Neural Octahedral Field: Octahedral prior for simultaneous smoothing and sharp edge regularization

TL;DR

The paper tackles the challenge of simultaneously smoothing while preserving sharp edges in neural implicit surface reconstructions from noisy unoriented point clouds. It introduces a neural octahedral field that assigns symmetry-aware octahedral frames to every 3D location via an MLP and aligns these frames with the distance field gradient using a pair of pointwise losses, effectively enabling edge-aware regularization in a fully implicit, pointwise framework. The method supports both signed and unsigned distance fields and demonstrates strong performance against a broad set of baselines on standard datasets, with extensive ablations validating initialization and weight choices. While exhibiting competitive results and edge-preserving behavior, the approach relies on faithful initialization and incurs higher computational cost, motivating future work on adaptive scaling and integration with data priors.

Abstract

Neural implicit representation, the parameterization of a continuous distance function as a Multi-Layer Perceptron (MLP), has emerged as a promising lead in tackling surface reconstruction from unoriented point clouds. In the presence of noise, however, its lack of explicit neighborhood connectivity makes sharp edges identification particularly challenging, hence preventing the separation of smoothing and sharpening operations, as is achievable with its discrete counterparts. In this work, we propose to tackle this challenge with an auxiliary field, the \emph{octahedral field}. We observe that both smoothness and sharp features in the distance field can be equivalently described by the smoothness in octahedral space. Therefore, by aligning and smoothing an octahedral field alongside the implicit geometry, our method behaves analogously to bilateral filtering, resulting in a smooth reconstruction while preserving sharp edges. Despite being operated purely pointwise, our method outperforms various traditional and neural implicit fitting approaches across extensive experiments, and is very competitive with methods that require normals and data priors. Code and data of our work are available at: https://github.com/Ankbzpx/frame-field.

Figures (20)

• Figure 1: Geometric intuition. (a) Consider a 2D smooth vector field evaluated at two spatial locations as a pair of orthogonal vectors. Due to spatial smoothness, the vectors associated with points in-between need to cover $90^\circ$ angle difference (b). If the vector field is the gradient field of a 2D SDF, and those two points are its zero level samples, then the underlying surface crossing them must have normal vectors covering at least $90^\circ$ on the Gauss map (visualized as solid color on the circle) (c). Without additional constraints or priors, it is difficult to reduce the neighborhood for the normal rotation to produce a visually sharp turning. (d) Now consider a special vector field, the 2D cross field, that exhibits $90^\circ$ symmetry. Since both vectors are equivalent under orthogonality, there is no angle difference between them (e). Therefore, when used as a guidance for the SDF gradient field, the cross field naturally induces a sharp geometric prior (f).
• Figure 2: The illustration of our pipeline. Given an unoriented point cloud (a), we initialize a distance field. By pairing with an aligned octahedral field and encouraging smoothness in octahedral space (b-d), we perform simultaneous smoothing and sharpening of the underlying geometry.
• Figure 3: Non-$90^\circ$ dihedral angle handling, the green strokes indicate the zero level sets under smooth vector interpolation, while the red strokes indicate the ones under our guidance. Although $90^\circ$ symmetry cannot precisely describe a non-$90^\circ$ angle, it can still serve as a prior for visually sharp features (a-d), and when the angle difference is small, it converges to smooth vector interpolation (e).
• Figure 4: Qualitative results of implicit fitting methods on ABC / Thingi10k at noise level $0.002L$. Our method outperforms others with cleaner shape features.
• Figure 5: Qualitative result of denoising methods on ABC / Thingi10k. Our method performs better at highlighting sharp edges and maintaining organic shape features.