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 a...

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Published in:	Algorithms Vol. 13; no. 10; p. 258
Main Authors:	Hajij, Mustafa, Rosen, Paul
Format:	Journal Article
Language:	English
Published:	Basel MDPI AG 01.10.2020
Subjects:	Algorithms Computer graphics Data analysis Data retrieval Demand analysis Domains Image processing Image segmentation Information retrieval Mathematical functions parallel algorithms Parallel processing reeb graph topological data analysis Topology Visualization
ISSN:	1999-4893, 1999-4893
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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.
AbstractList	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.
Author	Hajij, Mustafa Rosen, Paul
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SubjectTerms	Algorithms Computer graphics Data analysis Data retrieval Demand analysis Domains Image processing Image segmentation Information retrieval Mathematical functions parallel algorithms Parallel processing reeb graph topological data analysis Topology Visualization
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Title	An Efficient Data Retrieval Parallel Reeb Graph Algorithm
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