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

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 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.

VAPOR: Visual Analytics for the Exploration of Pelvic Organ Variability in Radiotherapy

“…The distance volumes are then unraveled into 1D vectors using the 3D spacefilling Hilbert Curve that allows us to analyze how the shape differentiation capabilities of our method changes if the sampling density is reduced. This has also been employed by Weissenböck et al [52] and by Demir et al [53] for volume data comparison. After unfolding, there is a unique vector for each organ, patient, and timestep.…”

open_iA: A tool for processing and visual analysis of industrial computed tomography datasets

“…Amirkhanov, Fröhler, Kastner, Gröller, & Heinzl, 2014) makes it possible to analyze spectral data, e.g., from X-Ray fluorescence spectral tomography, alongside with data from computed tomography for the same specimen. • Dynamic Volume Lines (Weissenböck, Fröhler, Gröller, Kastner, & Heinzl, 2019) facilitate the comparison of multiple slightly varying volumetric datasets, by mapping them to 1D and applying a nonlinear scaling to highlight regions with large differences. • With MetaTracts (Bhattacharya, Heinzl, Amirkhanov, Kastner, & Wenger, 2015, Bhattacharya et al (2017) one can characterize and analyze fiber bundles as well as weaving patterns in fiber-reinforced polymers.…”

Scale-Space Splatting: Reforming Spacetime for Cross-Scale Exploration of Integral Measures in Molecular Dynamics

“…Space reformation techniques are valuable tools for gaining insight into the spatial structure of the data. Recent publications present methods for a decomposition using a space-filling curve in MotionRugs [7] and Dynamic Volume Lines [52]. These works transform continuous volume data into one-dimensional representations by following a spacefilling curve through the volume.…”