. We call the network tangent represent learning network (TRNet). For each query point, the tangent space representation is a set of latent points spanning the tangent plane of it. The representation is generated using only the coordinates of its neighbors and regularized by a differentiable random sample consensus like component, which makes TRNet more compact and effective for normal estimation. We also design a compact multiscale network, denoted by multiresolution tangent representation learning network (MTRNet), to boost estimations from multiple TRNet trained with different fixed neighborhood size. Our TRNet and MTRNet perform favorably against state-of-the-art methods on synthesized data and real scenarios with far smaller model size.