Advancements in 3D curve skeletonization are accelerating progress across a wide range of applications. However, developing robust skeletonization algorithms that capture intricate object details remains challenging. Skeletonization via Local Separators (LS) offers an efficient graph-based approach but suffers from representation inaccuracies due to its discrete nature. To address this, we introduce CSCD, a novel framework for Curve Skeletonization in the Continuous Domain, generalizing LS to manifolds. Specifically, we present two realizations: CSCD-M for meshes and CSCD-PC for point clouds. CSCD-M leverages the intrinsic triangulation of a mesh for resilience to noise and improved topological preservation, while CSCD-PC employs tufted Laplacians for enhanced robustness. To our knowledge, CSCD-M is the first intrinsic method for curve skeletonization. Our results show CSCD-M matches LS performance across diverse meshes and outperforms LS (TOG'21) on benchmarks like Thingi10k dataset. CSCD-PC qualitatively outperforms CoverageAxis++ (Eurographics'24) and EPCS (CAG'23). Finally, we demonstrate the efficacy of CSCD in a few downstream tasks: object classification, shape segmentation, identifying handles, tunnels, and constrictions in objects. Project Website: https://cscd-skel.pages.dev

翻译：三维曲线骨架化技术的进步正在加速推进众多应用领域的发展。然而，开发能够捕捉复杂物体细节的鲁棒骨架化算法仍然面临挑战。基于局部分隔符的骨架化方法提供了一种高效的图论方案，但由于其离散本质导致表示精度不足。为解决这一问题，我们提出CSCD框架——一种在连续域实现曲线骨架化的新型方法，将LS方法推广至流形空间。具体而言，我们实现了两种方案：针对网格的CSCD-M和针对点云的CSCD-PC。CSCD-M利用网格的固有三角剖分以增强抗噪性和拓扑保持能力，而CSCD-PC则采用簇状拉普拉斯算子提升鲁棒性。据我们所知，CSCD-M是首个用于曲线骨架化的内蕴方法。实验结果表明，CSCD-M在多样化网格上的性能与LS方法相当，并在Thingi10k等基准测试中优于LS方法（TOG'21）。CSCD-PC在定性评估上超越CoverageAxis++（Eurographics'24）和EPCS（CAG'23）。最后，我们通过物体分类、形状分割、把手识别、孔洞检测及收缩区域识别等下游任务验证了CSCD的有效性。项目网站：https://cscd-skel.pages.dev