提出连续域曲线骨架化框架，提升网格与点云的细节保留能力
Curve Skeletonization in Continuous domain for Meshes and Point Clouds
- 基于流形的连续域方法，避免离散表示误差
- 在Thingi10k上性能超越现有最佳方法（LS TOG'21）
- 适用于形状分类、拓扑识别等下游任务，适合几何处理研究者
3D曲线骨架化技术在诸多应用中快速发展，但如何稳健捕捉复杂物体细节仍具挑战。现有的局部分离器（LS）方法虽高效，却因离散性导致表示失真。为此，我们提出CSCD——一种面向曲面与点云的连续域曲线骨架化新框架，将LS推广至流形空间。具体实现包括：针对网格的CSCD-M利用网格内在三角剖分，增强抗噪性与拓扑保真度；针对点云的CSCD-PC采用毛状拉普拉斯算子，提升鲁棒性。据我们所知，CSCD-M是首个内在式曲线骨架化方法。实验表明，CSCD-M在多种网格上性能媲美LS，且在Thingi10k数据集上优于LS（TOG'21）。CSCD-PC在定性表现上超越CoverageAxis++（Eurographics'24）和EPCS（CAG'23）。此外，我们在物体分类、形状分割及孔洞、隧道、狭窄区域识别等任务中验证了CSCD的有效性。
原文摘要 · Abstract (English)
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
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