Flexible Mesh Segmentation via Reeb Graph Representation of Geometrical and Topological Features
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912196205740032 |
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| author | Beguet, Florian Lanquetin, Sandrine Raffin, Romain |
| author_facet | Beguet, Florian Lanquetin, Sandrine Raffin, Romain |
| contents | This paper presents a new mesh segmentation method that integrates geometrical and topological features through a flexible Reeb graph representation. The algorithm consists of three phases: construction of the Reeb graph using the improved topological skeleton approach, topological simplification of the graph by cancelling critical points while preserving essential features, and generation of contiguous segments via an adaptive region-growth process that takes geometric and topological criteria into account. Operating with a computational complexity of O(n log(n)) for a mesh of n vertices, the method demonstrates both efficiency and scalability. An evaluation through case studies, including part-based decomposition with Shape Diameter Function and terrain analysis with Shape Index, validates the effectiveness of the method in completely different applications. The results establish this approach as a robust framework for advanced geometric analysis of meshes, connecting the geometric and topological features of shapes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_05335 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Flexible Mesh Segmentation via Reeb Graph Representation of Geometrical and Topological Features Beguet, Florian Lanquetin, Sandrine Raffin, Romain Graphics Computer Vision and Pattern Recognition This paper presents a new mesh segmentation method that integrates geometrical and topological features through a flexible Reeb graph representation. The algorithm consists of three phases: construction of the Reeb graph using the improved topological skeleton approach, topological simplification of the graph by cancelling critical points while preserving essential features, and generation of contiguous segments via an adaptive region-growth process that takes geometric and topological criteria into account. Operating with a computational complexity of O(n log(n)) for a mesh of n vertices, the method demonstrates both efficiency and scalability. An evaluation through case studies, including part-based decomposition with Shape Diameter Function and terrain analysis with Shape Index, validates the effectiveness of the method in completely different applications. The results establish this approach as a robust framework for advanced geometric analysis of meshes, connecting the geometric and topological features of shapes. |
| title | Flexible Mesh Segmentation via Reeb Graph Representation of Geometrical and Topological Features |
| topic | Graphics Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2412.05335 |