Information theory in computer graphics and visualization

We present a half-day course to review several information theory applications for computer graphics and visualization. Information theory tools, widely used in scientific fields such as engineering, physics, genetics and neuroscience, are also emerging as useful transversal tools in computer graphics and related fields. We introduce the basic concepts of information theory and how they map into application areas. Application areas in computer graphics include viewpoint selection, mesh saliency, scene exploration, ambient occlusion, geometry simplification, radiosity, adaptive ray-tracing and shape descriptors. Application areas in visualization are view selection for volume data, flow visualization, ambient occlusion, time-varying volume visualization, transfer function definition, time-varying volume visualization, iso-surface similarity maps and quality metrics. The applications fall broadly into two categories: the mapping of the problem to an information channel - as in viewpoint applications - and the direct use of measures such as entropy, Kullback-Leibler distance, Jensen-Shannon divergence, and f-divergences. These would be used to evaluate, for instance, the homogeneity of a set of samples being used as metrics. We will also discuss the potential applications of the information bottleneck method that allows us to progressively extract or merge information in a hierarchical structure.