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/

翻译：尽管行进立方体（MC）和行进四面体（MTet）因其简单高效而被广泛采用于三维重建流程中，但其可微分变体在网格提取方面仍不尽如人意。这通常限制了基于学习的框架中从点云或图像重建的三维网格质量。相比之下，裁剪质心Voronoi剖分（clipped CVT）提供了更强的理论保证并能生成更高质量的网格。然而，由于缺乏可微分形式，其一直未能被集成到现代机器学习流程中。为弥补这一差距，我们提出了DCCVT，一种利用裁剪CVT从含噪符号距离场（SDF）中提取高质量三维网格的可微分算法。我们推导了计算裁剪CVT的完全可微分形式，并展示了其与基于深度学习的SDF估计相结合，从输入点云重建精确三维网格的过程。我们在合成数据上的实验表明，DCCVT在网格质量和重建保真度方面优于现有先进方法。https://wylliamcantincharawi.dev/DCCVT.github.io/