Can we generate “foveated Image” in Mathematica

Question

\"Foveated imaging is a digital image processing technique in which the image resolution, or amount of detail, varies across the image according to one or more \"fixation po

Answer 1

WaveletMapIndexed can give a spatially-varying blur, as shown in the Mathematica documentation (WaveletMapIndexed->Examples->Applications->Image Processing). Here is an implementation of a foveatedBlur, using a compiled version of the acuity function from the other answer:

Clear[foveatedBlur];
foveatedBlur[image_, d_, cx_, cy_, blindspotradius_] := 
   Module[{sx, sy}, 
      {sy, sx} = ImageDimensions@image;
      InverseWaveletTransform@WaveletMapIndexed[ImageMultiply[#, 
          Image[acuityC[d, sx, sy, -cy + sy/2, cx - sx/2, blindspotradius]]] &, 
          StationaryWaveletTransform[image, Automatic, 6], {___,  1 | 2 | 3 | 4 | 5 | 6}]]

where the compiled acuity is

Clear[acuityC];
acuityC = Compile[{{distance, _Real}, {sx, _Integer}, {sy, _Integer}, {x0, _Real}, 
                   {y0, _Real}, {blindspotradius, _Real}}, 
            Table[With[{\[Theta] = ArcTan[distance, Sqrt[(x - x0)^2 + (y - y0)^2]]},  
                  (Exp[-Abs[\[Theta]]/(15 Degree)] - .05)/.95 
                  *(1. - Boole[(x - x0)^2 + (y - y0 + 0.25 sy)^2 <= blindspotradius^2])], 
                  {x, Floor[-sx/2], Floor[sx/2 - 1]}, {y, Floor[-sy/2], Floor[sy/2 - 1]}]];

The distance parameter sets the rate of falloff of the acuity. Focusing point {cx,cy}, and blind-spot radius are self-explanatory. Here is an example using Manipulate, looking right at Lena's right eye:

size = 256;
lena = ImageResize[ExampleData[{"TestImage", "Lena"}], size];

Manipulate[foveatedBlur[lena, d, p[[1]], p[[2]], 20], {{d, 250}, 50, 
    500}, {{p, ImageDimensions@lena/2}, Locator, Appearance -> None}]

See the blind spot?