An analytical approach to determining the ego-motion of a camera having free intrinsic parameters
Michael J. Brooks · 2002
this paper, we analyse the motion of a camera having free intrinsic parameters. We define a free parameter to be one that is unknown and may vary continuously. A time-dependent epipolar equation is presented, followed by a formal definition of the time-derivative of the fundamental matrix for the case of a mobile camera. Next, differential forms of the epipolar equation are obtained. This may be seen as a recasting of the recent work of Vieville and Faugeras [12] into an analytical framework. Critical to the approach is the determination, to within a common scalar factor, of two special matrices from optical flow data. The case of a camera with free focal length undergoing arbitrary motion is then considered in detail. Closed-form expressions are given, in terms of the entries of the two matrices, for the ego-motion parameters, as well as the focal length and its derivative. Key words and phrases. Self-calibration, ego-motion, epipolar equation, fundamental matrix, intrinsic parameters. 1 Introduction