Determining the Translational Speed of a Camera from Time-Varying Optical Flow

Abstract

Under certain assumptions, a moving camera can be self-calibrated solely on the basis of instantaneous optical flow. However, due to a fundamental indeterminacy of scale, instantaneous optical flow is insufficient to determine the magnitude of the camera’s translational velocity. This is equivalent to the baseline length indeterminacy encountered in conventional stereo self-calibration. In this paper we show that if the camera is calibrated in a certain weak sense, then, by using time-varying optical flow, the velocity of the camera may be uniquely determined relative to its initial velocity. This result enables the calculation of the camera’s trajectory through the scene over time. A closed-form solution is presented in the continuous realm, and its discrete analogue is experimentally validated.