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.

本研究解决了在大量扫描噪声存在时表面重建中过拟合或过于平滑的问题。提出了一种新型的神经场，八面体场，通过球面调和的表示，自动捕捉几何特征，确保在平滑的同时保留锐角。实验表明，该方法在各种传统和神经方法中表现出色，具有显著的实际应用潜力。

神经八面体场：用于同时平滑和锐边正则化的八面体先验