Mesh segmentation represents a crucial task in computer graphics and geometric analysis, with diverse applications spanning texture mapping, animation, and beyond. This paper introduces an innovative Reeb graph-based mesh segmentation method that seamlessly integrates geometric and topological features to achieve flexible and robust segmentation results. The proposed approach encompasses three primary phases. First, an enhanced topological skeleton construction efficiently captures the Reeb graph structure while preserving degenerate critical points. Second, a topological simplification process employing critical point cancellation reduces graph complexity while maintaining essential shape features and correspondences. Finally, a region growing algorithm leverages both Reeb graph adjacency and mesh vertex connectivity to generate contiguous, semantically meaningful segments. The presented method exhibits computational efficiency, achieving a complexity of $O(n \log n$) for a mesh containing n vertices. Its versatility and effectiveness are validated through application to both local geometry-based segmentation using the Shape Index and part-based decomposition utilizing the Shape Diameter Function. This flexible framework establishes a solid foundation for advanced analysis and applications across various domains, offering new possibilities for mesh processing and understanding.

翻译：网格分割是计算机图形学与几何分析中的关键任务，在纹理映射、动画制作等众多领域具有广泛应用。本文提出了一种创新的基于Reeb图的网格分割方法，通过无缝融合几何与拓扑特征，实现灵活且鲁棒的分割效果。该方法包含三个主要阶段：首先，通过增强的拓扑骨架构建高效捕获Reeb图结构，同时保留退化临界点；其次，采用临界点消除的拓扑简化过程在保持关键形状特征与对应关系的同时降低图结构复杂度；最后，利用Reeb图邻接关系与网格顶点连通性的区域生长算法生成连续且具有语义意义的片段。该方法展现出良好的计算效率，对于包含n个顶点的网格可实现$O(n \log n$)的时间复杂度。通过将其应用于基于形状指数的局部几何分割及基于形状直径函数的部件分解，验证了该框架的通用性与有效性。这一柔性框架为跨领域的高级分析与应用奠定了坚实基础，为网格处理与理解提供了新的可能性。