2021/08/06 by Tushar M. Athawale, Athawale, Tushar M., Sudhanshu Sane +3 · 3 citations
Computer Science · #Topological and Geometric Data Analysis #Data Visualization and Analytics #Data Management and Algorithms
paper · pdf · doi:10.48550/arxiv.2108.03066
Marching squares (MS) and marching cubes (MC) are widely used algorithms for\nlevel-set visualization of scientific data. In this paper, we address the\nchallenge of uncertainty visualization of the topology cases of the MS and MC\nalgorithms for uncertain scalar field data sampled on a uniform grid. The\nvisualization of the MS and MC topology cases for uncertain data is challenging\ndue to their exponential nature and the possibility of multiple topology cases\nper cell of a grid. We propose the topology case count and entropy-based\ntechniques for quantifying uncertainty in the topology cases of the MS and MC\nalgorithms when noise in data is modeled with probability distributions. We\ndemonstrate the applicability of our techniques for independent and correlated\nuncertainty assumptions. We visualize the quantified topological uncertainty\nvia color mapping proportional to uncertainty, as well as with interactive\nprobability queries in the MS case and entropy isosurfaces in the MC case. We\ndemonstrate the utility of our uncertainty quantification framework in\nidentifying the isovalues exhibiting relatively high topological uncertainty.\nWe illustrate the effectiveness of our techniques via results on synthetic,\nsimulation, and hixel datasets.\n