Reconstructing an image from overlapping patches

Question

The Mathematica function ImagePartition can create overlapping sub-images with the pixel offset options {dw, dh}:

ImagePartition[image, {w, h}, {dw, dh}]

Meanwhile, the ImageAssemble function has no such option documented.

Hence my question is: how would one reconstruct an image made up of overlapping patches?

• Is there an "easy" way?
• Or do I need to work through the list of patches one-by-one?

Update:

If I want each overlapping patch to contribute equally to the value of a single pixel in the final image, what would I do?

(Sorry, should have been clearer - have changed the title)

Answer 1

I think this could be what you're looking for. First let's create a list of patches:

img = ExampleData[{"TestImage", "Lena"}];
patches = ImagePartition[img, 256, {128, 128}]

I'm not going to use ImageAssemble to put these back together. The trick is to create black and white masks, one for each patch. This is one example:

And then to use ImageMultiply to create the following intermediate step:

Now since black is {0,0,0} and each image has a the right dimensions we can add them all together using ImageAdd. The implementation looks like this:

img = ExampleData[{"TestImage", "Lena"}];
{w, h} = ImageDimensions[img];
masks[{w_, h_}, {partW_, partH_}, {offsetX_, offsetY_}] := 
  Flatten@Table[
    Graphics[{
      Black, Rectangle[{0, 0}, {w, h}],
      White, Rectangle[{offx, offy}, {offx + partW, offy + partH}]
      }, ImageSize -> {w, h}, 
     Method -> {"ShrinkWrap" -> True}], {offx, 0, 
     offsetX Floor[(w - partW)/offsetX], offsetX}, {offy, 0, 
     offsetY Floor[(h - partH)/offsetY], offsetY}
    ];
patchesCombine[patches_, masks_] := Module[{masked},
  masked = ImageMultiply[img, #] & /@ masks;
  Fold[ImageAdd, First@masked, Rest@masked]
  ]

And can be used like this:

patchesCombine[
 patches,
 masks[ImageDimensions[img], {256, 256}, {128, 128}]
 ]

The arguments supplied to masks are the same arguments that you would supply to ImagePartition.

Answer 2

ip = ImagePartition[ExampleData[{"TestImage", "Lena"}], 40, {10, 10}] ;
ImageAssemble[Map[ImageCrop[#, {10, 10}] &, ip, {2}]]