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Keith Stroyan, Mark Nawrot; The peak motion/pursuit ratio and structure from motion parallax. Journal of Vision 2011;11(11):63. doi: 10.1167/11.11.63.
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The perception of relative depth from motion parallax relies on an internal pursuit signal generated to maintain stable fixation during observer translation (Nawrot & Joyce, 2007; Nadler, Nawrot, Angelaki, & DeAngelis, 2009). In (Nawrot & Stroyan, 2009) we mathematically derived a formula for relative depth from motion parallax using the ratio of the rate of retinal motion over the rate of smooth pursuit eye movement, the motion/pursuit ratio. The mathematics describes a laterally translating observer who fixates on one point and judges the depth of another point in central vision. We also confirmed, psychophysically, that judgments of relative depth agree with this dynamic geometric model. For points in central vision, the motion/pursuit ratio determines relative depth instantaneously, mathematically, and in less than 100 msec for people (Nawrot & Stroyan, 2010), but a single instantaneous observation does not give an accurate representation of the depth of points outside central vision. As an observer moves, the motion/pursuit ratio at a point changes and reaches a peak value at a time depending on that point. Mathematical recovery of the structure of objects that extend beyond central vision is possible using a longer duration integration of the motion/pursuit ratio over the points on the object. We present an analysis and computer simulation of how the motion/pursuit ratio gives accurate structure from motion parallax using the peak values of the motion/pursuit ratio.
While it is empirically known that the relative depth of points on an object may be perceived quickly and accurately in central vision, our mathematics suggests that the perception of the structure of an object that extends beyond central vision might be accurately perceived by longer duration integration of only the motion/pursuit ratio.
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