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".



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+