We present a visual analysis environment based on a multi-scale partitioning of a 2d domain intoregions bounded by cycles in weighted planar embedded graphs.The work has been inspired by anapplication in granular mate...We present a visual analysis environment based on a multi-scale partitioning of a 2d domain intoregions bounded by cycles in weighted planar embedded graphs.The work has been inspired by anapplication in granular materials research,where the question of scale plays a fundamental role inthe analysis of material properties.We propose an efficient algorithm to extract the hierarchical cyclestructure using persistent homology.The core of the algorithm is a filtration on a dual graph exploitingAlexander’s duality.The resulting partitioning is the basis for the derivation of statistical properties thatcan be explored in a visual environment.We demonstrate the proposed pipeline on a few syntheticand one real-world dataset.展开更多
基金the Wallenberg AI,Autonomous Systems and Software Program(WASP)funded by the Knut and Alice Wallenberg Foundation,the SeRC(Swedish e-Science Research Center)and the ELLIIT environment for strategic research in Sweden,the Swedish Research Council(VR)grant 2019–05487an Indo-Swedish joint network project:DST/INT/SWD/VR/P-02/2019 VR grant 2018–07085.
文摘We present a visual analysis environment based on a multi-scale partitioning of a 2d domain intoregions bounded by cycles in weighted planar embedded graphs.The work has been inspired by anapplication in granular materials research,where the question of scale plays a fundamental role inthe analysis of material properties.We propose an efficient algorithm to extract the hierarchical cyclestructure using persistent homology.The core of the algorithm is a filtration on a dual graph exploitingAlexander’s duality.The resulting partitioning is the basis for the derivation of statistical properties thatcan be explored in a visual environment.We demonstrate the proposed pipeline on a few syntheticand one real-world dataset.
