# A Model of Information Visualization Interpretation
## 1 Introduction  
The visual display of quantitative data requires the viewer to decode numerical information from visual objects [1], as shown in Figure 1. As the volume and dimension of data increase, the associated visualizations become increasingly more complex [2], making the decoding process more challenging. Much attention has been given to the success or failure of the decoding process. Research agendas have had a variety of objectives and have utilized various methodologies. A discussion of topics relevant to this paper follows. An information visualization communicates numeric data using objects such as lines, rectangles, bars, circles, and so forth [1]. [PERSON] and [PERSON], in their classic work on graphical perception [3], studied how the viewer assigns numbers to these objects using their geometric properties of points, lengths, areas, and so forth. Their results were repeated and extended on a larger experimental scale using crowd sourcing on Amazon's Mechanical Turk platform by [PERSON] and [PERSON] [4]. The systemic difference they found between the user-perceived value and the desired numeric value is called the \"expected visual measurement error\" in this paper, and modeling it is one of the goals. All models are based on assumptions. In order to build ours, we need to clarify the situation and context in which the decoding occurs. This requires an understanding of how people approach a visualization to read it. [PERSON] and [PERSON] published a survey of graph comprehension research [5]. They found in the literature three major factors influencing a student's comprehension of graphs: visual characteristics of the graph, prior experience with visualizations, and knowledge and expectations with the content of the data in a graph. While measuring comprehension is not an objective of this research, it is assumed the viewer understands how to read a bar graph, which is not universally true. Here we encounter a subtle point, which is the reason the viewer is inspecting the graph. Is the the person seeking an answer to a specific question, or is the viewer free to explore and deduce meaning? This introduces the concept of top-down versus bottom-up viewing of a visualization [6; 7]. Top-down is goal-oriented, and visual attention is associated with the viewer's goals and expectations, whereas in bottom-up, visual attention is driven by the graphical characteristics of the image, such as color and contrast. Bottom-up is the free visual search. [PERSON] et al. have explored bottom-up situations in several studies using eye tracking [8; 9]. This can be complicated due to the matter of memory. If the viewer is given a limited period to investigate the visualization, then memory must be used to fulfill a task [10]. In this paper, the concern is with a viewer who is given a specific task to fulfill, making this a top-down situation. In moving from related cognitive issues to focus on the eye-tracking methodology, we find rich literature. [PERSON] and [PERSON] [11] offer a detailed historical review of eye tracking starting in the 1800s. Much early research tried to tie eye tracking to the cognitive process. That is, how eye movement relates to the thought process [12; 13; 14]. A thread of recent research seeks to use eye tracking to discover how a viewer seeks out the salient features of the visualization [15]. This can be tied to visualization design via a so-called saliency map [8; 16], which is used to predict user behavior. These maps are most applicable in a bottom-up situation. Important to the use of eye-tracking data in the development of models is the capability to quantize it. The most common approach is through various metrics. In [11], 21 usability studies utilizing eye tracking were surveyed, and the metrics were classified and counted. Some of this is relevant herein. First, the concept of a fixation is needed.