Flexible Mesh Segmentation via Reeb Graph Representation of Geometrical and Topological Features
This provides a robust framework for advanced geometric analysis of meshes, connecting geometric and topological features, but it appears incremental as it builds on existing Reeb graph and segmentation methods.
The paper tackles mesh segmentation by integrating geometrical and topological features using a flexible Reeb graph representation, achieving O(n log(n)) computational complexity and validating effectiveness in diverse applications like part-based decomposition and terrain analysis.
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.