![]() ![]() In reality the phenomena are complicated by the fact that, supposing our attention is attracted, not by some object moving along with us, but by stationary external objects, we are invariably in the habit of keeping the eyes fastened for a brief space on some definite point, by turning them so as to counteract the effect of the forward motion of the body. Lateral motion has no FoE at the crossing point.) However, von Kreis, in ( Helmholtz 1910, vol III, Note 4, p.371) writes, “… The changes of which he (Helmholtz) speaks are such as the observer would notice if he advanced forward without changing the attitude of his head or his eyes especially. (In more general cases with a component of forward motion, the “focus of expansion” is an important consideration. Helmholtz (1910, vol III, p.295) wrote about retinal motion and concentrated on the case of forward motion, a topic since studied in detail generally under the name “optic flow.” In the extreme case when one moves directly toward the fixate point the “flow” on the retina is pure expansion. The subject is complicated by the fact that there are different “dynamic geometries” of retinal motion depending on the direction of observer motion and movement of the head and eyes. However, we have only recently begun to understand the dynamic geometry in relation to the neural mechanisms serving the perception of depth. This motion parallax is an important monocular cue for the visual perception of depth. Observer translation while viewing a rigid scene creates a continuously varying retinal image because of the change in relative position of objects from the observer’s point of view. Our analysis shows that the motion/pursuit ratio determines an excellent 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 analyze the dynamic geometry of future experiments. 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. We show how the mathematical motion/pursuit cue varies with different points across the plane and with time as an observer translates. 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 also reported on psychophysical experiments indicating that this ratio is the important quantity for perception. 49, p.1969) 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. Visual perception of depth from lateral observer translation uses both retinal image motion and eye movement. This retinal movement of images provides a cue to the relative depth of objects in the environment, however retinal motion alone cannot mathematically determine relative depth of the objects. 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. ![]()
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