Estimating the heading direction using normal flow

Abstract

If an observer is moving rigidly with bounded rotation then normal flow measurements (i.e., the spatiotemporal derivatives of the image intensity function) give rise to a constraint on the oberver's translation. This novel constraint gives rise to a robust, qualitative solution to the problem of recovering the observer's heading direction, by providing an area where the Focus of Expansion lies. If the rotation of the observer is large then the solution area is large too, while small rotation causes the solution area to be small, thus giving rise to a robust solution. In the paper the relationship between the solution area and the rotation and translation vectors is studied and experimental results using synthetic and real calibrated image sequences are presented. This work demonstrates that the algorithm developed in (Horn and Weldon 1987) for the case of pure translation, if appropriately modified, results in a robust algorithm that works in the case of general rigid motion with bounded rotation. Subsequently, it has the potential to replace expensive accelerometers, inertial systems and inaccurate odometers in practical navigational systems for the problem of kinetic stabilization, which is a prerequisite for any other navigational ability.