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.

翻译：大量图像和地铁图等许多视觉图象,具有显著的信息损失。看一看,观众似乎有许多机会误解正在视觉化的数据,从而损害这些视觉图象的好处。实际上,这些视觉图象无疑是有用的。最近提出的分析视觉化过程成本-效益比的信息理论性衡量方法可以解释实际中经历的这种有用性,并假定观众的知识可以减少由于信息损失而可能造成的潜在扭曲(如误解)。这说明,通过比较潜在的扭曲而没有任何知识和实际扭曲与某些知识,观众的知识可以估计出很多机会。在本文件中,我们描述了一些案例研究,收集一些案例,以便(一) 支持对几种候选措施的评估,以估计视觉化过程可能的扭曲,和(二) 表明它们在实际情景中是否适用。由于关于选择一种适当约束性衡量方法来估计可能的扭曲的理论性论述仍然具有结论性,因此,关于视觉化的真实世界数据可以进一步为选择一种约束性衡量尺度提供实际证据,从而有助于我们进行理论性解释的精确性结论。同时,一旦我们能够进一步确定一种理论性结论,那么,我们就可以用一种理论性的方法来进行精确性解释。