Abstract
One of the greatest challenges for today’s visualization and analysis communities is the massive amounts of data generated from state of the art simulations. Traditionally, the increase in spatial resolution has driven most of the data explosion, but more recently ensembles of simulations with multiple results per data point and stochastic simulations storing individual probability distributions are increasingly common. This chapter describes a relatively new data representation for scalar data, called hixels, that stores a histogram of values for each sample point of a domain. The histograms may be created by spatial down-sampling, binning ensemble values, or polling values from a given distribution. In this manner, hixels form a compact yet information rich approximation of large scale data. In essence, hixels trade off data size and complexity for scalar-value “uncertainty”.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bremer, P.T., Edelsbrunner, H., Hamann, B., Pascucci, V.: A topological hierarchy for functions on triangulated surfaces. IEEE Trans. Vis. Comp. Graph. 10(4), 385–396 (2004)
Edelsbrunner, H., Harer, J., Zomorodian, A.: Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds. Discrete Comput. Geom. 30(1), 87–107 (2003)
Feller, W.: An Introduction to Probability Theory and its Applications, vol. 1. Wiley, New York (1968)
Forman, R.: A user’s guide to discrete Morse theory. In: Proceedings of the 2001 Internat. Conference on Formal Power Series and Algebraic Combinatorics. A Special Volume of Advances in Applied Mathematics, p. 48 (2001)
Gyulassy, A., Bremer, P.T., Hamann, B., Pascucci, V.: A practical approach to Morse-Smale complex computation: scalability and generality. IEEE Trans. Vis. Comput. Graph. 14(6), 1619–1626 (2008)
King, H., Knudson, K., Mramor, N.: Generating discrete morse functions from point data. Exp. Math. 14(4), 435–444 (2005)
Lewiner, T., Lopes, H., Tavares, G.: Applications of forman’s discrete morse theory to topology visualization and mesh compression. IEEE Trans. Vis. Comp. Graph. 10(5), 499–508 (2004)
Matsumoto, Y.: An Introduction to Morse Theory. Translations of Mathematical Monographs, vol. 208. American Mathematical Society, Providence (2002)
Milnor, J.: Morse Theory. Princeton University Press, Princeton (1963)
Thompson, D., Levine, J., Bennett, J., Bremer, P.T., Gyulassy, A., Pascucci, V., Pebay, P.: Analysis of large-scale scalar data using hixels. In: IEEE Symposium on Large-Scale Data Analysis and Visualization (LDAV) (2011)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag London
About this chapter
Cite this chapter
Levine, J.A. et al. (2014). Analysis of Uncertain Scalar Data with Hixels. In: Hansen, C., Chen, M., Johnson, C., Kaufman, A., Hagen, H. (eds) Scientific Visualization. Mathematics and Visualization. Springer, London. https://doi.org/10.1007/978-1-4471-6497-5_3
Download citation
DOI: https://doi.org/10.1007/978-1-4471-6497-5_3
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-4471-6496-8
Online ISBN: 978-1-4471-6497-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)