Fig. 3: Geometry of a more generalized viewing scenario.

A The eye translates to the right while maintaining fixation on a moving target (yellow square) by making a smooth eye movement with velocity ω_eye. The eye velocity is comprised of a compensatory rotation for the translation, \({\omega }_{{\mathrm{eye}}}^{T}\), and a component related to tracking the moving target, \({\omega }_{{\mathrm{eye}}}^{P}\). The rotation pivot of the optic flow field, p, is located between the eye and the fixation target. The amplitude of eye translation and rotation is exaggerated for the purpose of illustration. B When an object (soccer ball shape) is located at depth, d, and moves independently in the world, its retinal image velocity, ω_ret, is determined by its own motion in the world, ω_obj, motion parallax produced by the observer’s translation, \({\omega }_{{\mathrm{ret}}}^{T}\), and image motion resulting from the pursuit eye movement, \({\omega }_{{\mathrm{ret}}}^{P}\). ω_eye, \({\omega }_{{\mathrm{eye}}}^{T}\), \({\omega }_{{\mathrm{eye}}}^{P}\), and ω_obj are defined relative to a fixed point in the world, and ω_ret, \({\omega }_{{\mathrm{ret}}}^{T}\), and \({\omega }_{{\mathrm{ret}}}^{P}\) are relative to the eye.