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1077-2626 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVCG.2018.2864510, IEEE Transactions on Visualization and Computer Graphics Dynamic Volume Lines: Visual Comparison of 3D Volumes through Space-filling Curves Johannes Weissenb¨ock, Bernhard Fr¨ohler, Eduard Gr¨oller, Johann Kastner and Christoph Heinzl Hilbert index 0 80 40 120 160 210 240 280 320 360 400 511 Intensities HilbertIdx: 345 Intensity: 52206 a b c d Intensity frequencies Low (0) High (1) Local ensemble variation Low (0) High (1) Volume 1 Volume 2 Volume 3 Volume 4 Volume 5 Volume 6 Volume 7 Volume 8 Interquartile range Median Upper whisker Lower whisker Fig. 1. Dynamic Volume Lines depicts sets of volumes (a) in an overview visualization, i.e., an interactive nonlinearly scaled histogram heatmap, which encodes intensity frequencies, or (b) in a detailed view, as interactive nonlinearly scaled 1D Hilbert line plots. Based on the individual 1D Hilbert line plots, functional boxplots (c) are generated on demand. The scaling widget (d) depicts the ensemble variation on each level of detail. Abstract — The comparison of many members of an ensemble is difficult, tedious, and error-prone, which is aggravated by often just subtle differences. In this paper, we introduce Dynamic Volume Lines for the interactive visual analysis and comparison of sets of 3D volumes. Each volume is linearized along a Hilbert space-filling curve into a 1D Hilbert line plot, which depicts the intensities over the Hilbert indices. We present a nonlinear scaling of these 1D Hilbert line plots based on the intensity variations in the ensemble of 3D volumes, which enables a more effective use of the available screen space. The nonlinear scaling builds the basis for our interactive visualization techniques. An interactive histogram heatmap of the intensity frequencies serves as overview visualization. When zooming in, the frequencies are replaced by detailed 1D Hilbert line plots and optional functional boxplots. To focus on important regions of the volume ensemble, nonlinear scaling is incorporated into the plots. An interactive scaling widget depicts the local ensemble variations. Our brushing and linking interface reveals, for example, regions with a high ensemble variation by showing the affected voxels in a 3D spatial view. We show the applicability of our concepts using two case studies on ensembles of 3D volumes resulting from tomographic reconstruction. In the first case study, we evaluate an artificial specimen from simulated industrial 3D X-ray computed tomography (XCT). In the second case study, a real-world XCT foam specimen is investigated. Our results show that Dynamic Volume Lines

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