Determining the egomotion of an uncalibrated camera from instantaneous optical flow

Abstract

A procedure is described for self-calibration of a moving camera from instantaneous optical flow. Under certain assumptions this procedure allows the egomotion and some intrinsic parameters of the camera to be determined solely from the instantaneous positions and velocities of a set of image features. The proposed method relies on the use of a differential epipolar equation that relates optical flow to the egomotion and the internal geometry of the camera. A detailed derivation of this equation is presented. This aspect of the work may be seen as a recasting into an analytical framework of the pivotal research of Vieville Faugeras [Proceedings of the Fifth International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1995), pp. 750–756]. The information about the camera's egomotion and internal geometry enters the differential epipolar equation via two matrices. It emerges that the optical flow determines the composite ratio of some of the entries of the two matrices. It is shown that a camera with unknown focal length undergoing arbitrary motion can be self-calibrated by means of closed-form expressions in the composite ratio. The corresponding formulas specify five egomotion parameters as well as the focal length and its derivative. A procedure is presented for reconstructing the viewed scene, up to a scale factor, from the derived self-calibration data and the optical flow data. Experimental results are given to demonstrate the correctness of the approach.