  Many visual representations, such as volume-rendered images and metro maps,
feature a noticeable amount of information loss. At a glance, there seem to be
numerous opportunities for viewers to misinterpret the data being visualized,
hence undermining the benefits of these visual representations. In practice,
there is little doubt that these visual representations are useful. The
recently-proposed information-theoretic measure for analyzing the cost-benefit
ratio of visualization processes can explain such usefulness experienced in
practice, and postulate that the viewers' knowledge can reduce the potential
distortion (e.g., misinterpretation) due to information loss. This suggests
that viewers' knowledge can be estimated by comparing the potential distortion
without any knowledge and the actual distortion with some knowledge. In this
paper, we describe several case studies for collecting instances that can (i)
support the evaluation of several candidate measures for estimating the
potential distortion distortion in visualization, and (ii) demonstrate their
applicability in practical scenarios. Because the theoretical discourse on
choosing an appropriate bounded measure for estimating the potential distortion
is yet conclusive, it is the real world data about visualization further
informs the selection of a bounded measure, providing practical evidence to aid
a theoretical conclusion. Meanwhile, once we can measure the potential
distortion in a bounded manner, we can interpret the numerical values
characterizing the benefit of visualization more intuitively.
