Visualize and Synthesize Stereograms
Looking at a stereogram with crossed eyes, one can see a 3D object emerging from a flat background. This effect is achieved by a repeated pattern with subtle local shifts that encode the parallax and thus the depth of a 3D object. ImageDisplacements can detect these subtle shifts and enables you to reconstruct the depth map of the underlying object.
A stereogram that displays a Spikey.
stereogram = \!\(\*
GraphicsBox[
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dWZC+um0d9T+h1TBb5muvh0dbbu6aGJCsrrNKb3NX/suoaH5OCrpa2HZ3bJy
9ohUcVZA3g/yRSdWshgmYL7G1cL/A3lLgG4=
"], {{0, 384}, {512, 0}}, {0,
255},
ColorFunction->RGBColor],
BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> False],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{512, 384},
PlotRange->{{0, 512}, {0, 384}}]\)
To view it, look closely, cross your eyes, and slowly reduce the distance to the screen. Then release your eyes, and with some patience you should see the extruded image of a stellated icosahedron.
To decode a stereogram, first determine the width of the pattern period.
period = Length@
Last@FindTransientRepeat[First@ImageData@Binarize@stereogram, 3]
Utilize ImageDisplacements to determine the subtle shifts in the pattern.
shifts = Map[Norm, First@ImageDisplacements[
{ImageTake[stereogram, All, {period + 1, -1}],
ImageTake[stereogram, All, {1, -period - 1}]}
], {2}];
Convert the pattern shifts into a corresponding depth map, assuming a typical screen observer configuration.
shiftToDepth[shift_] := 1600 shift/(160 + shift);
depthEstimate =
ImagePad[Image[
shiftToDepth@shifts], {{period + 1 - Max[shifts],
Max[shifts]}, {0, 0}}, Black];
depthEstimate // ImageAdjust
Use the following code to create your own stereogram with any pattern and depth map.
pattern = \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
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"], {{0, 360}, {600, 0}}, {0, 255},
ColorFunction->GrayLevel],
BoxForm`ImageTag[
"Byte", ColorSpace -> "Grayscale", Interleaving -> None],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{600, 360},
PlotRange->{{0, 600}, {0, 360}}]\);
stereogram = CreateStereogram[pattern, depth]