# Curve Skeletonization in Continuous domain for Meshes and Point Clouds

arXiv: https://arxiv.org/abs/2605.25921 · HTML: https://mlsanity.com/paper/2605.25921/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 68 references that are in the map.
- First posted on arXiv 25 May 2026.

## Builds on (most cited first, 13 of 13)

- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Voxel2Mesh: 3D Mesh Model Generation from Volumetric Data](https://mlsanity.com/paper/1912.03681/) (2019)
- [Point2Skeleton: Learning Skeletal Representations from Point Clouds](https://mlsanity.com/paper/2012.00230/) (2020)
- [Coverage Axis: Inner Point Selection for 3D Shape Skeletonization](https://mlsanity.com/paper/2110.00965/) (2021)
- [Computing Medial Axis Transform with Feature Preservation via Restricted Power Diagram](https://mlsanity.com/paper/2210.13676/) (2022)
- [A Survey of Algorithms for Geodesic Paths and Distances](https://mlsanity.com/paper/2007.10430/) (2020)
- [Coverage Axis++: Efficient Inner Point Selection for 3D Shape Skeletonization](https://mlsanity.com/paper/2401.12946/) (2024)
- [Voxel Structure-based Mesh Reconstruction from a 3D Point Cloud](https://mlsanity.com/paper/2104.10622/) (2021)
- [Skeletonization via Local Separators](https://mlsanity.com/paper/2007.03483/) (2020)
- [Integer Coordinates for Intrinsic Geometry Processing](https://mlsanity.com/paper/2106.00220/) (2021)
- [EPCS: Endpoint-based Part-aware Curve Skeleton Extraction for Low-quality Point Clouds](https://mlsanity.com/paper/2211.09488/) (2022)
- [New Greedy Heuristics For Set Cover and Set Packing](https://mlsanity.com/paper/1305.3584/) (2013)
- [Multilevel Skeletonization Using Local Separators](https://mlsanity.com/paper/2303.07210/) (2023)

## Abstract (arXiv)

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