Matlab: Matrix Neighbour Extraction - matlab

Question

I have a large number of images which I've broken down into segments such that their matrices look like:
img = [ 1 1 1 1 1 2 2 2 3 3 3 3
1 1 1 1 2 2 2 2 2 3 3 3
1 1 1 4 4 4 2 2 2 3 3 3
5 5 5 5 5 5 5 2 2 3 3 3 ];
where each number represents a different region and each region is arbitrarily shaped. So in this case, region 1 has neighbours 2, 4 and 5, region 2 has neighbours 1, 3 and 4 and so on.
I've extracted all of the regions into separate cells and obtained statistics (mean, variance, etc) which I plan to use to merge regions with statistics within a certain tolerance. I'm struggling to think of an efficient way to obtain the neighbours of each region to allow that merging to occur.
I have a horrible solution which takes a very long time for even one image:
referenceImage = [ 1 1 1 1 1 2 2 2 3 3 3 3;
1 1 1 1 2 2 2 2 2 3 3 3;
1 1 1 4 4 4 2 2 2 3 3 3;
5 5 5 5 5 5 5 2 2 3 3 3];
% Wish to extract each region into a separate cell
lastSP = 5;
sps = 1:lastSP;
% Could be a way to vectorise the below loop but it escapes me
superPixels(lastSP) = struct('Indices', 0, 'Neighbours', 0);
% Split data into separate cells
parfor a = 1 : lastSP
inds = find(referenceImage == sps(a));
superPixels(a).Indices = inds;
end
szs = size(referenceImage); % Sizes of RGB Image
for a = 1 : lastSP + 1
mask = zeros(szs(1), szs(2)); % Just bin mask wanted
mask(superPixels(a).Indices) = 1; % Mark the region pixels as one
mask = xor(bwmorph(mask, 'thicken'), mask); % Obtain the outlying regions
inds = find(mask ==1); % Fetch the external region indices
neighbours = []; % Have to dynamically grow neighbours matrix
neigh = 1;
for b = 1 : length(inds)
found = false;
if ~isempty(neighbours) % Check neighbours first
for c = 1 : length(neighbours)
if any(superPixels(neighbours(c)).Indices == inds(b))
found = true;
break;
end
end
end
if ~found
for c = 1 : lastSP + 1 % Check every other region
if any(superPixels(c).Indices == inds(b))
neighbours(neigh) = c;
neigh = neigh + 1;
break;
end
end
end
end
superPixels(a).Neighbours = neighbours;
end
I'm wondering if this is actually the best way to approach this problem. I know the very last loop is the main problem but I can't think of another way to reasonably write this, unless I recurse and check the neighbours of known neighbours.
Any help or nudges in the right direction would be greatly appreciated; thanks!

Answer 1

A simple (but probably not maximally efficient) solution is to dilate each region mask to pick neighbors:
labels = unique(img);
nLabels = length(labels);
neighbors = cell(nLabels,1);
for iLabel = 1:nLabels
msk = img == labels(iLabel);
adjacentPixelMask = imdilate(msk,true(3)) & ~msk;
neighbors{iLabel} = unique(img(adjacentPixelMask));
end
neighbors{1}
ans =
2
4
5