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The paper introduces S2MDF, a plug-and-play module that enforces a hard constraint on vector-valued Signed Distance Fields (SDFs) to eliminate interpenetration artifacts in compositional implicit surface representations. Unlike existing methods that rely on soft penalty terms, S2MDF guarantees intersection-free geometries to numerical precision without architectural changes or significant computational overhead. Experiments demonstrate that S2MDF outperforms state-of-the-art methods by achieving intersection-free results while maintaining reconstruction quality.
Finally, a way to guarantee intersection-free multi-object SDFs without finicky loss weighting or architectural surgery.
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.
