Can Mathematica be used to make anamorphic distortions like these?

h = 6.0;  (* eye height *)
h0 = 4.0;  (* apparent image height *)
d = 10.0;  (* apparent image distance *)
a = d h0/(h - h0);  (* actual length of painting *)

The geometry is like this:

enter image description here

Now do the transformation.

myimage = ImageResize[Import@"https://i.stack.imgur.com/k78e8.jpg", Scaled[1/5]];

f[{x_, y_}] := h/(h - y) {x, d}

w0 = h0 Divide @@ ImageDimensions[myimage]
(* 3.20667 *)

i = ImageForwardTransformation[myimage, f,
   DataRange -> {{-w0/2, w0/2}, {0, h0}},
   PlotRange -> All, Background -> White];

b = a Divide @@ ImageDimensions[i]
(* 4.81791 *)

The resulting transformed image i:

enter image description here

Using Mathematica's 3D graphics we can paint the transformed image on the ground and view from the appropriate point:

Graphics3D[{Table[{Orange,
    Cylinder[{{-b/2, y, 0}, {-b/2, y, 1}}, 0.1],
    Cylinder[{{b/2, y, 0}, {b/2, y, 1}}, 0.1]}, {y, d, a + d, 2}],
  Texture[i],
  Polygon[{{-b/2, d, 0}, {-b/2, d + a, 0}, {b/2, d + a, 0}, {b/2, d, 0}}, 
   VertexTextureCoordinates -> {{0, 0}, {0, 1}, {1, 1}, {1, 0}}]},
 ViewVector -> {{0, 0, h}, {0, (d + a)/2, 0}},
 ViewAngle -> 0.5, Lighting -> "Neutral", Boxed -> False]

enter image description here


Yes. Simply use: ImagePerspectiveTransformation[]

myimage = Import@"https://i.stack.imgur.com/k78e8.jpg";

For example, define myimage to be your image. Then:

ImagePerspectiveTransformation[myimage, TransformationFunction[( \!\(\*
TagBox[GridBox[{
{"0", "1", "0.5"},
{"2", "0.5", "0.1"},
{"2", "0", "1.5"}
},
AutoDelete->False,
GridBoxDividers->{
        "Columns" -> {{False}}, "ColumnsIndexed" -> {-2 -> True}, 
         "Rows" -> {{False}}, "RowsIndexed" -> {-2 -> True}, 
         "Items" -> {}, "ItemsIndexed" -> {}},
GridBoxItemSize->{
        "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, 
         "Rows" -> {{Automatic}}, "RowsIndexed" -> {}, "Items" -> {}, 
         "ItemsIndexed" -> {}}],
#& ]\) )]]

enter image description here

The way to set the geometry for a given viewing position is illustrated here (see Seeing the light: Optics in nature, photography, color, vision and holography by Falk, Brill and Stork): the height of the viewer's eye is given by the top of the right vertical line, a C. Draw a straight line from that point through the right of the base of the transformed image and then continue to the bottom left and use a straightedge accordingly. When viewed from that upper right point, the picture will appear undistorted.

enter image description here

Tags:

Image Processing

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