矩阵“之字形"重新排序 [英] Matrix "Zigzag" Reordering

问题描述

我在MATLAB中有一个NxM矩阵，我想以与JPEG重新排序其子块像素的方式类似的方式重新排序:

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

^{(来自维基百科的图片)}

我希望算法是通用的，这样我就可以传递任何尺寸的2D矩阵.我是一名C ++程序员，非常想写一个老式的循环来完成此任务，但是我怀疑在MATLAB中有更好的方法来实现它.

I would like the algorithm to be generic such that I can pass in a 2D matrix with any dimensions. I am a C++ programmer by trade and am very tempted to write an old school loop to accomplish this, but I suspect there is a better way to do it in MATLAB.

我宁愿要一种在NxN矩阵上工作并从那里开始的算法.

I'd be rather want an algorithm that worked on an NxN matrix and go from there.

1 2 3
4 5 6  -->  1 2 4 7 5 3 6 8 9
7 8 9

推荐答案

考虑代码:

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

具有4x4矩阵的示例:

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

以及具有非平方矩阵的示例:

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

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