When viewers read a data visualization, they are translating visual marks into quantitative judgments that are systematically imperfect. Decades of graphical perception research have documented these errors, but most findings take the form of ordinal rankings or categorical taxonomies. While helpful, these descriptions do not make quantitative predictions: they cannot predict how large a viewer's error will be for a specific chart design, dataset, and task, nor can they generalize to combinations not yet tested experimentally.

This dissertation develops computational models that make quantitative predictions about how viewers interpret data visualizations. Four studies model different aspects of visualization perception with increasing generality. First, I develop a formal model of y-axis truncation in bar charts that defines task-dependent conditions under which truncation preserves or distorts data structure, replacing heuristics with formally grounded, computable design guidance. Second, I test whether deep neural network features trained on natural images can serve as computational proxies for human similarity judgments of visualizations. Third, I apply signal detection theory (SDT) to visual lineup analysis, demonstrating that SDT provides a richer computational model of lineup perception than accuracy-based approaches by separating viewer sensitivity from decision criterion. Finally, I propose visual decoding operators --- composable perceptual primitives, each with estimable bias and variance --- and provide an existence proof that operators characterized on PDF and CDF charts compose to predict scatterplot mean-estimation performance with no parameters fit to the target data.

Together, these studies demonstrate that computational models of visualization perception are both feasible and productive: they predict quantities that ordinal rankings cannot, expose mechanisms that holistic accuracy measures obscure, and generalize across chart types and tasks.