The retinal motion of a distractor viewed by a translating observer is not sufficient by itself to determine the relative depth of an object. This is similar to the static situation where binocular disparity does not determine depth by itself, but together with convergence does determine it.
Consider the case where the fixate and distractor lie on the axis and the observer moves to the right along the axis at 6.5 cm/sec (interocular distance/sec). Suppose the right eye crosses the axis at as shown next.
The derivative in terms of the eye parameters, = node percent, = interocular distance, and = eye radius at is
Solving for gives
Solving the equation for gives .
Define the function ; then at fixate and distractor for all values of .
For fixate and distractor on the axis,
, and when , .
The Demonstration "Motion Parallax versus Depth, 3D (Visual Depth Perception 13)" (see Related Links) shows both fixate distance and pursuit on a single 3D curve.
The Demonstration "Motion/Pursuit Law in 1D (Visual Depth Perception 1)" (see Related Links) shows how the ratio of motion to pursuit does determine relative depth in this basic case.