{"id":362,"date":"2011-02-04T15:32:27","date_gmt":"2011-02-04T20:32:27","guid":{"rendered":"https:\/\/blogs.mathworks.com\/steve\/2011\/02\/04\/more-on-segmenting-in-a-b-space\/"},"modified":"2019-10-29T13:54:07","modified_gmt":"2019-10-29T17:54:07","slug":"more-on-segmenting-in-a-b-space","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/steve\/2011\/02\/04\/more-on-segmenting-in-a-b-space\/","title":{"rendered":"More on segmenting in a*-b* space"},"content":{"rendered":"
\r\n

I'm back to looking at M&Ms today. (Previous posts: 17-Dec-2010<\/a>, 23-Dec-2010<\/a>, 30-Dec-2010<\/a>, 11-Jan-2011<\/a>)\r\n <\/p>

url = 'https:\/\/blogs.mathworks.com\/images\/steve\/2010\/mms.jpg'<\/span>;\r\nrgb = imread(url);\r\nimshow(rgb)<\/pre> 
Last time I showed how I used imfreehand<\/tt> to segment the region in the a*-b* plane corresponding to the green M&Ms.\r\n   <\/p>\r\n   
 <\/p>\r\n   
This time I'll use connected-components labeling and regionprops<\/tt> to segment the image based on all the colors, including the desk background.\r\n   <\/p>\r\n   
I saved the previously computed a*-b* histogram in a MAT-file online; here's how to retrieve and display it.<\/p>
matfile_url = 'https:\/\/blogs.mathworks.com\/images\/steve\/2011\/freehand_segment.mat'<\/span>;\r\ntemp_matfile = [tempname '.mat'<\/span>];\r\nurlwrite(matfile_url, temp_matfile);\r\ns = load(temp_matfile);\r\ndelete(temp_matfile)\r\nH = s.H;\r\nimshow(H, [0 1000], 'InitialMagnification'<\/span>, 300, 'XData'<\/span>, [-100 100], ...<\/span>\r\n    'YData'<\/span>, [-100 100])\r\naxis on<\/span><\/pre> 
Next, let's threshold the image. (Magic Number Alert! I chose the threshold manually based on visual inspection of pixel values.)<\/p>
mask = H > 100;<\/pre>
imshow(mask, 'InitialMagnification'<\/span>, 300, 'XData'<\/span>, [-100 100], ...<\/span>\r\n    'YData'<\/span>, [-100 100])\r\naxis on<\/span><\/pre> 
So we've got seven \"blobs\". Let's measure their centroids.<\/p>
props = regionprops(mask, s.H, 'Centroid'<\/span>);\r\nprops(1)<\/pre>
\r\nans = \r\n\r\n    Centroid: [20.2143 82.5357]\r\n\r\n<\/pre>
centers = cat(1, props.Centroid)<\/pre>
\r\ncenters =\r\n\r\n   20.2143   82.5357\r\n   45.4706   92.2353\r\n   49.2973   29.0541\r\n   51.6029   67.1765\r\n   52.2667   53.4667\r\n   77.8000   67.8000\r\n   80.1724   84.4483\r\n\r\n<\/pre>
These centroid values are in the intrinsic pixel coordinates of the image. To convert them to a* and b* values, we have to\r\n      scale and shift.\r\n   <\/p>
ab_centers = 2*centers - 102<\/pre>
\r\nab_centers =\r\n\r\n  -61.5714   63.0714\r\n  -11.0588   82.4706\r\n   -3.4054  -43.8919\r\n    1.2059   32.3529\r\n    2.5333    4.9333\r\n   53.6000   33.6000\r\n   58.3448   66.8966\r\n\r\n<\/pre>
a_centers = ab_centers(:,1);\r\nb_centers = ab_centers(:,2);<\/pre>
Next question: where are these centers, and what are the regions in the a*-b* plane closest to each one? The voronoi<\/tt> function shows you both.\r\n   <\/p>
hold on<\/span>\r\nvoronoi(a_centers, b_centers, 'r'<\/span>)\r\nhold off<\/span><\/pre> 
To perform a nearest-neighbor classification of all the pixels, let's compute the Delaunay triangulation, from which we can\r\n      easily do the nearest-neighbor calculation.\r\n   <\/p>
dt = DelaunayTri(a_centers, b_centers)<\/pre>
\r\ndt = \r\n\r\n  DelaunayTri\r\n\r\n  Properties:\r\n      Constraints: []\r\n                X: [7x2 double]\r\n    Triangulation: [7x3 double]\r\n\r\n\r\n<\/pre>
Compute the a* and b* values of all the pixels:<\/p>
lab = lab2double(applycform(rgb, makecform('srgb2lab'<\/span>)));\r\nL = lab(:,:,1);\r\na = lab(:,:,2);\r\nb = lab(:,:,3);<\/pre>
For every pixel in the original image, find the closest a*-b* centroid by using the nearestNeighbor<\/tt> function with the Delaunay triangulation.\r\n   <\/p>
X = nearestNeighbor(dt, a(:), b(:));\r\nX = reshape(X, size(a));<\/pre>
I would like to make a colormap of the seven colors in our segmentation. We have a* and b* values for each of the colors,\r\n      but not L* values. We could just make up a constant L* value. Instead, I'll compute the mean L* value for all the pixels closest\r\n      to the centroid of each of the histogram blobs.\r\n   <\/p>
L_mean = zeros(size(a_centers));\r\nfor<\/span> k = 1:numel(L_mean)\r\n    L_mean(k) = mean(L(X == k));\r\nend<\/span><\/pre>
Now we convert the L*a*b* values corresponding to each of our seven colors back to RGB using applycform<\/tt>.\r\n   <\/p>
map = applycform([L_mean, a_centers, b_centers], makecform('lab2srgb'<\/span>))<\/pre>
\r\nmap =\r\n\r\n    0.2587    0.8349    0.1934\r\n    0.8724    0.8465    0.0271\r\n    0.1095    0.4111    0.6803\r\n    0.8382    0.7591    0.5286\r\n    0.3304    0.2993    0.2751\r\n    0.7264    0.2055    0.2008\r\n    0.9653    0.3595    0.0690\r\n\r\n<\/pre>
And finally we can use X<\/tt> and map<\/tt> to display our segmented result as an indexed image.\r\n   <\/p>
close all<\/span>\r\nimshow(X, map)<\/pre> 
Not bad!<\/p>\r\n   
Unless I have some inspiration between now and next week, I might be ready to let this image go and search for something else\r\n      to write about.\r\n   <\/p>