This manuscript describes the elements of a theory of information tailored to control and decision tasks and specifically to visual data. The concept of Actionable Information is described, that relates to a notion of information championed by J. Gibson, and a notion of "complete information" that relates to the minimal sufficient statistics of a complete representation. It is shown that the "actionable information gap" between the two can be reduced by exercising control on the sensing

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... Thus, senging, control and information are inextricably tied. This has consequences in the so-called "signal-to-symbol barrier" problem, as well as in the analysis and design of active sensing systems. It has ramifications in vision-based control, navigation, 3-D reconstruction and rendering, as well as detection, localization, recognition and categorization of objects and scenes in live video. This manuscript has been developed from a set of lecture notes for a summer course at the First International Computer Vision Summer School (ICVSS) in Scicli, Italy, in July of 2008. They were later expanded and amended for subsequent lectures in the same School in July 2009. Starting on November 1, 2009, they were further expanded for a special topics course, CS269, taught at UCLA in the Spring term of 2010.