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Issue No. 02 - Feb. (2013 vol. 19)
ISSN: 1077-2626
pp: 263-277
B. Duffy , Oxford Centre for Collaborative Appl. Math. (OCCAM), Univ. of Oxford, Oxford, UK
H. Carr , Visualization & Virtual Reality Group, Univ. of Leeds, Leeds, UK
T. Moller , Graphics, Usability, & Visualization (GrUVi) Lab., Simon Fraser Univ., Burnaby, BC, Canada
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.
statistics, data visualisation, geometry, geometric approximations, isosurface statistics, histograms, data sets, regular lattices, Histograms, Size measurement, Jacobian matrices, Lattices, Quantization, Extraterrestrial measurements, Approximation methods, geometric statistics, Histograms, frequency distribution, integration

H. Carr, B. Duffy and T. Moller, "Integrating Isosurface Statistics and Histograms," in IEEE Transactions on Visualization & Computer Graphics, vol. 19, no. , pp. 263-277, 2013.
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