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.

翻译：中轴变换（MAT）是一种完整的形状描述子，能够重建原始域几何结构。高质量的中轴变换不仅要实现高保真重建，还应捕获结构特征——例如，使MAT边界与倒圆区域中滚球中心轨迹对齐。然而，计算这种理想MAT仍面临重大挑战，尤其是当输入为离散三角形网格时。本文遵循先通过表面样本的三维Voronoi图初始化MAT、再经由类似QEM的简化方案精简Voronoi结构的成熟技术路线。我们的核心洞见是：在渐进简化过程中显式追踪MAT顶点与表面区域之间的对应关系，确保生成的MAT三角形准确反映表面贴片间的内在对称性。我们将这些几何要求转化为一系列优先级控制策略，用以调控边折叠的顺序。通过与当前最优MAT算法的广泛对比，验证了本方法在运行效率、结构对齐性、边界规则性、三角形质量及噪声鲁棒性方面的强劲性能。即使在极端简化条件下，本方法生成的MAT对关节类形状和CAD模型仍保持高表现力——仅用数百个顶点即可有效捕获复杂几何体的全局结构。