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

2026-05-28

AI Summary

This work addresses the lack of physical plausibility in multi-object signed distance field (SDF) modeling, which often suffers from geometric interpenetration. The authors propose S2MDF—a lightweight, plug-and-play hard-constraint module that enforces non-overlapping conditions on vector-valued SDFs without modifying the underlying network architecture. To the best of our knowledge, this is the first approach to completely eliminate geometric intersections among multiple SDFs through hard constraints, avoiding the need for intricate loss function tuning. S2MDF can be flexibly applied during either training or post-processing and, when combined with a Marching Cubes–compatible linear interpolation-based meshing strategy, reduces object overlap to numerical precision across several state-of-the-art methods while preserving high-fidelity geometry reconstruction—significantly outperforming existing soft-constraint alternatives.

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.

Problem

• Signed Distance Field
• Multi-Object
• Intersection-Free
• Implicit Surface
• Geometric Interpenetration

Innovation

• Signed Distance Field
• intersection-free
• plug-and-play
• compositional representation
• hard constraint