Fast way to find the neighboor of pixel - matlab

Question

I am programming for task that finds the neighbor of a given pixel x in image Dthat can formula as:
The formula shown pixels y which satisfy the distance to pixel x is 1, then they are neighbor of pixel x. This is my matlab code. However, it still takes long time to find. Could you suggest a faster way to do it. Thank you so much
%-- Find the neighborhood of one pixel
% x is pixel coordinate
% nrow, ncol is size of image
function N = find_neighbor(x,nrow,ncol)
i = x(1);
j = x(2);
I1 = i+1;
if (I1 > nrow)
I1 = nrow;
end
I2 = i-1;
if (I2 < 1)
I2 = 1;
end
J1 = j+1;
if (J1 > ncol)
J1 = ncol;
end
J2 = j-1;
if (J2 < 1)
J2 = 1;
end
N = [I1, I2, i, i; j, j, J1, J2];
For example: ncol=128; nrow=128; x =[30;110] then output
N =31 29 30 30; 110 110 111 109]
For calling the function in loop
x=[30 31 32 33; 110 123 122 124]
for i=1:length(x)
N = find_neighbor(x(:,i),nrow,ncol);
end

Answer 1

Here's a vectorized approach using bsxfun:
% define four neighbors as coordinate differences
d = [-1 0 ; 1 0 ; 0 -1 ; 0 1]';
% add to pixel coordinates
N = bsxfun(#plus, x, permute(d, [1 3 2]));
% make one long list for the neighbors of all pixels together
N = reshape(N, 2, []);
% identify out-of-bounds coordinates
ind = (N(1, :) < 1) | (N(1, :) > nrow) | (N(2, :) < 1) | (N(2, :) > ncol);
% and remove those "neighbors"
N(:, ind) = [];
The permute is there to move the "dimension" of four different neighbors into the 3rd array index. This way, using bsxfun, we get the combination of every pair of original pixel coordinates with every pair of relative neighbor coordinates. The out-of-bounds check assumes that nrow belongs to the first coordinate and ncol to the second coordinate.
With
ncol=128;
nrow=128;
x = [30 31 32 33; 110 123 122 124];
the result is
N =
29 30 31 32 31 32 33 34 30 31 32 33 30 31 32 33
110 123 122 124 110 123 122 124 109 122 121 123 111 124 123 125
Different neighbors of different pixels can end up to be the same pixel, so there can be duplicates in the list. If you only want each resulting pixel once, use
% remove duplicates?
N = unique(N', 'rows')';
to get
N =
29 30 30 30 31 31 31 32 32 32 33 33 33 34
110 109 111 123 110 122 124 121 123 124 122 123 125 124

Answer 2

Matlab's performance is horrible when calling small functions many time. The Matlab approach is to do vectorize as much as possible. A vectorized version of your code:
function N = find_neighbor(x,nrow,ncol)
N = [min(x(1,:)+1,nrow), max(x(1,:)-1,1), x(1,:), x(1,:); x(2,:), x(2,:),min(x(2,:)+1,ncol), max(x(2,:)-1,1)];
end
and usage
x=[30 31 32 33; 110 123 122 124]
N = find_neighbor(x,nrow,ncol);
BTW, for pixels on the border , your solution always gives 4 neighbors. This is wrong. the neighbors of (1,1) for examples should be only (2,1) and (1,2), while you add two extra (1,1).
The solution to this is quite simple - delete all neighbors that are outside the image
function N = find_neighbor(x,nrow,ncol)
N = [x(1,:)+1, x(1,:)-1, x(1,:), x(1,:); x(2,:), x(2,:),x(2,:)+1, x(2,:)-1];
N(:,N(1,:)<1 | N(1,:)> nrow | N(2,:)<1 | N(2,:)>ncol)=[];
end