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High performance level-set based topological data analysis

Abstract : Topological Data Analysis requires efficient algorithms to deal with the continuously increasing size and level of details of data sets. In this manuscript, we focus on three fundamental topological abstractions based on level sets: merge trees, contour trees and Reeb graphs. We propose three new efficient parallel algorithms for the computation of these abstractions on multi-core shared memory workstations. The first algorithm developed in the context of this thesis is based on multi-thread parallelism for the contour tree computation. A second algorithm revisits the reference sequential algorithm to compute this abstraction and is based on local propagations expressible as parallel tasks. This new algorithm is in practice twice faster in sequential than the reference algorithm designed in 2000 and offers one order of magnitude speedups in parallel. A last algorithm also relying on task-based local propagations is presented, computing a more generic abstraction: the Reeb graph. Contrary to concurrent approaches, these methods provide the augmented version of these structures, hence enabling the full extend of level-set based analysis. Algorithms presented in this manuscript result today in the fastest implementations available to compute these abstractions. This work has been integrated into the open-source platform: the Topology Toolkit (TTK).
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Submitted on : Wednesday, September 23, 2020 - 2:22:25 PM
Last modification on : Thursday, October 22, 2020 - 11:19:06 AM


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  • HAL Id : tel-02141632, version 2


Charles Gueunet. High performance level-set based topological data analysis. Image Processing [eess.IV]. Sorbonne Université, 2019. English. ⟨NNT : 2019SORUS120⟩. ⟨tel-02141632v2⟩



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