# Metric--Phase Fields: Decoupling Distance and Sign for Thin-Structure Reconstruction from Unoriented Point Clouds

arXiv: https://arxiv.org/abs/2605.25503 · HTML: https://mlsanity.com/paper/2605.25503/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 48 references that are in the map.
- First posted on arXiv 25 May 2026.

## Builds on (most cited first, 3 of 3)

- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [Voronoi-Assisted Optimization for Diffusing Unsigned Distance Fields from Unoriented Points](https://mlsanity.com/paper/2510.12524/) (2025)

## Built on by (most cited first, 2 of 2)

- [Projective Normal Fields: A Convex Optimization Method for Constructing Smooth UDFs](https://mlsanity.com/paper/2609.34784/) (2026)
- [Volume Rendering with Metric--Phase Fields for Thin Structures and Sign-Ambiguous Geometry](https://mlsanity.com/paper/2610.13088/) (2026)

## Abstract (arXiv)

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 hrefhttps://github.com/JIAYI-Scarlett/ICML2026-MPFMPFs-GitHub for source code and test models.