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

TL;DR

This paper introduces an octahedral field prior for neural implicit surface reconstruction, enabling simultaneous smoothing and sharp edge preservation from noisy point clouds without explicit neighborhood information.

Contribution

The paper proposes the octahedral field as an auxiliary prior to improve neural implicit surface reconstruction, allowing explicit control over smoothing and sharp edges in a pointwise manner.

Findings

Outperforms traditional and neural implicit methods in experiments

Achieves sharp edge preservation without explicit neighborhood info

Competitive with methods requiring normals and 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.