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.

翻译：组合隐式表面表示将场景建模为物体的集合，每个物体由符号距离场（SDF）编码。该方法的一个根本限制是多个SDF可能产生相互穿透的几何结构，从而违反物理合理性。现有的缓解策略依赖于软惩罚项，该方法虽能减少但无法消除交叉，且需要精细的损失权重调整。为真正防止相互穿透，我们提出对向量值SDF施加硬约束，并引入S2MDF——一种轻量级即插即用模块，可在无需修改架构的情况下对任意物体组合SDF表示实施该约束。该模块引入的计算开销可忽略不计，且兼容线性插值的标准网格化算法（如Marching Cubes）。它可应用于训练阶段或作为后处理步骤。在多种先进组合方法上的实验表明，S2MDF在保持重建质量的同时将交叉降至数值精度水平，性能优于现有缓解策略。