Multi-Charts for Comparative 3D Ensemble Visualization

A comparative visualization of multiple volume data sets is challenging due to the inherent occlusion effects, yet it is important to effectively reveal uncertainties, correlations and reliable trends in 3D ensemble fields. In this paper we present bidirectional linking of multi-charts and volume visualization as a means to analyze visually 3D scalar ensemble fields at the data level. Multi-charts are an extension of conventional bar and line charts: They linearize the 3D data points along a space-filling curve and draw them as multiple charts in the same plot area. The bar charts encode statistical information on ensemble members, such as histograms and probability densities, and line charts are overlayed to allow comparing members against the ensemble. Alternative linearizations based on histogram similarities or ensemble variation allow clustering of spatial locations depending on data distribution. Multi-charts organize the data at multiple scales to quickly provide overviews and enable users to select regions exhibiting interesting behavior interactively. They are further put into a spatial context by allowing the user to brush or query value intervals and specific distributions, and to simultaneously visualize the corresponding spatial points via volume rendering. By providing a picking mechanism in 3D and instantly highlighting the corresponding data points in the chart, the user can go back and forth between the abstract and the 3D view to focus the analysis.

1 Introduction

Volume rendering is a standard method to visually convey the information content in 3D scalar fields. Especially when transfer functions in combination with interactive approaches are used, volume rendering allows effectively revealing the location and shape of relevant features, as well as their spatial relationships. Volume rendering, on the other hand, faces the problem of spatial occlusions and attenuation effects. This limits the number of features that can be visualized simultaneously, and it lowers the effectiveness of volume rendering without prior knowledge of features and their locations in space. In particular when volume rendering is used to explore multi-variate fields, requiring quantitative comparisons across multiple parameters, these limitations are further increased.