An Efficient Data Retrieval Parallel Reeb Graph Algorithm
This work addresses the need for scalable topological analysis in fields like geometric processing and computer graphics, but it appears incremental as it builds on existing Reeb graph methods with parallelization.
The authors tackled the problem of efficiently computing Reeb graphs for large datasets by proposing a parallel algorithm on triangulated meshes, demonstrating its running time on standard datasets and applying it to mesh segmentation.
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.