On automatic determination of varying focal lengths using semidefinite programming

We describe a novel approach to the determination of the focal length of a moving camera with rectangular pixels. The principal point of the camera assumed to be known and fixed, whereas the focal length is allowed to vary across the sequence. Given three or more such images and a projective reconstruction, we describe a novel auto-calibration technique to obtain a metric reconstruction. Our technique uses semidefinite programming to recover these focal lengths (and hence the metric reconstruction). Our approach is efficient, well behaved with guaranteed convergence, and can be applied to long sequences of video. We present results for our approach using both simulated and real video sequences.