When we make a smooth eye movement to track a moving object, the visual system must take the eye's movement into account in order to estimate the object's velocity relative to the head. This can be done by using extra-retinal signals to estimate eye velocity and then subtracting expected from observed retinal motion. Two familiar illusions of perceived velocity--the Filehne illusion and Aubert-Fleischl phenomenon--are thought to be the consequence of the extra-retinal signal underestimating eye velocity. These explanations assume that retinal motion is encoded accurately, which is questionable because perceived retinal speed is strongly affected by several stimulus properties. We develop and test a model of head-centric velocity perception that incorporates errors in estimating eye velocity and in retinal-motion sensing. The model predicts that the magnitude and direction of the Filehne illusion and Aubert-Fleischl phenomenon depend on spatial frequency and this prediction is confirmed experimentally.