Duffy, B, Carr, HA and Möller, T (2013) Integrating isosurface statistics and histograms. IEEE Transactions on Visualization and Computer Graphics, 19 (2). 263 - 277 (14). ISSN 1077-2626
Abstract
Many data sets are sampled on regular lattices in two, three or more dimensions, and recent work has shown that statistical properties of these data sets must take into account the continuity of the underlying physical phenomena. However, the effects of quantization on the statistics have not yet been accounted for. This paper therefore reconciles the previous papers to the underlying mathematical theory, develops a mathematical model of quantized statistics of continuous functions, and proves convergence of geometric approximations to continuous statistics for regular sampling lattices. In addition, the computational cost of various approaches is considered, and recommendations made about when to use each type of statistic.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. |
Keywords: | Frequency distribution; geometric statistics; histograms; integration |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 30 Jun 2014 11:07 |
Last Modified: | 21 Jan 2018 23:54 |
Published Version: | http://dx.doi.org/10.1109/TVCG.2012.118 |
Status: | Published |
Publisher: | Institute of Electrical and Electronics Engineers (IEEE) |
Identification Number: | 10.1109/TVCG.2012.118 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:79281 |