Overview and State-of-the-Art of Uncertainty Visualization - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 12

only low-level visual processing but also high-level cognitive treatment of the visual
information. Standard tasks as an example may consist in counting the number of
local minima in a dataset, find the location of the maximum or minimum value,
find the direction of rotation of a vortex. The task completion time, task completion
accuracy, user's rating of efficiency and usability may be recorded. A statistical
analysis of the recorded data is done. Typical analyses include analysis of variance
(ANOVA), used to check in particular if the difference in the mean value of two
distributions is significant. Examples of uncertainty visualization papers with a task-
based evaluation include [ 20 , 21 , 69 , 91 ].
1.5 Review of Current State of the Art
The goal of visualization is to effectively present large amounts of information in
a comprehensible manner, however, most visualizations lack indications of uncer-
tainty [ 42 , 43 , 63 , 83 ].
1.5.1 Traditional Representations
Tukey [ 103 ] proposed graphical techniques to summarize and convey interesting
characteristics of a data set not only to facilitate an understanding of the given data but
also to further investigation and hypothesis testing. These tested graphical methods,
such as the boxplot, histogram, and scatter plot, provide identifiable representations
of a data distribution, and their simplicity allows for quick recognition of important
features and comparison of data sets. In addition, they can be substituted for the
actual display of data, specifically when data sets are too large to plot efficiently.
1.5.1.1 1D
One of the most ubiquitous approaches to displaying uncertainty information is
the boxplot [ 28 , 34 , 94 , 103 ], which is the standard technique for presenting the
five-number summary , consisting of the minimum and maximum range values, the
upper and lower quartiles, and the median, as illustrated in Fig. 1.2 a. This collec-
tion of values quickly summarizes the distribution of a data set, including range and
expected value, and provides a straightforward way to compare data sets. In addi-
tion, the reduced representation afforded by the five-number summary provides a
concise tool for data analysis, since only these characteristic values need to be ana-
lyzed. Figure 1.2 b and c show visual modifications of the boxplot. Surveys on the
introduction and evolution of the boxplot can be found in [ 16 , 81 ].
The box plot is often adapted to include information about the underlying distrib-
ution, as demonstrated in Fig. 1.2 d-g. The most common modification adds density