Lifted Wasserstein Matcher for Fast and Robust Topology Tracking
Autor: | Bruno Conche, Julien Tierny, Mélanie Plainchault, Maxime Soler |
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Přispěvatelé: | Performance et Qualité des Algorithmes Numériques (PEQUAN), LIP6, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), TOTAL S.A., TOTAL FINA ELF |
Jazyk: | angličtina |
Rok vydání: | 2018 |
Předmět: |
Computational Geometry (cs.CG)
FOS: Computer and information sciences Topological Data Analysis Optimal matching Computer science Computer Vision and Pattern Recognition (cs.CV) Feature extraction Computer Science - Computer Vision and Pattern Recognition 02 engineering and technology [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] Topology [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG] Upsampling Computer Science - Graphics Robustness (computer science) Hungarian algorithm Wasserstein metric FOS: Electrical engineering electronic engineering information engineering 0202 electrical engineering electronic engineering information engineering [INFO.INFO-MS]Computer Science [cs]/Mathematical Software [cs.MS] Optimal Transport Image and Video Processing (eess.IV) [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV] 020207 software engineering Electrical Engineering and Systems Science - Image and Video Processing Graphics (cs.GR) [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR] [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] Computer Science - Computational Geometry 020201 artificial intelligence & image processing Topological data analysis Feature Tracking Assignment problem |
Zdroj: | IEEE Symposium on Large Data Analysis and Visualization IEEE Symposium on Large Data Analysis and Visualization, Oct 2018, Berlin, Germany LDAV |
Popis: | International audience; This paper presents a robust and efficient method for tracking topological features in time-varying scalar data. Structures are tracked based on the optimal matching between persistence diagrams with respect to the Wasserstein metric. This fundamentally relies on solving the assignment problem, a special case of optimal transport, for all consecutive timesteps. Our approach relies on two main contributions. First, we revisit the seminal assignment algorithm by Kuhn and Munkres which we specifically adapt to the problem of matching persistence diagrams in an efficient way. Second, we propose an extension of the Wasserstein metric that significantly improves the geometrical stability of the matching of domain-embedded persistence pairs. We show that this geometrical lifting has the additional positive side-effect of improving the assignment matrix sparsity and therefore computing time. The global framework implements a coarse-grained parallelism by computing persistence diagrams and finding optimal matchings in parallel for every couple of consecutive timesteps. Critical trajectories are constructed by associating successively matched persistence pairs over time. Merging and splitting events are detected with a geometrical threshold in a post-processing stage. Extensive experiments on real-life datasets show that our matching approach is an order of magnitude faster than the seminal Munkres algorithm. Moreover, compared to a modern approximation method, our method provides competitive runtimes while yielding exact results. We demonstrate the utility of our global framework by extracting critical point trajectories from various simulated time-varying datasets and compare it to the existing methods based on associated overlaps of volumes. Robustness to noise and temporal resolution downsampling is empirically demonstrated. |
Databáze: | OpenAIRE |
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