Novel Neural Network Method Improves Accuracy of Signed Distance Function Computation from Point Clouds
Researchers have proposed a novel neural-network-based variational method for computing highly accurate signed distance functions (SDFs) from unoriented point clouds by explicitly incorporating the medial axis of a surface. The approach uses a phase field approximation of Ambrosio-Tortorelli type to handle the gradient discontinuity at the medial axis, enforcing the eikonal equation and zero-level set as constraints. The method demonstrates improved accuracy both near and far from the surface compared to existing approaches, with potential implications for 3D reconstruction, computer graphics, and geometric deep learning.
A preprint posted to arXiv introduces a variational framework for computing signed distance functions (SDFs) from unoriented point clouds that explicitly accounts for the medial axis — the locus of points equidistant from two or more surface points where the SDF gradient is discontinuous. Traditional SDF learning methods often struggle with global accuracy because they do not handle this discontinuity set, leading to artifacts away from the surface. The proposed method addresses this by adopting a higher-order variational formulation that enforces linear gradient growth away from the medial axis, combined with a phase field approximation of Ambrosio-Tortorelli type that implicitly represents the medial axis. Both the SDF and the phase field are parameterized as neural networks, making the approach compatible with modern deep learning pipelines. The eikonal equation — which constrains the SDF gradient magnitude to one — and the zero-level set condition are imposed as hard constraints. Quantitative and qualitative experiments show the method outperforms competing approaches in both near-field and global accuracy. The work spans computer vision, computational geometry, graphics, machine learning, and numerical analysis.
What's missing
It is not yet peer-reviewed, so independent validation of the claimed accuracy improvements is pending.
What different sources said
- arXiv cs.LGCenter
Medial Axis Aware Learning of Signed Distance Functions
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