Diminished reality is as important as augmented reality, and both are possible with a device called the Reality Mediator. Over the past two decades, we have designed, built, worn, and tested many different embodiments of this device in the context of wearable computing. Incorporated into the Reality Mediator is an “EyeTap” system, which is a device that quantifies and resynthesizes light that would otherwise pass through one or both lenses of the eye(s) of a wearer. The functional principles of EyeTap devices are discussed, in detail. The EyeTap diverts into a spatial measurement system at least a portion of light that would otherwise pass through the center of projection of at least one lens of an eye of a wearer. The Reality Mediator has at least one mode of operation in which it reconstructs these rays of light, under the control of a wearable computer system. The computer system then uses new results in algebraic projective geometry and comparametric equations to perform head tracking, as well as to track motion of rigid planar patches present in the scene. We describe how our tracking algorithm allows an EyeTap to alter the light from a particular portion of the scene to give rise to a computer-controlled, selectively mediated reality. An important difference between mediated reality and augmented reality includes the ability to not just augment but also deliberately diminish or otherwise alter the visual perception of reality. For example, diminished reality allows additional information to be inserted without causing the user to experience information overload. Our tracking algorithm also takes into account the effects of automatic gain control, by performing motion estimation in both spatial as well as tonal motion coordinates.