A Simple and Stable Centeredness Measure for 3D Curve Skeleton Extraction

Area of Science:

• Computer Graphics
• Computational Geometry
• 3D Shape Analysis

Background:

• Existing 3D curve skeleton extraction methods struggle with identifying central points and require manual threshold adjustments.
• Shape boundary perturbations often lead to spurious branches in extracted skeletons.
• Current techniques are sensitive to noise and details, complicating skeletonization.

Purpose of the Study:

• To present a novel, fast, and convenient method for extracting high-quality 3D curve skeletons.
• To introduce a stable centeredness measure based on inside-out fire propagation simulation.
• To effectively prune spurious branches and optimize skeleton compactness without manual threshold tuning.

Main Methods:

• Utilizes medial surfaces of 3D shapes for skeleton extraction.
• Employs an inside-out fire propagation simulation for a localized and parallelizable centeredness measure.
• Incorporates measures to suppress noise and details for stable measurements.
• Applies minimum set covers to optimize center points and generate compact skeletons.

Main Results:

• The proposed method successfully extracts clean, compact, and centered 3D curve skeletons.
• It demonstrates superior performance compared to existing state-of-the-art methods.
• The new approach significantly reduces the need for manual adjustments and threshold tuning.
• Experimental results confirm the method's speed and robustness.

Conclusions:

• The medial surface-based approach offers a convenient and fast solution for 3D curve skeleton extraction.
• The inside-out centeredness measure provides stability and robustness against boundary perturbations.
• This method effectively generates high-quality skeletons, outperforming previous techniques in efficiency and quality.