Computation of 3D-motion parameters using the log-polar transform

Abstract

Arificial vision systems for mobile robots necessitate sensors and representations that enable a real-time reactive behavior. The log-polar transform has been shown to be a variable resolution scheme that achieves a high compression of the non-foveal part of an image. Such space variant sensors must inevitably be active in order to utilize the high- and homogeneous resolution fovea. We study here the computation of the heading direction using a log-polar sensor able to fixate. The polar nature of the complex logarithmic mapping produces a computationally superior representation of the optical flow. Based on an insight for the translational case we present a new algorithm for computing the focus of expansion by applying fixation in case of general motion.