Matlab adding rows and columns elegantly

Question

Say that we have the following random matrix:

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

I'd like to transform it into the following:

1 0 2 0 3 0 4 0
0 0 0 0 0 0 0 0
5 0 6 0 7 0 8 0
0 0 0 0 0 0 0 0
9 0 8 0 7 0 6 0
0 0 0 0 0 0 0 0
5 0 4 0 3 0 2 0
0 0 0 0 0 0 0 0

For some reason I cannot use mathjax format so it looks a bit awful, sorry for this. Point, is, that I want to add row and columns of zeros in between of my current rows and columns so that I increase its size 2x.

I came up with the following code, but it only works for very small matrixes if i use it on a a big image it cannot finish due to memory limitation problems.

clear all

I=imread('image.png');
I=rgb2gray(I);

B=zeros(2*size(I));

[x, y]=find(-inf<I<inf);

xy=[x,y];
nxy=xy;

%coord change
nxy=2*xy-1;

B(nxy(:,1),nxy(:,2))=I(xy(:,1),xy(:,2)); 

I expected to be fast because it is fully vectorised with maltlab functions but it fails miserably. Is there some other elegant way to do this?

Answer 1

If you take a look at your indexing vectors, this is something like I([1 1 2 2] ,[1 2 1 2] ); for a 2x2 matrix which means you index each row and column twice. The right solution is B(1:2:end,1:2:end)=I; which indexes every second row and every second column.

Answer 2

This can be also done via the one liner, say your original matrix is called A, then

kron(A,[1,0;0,0])