Convection Augmented Gauss Reconstruction for Unoriented Point Clouds

Abstract

Unoriented surface reconstructions based on the Gauss formula have attracted much attention due to their mathematical formulation and good experimental performance. However, the formula’s isotropy limits its capacity to leverage the directional features of point clouds. In this study, we introduce a convection augmentation term to extend the classic Gauss formula. This new term allows our method to leverage point clouds’ directional characteristics effectively. With the proper choice of the velocity field, this method could construct more equations to calculate a more precise indicator function. Furthermore, an adaptive selection strategy of the velocity field is proposed. For large-scale point clouds, we propose a CUDA-and-octree-based acceleration algorithm with O ( N ) space complexity and O ( N log N ) time complexity. Our method can complete the orientation and reconstruction tasks of point clouds with up to 500K within a few seconds. Extensive experiments demonstrate that our method achieves state-of-the-art performance and manages various challenging situations, especially for models with thin structures or small holes. The source code is publicly available at https://github.com/mayueji/CAGR .