Here we use the dynamic geometry of motion parallax to show that the visual system relies on a ratio of retinal image motion and pursuit eye movement to disambiguate near and far depth from motion parallax, and to show that this ratio provides a reliable metric for relative depth of objects in a scene. Another important monocular depth perception cue is motion parallax, the relative movement of objects in a scene created by the translation of an observer ( Gibson, 1950). This retinal disparity is an important cue for the perception of relative depth from binocular stereopsis. Historically, knowledge of the underlying static geometry was central to understanding how the lateral separation of the two eyes creates retinal images with objects in different positions ( Wheatstone, 1838 Wade, 1998). Therefore, geometry provides a crucial starting point for understanding how the visual system produces a neural representation of relative depth. To perceive a three-dimensional world the human visual system must rely on the information falling upon a two-dimensional retina. The theoretical framework provided by the motion/pursuit law provides the quantitative foundation necessary to study this fundamental visual depth perception ability. Results of a psychophysical experiment show that changes in the motion/pursuit ratio have a much better relationship to changes in the perception of depth from motion parallax than do changes in motion or pursuit alone. We show that this could have been obtained with the approaches of Nakayama and Loomis (1974) or Longuet-Higgins and Prazdny (1980) by adding pursuit to their treatments. Mathematically, the ratio of retinal image motion (motion) and smooth pursuit of the eye (pursuit) provides the necessary information for the computation of relative depth from motion parallax. While the static optical geometry of retinal disparity explains the perception of depth from binocular stereopsis, we propose a new formula to link the pertinent dynamic geometry to the computation of depth from motion parallax. One of vision’s most important functions is specification of the layout of objects in the 3D world.
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