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

Zimeng Wang, Zhiyang Dou, Rui Xu, Cheng Lin, Yuan Liu, Xiaoxiao Long, Shiqing Xin, Taku Komura, Xiaoming Yuan, Wenping Wang

TL;DR

Coverage Axis++ introduces a fast, heuristic method for 3D shape skeletonization that approximates the Medial Axis Transform without strict watertightness requirements. It leverages a triadic scoring scheme—coverage, uniformity, and centrality—to greedily select inner skeletal points from a large set of random candidates, and constructs connectivity via Voronoi or Power Diagram-based schemes depending on input type. The approach achieves competitive or superior reconstruction accuracy with substantially reduced runtime compared to state-of-the-art methods, and it supports arbitrary input representations (meshes, triangle soups, point clouds) and explicit skeletal-point counts. This yields a practical, versatile MAT approximation suitable for downstream applications like reconstruction, segmentation, and meshing, with potential extensions to feature preservation and broader sampling tasks.

Abstract

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.

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

TL;DR

Coverage Axis++ introduces a fast, heuristic method for 3D shape skeletonization that approximates the Medial Axis Transform without strict watertightness requirements. It leverages a triadic scoring scheme—coverage, uniformity, and centrality—to greedily select inner skeletal points from a large set of random candidates, and constructs connectivity via Voronoi or Power Diagram-based schemes depending on input type. The approach achieves competitive or superior reconstruction accuracy with substantially reduced runtime compared to state-of-the-art methods, and it supports arbitrary input representations (meshes, triangle soups, point clouds) and explicit skeletal-point counts. This yields a practical, versatile MAT approximation suitable for downstream applications like reconstruction, segmentation, and meshing, with potential extensions to feature preservation and broader sampling tasks.

Abstract

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.
Paper Structure (41 sections, 12 equations, 17 figures, 7 tables, 1 algorithm)

This paper contains 41 sections, 12 equations, 17 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Medial Axis Transform
  5. Voronoi Diagram & Power Diagram
  6. Method
  7. Coverage Score
  8. Uniformity Score
  9. Centrality Score
  10. Final Score
  11. Candidate and Surface Point Generation
  12. Connectivity of Skeletal Points
  13. Mesh Input
  14. Point Cloud Input
  15. Discussion
  16. ...and 26 more sections

Figures (17)

  • Figure 1: The pipeline of Coverage Axis++. (a) Input point cloud. (b) Inner point candidates. (c) Candidate inner balls with original radius. (d) Selected inner balls with original radius. (e) Selected inner points. (f) Skeletonization result.
  • Figure 2: An illustration of the edge collapse process. The surface is in black, with selected skeletal points highlighted in red. The collapsed edges are shown with dashed lines.
  • Figure 3: Qualitative comparisons. (a-c) SAT. (d) MATFP. (e) QMAT. (f) QMAT+. (g) Coverage Axis. (h) Coverage Axis++.
  • Figure 4: A gallery of skeletonization results of point clouds using Coverage Axis++.
  • Figure 5: Comparison with existing shape skeletonization methods for point clouds.
  • ...and 12 more figures