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

Paper accepted to NeurIPS 2026

Deniz Sayin Mercadier, Federico Stella, Aurel Bizeau, Nicolas Talabot, Pascal Fua

* equal contribution

Feel free to contact us for any questions!

S2MDF at a glance

Each object of a compositional scene has its own Signed Distance Field (SDF), so nothing prevents two objects from interpenetrating. We require the two smallest SDF values at every point to sum to a non-negative number: the MDF constraint, which rules out intersections (Theorem 1). S2MDF enforces it in closed form by shifting all SDFs together (Shift-All), and since linear interpolation preserves the constraint (Theorem 2), standard Marching Cubes / Tetrahedra produce intersection-free meshes.

Abstract

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.

Presentation

A plug-and-play layer

p goes through a multi-object SDF network, giving SDF(p); the S2MDF layer turns it into MDF(p)

S2MDF sits on top of any network that predicts one SDF per object, without changing its architecture. It acts point-wise, adds no parameters and only a negligible cost, and can be used while training or as post-processing on an already-trained model.

Results

We plug S2MDF into three state-of-the-art compositional methods: ObjectSDF++ (indoor scenes), PartSDF (part-based shapes) and MedTet (medical shapes). Each video zooms in and then shows the objects in transparency: red regions are intersections between objects, green regions are contacts without interpenetration.

Vanilla

S2MDF Shift-All (PP)

S2MDF Shift-All (Train)

ObjectSDF++

Replica room 0, 256³ grid. (Train) uses the skip-connection variant.

PartSDF

PartNet chairs, 128³ grid.

MedTet

MM-WHS heart, 64³ tetrahedral grid subdivided once.

intersectioncontact

PP: post-processing of the trained vanilla model. Train: S2MDF used during training.

Quantitative results

	MCD ↓	MNC ↑	F1 ↑	IoU ↑	IV ↓
ObjectSDF++ · Replica, 8 scenes · MCD ×10⁻²
Vanilla ObjectSDF++	10.677	77.953	66.946	–	1.4·10⁻³
S2MDF Shift-All (PP)	3.345	78.058	68.325	–	1.3·10⁻⁷
S2MDF Shift-All (Train)*	3.942	78.430	68.623	–	1.5·10⁻⁶
PartSDF · PartNet chairs · MCD ×10⁻⁴
Vanilla PartSDF	4.331	95.119	96.731	85.630	1.9·10⁻³
S2MDF Shift-All (PP)	1.973	94.824	98.005	89.173	5.2·10⁻⁹
S2MDF Shift-All (Train)	2.120	94.823	98.039	89.297	5.7·10⁻⁹
MedTet · MM-WHS heart · MCD ×10⁻⁴
Vanilla MedTet	23.863	94.333	97.470	83.580	3.4·10⁻⁴
S2MDF Shift-All (PP)	31.099	94.316	97.297	83.694	9.9·10⁻¹²
S2MDF Shift-All (Train)	23.094	94.407	97.556	83.901	4.6·10⁻¹¹

Same reconstruction quality, with the intersection volume (IV) down to numerical precision. MCD: mean Chamfer distance, MNC: mean normal consistency, IV: intersection volume. *Skip-connection variant. Mean over 3 runs. See the paper for comparisons with existing mitigation strategies.

BibTeX

If you find our work useful, please cite it:

@inproceedings{sayinmercadierstella2026s2mdf,
  author    = {Sayin Mercadier, Deniz and Stella, Federico and Bizeau, Aurel and Talabot, Nicolas and Fua, Pascal},
  title     = {{S2MDF}: A Plug-And-Play Layer for Intersection-Free Multi-Object Signed Distance Fields},
  booktitle = {Advances in Neural Information Processing Systems},
  year      = {2026}
}