Reproduce image effect in Mathematica

Load image

img = Import["http://i.stack.imgur.com/qzMGE.jpg"]

ImagePartition and DominantColors

Make an array of Disk of the DominantColors in each part of ImagePartition.

Rotate[
 Graphics@MapIndexed[
    {First@DominantColors[#1, 1], Disk[#2, 1/2]} &
    , ImagePartition[img, 10], {2} ]
 , -π/2]

ImageResize and ImageData

But I find the solution by @Szabolcs better, here I just do the rotation differently and add Background -> Black

Graphics[
 MapIndexed[
  {RGBColor[#1], Disk[{{0, 1}, {-1, 0}}.#2, 1/2]} &, 
  ImageData@ImageResize[img, {Automatic, 80}]
  , {2}
  ], Background -> Black]

Removing Moiré pattern

And yet another rotation option.

Export[
 "Q106165.PDF",
 Graphics[
  MapIndexed[
   {RGBColor[#1], , Disk[#2, 1/2]} &, 
   Transpose@
    ImageData[ImageResize[img, {Automatic, 80}], DataReversed -> True]
   , {2}
   ], Background -> Black]]

Here's my solution. Change CompilationTarget -> "C" to CompilationTarget -> "WVM" if you don't have a C compiler available.

cf = Compile[{{v, _Real}, {kernel, _Real, 2}},
   v*kernel,
   RuntimeAttributes -> {Listable},
   Parallelization -> True,
   CompilationTarget -> "C",
   RuntimeOptions -> "Speed"
   ];

shapedPixels[img_, kernel_] := With[{dim = ImageDimensions[img]},
   ImageCrop[
    Image[Join @@ 
      Transpose[
       Join @@@ 
        Transpose[
         cf[ImageData[
           ImageResize[img, 
            Ceiling[dim/Reverse[Dimensions[kernel]]]]], kernel], {1, 
          2, 5, 4, 3}], {1, 3, 2, 4}]], dim]];

Manipulate[
 shapedPixels[pic, 
  ArrayPad[If[invert, 1 - matrix[r], matrix[r]], padding]], {r, 1, 20,
   1}, {padding, 0, 10, 
  1}, {matrix, {DiskMatrix, DiamondMatrix, BoxMatrix, IdentityMatrix, 
   CrossMatrix}}, {{invert, False}, {True, False}}]

Another approach:

pic = Import@"http://i.stack.imgur.com/qzMGE.jpg"

Image @ ArrayFlatten @ Map[
   Map[Function[x, x #], DiskMatrix[5], {2}]&, 
   ImageData@ImageResize[pic, {Automatic, 50}],
   {2}
]

I'm not taking care about preserving image size, it is governed by Resize and DiskMatrix size.

just put e.g. DiamondMatrix[5] or Rescale@GaussianMatrix[10] to get more fun: