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Most existing approaches for point cloud normal estimation aim to locally fita geometric surface and calculate the normal from the fitted surface. Recently,learning-based methods have adopted a routine of predicting point-wise weightsto solve the weighted least-squares surface fitting problem. Despite achievingremarkable progress, these methods overlook the approximation error of thefitting problem, resulting in a less accurate fitted surface. In this paper, wefirst carry out in-depth analysis of the approximation error in the surfacefitting problem. Then, in order to bridge the gap between estimated and precisesurface normals, we present two basic design principles: 1) applies the$Z$-direction Transform to rotate local patches for a better surface fittingwith a lower approximation error; 2) models the error of the normal estimationas a learnable term. We implement these two principles using deep neuralnetworks, and integrate them with the state-of-the-art (SOTA) normal estimationmethods in a plug-and-play manner. Extensive experiments verify our approachesbring benefits to point cloud normal estimation and push the frontier ofstate-of-the-art performance on both synthetic and real-world datasets.

Rethinking the Approximation Error in 3D Surface Fitting for Point Cloud Normal Estimation