VortSDF: 3D Modeling with Centroidal Voronoi Tesselation on Signed Distance Field

TL;DR

VortSDF introduces a hierarchical Centroidal Voronoi Tessellation to adaptively discretize space around a surface and jointly optimize an explicit $SDF$ together with shallow color networks for multi-view reconstruction. By operating on the CVT dual tetrahedral mesh and employing differentiable rendering, the method concentrates samples near the surface, enabling detailed geometry with far fewer points and faster convergence than uniform-grid baselines. The approach includes an approximate, scalable CVT optimization guided by bisectors, a tetrahedral ray marching scheme, and regularization strategies to stabilize the $SDF$ field, yielding state-of-the-art or competitive results on BlendedMVS and 4D Human Outfit datasets while reducing computational cost. This work demonstrates that nonuniform, surface-aware discretizations can substantially improve reconstruction quality and efficiency, with practical implications for large-scale scene capture and animation pipelines.

Abstract

Volumetric shape representations have become ubiquitous in multi-view reconstruction tasks. They often build on regular voxel grids as discrete representations of 3D shape functions, such as SDF or radiance fields, either as the full shape model or as sampled instantiations of continuous representations, as with neural networks. Despite their proven efficiency, voxel representations come with the precision versus complexity trade-off. This inherent limitation can significantly impact performance when moving away from simple and uncluttered scenes. In this paper we investigate an alternative discretization strategy with the Centroidal Voronoi Tesselation (CVT). CVTs allow to better partition the observation space with respect to shape occupancy and to focus the discretization around shape surfaces. To leverage this discretization strategy for multi-view reconstruction, we introduce a volumetric optimization framework that combines explicit SDF fields with a shallow color network, in order to estimate 3D shape properties over tetrahedral grids. Experimental results with Chamfer statistics validate this approach with unprecedented reconstruction quality on various scenarios such as objects, open scenes or human.

Figures (6)

• Figure 1: We propose a volumetric optimization framework that combines explicit SDF fields and learnable features with two shallow color networks, in order to estimate 3D shape properties over tetrahedral grids.
• Figure 2: The site locations are optimized using an approximated CVT algorithm that does not explicitly identify the Voronoi cells (left) but consider the neighboring bisectors instead (right).
• Figure 3: a) The SDF values at the intersecting segments extremities are obtained by linear interpolation of the SDF values at the entry and exit faces. Features at sampled points are linearly interpolated from the $4$ vertices of the tetrahedron. b) The viewing ray exit face is the face to which camera center belongs after projecting the tetrahedron into the plane perpendicular to the viewing ray.
• Figure 4: Comparative results we obtained with our method, NeuS and Voxurf on data "Stone", "Durian" and "Man" of BlendedMVS. We output the final 3D meshes using Marching Cubes (MC) for NeuS and Voxurf and Marching Tetrahedra for our method. We also show errors from ground truth meshes to predicted meshes as heatmaps.
• Figure 5: Comparative results we obtained with our method, NeuS and Voxurf on the 4D Human Outfit dataset. We output the final 3D meshes using Marching Cubes (MC) for NeuS and Voxurf and Marching Tetrahedra for our method.