Dynamic Analysis of Optic Flow and Eye Pursuit

The brain uses a variety of cues to reconstruct 3-dimensional environments.  Our work studies the mathematics of a combination of moving 2-dimensional projections on the retina and motor-control of the eye.  A translating observer who is fixated on a particular point requires "smooth eye pursuit" to keep the special point in central vision. Retinal images of other points in the environment move on the retina, creating "motion parallax.” Experiments suggest that the ratio of these two rates is used in the brain to perceive depth.  

This motion-pursuit ratio dΘ/dΒ (Nawrot & Stroyan, 2009) helps an observer determine the depth of objects relative to a given fixate. Using knowledge of fixate position, we then mathematically reconstruct shapes in the horizontal plane. We find that dynamic approximations of object distance in two dimensions using the motion-pursuit ratio are more accurate than previous expectations.

Optic flow is the more general motion of external 3-dimensional points on the 2-dimenaional retina that depends on the shape of the object and the observer's motion.  For this part of our project, we use Mathematica to create and analyze animations of the optic flow of various 3-dimensional objects.