"Where are you driving to?" Heading direction for a mobile robot from optical flow

If a camera moves on a straight line, the optic flow field is a diverging vector field, of which the singularity is called "focus of expansion" (FOE). An object which is seen in this FOE is located on the future path of the camera. If the camera is also rotating, the future path is no longer a point in the image domain, but a line. All objects which are on the future path (and thus will cause collisions) are projected on this line. However, the reverse is not necessary true - not all points on the line are collision points. In this paper we derive how the optic flow can be used to compute which points in the image are projections of collision points.