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2011 Visual depth from motion parallax and eye pursuit, with Mark Nawrot, J. Math. Biol. (2012) 64:1157–1188, DOI 10.1007/s00285-011-0445-1
A translating observer viewing a rigid environment experiences “motion parallax”, the relative movement upon the observer’s retina of variously positioned objects in the scene. This retinal movement of images provides a cue to the relative depth of objects in the environment, however retinal motion alone cannot mathemati- cally determine relative depth of the objects. Visual perception of depth from lateral observer translation uses both retinal image motion and eye movement. In Nawrot and Stroyan (Vision Res 49:1969–1978, 2009) we showed mathematically that the ratio of the rate of retinal motion over the rate of smooth eye pursuit mathematically determines depth relative to the fixation point in central vision. We also reported on psychophysical experiments indicating that this ratio is the important quantity for perception. Here we analyze the motion/pursuit cue for the more general, and more complicated, case when objects are distributed across the horizontal viewing plane beyond central vision. We show how the mathematical motion/pursuit cue varies with different points across the plane and with time as an observer translates. If the time varying retinal motion and smooth eye pursuit are the only signals used for this visual process, it is important to know what is mathematically possible to derive about depth and structure. Our analysis shows that the motion/pursuit ratio determines an excel- lent description of depth and structure in these broader stimulus conditions, provides a detailed quantitative hypothesis of these visual processes for the perception of depth and structure from motion parallax, and provides a computational foundation to ana- lyze the dynamic geometry of future experiments.