Time to Contact Relative to a Planar Surface

We show how to determine the time to contact from time varying images using only accumulated sums of suitable products of image brightness derivatives. There is no need for feature or object detection, tracking of features, estimation of optical flow, or any "higher level" processing. This so-called "direct" method for determining the time to contact is based on analysis of the motion field resulting from rigid body motion under perspective projection and the constant brightness assumption. The method has essentially no latency, since it can be based on analysis of just two frames of a video sequence, and does not require a calibrated camera. An implementation of the method is demonstrated on synthetic image sequences and stop motion sequences - where the ground truth is accurately know - as well as on video sequences taken by a camera mounted on moving vehicles.