The Reeb graph of a scalar function defined on a domain gives a topological 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 to compute large data sets has increased in the last decade and hence the consideration of the parallelization of topological computations  . We propose a parallel augmented Reeb graph algorithm on triangulated meshes with and without a boundary. In other words, besides our parallel algorithm for  Reeb graph, we give a description for extracting the original manifold data from the Reeb graph structure  . As an application, we show how our algorithm can be utilized in mesh segmentation algorithms.
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.
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