Dynamic Volume Lines: Visual Comparison of 3D Volumes through Space-filling Curves

Johannes Weissenböck, Bernhard Fröhler, Eduard Gröller, Johann Kastner, Christoph Heinzl

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


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 can identify regions with high local intensity variations, allowing the user to draw conclusions, for example, about the choice of reconstruction parameters. Furthermore, it is possible to detect ring artifacts in reconstructions volumes.
Original languageEnglish
Article number8440038
Pages (from-to)1040-1049
Number of pages10
JournalIEEE Transactions on Visualization and Computer Graphics (TVCG)
Issue number1
Publication statusPublished - Jan 2019


  • Ensemble data
  • Hilbert curve
  • X-ray computed tomography
  • comparative visualization
  • nonlinear scaling
  • Visual Analysis
  • Visualization
  • Visual Computing
  • visual analysis


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