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 featu...
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Zusammenfassung: | 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. |
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DOI: | 10.48550/arxiv.2412.05335 |