Point cloud denoising and normal estimation are two fundamental yet dependent problems in digital geometry processing. However, both are often independently researched, leading to inconsistent geometry on 3D surfaces. To address it, we propose PN-Internet, an end-to-end Point-and-Normal Interactive Network for joint point cloud denoising and normal estimation. PN-Internet leverages the geometric dependency between point positions and normals to design two interactive graph convolution networks (GCNs): a point-to-normal network and a normal-to-point network. It adopts a coarse-to-fine learning paradigm, where two GCNs are exploited to respectively perform point cloud denoising and normal estimation. The point-to-normal network improves the quality of the normals using an MLP module, while the normal-to-point network refines the point positions using a parameter-free projection module based on the constraints from the normals. In addition, we introduce a feature-aware loss function to preserve the quality of 3D shape features. Unlike most existing methods, PN-Internet takes advantage of the geometric dependency between points and normals and benefits from training data. Our experimental results demonstrate that PN-Internet achieves geometric consistency between point cloud denoising and normal estimation. Furthermore, we show significant improvements over state-of-the-art methods.

Convolution on 3D point clouds is widely researched yet far from perfect in geometric deep learning. The traditional wisdom of convolution characterises feature correspondences indistinguishably among 3D points, arising an intrinsic limitation of poor distinctive feature learning. In this article, we propose Adaptive Graph Convolution (AGConv) for wide applications of point cloud analysis. AGConv generates adaptive kernels for points according to their dynamically learned features. Compared with the solution of using fixed/isotropic kernels, AGConv improves the flexibility of point cloud convolutions, effectively and precisely capturing the diverse relations between points from different semantic parts. Unlike the popular attentional weight schemes, AGConv implements the adaptiveness inside the convolution operation instead of simply assigning different weights to the neighboring points. Extensive evaluations clearly show that our method outperforms state-of-the-arts of point cloud classification and segmentation on various benchmark datasets. Meanwhile, AGConv can flexibly serve more point cloud analysis approaches to boost their performance. To validate its flexibility and effectiveness, we explore AGConv-based paradigms of completion, denoising, upsampling, registration and circle extraction, which are comparable or even superior to their competitors.