Matrix “Zigzag” Reordering

Question

I have an NxM matrix in MATLAB that I would like to reorder in similar fashion to the way JPEG reorders its subblock pixels:

Answer 1

Here's a way how to do this. Basically, your array is a hankel matrix plus vectors of 1:m, where m is the number of elements in each diagonal. Maybe someone else has a neat idea on how to create the diagonal arrays that have to be added to the flipped hankel array without a loop.

I think this should be generalizeable to a non-square array.

% for a 3x3 array 
n=3;

numElementsPerDiagonal = [1:n,n-1:-1:1];
hadaRC = cumsum([0,numElementsPerDiagonal(1:end-1)]);
array2add = fliplr(hankel(hadaRC(1:n),hadaRC(end-n+1:n)));

% loop through the hankel array and add numbers counting either up or down
% if they are even or odd
for d = 1:(2*n-1)
   if floor(d/2)==d/2
      % even, count down
      array2add = array2add + diag(1:numElementsPerDiagonal(d),d-n);
   else
      % odd, count up
      array2add = array2add + diag(numElementsPerDiagonal(d):-1:1,d-n);
   end
end

% now flip to get the result
indexMatrix = fliplr(array2add)

result =
     1     2     6
     3     5     7
     4     8     9

Afterward, you just call reshape(image(indexMatrix),[],1) to get the vector of reordered elements.

EDIT

Ok, from your comment it looks like you need to use sort like Marc suggested.

indexMatrixT = indexMatrix';   % ' SO formatting
[dummy,sortedIdx] = sort(indexMatrixT(:));

sortedIdx =
     1     2     4     7     5     3     6     8     9

Note that you'd need to transpose your input matrix first before you index, because Matlab counts first down, then right.