DCCVT: Differentiable Clipped Centroidal Voronoi Tessellation

TL;DR

DCCVT introduces a differentiable clipped Centroidal Voronoi Tessellation framework to extract high-quality 3D meshes from noisy SDFs by jointly optimizing Voronoi site positions and SDF values, with robust projection of 0-crossing vertices and adaptive upsampling. The method combines CVT regularization, Eikonal SDF constraints, and MbMC smoothing to produce regular, watertight meshes and demonstrates superior reconstruction fidelity on the Thingi32 dataset compared to differentiable baselines like DMC and DMTet. The work enables end-to-end differentiable mesh extraction within learning pipelines and shows robustness to incomplete or imperfect SDF initializations, highlighting potential for integration with strong shape priors and advanced SDF estimators. Overall, DCCVT advances mesh quality and optimization coherence by unifying mesh extraction with SDF optimization through a differentiable clipped CVT formulation, with practical impact for learning-based 3D reconstruction from point clouds and images.

Abstract

While Marching Cubes (MC) and Marching Tetrahedra (MTet) are widely adopted in 3D reconstruction pipelines due to their simplicity and efficiency, their differentiable variants remain suboptimal for mesh extraction. This often limits the quality of 3D meshes reconstructed from point clouds or images in learning-based frameworks. In contrast, clipped CVTs offer stronger theoretical guarantees and yield higher-quality meshes. However, the lack of a differentiable formulation has prevented their integration into modern machine learning pipelines. To bridge this gap, we propose DCCVT, a differentiable algorithm that extracts high-quality 3D meshes from noisy signed distance fields (SDFs) using clipped CVTs. We derive a fully differentiable formulation for computing clipped CVTs and demonstrate its integration with deep learning-based SDF estimation to reconstruct accurate 3D meshes from input point clouds. Our experiments with synthetic data demonstrate the superior ability of DCCVT against state-of-the-art methods in mesh quality and reconstruction fidelity. https://wylliamcantincharawi.dev/DCCVT.github.io/

Figures (12)

• Figure 1: Comparison of 3D mesh reconstruction from an unoriented point cloud. (a) Input point cloud. (b) Input Signed Distance Field (SDF) reconstructed using Marching Cubes at $256^3$ resolution. (c) Voromesh baseline with $32^3$ sites. (d) Our proposed DCCVT method with $24^3$ sites plus near sampling sites, achieving more accurate and regular surface reconstruction.
• Figure 2: Overview of our proposed method. Starting from an unoriented 3D point cloud and an inferred SDF estimation from the point cloud (a), we initialize Voronoi sites (b), which yield a discretized SDF (zero-level shown in green). We then project zero-crossing Voronoi vertices (green stars) and edge midpoints (green squares) onto the SDF zero-level and minimize the Chamfer distance to the input point cloud (c–d). This optimization produces an improved site distribution and SDF representation (e), from which we extract the final mesh using our Voronoi-based meshing strategy (f), with Voronoi vertices shown in purple.
• Figure 3: After selecting a site, we compute the minimal distance $\mathrm{d}_{\mathrm{min}}$ and insert a tetrahedron aligned with the SDF gradient (a). This preserves the local site connectivity (b). Our upsampling strategy results in a non-uniform site distribution (c).
• Figure 4: Optimized results for different resolution of sites with an accurate SDF representation.
• Figure 5: Results for different upsampling methods on an inaccurate SDF representation. Every optimization uses the same number of sites.

Theorems & Definitions (2)

• proof
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