Image and Signal Processing

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.

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Out[1]=

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.

In[2]:=
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period = Length@ Last@FindTransientRepeat[First@ImageData@Binarize@stereogram, 3]
Out[2]=

Utilize ImageDisplacements to determine the subtle shifts in the pattern.

In[3]:=
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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.

In[4]:=
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shiftToDepth[shift_] := 1600 shift/(160 + shift);
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depthEstimate = ImagePad[Image[ shiftToDepth@shifts], {{period + 1 - Max[shifts], Max[shifts]}, {0, 0}}, Black];
In[6]:=
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depthEstimate // ImageAdjust
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Use the following code to create your own stereogram with any pattern and depth map.

show complete Wolfram Language input
In[7]:=
Click for copyable input
StereogramShift[maxshift_][pattern_Image, depth_Image] := Block[ {array, trafo, shifted, widht, height}, {widht, height} = {1/2, 1} ImageDimensions[pattern]; array = maxshift Transpose@ImageData[depth, DataReversed -> True]; trafo = position \[Function] (position + {Extract[array, Ceiling[position]], 0}); shifted = ImageTransformation[pattern, trafo, DataRange -> All, PlotRange -> {{0, widht}, {0, height}}, Resampling -> "Cubic", Padding -> "Periodic"]; ImageAssemble[{{ImageTake[pattern, All, {-widht, -1}], shifted}}] ]; CreateStereogram[pattern_Image, depth_Image, maxshift_: 24] := Module[ {W, H, w, h, depthMap, patternStrip}, {w, h} = ImageDimensions[pattern]; {W, H} = ImageDimensions[depth]; depthMap = ImageCrop[ ImageClip@ColorConvert[depth, "Grayscale"], {Ceiling[W, w], Full}]; patternStrip = ImageCrop[ ImageAssemble@ Transpose@{ConstantArray[pattern, {Ceiling[H/h]}]}, {w, H}]; ImageCrop[ ImageAssemble@List@ Map[ strip \[Function] ImageTake[strip, All, {w/2 + 1, -1}], FoldList[ StereogramShift[maxshift], patternStrip, Flatten@ ImagePartition[ depthMap, {1/2, 1} ImageDimensions[patternStrip]] ] ], {W, H} ] ]
In[8]:=
Click for copyable input
pattern = \!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJx83AVQXXfax/FuVypJ4+4khJDg7u7ubhd3Lu7uXNz9Ahd3d3eXACFAAkmA uCeNS9+H/LMntzd5t/OdZ08yszOdz/zOod3tLpUJXtXi559++snlVziqxh4i zs7GXmp74BcaDi7Wlg7mZjIOruaW5s7cJv+E3wz8x08/mcG/bj8b86xamC2N JZV+TI9HvXQr2GAfWRG4uiK43C11VcVyKsOiusGllqJq12qZsVLu+txDjk4o 2oBo+7ZHTp3PFR1Kj2hOoXgVKyM0ytrtbnbhN7o8buQYdHnwZDowBnYQax5l nPhQdPxDov6HAOJ8rdNMsx1qqsxsLHJ4Pfx1R/qk1rCG3piDCvOYBvWUDs10 pup6q93t4qSBHsHUHClCozTBJVnbtAVXN3y7c+wTqqdp7V2F1fed31g7cPrx oX8/pjlya+amzb2/tOdWjMpM9VMiTecXu//666/Pnz8vkXoXsjrIm0htlPIK RoEVykV8LlJ5ZFxgeINpAlrlXxpRnPF2GEpmeFYmuvK9FYTrqz3/pvawjzvG ZVOaEF1pJ2/HzKNzklePMzrEYr7IP8clLMYqry1uaTB+DTWUcm26aX4bCor0 Bas1kh8o9RebRekJuouyxikbLvisb4S9H0t/qmt5FaCgMIsprd4Uzsu+cG0j Cve4mx90tYhUDu9peoJBoTZrkimgKvqSf3v2hENrXcaiD0FBa1VWVxzcoSUP n/dPnn5894ECCqXoHYasLO27Ma4kjgUEdZNtdKoUPzYlVy6yRDr5voRr84dW ipdrz32oO5oUCEpH3TwZkklSZTWCkR7cRhe4tY+hWlI1ntW7DaROY1CovsSV 0YAzTc5H7wTrgdWbkCzgIuiJABQKuMDqRvg7baUFgJIV7NqzafzPx1qo3VtG 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In[9]:=
Click for copyable input
stereogram = CreateStereogram[pattern, depth]
Out[9]=

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