Wavelet-based Global Orientation and Surface Reconstruction for Point Clouds

2025-06-19

AI Summary

This paper addresses surface reconstruction from sparse, unoriented point clouds. Methodologically, it introduces a unified wavelet-based framework that jointly solves normal orientation and surface reconstruction: (1) It represents the smoothed indicator function using compactly supported orthogonal wavelet bases—leveraging both compact support and orthogonality for robust normal estimation on unoriented point clouds; (2) it enforces geometric consistency via a divergence-free vector field to impose homogeneous constraints; and (3) it transfers modified kernel smoothing into the wavelet domain to accelerate optimization and suppress surface discontinuities. Experiments demonstrate state-of-the-art performance in both reconstruction accuracy and normal orientation quality on sparse point clouds. The method is computationally efficient and scalable on CPU platforms, and its implementation is publicly available.

Technology Category

• Machine Learning: Learning with Manifolds
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Computer Vision: 3D Computer Vision

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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.

Problem

• Reconstructing surfaces from unoriented sparse point clouds
• Improving orientation and reconstruction using wavelet-based methods
• Accelerating computation via wavelet basis and kernel optimization

Innovation

• Wavelet-based mollified indicator function representation
• Divergence-free function field for homogeneous constraints
• Compact support alignment for accelerated matrix construction