Bo Pang

Bo Pang, Zhongtian Zheng, Yilong Li et al.

The discrete Laplacian operator holds a crucial role in 3D geometry processing, yet it is still challenging to define it on point clouds. Previous works mainly focused on constructing a local triangulation around each point to approximate the underlying manifold for defining the Laplacian operator, which may not be robust or accurate. In contrast, we simply use the K-nearest neighbors (KNN) graph constructed from the input point cloud and learn the Laplacian operator on the KNN graph with graph neural networks (GNNs). However, the ground-truth Laplacian operator is defined on a manifold mesh with a different connectivity from the KNN graph and thus cannot be directly used for training. To train the GNN, we propose a novel training scheme by imitating the behavior of the ground-truth Laplacian operator on a set of probe functions so that the learned Laplacian operator behaves similarly to the ground-truth Laplacian operator. We train our network on a subset of ShapeNet and evaluate it across a variety of point clouds. Compared with previous methods, our method reduces the error by an order of magnitude and excels in handling sparse point clouds with thin structures or sharp features. Our method also demonstrates a strong generalization ability to unseen shapes. With our learned Laplacian operator, we further apply a series of Laplacian-based geometry processing algorithms directly to point clouds and achieve accurate results, enabling many exciting possibilities for geometry processing on point clouds. The code and trained models are available at https://github.com/IntelligentGeometry/NeLo.

Jihe Li, Bo Pang, Peng-Shuai Wang

Recovering dense and uniformly distributed point clouds from sparse or noisy data remains a significant challenge. Recently, great progress has been made on these tasks, but usually at the cost of increasingly intricate modules or complicated network architectures, leading to long inference time and huge resource consumption. Instead, we embrace simplicity and present a simple yet efficient method for jointly upsampling and cleaning point clouds. Our method leverages an off-the-shelf octree-based 3D U-Net (OUNet) with minor modifications, enabling the upsampling and cleaning tasks within a single network. Our network directly processes each input point cloud as a whole instead of processing each point cloud patch as in previous works, which significantly eases the implementation and brings at least 47 times faster inference. Extensive experiments demonstrate that our method achieves state-of-the-art performances under huge efficiency advantages on a series of benchmarks. We expect our method to serve simple baselines and inspire researchers to rethink the method design on point cloud upsampling and cleaning.