Deniz Sayin Mercadier

Deniz Sayin Mercadier, Federico Stella, Aurel Bizeau et al.

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.

Deniz Sayin Mercadier, Hieu Le, Yihong Chen et al.

Human organs are composed of interconnected substructures whose geometry and spatial relationships constrain one another. Yet, most deep-learning approaches treat these parts independently, producing anatomically implausible reconstructions. We introduce PrIntMesh, a template-based, topology-preserving framework that reconstructs organs as unified systems. Starting from a connected template, PrIntMesh jointly deforms all substructures to match patient-specific anatomy, while explicitly preserving internal boundaries and enforcing smooth, artifact-free surfaces. We demonstrate its effectiveness on the heart, hippocampus, and lungs, achieving high geometric accuracy, correct topology, and robust performance even with limited or noisy training data. Compared to voxel- and surface-based methods, PrIntMesh better reconstructs shared interfaces, maintains structural consistency, and provides a data-efficient solution suitable for clinical use.