Attentive vision is characterized by selective sensing in space and time as well as selective processing with respect to a specic task. Selection in space involves the splitting of the visual eld in a high resolution area -the fovea -and a space-variant resolution areathe periphery. Both in neurobiology and in robot vision, models of the resolution decrease towards the image boundaries have been established. The most convincing model is the theory of log-polar mapping where very high data compression rates are achieved.In combination with the complexity reduction we believe that the log-polar mapping has further computational advantages which we elaborate in this study. Based on the optical ow we study the computation of 3D motion and structure globally and locally. We present a global method to compute the Focus of Expansion in the case of pure translation. By xating on an object we show how to estimate ego motion in the presence of translation and rotation of the observer from the ow in the log-polar periphery. Then, we turn to local dierential computations and we establish both approximate and exact expressions for the time to collision.