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

Consider the code:

M = randi(100, [3 4]);                      %# input matrix

ind = reshape(1:numel(M), size(M));         %# indices of elements
ind = fliplr( spdiags( fliplr(ind) ) );     %# get the anti-diagonals
ind(:,1:2:end) = flipud( ind(:,1:2:end) );  %# reverse order of odd columns
ind(ind==0) = [];                           %# keep non-zero indices

M(ind)                                      %# get elements in zigzag order

An example with a 4x4 matrix:

» M
M =
    17    35    26    96
    12    59    51    55
    50    23    70    14
    96    76    90    15

» M(ind)
ans =
    17  35  12  50  59  26  96  51  23  96  76  70  55  14  90  15

and an example with a non-square matrix:

M =
    69     9    16   100
    75    23    83     8
    46    92    54    45
ans =
    69     9    75    46    23    16   100    83    92    54     8    45