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".
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