Determining the egomotion of an uncalibrated camera from instantaneous optical flow

Abstract. The main result of this paper is a procedure for self-calibration of a moving camera from instantaneous optical ow. Under certain assump-tions, this procedure allows the ego-motion and some intrinsic parameters of the camera to be determined solely from the instantaneous positions and ve-locities of a set of image features. The proposed method relies upon the use of a dierential epipolar equation that relates optical ow to the ego-motion and internal geometry of the camera. The paper presents a detailed derivation of this equation. This aspect of the work may be seen as a recasting into an analytical framework of the pivotal research of Vieville and Faugeras.1 The information about the camera's ego-motion and internal geometry enters the dierential epipolar equation via two matrices. It emerges that the optical ow 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 mo-tion can be self-calibrated via closed-form expressions in the composite ratio. The corresponding formulae specify ve ego-motion parameters, as well as the focal length and its derivative. An accompanying procedure is presented for reconstructing the viewed scene, up to scale, from the derived self-calibration data and the optical ow data. Experimental results are given to demonstrate the correctness of the approach. 1