Flexible Mesh Segmentation through Integration of Geometric andTopological Features of Reeb Graphs

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.