Motion from projection: a forward model

One of the most fundamental properties of the Radon (projection) transform is that shifting of the image results in shifted projections. This useful property relates translational motion in the image to simple displacement in the projections. It is far from clear, however, how more general types of motion in the image domain will be manifested in the projections. In this paper, we present a model for this phenomenon in the general case; namely, we develop a generalization of the shift property of the Radon transform. We study various properties of the apparent projected motion applied by the model, and study the case of affine motion in particular. We also present illustrative examples, and briefly discuss the inverse problem implied by the forward model developed herein, along with some possible applications