Visual Entropy and the Visualization of Uncertainty
Background: It is possible to find many different visual representations of data values in visualizations, it is less common to see visual representations that include uncertainty, especially in visualizations intended for non-technical audiences. Objective: our aim is to rigorously define and evaluate the novel use of visual entropy as a measure of shape that allows us to construct an ordered scale of glyphs for use in representing both uncertainty and value in 2D and 3D environments. Method: We use sample entropy as a numerical measure of visual entropy to construct a set of glyphs using R and Blender which vary in their complexity. Results: A Bradley-Terry analysis of a pairwise comparison of the glyphs shows participants (n=19) ordered the glyphs as predicted by the visual entropy score (linear regression R2 >0.97, p<0.001). We also evaluate whether the glyphs can effectively represent uncertainty using a signal detection method, participants (n=15) were able to search for glyphs representing uncertainty with high sensitivity and low error rates. Conclusion: visual entropy is a novel cue for representing ordered data and provides a channel that allows the uncertainty of a measure to be presented alongside its mean value.