Code to rebuild a patchwork image

Question

I'm trying to rebuild an image which has been cut into strips vertically and horizontally then the ordering of the strips has been rearranged.

For example:

So far I've only been able to come up with code which requires manual entry of the block size as well as the column/row reordering. What tools should I be using to automate the process of rebuilding the image without explicitly giving the code the block size and reordering needed.

For reference I am on Mathematica 10.2 but will welcome answers which use newer features as I plan to upgrade soon.

Thanks in advance.

Answer 1

There are other questions about reconstruction such as this one and this one. I wanted to specifically address automatically finding the block size. This is kind of hard in general as the shuffled image may not necessarily contain hard edges. Below is my crude attempt:

(* get the image *)
img = Import["https://i.stack.imgur.com/fJb9a.png"];

(** Mush all the rows of the image together and look at differences.
   Hopefully should see the seams become big jumps in the list **) 
diffs = Abs@Differences[Mean[ImageData[ColorConvert[img, "Grayscale"]]], 1];

(* get the peaks that survive a high level of filtering *)
peaks = FindPeaks[diffs, 8];
ListLinePlot[diffs, PlotRange -> All, Epilog -> {Red, Point[peaks]}]

(* get the median distance between peaks *)
estimatedBS = Median[Differences[peaks[[All, 1]]]]; (* 60 *)

(* extract pieces with estimated block size so we can feed to reconstruction later *)
pieces = Flatten@ImagePartition[img, estimatedBS]