Neural implicit representation, the parameterization of distance function as a coordinate neural field, has emerged as a promising lead in tackling surface reconstruction from unoriented point clouds. To enforce consistent orientation, existing methods focus on regularizing the gradient of the distance function, such as constraining it to be of the unit norm, minimizing its divergence, or aligning it with the eigenvector of Hessian that corresponds to zero eigenvalue. However, under the presence of large scanning noise, they tend to either overfit the noise input or produce an excessively smooth reconstruction. In this work, we propose to guide the surface reconstruction under a new variant of neural field, the octahedral field, leveraging the spherical harmonics representation of octahedral frames originated in the hexahedral meshing. Such field automatically snaps to geometry features when constrained to be smooth, and naturally preserves sharp angles when interpolated over creases. By simultaneously fitting and smoothing the octahedral field alongside the implicit geometry, it behaves analogously to bilateral filtering, resulting in smooth reconstruction while preserving sharp edges. Despite being operated purely pointwise, our method outperforms various traditional and neural approaches across extensive experiments, and is very competitive with methods that require normal and data priors. Our full implementation is available at: https://github.com/Ankbzpx/frame-field.

翻译：神经隐式表示——将距离函数参数化为坐标神经场——已成为处理无定向点云表面重建的一个有前景的方向。为强制实现一致的方向性，现有方法侧重于对距离函数的梯度进行正则化，例如约束其为单位范数、最小化其散度，或将其与海森矩阵对应零特征值的特征向量对齐。然而，在大扫描噪声存在的情况下，这些方法往往要么过度拟合噪声输入，要么产生过度平滑的重建结果。在本工作中，我们提出在一种新型神经场变体——八面体场的引导下进行表面重建，该场利用了源自六面体网格化的八面体框架的球谐函数表示。这种场在约束为平滑时会自动贴合几何特征，并在跨越折痕插值时自然地保持锐利角度。通过同时拟合和平滑八面体场与隐式几何，其行为类似于双边滤波，从而在保持锐利边缘的同时实现平滑重建。尽管我们的方法完全基于逐点操作，但在大量实验中超越了多种传统及神经方法，并且与需要法向量和数据先验的方法相比极具竞争力。我们的完整实现可在以下网址获取：https://github.com/Ankbzpx/frame-field。