3D point clouds are often perturbed by noise due to the inherent limitation of acquisition equipments, which obstructs downstream tasks such as surface reconstruction, rendering and so on. Previous works mostly infer the displacement of noisy points from the underlying surface, which however are not designated to recover the surface explicitly and may lead to sub-optimal denoising results. To this end, we propose to learn the underlying manifold of a noisy point cloud from differentiably subsampled points with trivial noise perturbation and their embedded neighborhood feature, aiming to capture intrinsic structures in point clouds. Specifically, we present an autoencoder-like neural network. The encoder learns both local and non-local feature representations of each point, and then samples points with low noise via an adaptive differentiable pooling operation. Afterwards, the decoder infers the underlying manifold by transforming each sampled point along with the embedded feature of its neighborhood to a local surface centered around the point. By resampling on the reconstructed manifold, we obtain a denoised point cloud. Further, we design an unsupervised training loss, so that our network can be trained in either an unsupervised or supervised fashion. Experiments show that our method significantly outperforms state-of-the-art denoising methods under both synthetic noise and real world noise. The code and data are available at https://github.com/luost26/DMRDenoise

本文提出了一种基于自编码器的3D点云去噪方法，该方法通过学习嵌入式邻域特征的稀疏点的局部和非局部特征表示，对3D点云中的噪声进行去除，并通过重建的流形重新采样得到去噪后的点云，该方法在合成噪声和真实世界噪声下均表现出显著的性能优于现有的去噪方法。

点云去噪的可微流形重建