VoroFacet: Junction-aware Mesh Extraction from Neural Unsigned Distance Fields

Unsigned distance fields (UDFs) can represent surfaces of arbitrary topology, but recovering mesh connectivity from neural UDFs remains challenging, especially at non-manifold junctions where multiple sheets meet. To this end, we propose VoroFacet, a novel pipeline that extracts single-layer meshes from neural UDFs and reconstructs junction connectivity accurately through Voronoi facets. Specifically, we first use a near-surface double-layered proxy derived from the UDF as a local spatial partition for facet selection, where the facets belong to the Voronoi diagram of the sites generated by an adaptive ball cover of the proxy. We then estimate junctions from the mesh of this first extraction and place balls along them, so that in a re-extraction process, the resulting cospherical sites make incident sheets share Voronoi vertices and edges at these junctions. Finally, we propose a three-stage optimization to refine the geometry of the extracted mesh. Experiments demonstrate superior reconstruction quality over state-of-the-art methods, particularly at non-manifold junctions. The source code will be publicly available.