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 non-loop solution zig_zag.m. It looks ugly but it works!:

function [M,index] = zig_zag(M)
  [r,c] = size(M);
  checker = rem(hankel(1:r,r-1+(1:c)),2);
  [rEven,cEven] = find(checker);
  [cOdd,rOdd] = find(~checker.'); %'#
  rTotal = [rEven; rOdd];
  cTotal = [cEven; cOdd];
  [junk,sortIndex] = sort(rTotal+cTotal);
  rSort = rTotal(sortIndex);
  cSort = cTotal(sortIndex);
  index = sub2ind([r c],rSort,cSort);
  M = M(index);
end

And a test matrix:

>> M = [magic(4) zeros(4,1)];

M =

    16     2     3    13     0
     5    11    10     8     0
     9     7     6    12     0
     4    14    15     1     0

>> newM = zig_zag(M)    %# Zig-zag sampled elements

newM =

    16
     2
     5
     9
    11
     3
    13
    10
     7
     4
    14
     6
     8
     0
     0
    12
    15
     1
     0
     0