Data-Driven Space-Filling Curves

Zhou, Liang; Johnson, Chris R.; Weiskopf, Daniel

doi:10.1109/tvcg.2020.3030473

Cited by 22 publications

(23 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such situations are sub-optimal for filling a static SFC grid as many collisions occur (see supplemental material for examples). A possible enhancement-reducing the sensitivity of HAGRID to extreme outliers-could be the used of adaptive SFC's (Zhou et al 2020).…”

Section: Discussionmentioning

confidence: 99%

Hagrid: using Hilbert and Gosper curves to gridify scatterplots

Cutura

Morariu

Cheng

et al. 2022

J Vis

Self Cite

View full text Add to dashboard Cite

A common enhancement of scatterplots represents points as small multiples, glyphs, or thumbnail images. As this encoding often results in overlaps, a general strategy is to alter the position of the data points, for instance, to a grid-like structure. Previous approaches rely on solving expensive optimization problems or on dividing the space that alter the global structure of the scatterplot. To find a good balance between efficiency and neighborhood and layout preservation, we propose Hagrid, a technique that uses space-filling curves (SFCs) to “gridify” a scatterplot without employing expensive collision detection and handling mechanisms. Using SFCs ensures that the points are plotted close to their original position, retaining approximately the same global structure. The resulting scatterplot is mapped onto a rectangular or hexagonal grid, using Hilbert and Gosper curves. We discuss and evaluate the theoretic runtime of our approach and quantitatively compare our approach to three state-of-the-art gridifying approaches, DGrid, Small multiples with gaps SMWG, and CorrelatedMultiples CMDS, in an evaluation comprising 339 scatterplots. Here, we compute several quality measures for neighborhood preservation together with an analysis of the actual runtimes. The main results show that, compared to the best other technique, Hagrid is faster by a factor of four, while achieving similar or even better quality of the gridified layout. Due to its computational efficiency, our approach also allows novel applications of gridifying approaches in interactive settings, such as removing local overlap upon hovering over a scatterplot. Graphical abstract

show abstract

Section: Discussionmentioning

confidence: 99%

Hagrid: using Hilbert and Gosper curves to gridify scatterplots

Cutura

Morariu

Cheng

et al. 2022

J Vis

Self Cite

View full text Add to dashboard Cite

show abstract

“…For example, 3D volume data can first be reduced to a 1D curve by letting a space-filling curve cut through the volume; afterward, we can apply bands or range representations around the curve ( Demir et al, 2014 ). Figure 5 shows an example that uses a data-adaptive space-filling curve to perform the reduction to 1D ( Zhou et al, 2021 ). Here, the data comes from a heart ischemia simulation; see Rosen et al (2016) for background reading.…”

Section: Visual Mappingmentioning

confidence: 99%

Uncertainty Visualization: Concepts, Methods, and Applications in Biological Data Visualization

Weiskopf

2022

Front. Bioinform.

Self Cite

View full text Add to dashboard Cite

This paper provides an overview of uncertainty visualization in general, along with specific examples of applications in bioinformatics. Starting from a processing and interaction pipeline of visualization, components are discussed that are relevant for handling and visualizing uncertainty introduced with the original data and at later stages in the pipeline, which shows the importance of making the stages of the pipeline aware of uncertainty and allowing them to propagate uncertainty. We detail concepts and methods for visual mappings of uncertainty, distinguishing between explicit and implict representations of distributions, different ways to show summary statistics, and combined or hybrid visualizations. The basic concepts are illustrated for several examples of graph visualization under uncertainty. Finally, this review paper discusses implications for the visualization of biological data and future research directions.

show abstract

“…In contrast, we focus on the temporal changes in spatial regions, and extend their static overview of the data with interactive means for exploring data instances in detail to support more flexible, in‐depth analyses of visual patterns in their spatial context. Space‐filling curves have also been applied for the exploration of volume data [WFG∗18; ZJW21] on grid‐based data layouts. Other approaches include creating layouts for large graphs [MM08] and jigsaw maps [Wat05].…”

Section: Related Workmentioning

confidence: 99%

“…Dafner et al [DCM00] introduced context‐based space‐filling curves which are sensitive to coherent regions in images. Zhou et al [ZJW21] extend this concept by traversing on a Hamiltonian path based on a space‐filling curve. Ngo and Linsen [NL20] combine dimensionality reduction to 2D with interactive 2D to 1D mapping.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Visual Analysis of Spatio‐temporal Phenomena with 1D Projections

Franke

Henry

Koch

et al. 2021

Computer Graphics Forum

View full text Add to dashboard Cite

It is crucial to visually extrapolate the characteristics of their evolution to understand critical spatio‐temporal events such as earthquakes, fires, or the spreading of a disease. Animations embedded in the spatial context can be helpful for understanding details, but have proven to be less effective for overview and comparison tasks. We present an interactive approach for the exploration of spatio‐temporal data, based on a set of neighborhood‐preserving 1D projections which help identify patterns and support the comparison of numerous time steps and multivariate data. An important objective of the proposed approach is the visual description of local neighborhoods in the 1D projection to reveal patterns of similarity and propagation. As this locality cannot generally be guaranteed, we provide a selection of different projection techniques, as well as a hierarchical approach, to support the analysis of different data characteristics. In addition, we offer an interactive exploration technique to reorganize and improve the mapping locally to users' foci of interest. We demonstrate the usefulness of our approach with different real‐world application scenarios and discuss the feedback we received from domain and visualization experts.

show abstract

Data-Driven Space-Filling Curves

Cited by 22 publications

References 26 publications

Hagrid: using Hilbert and Gosper curves to gridify scatterplots

Hagrid: using Hilbert and Gosper curves to gridify scatterplots

Uncertainty Visualization: Concepts, Methods, and Applications in Biological Data Visualization

Visual Analysis of Spatio‐temporal Phenomena with 1D Projections

Contact Info

Product

Resources

About