Abstract:Distributions are often used to model uncertainty in many scientific datasets. To preserve the correlation among the spatially sampled grid locations in the dataset, various standard multivariate distribution models have been proposed in visualization literature. These models treat each grid location as a univariate random variable which models the uncertainty at that location. Standard multivariate distributions (both parametric and nonparametric) assume that all the univariate marginals are of the same type/family of distribution. But in reality, different grid locations show different statistical behavior which may not be modeled best by the same type of distribution. In this paper, we propose a new multivariate uncertainty modeling strategy to address the needs of uncertainty modeling in scientific datasets. Our proposed method is based on a statistically sound multivariate technique called Copula, which makes it possible to separate the process of estimating the univariate marginals and the process of modeling dependency, unlike the standard multivariate distributions. The modeling flexibility offered by our proposed method makes it possible to design distribution fields which can have different types of distribution (Gaussian, Histogram, KDE etc.) at the grid locations, while maintaining the correlation structure at the same time. Depending on the results of various standard statistical tests, we can choose an optimal distribution representation at each location, resulting in a more cost efficient modeling without significantly sacrificing on the analysis quality. To demonstrate the efficacy of our proposed modeling strategy, we extract and visualize uncertain features like isocontours and vortices in various real world datasets. We also study various modeling criterion to help users in the task of univariate model selection.
Paper: S.Hazarika, A. Biswas, H-W. Shen: “Uncertainty Visualization Using Copula-Based Analysis in Mixed Distribution Models”, IEEE Transactions on Visualization and Computer Graphics , 24(1): 934-943 (2018) . [bib,pdf,preview,presentation]
Abstract:Visualizing the similarities and differences among an ensemble of isosurfaces is a challenging problem mainly because the isosurfaces cannot be displayed together at the same time. For ensemble of isosurfaces, visualizing these spatial differences among the surfaces is essential to get useful insights as to how the individual ensemble simulations affect different isosurfaces. We propose a scheme to visualize the spatial variations of isosurfaces with respect to statistically significant isosurfaces within the ensemble. Understanding such variations among ensemble of isosurfaces at different spatial regions is helpful in analyzing the influence of different ensemble runs over the spatial domain. In this regard, we propose an isosurface-entropy based clustering scheme to divide the spatial domain into regions of high and low isosurface variation. We demonstrate the efficacy of our method by successfully applying it on real-world ensemble data sets from ocean simulation experiments and weather forecasts.
Abstract:We provide a visualization based answer to understanding the evolution and structure of dark matter halos by addressing the tasks assigned in 2015 IEEE Scientific Visualization Contest. The data released this year is a Cosmological Simulation dataset generated from the Dark Sky Simulation experiments. Out of the assigned tasks we are addressing the following: data integration and browsing, halo identification and visualization and diving deep into halo substructure.
Abstract:A heuristic ‘GRP_CH’ has been proposed to generate a random simple polygon from a given set of ‘n’ points in 2-Dimensional plane. The “2-Opt Move” heuristic with time complexity O(n^4) is the best known among the existing heuristics to generate a simple polygon. The proposed heuristics, ‘GRP_CH’ first computes the convex hull of the point set and then generates a random simple polygon from that convex hull. The ‘GRP_CH’ heuristic takes O(n^3) time which is less than that of “2-opt Move” heuristic. We have compared our results with “2-Opt Move” and it shows that the randomness behaviour of ‘GRP_CH’ heuristic is better than that of “2-Opt Move” heuristic.
Paper: S.Sadhu, S.Hazarika, K.Jain, S.Basu, T.De : “GRP-CH Heuristic for Generating Random Simple Polygon”, 23rd International Workshop on Combinatorial Algorithms 2012, 293-302, Springer LNCS Volume. [bib,pdf]