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The Reeb graph of a scalar function defined on a domain gives a topologicallymeaningful summary of that domain. Reeb graphs have been shown in the pastdecade to be of great importance in geometric processing, image processing,computer graphics, and computational topology. The demand for analyzing largedata sets has increased in the last decade. Hence the parallelization oftopological computations needs to be more fully considered. We propose aparallel augmented Reeb graph algorithm on triangulated meshes with and withouta boundary. That is, in addition to our parallel algorithm for computing a Reebgraph, we describe a method for extracting the original manifold data from theReeb graph structure. We demonstrate the running time of our algorithm onstandard datasets. As an application, we show how our algorithm can be utilizedin mesh segmentation algorithms.

An Efficient Data Retrieval Parallel Reeb Graph Algorithm