用球面相交优化生成点，让三维形状重建更平滑
VoroLight: Learning Voronoi Surface Meshes via Sphere Intersection
- 为每个表面顶点配一个可训练球，通过球面相交损失控制几何均匀性
- 在点云、网格、多视角图像等多模态输入下实现高保真重建
- 保持拓扑一致性与封闭性，适合需要规则表面的3D建模任务
Voronoi图天然具备凸性、封闭性和拓扑一致性，是三维形状重建的理想表示。然而传统可微Voronoi方法仅优化生成点位置，易导致表面局部不均。本文提出VoroLight，一种通过球面相交损失引导高阶等距关系的可微框架，使每个Voronoi表面顶点关联一个可训练球体，从而促进表面几何平滑。该方法直接在表面顶点上定义损失，支持来自隐式场、点云、网格和多视角图像的多模态监督。通过引入内部生成点并施加重心Voronoi分割目标，框架可自然扩展至具有一致表面-内部拓扑的体素Voronoi网格。在多种输入模态下，VoroLight实现了媲美现有方法的重建保真度，同时生成更光滑、更几何规则的Voronoi表面。
原文摘要 · Abstract (English)
Voronoi diagrams naturally produce convex, watertight, and topologically consistent cells, making them an appealing representation for 3D shape reconstruction. However, standard differentiable Voronoi approaches typically optimize generator positions in stable configurations, which can lead to locally uneven surface geometry. We present VoroLight, a differentiable framework that promotes controlled Voronoi degeneracy for smooth surface reconstruction. Instead of optimizing generator positions alone, VoroLight associates each Voronoi surface vertex with a trainable sphere and introduces a sphere--intersection loss that encourages higher-order equidistance among face-incident generators. This formulation improves surface regularity while preserving intrinsic Voronoi properties such as watertightness and convexity. Because losses are defined directly on surface vertices, VoroLight supports multimodal shape supervision from implicit fields, point clouds, meshes, and multi--view images. By introducing additional interior generators optimized under a centroidal Voronoi tessellation objective, the framework naturally extends to volumetric Voronoi meshes with consistent surface--interior topology. Across diverse input modalities, VoroLight achieves competitive reconstruction fidelity while producing smoother and more geometrically regular Voronoi surfaces. Project page: https://jiayinlu19960224.github.io/vorolight/
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