# Coverage Axis++: Efficient Inner Point Selection for 3D Shape Skeletonization

arXiv: https://arxiv.org/abs/2401.12946 · HTML: https://mlsanity.com/paper/2401.12946/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 100 references that are in the map.
- First posted on arXiv 23 Jan 2024.

## Builds on (most cited first, 27 of 27)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [HybrIK: A Hybrid Analytical-Neural Inverse Kinematics Solution for 3D Human Pose and Shape Estimation](https://mlsanity.com/paper/2011.14672/) (2020)
- [Mosaic-SDF for 3D Generative Models](https://mlsanity.com/paper/2312.09222/) (2023)
- [TORE: Token Reduction for Efficient Human Mesh Recovery with Transformer](https://mlsanity.com/paper/2211.10705/) (2022)
- [Predicting Animation Skeletons for 3D Articulated Models via Volumetric Nets](https://mlsanity.com/paper/1908.08506/) (2019)
- [A Skeleton-bridged Deep Learning Approach for Generating Meshes of Complex Topologies from Single RGB Images](https://mlsanity.com/paper/1903.04704/) (2019)
- [Point2Skeleton: Learning Skeletal Representations from Point Clouds](https://mlsanity.com/paper/2012.00230/) (2020)
- [Learning Dynamics via Graph Neural Networks for Human Pose Estimation and Tracking](https://mlsanity.com/paper/2106.03772/) (2021)
- [Globally Consistent Normal Orientation for Point Clouds by Regularizing the Winding-Number Field](https://mlsanity.com/paper/2304.11605/) (2023)
- [SkeletonNet: A Topology-Preserving Solution for Learning Mesh Reconstruction of Object Surfaces from RGB Images](https://mlsanity.com/paper/2008.05742/) (2020)
- [Coverage Axis: Inner Point Selection for 3D Shape Skeletonization](https://mlsanity.com/paper/2110.00965/) (2021)
- [Modeling 3D Shapes by Reinforcement Learning](https://mlsanity.com/paper/2003.12397/) (2020)
- [Surface Extraction from Neural Unsigned Distance Fields](https://mlsanity.com/paper/2309.08878/) (2023)
- [Computing Medial Axis Transform with Feature Preservation via Restricted Power Diagram](https://mlsanity.com/paper/2210.13676/) (2022)
- [Deep Medial Fields](https://mlsanity.com/paper/2106.03804/) (2021)
- [SPEAL: Skeletal Prior Embedded Attention Learning for Cross-Source Point Cloud Registration](https://mlsanity.com/paper/2312.08664/) (2023)
- [Top-Down Shape Abstraction Based on Greedy Pole Selection](https://mlsanity.com/paper/1910.08954/) (2019)
- [SEG-MAT: 3D Shape Segmentation Using Medial Axis Transform](https://mlsanity.com/paper/2010.11488/) (2020)
- [Skeletonization via Local Separators](https://mlsanity.com/paper/2007.03483/) (2020)
- [Medial Skeletal Diagram: A Generalized Medial Axis Approach for 3D Shape Representation](https://mlsanity.com/paper/2310.09395/) (2023)
- [LSMAT Least Squares Medial Axis Transform](https://mlsanity.com/paper/2010.05066/) (2020)
- [Neural Parametric Surfaces for Shape Modeling](https://mlsanity.com/paper/2309.09911/) (2023)
- [Surface Simplification using Intrinsic Error Metrics](https://mlsanity.com/paper/2305.06410/) (2023)
- [Patch-Grid: An Efficient and Feature-Preserving Neural Implicit Surface Representation](https://mlsanity.com/paper/2308.13934/) (2023)
- [EPCS: Endpoint-based Part-aware Curve Skeleton Extraction for Low-quality Point Clouds](https://mlsanity.com/paper/2211.09488/) (2022)
- [Medial Meshes for Volume Approximation](https://mlsanity.com/paper/1308.3917/) (2013)

## Built on by (most cited first, 10 of 10)

- [RigGS: Rigging of 3D Gaussians for Modeling Articulated Objects in Videos](https://mlsanity.com/paper/2503.16822/) (2025)
- [CWF: Consolidating Weak Features in High-quality Mesh Simplification](https://mlsanity.com/paper/2404.15661/) (2024)
- [Auto-Connect: Connectivity-Preserving RigFormer with Direct Preference Optimization](https://mlsanity.com/paper/2506.11430/) (2025)
- [Dynamic Realms: 4D Content Analysis, Recovery and Generation with Geometric, Topological and Physical Priors](https://mlsanity.com/paper/2409.14692/) (2024)
- [MorphoSkel3D: Morphological Skeletonization of 3D Point Clouds for Informed Sampling in Object Classification and Retrieval](https://mlsanity.com/paper/2501.12974/) (2025)
- [SkeletonGaussian: Editable 4D Generation through Gaussian Skeletonization](https://mlsanity.com/paper/2602.04271/) (2026)
- [SHARC: Reference point driven Spherical Harmonic Representation for Complex Shapes](https://mlsanity.com/paper/2604.01894/) (2026)
- [GaussiAnimate: Rig Animatable Categories with Level of Dynamics](https://mlsanity.com/paper/2604.08547/) (2026)
- [Soft Anisotropic Diagrams for Differentiable Image Representation](https://mlsanity.com/paper/2604.21984/) (2026)
- [Curve Skeletonization in Continuous domain for Meshes and Point Clouds](https://mlsanity.com/paper/2605.25921/) (2026)

## Abstract (arXiv)

We introduce Coverage Axis++, a novel and efficient approach to 3D shape skeletonization. The current state-of-the-art approaches for this task often rely on the watertightness of the input or suffer from substantial computational costs, thereby limiting their practicality. To address this challenge, Coverage Axis++ proposes a heuristic algorithm to select skeletal points, offering a high-accuracy approximation of the Medial Axis Transform (MAT) while significantly mitigating computational intensity for various shape representations. We introduce a simple yet effective strategy that considers shape coverage, uniformity, and centrality to derive skeletal points. The selection procedure enforces consistency with the shape structure while favoring the dominant medial balls, which thus introduces a compact underlying shape representation in terms of MAT. As a result, Coverage Axis++ allows for skeletonization for various shape representations (e.g., water-tight meshes, triangle soups, point clouds), specification of the number of skeletal points, few hyperparameters, and highly efficient computation with improved reconstruction accuracy. Extensive experiments across a wide range of 3D shapes validate the efficiency and effectiveness of Coverage Axis++. Our codes are available at https://github.com/Frank-ZY-Dou/Coverage_Axis.