Perrone [(1992) Journal of the Optical Society of America A, 9, 177-194] recently proposed a template-based model of self-motion estimation which uses direction- and speed-tuned input sensors similar to neurons in area MT of primate visual cortex. Such an approach would generally require an unrealistically large number of templates (five continuous dimensions). However, because primates, including humans, have a number of oculomotor mechanisms which stabilize gaze during locomotion, we can greatly reduce the number of templates required (two continuous dimensions and one compressed and bounded dimension). We therefore refined the model to deal with the gaze-stabilization case and extended it to extract heading and relative depth simultaneously. The new model is consistent with previous human psychophysics and has the emergent property that its output detectors have similar response properties to neurons in area MST.