MATStruct: High-Quality Medial Mesh Computation via Structure-aware Variational Optimization

2025-10-12

AI Summary

This paper addresses the longstanding challenge in medial axis transform (MAT) computation of simultaneously preserving structural integrity and ensuring high-quality intermediate mesh generation. We propose a structure-aware variational optimization framework. Methodologically, we introduce structure awareness into MAT optimization for the first time: (i) employing constrained power diagram partitioning for topology-preserving domain decomposition; (ii) applying spherical quadric error metrics for geometrically accurate projection onto the medial surface; and (iii) designing a particle-based optimization scheme incorporating a Gaussian kernel energy term to enforce medial axis connectivity and spatial uniformity. Compared with state-of-the-art approaches, our method achieves superior performance in three key aspects—structural decomposition clarity, geometric fidelity, and mesh robustness—while maintaining both geometric accuracy and topological correctness of the medial axis.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Matrix & Tensor Methods
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

We propose a novel optimization framework for computing the medial axis transform that simultaneously preserves the medial structure and ensures high medial mesh quality. The medial structure, consisting of interconnected sheets, seams, and junctions, provides a natural volumetric decomposition of a 3D shape. Our method introduces a structure-aware, particle-based optimization pipeline guided by the restricted power diagram (RPD), which partitions the input volume into convex cells whose dual encodes the connectivity of the medial mesh. Structure-awareness is enforced through a spherical quadratic error metric (SQEM) projection that constrains the movement of medial spheres, while a Gaussian kernel energy encourages an even spatial distribution. Compared to feature-preserving methods such as MATFP and MATTopo, our approach produces cleaner and more accurate medial structures with significantly improved mesh quality. In contrast to voxel-based, point-cloud-based, and variational methods, our framework is the first to integrate structural awareness into the optimization process, yielding medial meshes with superior geometric fidelity, topological correctness, and explicit structural decomposition.

Problem

• Computing medial axis transform with preserved structure
• Ensuring high quality medial mesh through optimization
• Integrating structural awareness into medial mesh computation

Innovation

• Structure-aware variational optimization for medial axis computation
• Restricted power diagram partitions volume into convex cells
• Spherical quadratic error metric projection constrains medial spheres