The motion/pursuit law for visual depth perception from motion parallax

One of vision's most important functions is specification of the layout of objects in the 3D world. 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. 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. We show that this could have been obtained with the approaches of Nakayama and Loomis [Nakayama, K., & Loomis, J. M. (1974). Optical velocity patterns, velocity-sensitive neurons, and space perception: A hypothesis. Perception, 3, 63-80] or Longuet-Higgens and Prazdny [Longuet-Higgens, H. C., & Prazdny, K. (1980). The interpretation of a moving retinal image. Proceedings of the Royal Society of London Series B, 208, 385-397] by adding pursuit to their treatments. 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. The theoretical framework provided by the motion/pursuit law provides the quantitative foundation necessary to study this fundamental visual depth perception ability.