Matching values from a matrix in a 3-D array - matlab

Question

I am trying to match RGB values in an image.
% R G B
RGBset = [ 3 9 12;
4 8 13;
11 13 13;
8 3 2]
img(:,:,1) = [1 2 3
6 5 4
7 9 8
10 11 12];
img(:,:,2) = [3 4 8;
6 7 8;
11 10 9;
12 13 14];
img(:,:,3)= [3 7 2;
4 9 10;
5 11 12;
6 13 14]
In this image, only one RGB value matches from the RGBset which is [11,13,13], so the expected output is:
[0 0 0;
0 0 0;
0 0 0;
0 1 0]; % reshape(img(4,2,:),1,3) = [11, 13 13] is available in RGBset
% no other RGB value is present in the image
I have made this code but it is very slow for larger images.
matched= zeros(img(:,:,1));
for r=1:size(img(:,:,1),1)
for c=1:size(img(:,:,2),2)
matched(r,c)=ismember(reshape(img(r,c,:),1,3),RGBset,'rows');
end
end
What will be the solution with more speed?

Answer 1

We can reduce each RGB triplet into a scalar each and we will do this for both RGBset and img. This would reduce them to 2D and 1D matrices respectively. We are calling this as dimensionality-reduction. With this reduced data, we are achieving memory efficiency and that hopefully should lead to performance boost.
Thus, a solution with those bases covered would look something like this -
% Scaling array for dim reduction
s = [256^2, 256, 1].';
% Reduce dims for RGBset and img
RGBset1D = RGBset*s;
img1D = reshape(img,[],3)*s;
% Finally use find membership and reshape to 2D
out = reshape(ismember(img1D, RGBset1D), size(img,1), []);
Benchmarking for the vectorized solutions
Benchmarking code -
% R G B
RGBset = [ 3 9 12;
4 8 13;
11 13 13;
8 3 2]
% Setup inputs
img = randi(255, 2000, 2000, 3);
img(3,2,:) = RGBset(4,:);
% Luis's soln
disp('--------------------- Reshape + Permute ------------------')
tic
img2 = reshape(permute(img, [3 1 2]), 3, []).';
matched = ismember(img2, RGBset, 'rows');
matched = reshape(matched, size(img,1), []);
toc
% Proposed in this post
disp('--------------------- Dim reduction ------------------')
tic
s = [256^2, 256, 1].';
RGBset1D = RGBset*s;
img1D = reshape(img,[],3)*s;
out = reshape(ismember(img1D, RGBset1D), size(img,1), []);
toc
Benchmarking output -
--------------------- Reshape + Permute ------------------
Elapsed time is 3.101870 seconds.
--------------------- Dim reduction ------------------
Elapsed time is 0.031589 seconds.

Answer 2

You can replace the loops by permute and reshape:
img2 = reshape(permute(img, [3 1 2]), 3, []).';
matched = ismember(img2, RGBset, 'rows');
matched = reshape(matched, size(img,1), []);
This creates a 3-column matrix img2 in which each row corresponds to one pixel from img. That way ismember(..., 'rows') can be applied in a vectorized manner. The obtained result is then reshaped as needed.

Answer 3

You can just loop over the colours, which is much quicker than looping over each pixel.
% Set up your colours into the 3rd dimension, so they match along the same axis
RGB3D = reshape(RGBset,[],1,3);
% Loop over them
for ii = 1:size(RGB3D, 1)
% See if all 3 members of the colour match any pixel
matched = all(ismember(img, RGB3D(ii,:,:)),3)
if any(matched)
disp(matched)
disp(['matched color: ' num2str(ii)]);
% do something else with the matched pixels
end
end