This paper presents a practical approach for the optimization of topological simplification, a central pre-processing step for the analysis and visualization of scalar data. Given an input scalar field f and a set of "signal" persistence pairs to maintain, our approaches produces an output field g that is close to f and which optimizes (i) the cancellation of "non-signal" pairs, while (ii) preserving the "signal" pairs. In contrast to pre-existing simplification algorithms, our approach is not restricted to persistence pairs involving extrema and can thus address a larger class of topological features, in particular saddle pairs in three-dimensional scalar data. Our approach leverages recent generic persistence optimization frameworks and extends them with tailored accelerations specific to the problem of topological simplification. Extensive experiments report substantial accelerations over these frameworks, thereby making topological simplification optimization practical for real-life datasets. Our approach enables a direct visualization and analysis of the topologically simplified data, e.g., via isosurfaces of simplified topology (fewer components and handles). We apply our approach to the extraction of prominent filament structures in three-dimensional data. Specifically, we show that our pre-simplification of the data leads to practical improvements over standard topological techniques for removing filament loops. We also show how our approach can be used to repair genus defects in surface processing. Finally, we provide a C++ implementation for reproducibility purposes.
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http://dx.doi.org/10.1109/TVCG.2024.3456345 | DOI Listing |
Sci Total Environ
December 2024
State Key Laboratory of Mariculture Biobreeding and Sustainable Goods, Yellow Sea Fisheries Research Institute, Chinese Academy of Fishery Sciences, Qingdao, Shandong 266071, China; Laboratory for Marine Fisheries Science and Food Production Processes, Qingdao Marine Science and Technology Center, Shandong 266237, China.
The water-sediment regulation scheme (WSRS) in the Yellow River is a large-scale initiative to artificially regulate the flow of sediment to the sea, thereby increasing the flood-carrying capacity of the riverbed and reservoirs. Currently, systematic studies on ecological impacts of WSRS at ecosystem-level are still insufficient. This limitation hampers the pursuit of a 'green', healthy, ecosystem and sustainable fisheries.
View Article and Find Full Text PDFChem Mater
October 2024
Department of Chemical Engineering, University College London, London WC1E 7JE, United Kingdom.
Metal-organic frameworks (MOFs) began to emerge over two decades ago, resulting in the deposition of 120 000 MOF-like structures (and counting) into the Cambridge Structural Database (CSD). Topological analysis is a critical step toward understanding periodic MOF materials, offering insight into the design and synthesis of these crystals via the simplification of connectivity imposed on the complete chemical structure. While some of the most prevalent topologies, such as face-centered cubic (), square lattice (), and diamond (), are simple and can be easily assigned to structures, MOFs that are built from complex building blocks, with multiple nodes of different symmetry, result in difficult to characterize topological configurations.
View Article and Find Full Text PDFSci Rep
October 2024
The Alan Turing Institute, The British Library, London, NW1 2DB, UK.
IEEE Trans Vis Comput Graph
September 2024
Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was developed allowing hypergraphs with thousands of hyperedges to be simplified and examined at different levels of detail.
View Article and Find Full Text PDFIEEE Trans Vis Comput Graph
September 2024
This paper presents a practical approach for the optimization of topological simplification, a central pre-processing step for the analysis and visualization of scalar data. Given an input scalar field f and a set of "signal" persistence pairs to maintain, our approaches produces an output field g that is close to f and which optimizes (i) the cancellation of "non-signal" pairs, while (ii) preserving the "signal" pairs. In contrast to pre-existing simplification algorithms, our approach is not restricted to persistence pairs involving extrema and can thus address a larger class of topological features, in particular saddle pairs in three-dimensional scalar data.
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