Attentive Visual Motion Processing: Computations in the Log-Polar Plane

Attentive Visual Motion Processing: Computations in the Log-Polar Plane. Attentive vision is characterized by selective sensing in space and time as well as selective processing with respect to a specific task. Selection in space involves the splitting of the visual field in a high resolution area—the fovea—and a space-variant resolution area—the 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 flow 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 fixating on an object we show how to estimate ego motion in the presence of translation and rotation of the observer from the flow in the log-polar periphery. Then, we turn to local differential computations and we establish both approximate and exact expressions for the time to collision.