解决多物体隐式表面模型的穿透问题，让物体永不相交。
S2MDF: A Plug-And-Play Layer for Intersection-Free Multi-Object Signed Distance Fields
- 提出硬约束机制，强制多物体距离场不穿透。
- 在多个先进方法上实现零穿透，精度达数值极限。
- 轻量模块可直接插入现有流程，无需改架构。
组合隐式表面表示将场景建模为多个由符号距离场（SDF）编码的物体集合。该方法的根本局限在于多个SDF可能生成相互穿插的几何体，违背物理合理性。现有缓解策略依赖软惩罚项，仅减少但无法彻底消除交叠，且需精细调整损失权重。为真正杜绝穿插，我们提出对向量值SDF的硬约束，并引入S2MDF——一个轻量级即插即用模块，可在不修改架构的前提下，对任意组合式SDF表示强制该约束。该模块计算开销极小，兼容线性插值的标准网格化算法（如Marching Cubes），支持训练阶段或后处理阶段使用。在多个前沿组合方法上的实验表明，S2MDF将交叠降至数值精度，同时保持重建质量，显著优于现有缓解策略。
原文摘要 · Abstract (English)
Compositional implicit surface representations model scenes as collections of objects, each encoded by a Signed Distance Field (SDF). A fundamental limitation of this approach is that multiple SDFs can produce geometries that interpenetrate, violating physical plausibility. Existing mitigation strategies rely on soft penalty terms that reduce but do not eliminate intersections, and require careful loss weighting. To truly prevent interpenetration, we propose a hard constraint on vector-valued SDFs and introduce S2MDF, a lightweight plug-and-play module that enforces the constraint on any object-compositional SDF representation without architectural modifications. It introduces negligible computational overhead and is compatible with linearly-interpolated standard meshing algorithms such as Marching Cubes. It can be applied during training or as a post-processing step. Experiments on multiple state-of-the-art compositional methods show that S2MDF reduces intersections to numerical precision while preserving reconstruction quality, outperforming existing mitigation strategies.
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