# Wavelet-based Global Orientation and Surface Reconstruction for Point Clouds

arXiv: https://arxiv.org/abs/2506.16299 · HTML: https://mlsanity.com/paper/2506.16299/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 19 Jun 2025.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [Points2Surf: Learning Implicit Surfaces from Point Cloud Patches](https://mlsanity.com/paper/2007.10453/) (2020)
- [DiGS : Divergence guided shape implicit neural representation for unoriented point clouds](https://mlsanity.com/paper/2106.10811/) (2021)
- [Globally Consistent Normal Orientation for Point Clouds by Regularizing the Winding-Number Field](https://mlsanity.com/paper/2304.11605/) (2023)
- [Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian](https://mlsanity.com/paper/2309.01793/) (2023)
- [Orienting Point Clouds with Dipole Propagation](https://mlsanity.com/paper/2105.01604/) (2021)
- [Iterative Poisson Surface Reconstruction (iPSR) for Unoriented Points](https://mlsanity.com/paper/2209.09510/) (2022)
- [Stochastic Poisson Surface Reconstruction](https://mlsanity.com/paper/2206.15236/) (2022)
- [A Closed-Form Formulation of HRBF-Based Surface Reconstruction](https://mlsanity.com/paper/1507.02860/) (2015)

## Abstract (arXiv)

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.