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Tracking and Separation (Visual Depth Perception 11)

We study the case of an observer moving at right angles to the aim of the head, fixing his eyes on a (fixate) point F and also observing a distractor D. The important angles for depth perception by motion parallax are and . The angle is mathematically helpful.
To animate motion in time, click the [+] next to the "time " slider and click play [>]. The changing position of the distractor on the retina is "motion parallax".

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Fixation on causes the eyes to rotate because of the observer's continuous translation. We measure the tracking angle counterclockwise (+) from the axis (head aim direction) and call the time rate of change needed to maintain fixation the "pursuit". This is , the time derivative in the sense of calculus.
In terms of the eye parameters = node percent, = interocular distance, and = eye radius, the derivative is
.
This peaks at (when the denominator is largest):
.
The observer's translation also causes the angle separating the fixate and distraction to change, causing motion of the image of D on the retina. The time rate of change in angle from the distractor to the fixate is a "dynamic parallax" describing the moving retinal image of . This derivative is
This simplifies greatly at the time , when the eye crosses the axis:
.
When the distraction is in line with the eye, , and has the simple form
and the ratio of retinal motion over pursuit is
.
The basic case of the motion/pursuit law for relative depth from motion parallax is
.
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