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S2MDF: A Plug-And-Play Layer for Intersection-Free Multi-Object Signed Distance Fields

NeurIPS 2026 · 3D vision › Face and shape · approach: Neural implicit surface reconstruction · 0 citations (OpenAlex)

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Proposes S2MDF, a hard-constraint projection layer that makes vector-valued multi-object SDFs intersection-free (sum of two smallest values non-negative), usable during training or as post-processing, compatible with linear-interpolation meshing.

Problem

Compositional implicit surface representations built from multiple SDFs can produce interpenetrating objects; existing soft penalty losses reduce but do not eliminate intersections and need careful loss weighting.

Approach

Define a Multi-object Distance Field (MDF) via the constraint that the sum of the two smallest SDF values is non-negative, which is preserved under linear interpolation and thus safe for Marching Cubes/Tetrahedra; enforce it by projection, either via an exact QP or a cheap Shift-All heuristic, as a plug-in layer.

Key results

• On PartSDF chairs, QP and Shift-All post-processing reduce intersection volume from 1.876e-3 to roughly 5e-9 to 6e-9 while MCD improves from 4.331e-4 to about 2e-4.
• On MedTet TS-Lung, Shift-All (Train) reduces intersection volume from 2.755e-4 to 1.4e-7 with reconstruction metrics close to vanilla.
• Shift-All adds no measurable overhead in training or post-processing, whereas QP training on ObjectSDF++ was infeasible due to the number of objects.

Surprising findings

• Shift-All, a simple heuristic, matches or slightly beats the exact QP projection in reconstruction quality.
• Applying the constraint during training with the eikonal loss on the pre-constraint output gave lower MCD on ObjectSDF++.

Limitations

• QP projection becomes prohibitively slow for large numbers of objects (e.g. ObjectSDF++ scenes with dozens of objects).
• Small floating-point collisions can remain at touching regions; a margin epsilon is needed to fully eliminate them.
• Can introduce junction artifacts when ground-truth parts are non-watertight (PartNet chairs).

Experimental setup

Datasets: MM-WHS TS-Lung (TotalSegmentator) Replica PartNet

Benchmarks: MM-WHS TS-Lung Replica PartNet

Metrics: Mesh Chamfer Distance Mesh Normal Consistency F1 score Mesh IoU Intersection Volume

Baselines: Vanilla MedTet Vanilla ObjectSDF++ Vanilla PartSDF Min projection (appendix) intersection loss variant

Builds on: DeepSDF Deep Marching Tetrahedra ObjectSDF++ PartSDF Marching Cubes

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