Conventional approaches to object tracking through an image sequence either use area correlation or extraction of contrast edges and other features from the target image, taken as the target signature. However, it is often difficult to reliably extract the target signature when the target and background image, as well as target/background polarity and contrast, change drastically over time. One of the major neurobiological discoveries in the last two decades is that the visual "what" processes, which determine the identity of an object, are segregated from the "where" processes, which determine the spatial location and motion of an object. Biological visual motion tracking does not require continuously detecting the target signature. It simply maintains the target signature throughout the image sequence via an adaptive process of the receptive fields of neurons. Formulated as a pure "where" process that maintains the Gabor representation of the target surface signature, we reduce the tracking process to the analytical computation of affine transformations of the surface signature through the image sequence. Experiments on realistic infrared image sequences demonstrate the great simplicity, high accuracy, and robustness of the proposed analytical target tracking algorithm.