Task-based Augmented Reeb Graphs with Dynamic ST-Trees

Charles Gueunet (1, 2) , Pierre Fortin (3) , Julien Jomier (1) , Julien Tierny (2)

1 Kitware SAS
2 APR - Algorithmes, Programmes et Résolution
3 PEQUAN - Performance et Qualité des Algorithmes Numériques

This paper presents, to the best of our knowledge, the first parallel algorithm for the computation of the augmented Reeb graph of piecewise linear scalar data. Such augmented Reeb graphs have a wide range of applications , including contour seeding and feature based segmentation. Our approach targets shared-memory multi-core workstations. For this, it completely revisits the optimal, but sequential, Reeb graph algorithm, which is capable of handing data in arbitrary dimension and with optimal time complexity. We take advantage of Fibonacci heaps to exploit the ST-Tree data structure through independent local propagations, while maintaining the optimal, linearithmic time complexity of the sequential reference algorithm. These independent propagations can be expressed using OpenMP tasks, hence benefiting in parallel from the dynamic load balancing of the task runtime while enabling us to increase the parallelism degree thanks to a dual sweep. We present performance results on triangulated surfaces and tetrahedral meshes. We provide comparisons to related work and show that our new algorithm results in superior time performance in practice, both in sequential and in parallel. An open-source C++ implementation is provided for reproducibility.

Domaines: Traitement des images [eess.IV]; Mathématique discrète [cs.DM]; Logiciel mathématique [cs.MS]; Géométrie algorithmique [cs.CG]; Vision par ordinateur et reconnaissance de formes [cs.CV]; Synthèse d'image et réalité virtuelle [cs.GR]

Charles Gueunet, Pierre Fortin, Julien Jomier, Julien Tierny. Task-based Augmented Reeb Graphs with Dynamic ST-Trees. Eurographics Symposium on Parallel Graphics and Visualization, Jun 2019, Porto, Portugal. ⟨10.2312/pgv.20191107⟩. ⟨hal-02159825⟩