Neural Octahedral Field: Octahedral prior for simultaneous smoothing and sharp edge regularization
This addresses a key problem in 3D reconstruction for applications like computer graphics and robotics, offering an incremental improvement by integrating a novel auxiliary field into existing neural implicit frameworks.
The paper tackles the challenge of reconstructing surfaces from noisy, unoriented point clouds using neural implicit representations, which struggle with identifying sharp edges while smoothing. It introduces an octahedral field to simultaneously smooth surfaces and preserve sharp edges, outperforming various traditional and neural methods in experiments.
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.