  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.
