<title>Egomotion from optical flow with an uncalibrated camera</title>

The problem of automatically determining an uncalibrated camera's motion through space solely form its view of the static surroundings has only recently received attention. In this work, we present a new direct method for computing camera egomotion from optical flow data in the particular case of a camera having unknown and possibly varying local length. Here, egomotion refers to motion that is expressed with respect to the camera's local frame of reference. No restrictions are placed on the nature of the camera's motion other than that its translational and rotational components vary smoothly. Essential to the approach is the derivation of a differential form of the time-dependent epipolar equation for a single moving camera. The method requires that two special matrices be computed from optical flow data. Closed-form expressions, presented in terms of the entries of the tow matrices, are then given for the egomotion parameters, the focal length and its derivative. This self-calibration process constitutes as essential prerequisite to obtaining a reconstruction of the viewed scene from optical flow.