Resolution vs. Tracking Error: Zoom as a Gain Controller

Abstract

During tracking, lens zoom acts as a gain between scene dynamics and fixation errors, providing a trade-off between maximizing resolution and minimizing tracking error. Using a linear Kalman filter model, it is shown that when image measurement error scales with focal length, the filter is invariant to zoom. When the error is of fixed size, however, zooming alters the balance between process and measurement errors in a counter-intuitive manner. It is shown that this balance can be restored by appropriate adjustment of the process noise. With a zoom invariant filter, zoom can be used to ensure that fixation errors remain bounded. To this end, an error variance control method is proposed which gives high confidence that the target will not leave the image during tracking. To implement such a scheme, equipment delays and responses must be known, including those of the zoom lenses. Experiments to measure these are described, and overall results are presented for 30 Hz tracking of real scenes.