分离距离与符号信息，更精准重建薄结构点云。
Metric--Phase Fields: Decoupling Distance and Sign for Thin-Structure Reconstruction from Unoriented Point Clouds
- 解耦度量距离与拓扑相位，用双场建模几何
- 在薄壳和薄板上比SDF方法更保真，训练更稳定
- 适合处理无方向点云的复杂薄结构重建
神经符号距离函数（SDF）在重建封闭曲面时表现优异，但在薄结构和开放边界上因严格的内外约束而失效。相反，无符号距离场（UDF）虽能适应复杂几何，却在零等值面处出现梯度奇异，影响优化与提取。本文提出度量-相位场（MPFs），一种解耦度量接近性与拓扑相位的隐式表示。给定无方向点云，MPFs学习一个无符号度量场 $r$ 与一个平滑相位场 $θ$，通过 $ anh(βθ)$ 构造有界相位指示器 $P$，提供有意义的软内外提示。采用门控度量与残差相位注入机制，融合两场得到具有稳定近表面梯度的符号隐式函数。相位系数 $β$ 可学习，实现相位跃迁锐度与符号饱和度的自适应控制。在合成与扫描的薄壳、薄板数据集上的实验表明，MPFs在保留细长结构方面优于最新SDF方法，同时训练鲁棒性与表面提取可靠性超过UDF方法。
原文摘要 · Abstract (English)
Neural Signed Distance Functions (SDFs) excel at reconstructing watertight manifolds but fail on thin structures and open boundaries due to strict inside--outside constraints. Conversely, Unsigned Distance Fields (UDFs) accommodate general geometries but suffer from gradient singularities at the zero-level set, hindering optimization and extraction. We introduce Metric--Phase Fields (MPFs), a decoupled implicit representation that separates metric proximity from topological phase. Given an unoriented point cloud, MPFs learn (i) an unsigned metric field $r$ and (ii) a smooth phase field $θ$, for which we derive a bounded phase indicator $P=\tanh(βθ)$ that provides soft inside--outside cues where they are meaningful. We couple the two fields via a gated-metric formulation with a residual phase injection to obtain a signed implicit function with stable near-surface gradients. The phase coefficient $β$ is learnable, allowing MPFs to adaptively control the sharpness of the phase transition and the degree of saturation of the soft sign indicator. Experiments on both synthetic and scanned thin-shell and thin-plate shapes demonstrate that MPFs preserve thin and layered structures more faithfully than recent SDF-based methods, while also enabling more robust training and more reliable surface extraction than UDF-based approaches. Check out \href{https://github.com/JIAYI-Scarlett/ICML2026-MPF}{MPFs-GitHub} for source code and test models.
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