Created with Wolfram Mathematica 6
Geometric Inputs to Visual Depth Perception
We recently discovered a new formula for visual depth perception from motion parallax. Mathematica 6 played a role in this discovery and is very helpful in explaining both the new dynamic formula and the old static formula for depth from convergence and disparity. There is a remarkable relation between the new and old foumulas. This collection of demonstration NoteBooks explains the new and old formulas interactively. The "Motion/Pursuit Law" is the most important computation, but the other interactive computations help you understand how that formula works and how it compares with static inputs to depth perception. By downloading the free Mathematica Player program, you will be able to do the computations yourself.
Motion/Pursuit Law: The 1-D case
1) Interactive computation of the M/PL in 1-D Motion/Pursuit Law in 1D (Visual Depth Perception 1)
2) Interactive computation of the M/PL in 1-D showing pursuit and motion on the axes. Motion, Pursuit, Fixate & Distraction (Visual Depth Perception 2)
Motion/Pursuit Law: The 2-D case
3) Interactive computation of the M/PL t=0 and peak in 2-D with mouse-movable distractor
Motion/Pursuit Law in 2 D (Visual Depth Perception 3)
4) Interactive computation of the M/PL t=0 and peak in 2-D around time zero invariant circles
Motion/Pursuit Law on Invariant Circles (Visual Depth Perception 4)
The horizontal fixation plane
5) A basic program to show what "fixation" means. Fixation & Distraction (Visual Depth Perception 5)
Eye parameters
6) A program to show variable interocular distance, eye radius, node percent, base point, head aim. Eye Parameters (Visual Depth Perception 6)
Binocular and retinal disparity
7) Interactive computaton of binocular and retinal disparity
with variable node percent. Binocular Disparity (Visual Depth Perception 7)
8) The invariant
circles (incl. Vieth-Meuller circle, geometric hropter) for
binocular disparity. Vieth-Müller Circles (Visual Depth Perception 8)
Static inputs to depth
9) A program showing a curve of constant B.D. with variable
depth. In other words, disparity alone does NOT
determine depth. Binocular Disparity vs Depth (Visual Depth Perception 9)
10) The depth and relative depth formula using both B.D. and convergence.
Disparity, Convergence & Depth (Visual Depth Perception 10)
Motion parallax and depth
11) A basic program showing the tracking
and separation angles animated in time. Tracking & Separation (Visual Depth Perception 11)
12) A program showing a curve of constant motion and variable
depth. Motion Parallax vs Depth, 2D (Visual Depth Perception 12)
13) A program showing a 3D curve of constant motion and variable
depth and pursuit. Motion Parallax vs Depth, 3D (Visual Depth Perception 13)
Comparison between static and dynamic inputs
14) Interactive computation showing the asymptotic approximation of static and dynamic quantities. Dynamic Approximation of Static Quantities (Visual Depth Perception 14)
Knowledge of speed determines absolute depth
If an observer could determine speed from visual cues, d
and f could be determined rather than only d/f
15) f
& d from speed and motion Speed, Motion, Pursuit & Depth (Visual Depth Perception 15)
16) f
& d from speed and M/P Speed, Pursuit, M/P Ratio & Depth (Visual Depth Perception 16)
The Motion/Pursuit Ratio and the Motion/Pursuit Law
17) Under Esitmate from Ratio Alone 1D Motion/Pursuit Ratio & Depth in 1D (Visual Depth Perceptio 17)
18)
Under Esitmate from Ratio Alone 2D Motion/Pursuit Ratio & Depth in 2D(Visual Depth Perception 18)