Structural MAT: Clean and Scalable Medial Axis Simplification via Explicit Surface Correspondence

2026-05-04

AI Summary

Computing an ideal medial axis transform (MAT) on discrete triangle meshes that simultaneously achieves high fidelity and structural alignment—such as preserving the trajectory of rolling-ball centers in filleted regions—remains challenging. This work proposes a novel approach that initializes the MAT from a surface-sampled 3D Voronoi diagram and explicitly maintains correspondences between MAT vertices and their originating surface regions throughout simplification. A geometry-aware edge collapse prioritization strategy is introduced to preserve intrinsic symmetries among medial sheets. By explicitly modeling and tracking surface-to-MAT correspondences during simplification—a first in MAT processing—the method yields structurally aligned, boundary-regular, and noise-resilient simplified MATs. Experiments demonstrate that complex CAD and articulated models can be accurately represented with only a few hundred vertices while outperforming existing methods in overall quality.

Abstract

The Medial Axis Transform (MAT) is a complete shape descriptor capable of reconstructing the geometry of the original domain. A high-quality MAT should not only facilitate high-fidelity reconstruction but also capture structural features -- for instance, by aligning the MAT boundary with the locus of rolling ball centers within fillet regions. However, computing such an ideal MAT remains a significant challenge, particularly when the input is a discrete triangle mesh. In this paper, we follow the established technical pipeline of initializing the MAT via a 3D Voronoi diagram of surface samples and subsequently simplifying the Voronoi structure through a QEM-like scheme. Our key insight is to explicitly track the correspondence between MAT vertices and surface regions throughout the progressive simplification process, ensuring that the resulting MAT triangles accurately reflect the intrinsic symmetries between surface patches. We translate these geometric requirements into a suite of priority control strategies that govern the sequencing of edge collapses. Through extensive evaluation against state-of-the-art MAT algorithms, we validate the strong performance of our approach regarding runtime efficiency, structural alignment, boundary regularity, triangle quality, and robustness to noise. Our resulting MATs remain highly expressive for both articulated shapes and CAD models, even under extreme simplification -- effectively capturing the global structure of complex geometries with only a few hundred vertices.

Problem

• Medial Axis Transform
• structural features
• triangle mesh
• shape reconstruction
• geometric symmetry

Innovation

• Medial Axis Transform
• Surface Correspondence
• Progressive Simplification
• Voronoi Diagram
• Structural Alignment