Information visualizations of quantitative data are rapidly becoming more complex as the dimension and volume of data increases. Critical to modern applications, an information visualization is used to communicate numeric data using objects such as lines, rectangles, bars, circles, and so forth. Via visual inspection, the viewer assigns numbers to these objects using their geometric properties of size and shape. Any difference between this estimation and the desired numeric value we call the "visual measurement error". The research objective of this paper is to propose models of the visual measure error utilizing stochastic geometry. The fundamental technique in building our models is the conceptualization of eye fixation points as might be determined by an eye-tracking experiment of viewers estimating size and shape of a visualization's object configurations. The fixation points are first considered as a stochastic point process whose characteristics require comment before proceeding to the statistical shape analysis of the visualization. Once clarified the fixation points are reinterpreted as a sampling of the shape and size of the landmark configurations of geometric landmarks on the visualization. The ultimate end of these models is to find optimal shape and size parameters leading to minimum visual measurement error.