Binocular Disparity versus Depth (Visual Depth Perception 9)

Manipulate[
Module[{motion,df,d,δ,curve,valueΔ,valueδ,valueθ,i,n,r},
motion[ff_,df_]=df (i/((df+f)(f+n r)));
d[f_]=f((4 +((((i/f)))^2))/(2 ((i/f)-2 Tan[δ/2])))Tan[δ/2];
δ=π/180.;i=13/2;n=1/2;r=13/10;

curve=Plot[d[ff],{ff,10,150},AxesLabel->{Style["f",Italic],Style["d",Italic]},PlotStyle->{AbsoluteThickness[2],Red},AxesOrigin->{10,0},PlotRange->{{-15,170},{-15,110}}];
valueΔ=Graphics[{Blue,{Text[Row[{Style["d",Italic]," = ",Round[d[f],.01]}],{30,100}],Text[Row[{Style["d",Italic]/Style["f",Italic]," = ",Round[d[f]/f,.001]}],{30,90}],Text[Row[{Style["f",Italic]," = ",Round[f,.01]}],{30,80}],Line[{{f,0},{f,d[f]},{0,d[f]}}]}}];
valueδ=Graphics[{Red,Text[Row[{"δ"," = ",1, " °"}],{f-5,d[f]+5}]}];
valueθ=Graphics[{Brown,Text[Row[{HoldForm[((Style["d",Italic]θ)/((Style["d",Italic]t)))]," = ",Round[motion[f,d[f]]180/π,.001]}],{f+10,d[f]-8}]}];
Show[{curve,valueΔ,valueδ,valueθ},ImageSize->{500,400}]],
{{f,62,"symmetric fixate location f"},.1,150,Appearance->"Labeled"}]

CAPTION

This Demonstration shows that binocular disparity alone does NOT determine the relative depth of a distractor.

The slider f allows you to vary the symmetric fixate location (shown in the details), while the program computes the symmetric depth d needed to maintain a binocular disparity of δ=1 degree. Distances are in centimeters.

DETAILS

Binocular disparity is explained in more detail in the Demonstration "Binocular Disparity (Visual Depth Perception 7)" and the addition of convergence for depth is in "Disparity, Convergence, and Depth (Visual Depth Perception 10)" (see Related Links).

For this Demonstration, we also give the value of the retinal motion rate d θ/d t for an observer moving at 6.5 cm/sec (interocular distance per second).

Motion parallax is asymptotic to binocular disparity at long fixate distances; see the Demonstration "Dynamic Approximation of Static Quantities (Visual Depth Perception 14)" in the Related Links.

THIS NOTEBOOK IS THE SOURCE CODE FROM

"Binocular Disparity versus Depth (Visual Depth Perception 9)" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/BinocularDisparityVersusDepthVisualDepthPerception9/

Contributed by: Keith Stroyan

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