Flexible Mesh Segmentation via Reeb Graph Representation of Geometrical and Topological Features

TL;DR

This paper introduces a scalable mesh segmentation method that combines geometrical and topological features using a Reeb graph, validated across diverse applications for improved geometric analysis.

Contribution

It presents a novel, efficient Reeb graph-based framework for mesh segmentation that integrates geometric and topological features with adaptive region growth.

Findings

Operates with O(n log(n)) complexity for meshes of size n.

Effectively decomposes meshes in part-based and terrain analysis applications.

Demonstrates robustness and scalability across different geometric analysis tasks.

Abstract

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.