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Skeletonization Quality Evaluation: Geometric Metrics for Point Cloud Analysis in Robotics

Qingmeng Wen, Yu-Kun Lai, Ze Ji, Seyed Amir Tafrishi

TL;DR

The paper tackles the lack of quantitative criteria for skeletonization quality on noisy point clouds in robotics. It introduces four geometric metrics—topological similarity, boundedness, centeredness, and smoothness—and a numeric scoring framework based on persistent homology, sphere-projection, ellipse fitting, and tangent-plane analyses. The authors demonstrate the approach on real-scanned data, showing how input density and noise influence each metric and providing an open-source toolbox for community use. The work enables objective comparisons of skeletonization methods and informs application-specific needs in manipulation, navigation, and perception tasks. Overall, this framework advances the evaluation of skeleton models, offering practical insights for robust robotic planning and sensing pipelines.

Abstract

Skeletonization is a powerful tool for shape analysis, rooted in the inherent instinct to understand an object's morphology. It has found applications across various domains, including robotics. Although skeletonization algorithms have been studied in recent years, their performance is rarely quantified with detailed numerical evaluations. This work focuses on defining and quantifying geometric properties to systematically score the skeletonization results of point cloud shapes across multiple aspects, including topological similarity, boundedness, centeredness, and smoothness. We introduce these representative metric definitions along with a numerical scoring framework to analyze skeletonization outcomes concerning point cloud data for different scenarios, from object manipulation to mobile robot navigation. Additionally, we provide an open-source tool to enable the research community to evaluate and refine their skeleton models. Finally, we assess the performance and sensitivity of the proposed geometric evaluation methods from various robotic applications.

Skeletonization Quality Evaluation: Geometric Metrics for Point Cloud Analysis in Robotics

TL;DR

The paper tackles the lack of quantitative criteria for skeletonization quality on noisy point clouds in robotics. It introduces four geometric metrics—topological similarity, boundedness, centeredness, and smoothness—and a numeric scoring framework based on persistent homology, sphere-projection, ellipse fitting, and tangent-plane analyses. The authors demonstrate the approach on real-scanned data, showing how input density and noise influence each metric and providing an open-source toolbox for community use. The work enables objective comparisons of skeletonization methods and informs application-specific needs in manipulation, navigation, and perception tasks. Overall, this framework advances the evaluation of skeleton models, offering practical insights for robust robotic planning and sensing pipelines.

Abstract

Skeletonization is a powerful tool for shape analysis, rooted in the inherent instinct to understand an object's morphology. It has found applications across various domains, including robotics. Although skeletonization algorithms have been studied in recent years, their performance is rarely quantified with detailed numerical evaluations. This work focuses on defining and quantifying geometric properties to systematically score the skeletonization results of point cloud shapes across multiple aspects, including topological similarity, boundedness, centeredness, and smoothness. We introduce these representative metric definitions along with a numerical scoring framework to analyze skeletonization outcomes concerning point cloud data for different scenarios, from object manipulation to mobile robot navigation. Additionally, we provide an open-source tool to enable the research community to evaluate and refine their skeleton models. Finally, we assess the performance and sensitivity of the proposed geometric evaluation methods from various robotic applications.

Paper Structure

This paper contains 18 sections, 3 theorems, 24 equations, 12 figures, 1 table.

Table of Contents

  1. Introduction
  2. skeletonization Evaluation Metrics
  3. Topological Similarity
  4. Problem Statement & Preliminaries
  5. Methodology
  6. Boundedness
  7. Problem statement
  8. Methodology
  9. Centeredness
  10. Problem Statement & Preliminaries
  11. Methodology
  12. Smoothness
  13. Problem Statement
  14. Methodology
  15. Results & Discussion
  16. ...and 3 more sections

Key Result

Proposition 1

The topological similarity between two normalized point clouds, $P_o$ and $P_s$, within a bounding box of diagonal $\epsilon_{\text{max}}$, is determined by the distance between their most persistent homology features, calculated from the growth of the Vietoris–Rips complex (Definition def.vierips). As $d^* \to 0$ and $N_o \to \infty$, this comparison provides an accurate measure of topological si

Figures (12)

  • Figure 1: Some of the simplex examples.
  • Figure 2: An example of a Vietoris-Rips complexbeksi20163d.
  • Figure 3: Persistent Homology Analysis of Simple Geometries ($H_0$ features). Shape of (a), (c), (e), (g) are with 200 points, while shape of (i) are with 2000 points.
  • Figure 4: The barcode of persistent homology ($H_0$ features). The input point clouds are scaled to fit within a cubic bounding box whose diagonal is 1.6 and only the top 5% and bottom 5% of persistence bars are shown for clarity)
  • Figure 5: Distance vectors projected to a ball surface.
  • ...and 7 more figures

Theorems & Definitions (31)

  • Definition 1
  • Remark 1
  • Definition 2
  • Remark 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Remark 3
  • Proposition 1
  • ...and 21 more