Wavelet-based Global Orientation and Surface Reconstruction for Point Clouds

TL;DR

This paper introduces a wavelet-based approach for unoriented surface reconstruction from point clouds, effectively handling sparse data and improving accuracy and efficiency over previous methods.

Contribution

It proposes a novel wavelet-based method for joint orientation and surface reconstruction, including a divergence-free function field and optimized matrix construction for speed.

Findings

Achieves state-of-the-art results on sparse point clouds

Demonstrates improved stability and accuracy

Offers efficient CPU performance

Abstract

Unoriented surface reconstruction is an important task in computer graphics and has extensive applications. Based on the compact support of wavelet and orthogonality properties, classic wavelet surface reconstruction achieves good and fast reconstruction. However, this method can only handle oriented points. Despite some improved attempts for unoriented points, such as iWSR, these methods perform poorly on sparse point clouds. To address these shortcomings, we propose a wavelet-based method to represent the mollified indicator function and complete both the orientation and surface reconstruction tasks. We use the modifying kernel function to smoothen out discontinuities on the surface, aligning with the continuity of the wavelet basis function. During the calculation of coefficient, we fully utilize the properties of the convolutional kernel function to shift the modifying computation onto wavelet basis to accelerate. In addition, we propose a novel method for constructing the divergence-free function field and using them to construct the additional homogeneous constraints to improve the effectiveness and stability. Extensive experiments demonstrate that our method achieves state-of-the-art performance in both orientation and reconstruction for sparse models. We align the matrix construction with the compact support property of wavelet basis functions to further accelerate our method, resulting in efficient performance on CPU. Our source codes will be released on GitHub.