Speed estimation from a single image of a disc: theory

Abstract

We develop an approach to estimate the tangential speed of the edge of a rotating disc using a single image captured from a moving camera. The only dimensional information required for the estimate is the velocity of the camera relative to the ground. Notably, the size of the disc is not used, and the scene requires no calibration. The side of a tire and wheel assembly (TWA) on a motor vehicle can be a good approximation to a rotating disc, and, under reasonable assumptions, the tangential speed of the tire tread equals the speed of the vehicle. This indirect measurement of vehicle speed is passive, works independently of camera orientation, and is unaffected by obstructions between the vehicle and camera as long as one TWA is visible. The technique is readily adapted for application to a disc attached to a stationary mount.