Rethinking the Approximation Error in 3D Surface Fitting for Point Cloud Normal Estimation
This work addresses a specific bottleneck in 3D computer vision for applications like robotics and graphics, but it is incremental as it builds on existing methods.
The paper tackles the problem of inaccurate normal estimation in point clouds by addressing the approximation error in surface fitting, resulting in improved state-of-the-art performance on synthetic and real-world datasets.
Most existing approaches for point cloud normal estimation aim to locally fit a geometric surface and calculate the normal from the fitted surface. Recently, learning-based methods have adopted a routine of predicting point-wise weights to solve the weighted least-squares surface fitting problem. Despite achieving remarkable progress, these methods overlook the approximation error of the fitting problem, resulting in a less accurate fitted surface. In this paper, we first carry out in-depth analysis of the approximation error in the surface fitting problem. Then, in order to bridge the gap between estimated and precise surface normals, we present two basic design principles: 1) applies the $Z$-direction Transform to rotate local patches for a better surface fitting with a lower approximation error; 2) models the error of the normal estimation as a learnable term. We implement these two principles using deep neural networks, and integrate them with the state-of-the-art (SOTA) normal estimation methods in a plug-and-play manner. Extensive experiments verify our approaches bring benefits to point cloud normal estimation and push the frontier of state-of-the-art performance on both synthetic and real-world datasets.