An Efficient Data Retrieval Parallel Reeb Graph Algorithm

The Reeb graph of a scalar function that is 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.

Mustafa Hajij, and Paul Rosen. An Efficient Data Retrieval Parallel Reeb Graph Algorithm. Algorithms: Special Issue on Topological Data Analysis, 2020.

@article{hajij2020retrieval,
  title = {An Efficient Data Retrieval Parallel Reeb Graph Algorithm},
  author = {Hajij, Mustafa and Rosen, Paul},
  journal = {Algorithms: Special Issue on Topological Data Analysis},
  year = {2020},
  abstract = {The Reeb graph of a scalar function that is 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.}
}