Projected Field Similarity for Comparative Visualization of Multi‐Run Multi‐Field Time‐Varying Spatial Data

Abstract

The purpose of multi‐run simulations is often to capture the variability of the output with respect to different initial settings. Comparative analysis of multi‐run spatio‐temporal simulation data requires us to investigate the differences in the dynamics of the simulations' changes over time. To capture the changes and differences, aggregated statistical information may often be insufficient, and it is desirable to capture the local differences between spatial data fields at different times and between different runs. To calculate the pairwise similarity between data fields, we generalize the concept of isosurface similarity from individual surfaces to entire fields and propose efficient computation strategies. The described approach can be applied considering a single scalar field for all simulation runs or can be generalized to a similarity measure capturing all data fields of a multi‐field data set simultaneously. Given the field similarity, we use multi‐dimensional scaling approaches to visualize the similarity in two‐dimensional or three‐dimensional projected views as well as plotting one‐dimensional similarity projections over time. Each simulation run is depicted as a polyline within the similarity maps. The overall visual analysis concept can be applied using our proposed field similarity or any other existing measure for field similarity. We evaluate our measure in comparison to popular existing measures for different configurations and discuss their advantages and limitations. We apply them to generate similarity maps for real‐world data sets within the overall concept for comparative visualization of multi‐run spatio‐temporal data and discuss the results.

Voreen -- An Open-source Framework for Interactive Visualization and Processing of Large Volume Data

“…To generate such a single overview plot, we transform the set of volumes to a similarity space. Here, we make use of the multi-run similarity plots proposed by Fofonov et al [13]. The idea is to create a lower-dimensional embedding of the whole ensemble in which each time step of each ensemble member is represented by a single point in the embedding such that Euclidean distances of the points in the embedding represent dissimilarities of the respective fields.…”

“…Isosurfaces were shown to be good scalar field descriptors and can therefore be used for this purpose, but do not capture the entire field. Fofonov et al [13] generalized the idea of isosurface similarity to a field similarity that was proven to have more desirable results to create embeddings than other metrics based on gradients or correlation. For this reason, we decided to integrate the scalar field similarity by Fofonov et al, which is used by default.…”

“…A screenshot of the Voreen application mode interface with multiple linked views providing insights in the 840 GB deep water asteroid impact ensemble data set [35]. It features a multi-run similarity plot (upper left) as proposed by Fofonov et al [13], the ensemble variance at the selected point in time (upper right), and two juxtaposed volume renderings of two individual simulation runs (bottom). The analyzed scalar field is the volume fraction of water.…”

“…When it comes to analyzing cohorts or ensembles, Voreen provides high-level visualizations (such as Multi-run Similarity Plots [13], Parallel Coordinates, time histograms, and variance calculation) as well as low-level operations and routines (such as filtering and transparent out-of-core-processing) for spatio-temporal multi-field or multi-channel ensemble data sets. When combined with other existing features, these methods allow developers to implement all sorts of analysis workflows including visual encodings that operate at multiple levels of detail and abstraction.…”

Comparative Layouts Revisited: Design Space, Guidelines, and Future Directions

“…This seems a strong advantage for explicit-encoding since the other three layouts are commonly complained of their limited scalability. For this reason, explicit-encoding was favored by researchers when dealing with small screen space or a large number of visualizations [17,59,74]. However, the scalability of the rest seems to depend on other factors such as screen space availability and visual representation complexity, leading to the consideration between space efficiency and visual interference.…”