Introducing the Taubin-Weingarten algorithm to compute second-order geometric descriptors in 3D point clouds

We propose the Taubin-Weingarten algorithm to compute second-order geometric features in 3D point clouds. This method is well-suited for working with large-scale 3D datasets due to its embarrassingly parallel nature. The speedup of our open-source C++ implementation is systematically above 30 for a high-performance CPU with 32 cores. It provides reliable estimates for standard quantifications in differential geometry, such as the Gaussian and mean curvatures of a surface, when compared to other approaches. Additionally, it achieves improvements of between 1.6 % and 10 % in F1-score compared to the standard first-order approach in point-wise classification tasks, such as object part segmentation and large-scale semantic scene segmentation. The results demonstrate that the Taubin-Weingarten algorithm is both efficient and robust, enabling consistent improvements in machine learning performance across various tasks.