An Efficient Data Retrieval Parallel Reeb Graph Algorithm

TL;DR

This paper introduces a parallel algorithm for computing Reeb graphs on triangulated meshes, significantly improving efficiency for large datasets and enabling applications like mesh segmentation.

Contribution

The paper presents a novel parallel Reeb graph algorithm for triangulated meshes, including a method for extracting original data from the graph, enhancing scalability and utility.

Findings

Demonstrates improved running times on standard datasets.

Enables efficient mesh segmentation applications.

Provides a method for data extraction from Reeb graphs.

Abstract

The Reeb graph of a scalar function defined on a domain gives a topologically meaningful summary of that domain. Reeb graphs have been shown in the past decade to be of great importance in geometric processing, image processing, computer graphics, and computational topology. The demand for analyzing large data sets has increased in the last decade. Hence the parallelization of topological computations needs to be more fully considered. We propose a parallel augmented Reeb graph algorithm on triangulated meshes with and without a boundary. That is, in addition to our parallel algorithm for computing a Reeb graph, we describe a method for extracting the original manifold data from the Reeb graph structure. We demonstrate the running time of our algorithm on standard datasets. As an application, we show how our algorithm can be utilized in mesh segmentation algorithms.