Curve Skeletonization in Continuous domain for Meshes and Point Clouds

2026-05-25

AI Summary

Existing graph-based skeletonization methods, such as Local Separators, struggle to simultaneously preserve topological fidelity and geometric detail in complex 3D shapes due to their discrete representations. This work proposes CSCD, a continuous-domain curve skeletonization framework that unifies processing of meshes (CSCD-M) and point clouds (CSCD-PC) directly on the intrinsic geometry of manifolds. CSCD-M leverages intrinsic triangulation, while CSCD-PC introduces a tufted Laplacian operator, both overcoming the expressiveness limitations of discrete approaches. Experiments demonstrate that CSCD-M outperforms Local Separators on benchmarks like Thingi10k, and CSCD-PC qualitatively surpasses CoverageAxis++ and EPCS. Furthermore, the resulting skeletons exhibit strong performance in downstream tasks including shape classification, segmentation, and topological recognition.

Abstract

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

Problem

• curve skeletonization
• continuous domain
• meshes
• point clouds
• topological preservation

Innovation

• Curve Skeletonization
• Continuous Domain
• Intrinsic Triangulation
• Tufted Laplacians
• Local Separators