Matlab: Find the distance from an element to the matrix border

Question

Say in Matlab I have a matrix like this:

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

I now need to find submatrixes 3x3 around every element (so each element in turn is the center of a 3x3 submatrix). When in the middle, it is no problem to find fx

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

which is the submatrix:

2 3 4
2 3 4
2 3 4

But when in the border of the matrix, that is elements in the first og last row or column, it of course isn't possible to find a 3x3 submatrix. Instead I need the submatrix that fits. In the corner fx I would get

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

where the submatrix is:

1 2
1 2

and in the middle of the border, I get fx:

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

which gives:

4 5 6
4 5 6

or as another example:

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

which gives:

6 7 8
6 7 8

I hope you understand my point. I am missing some feature that lets me find the distance from an element to the border.

I can treat every element as a center of a submatrix, and if I can just test, if the distance from the element to the border is below the submatrix's border (the submatrix dimension will namely change, to fx a 5x5 submatrix), then I can truncate a part of the submatrix while it is being made.

How do I find the distance from an element to the border of the matrix in the most efficient way?

Answer 1

Though it doesn't answer your question directly, I guess that your problem in a higher context is to do some kind of filter or processing on the 3x3 elements. Usually the solution is to pad the array with extra values, say NaN. Then you can safely extract 3x3 sub-matrix, which might have some NaNs.

You can do the padding using padarray command.

Edit(1): I've read your comments to another answer. It looks like you are more interested in detecting the border cases, rather then computing the distance. If you want to know when you are close to a border, how about creating a mask?

mask = false(size(A));
mask(1:2,:) = true;
mask(end-1:end,:) = true;
mask(:,1:2) = true;
mask(:,end-1:end) = true;

Answer 2

Let's specify the question a bit further: You have a matrix of the size nxm and you pick an element i,j. You want to know the distance of element i,j from the border? That would be: min(i,j,n-i,m-j)