Activity 16: Color Image Segmentation

The objective of this activity is to "segment" or select a region of interest from an image according to its color. To do this, we have to transform the RGB space into normalized chromaticity coordinates (NCC). We do this obtaining this by dividing each pixel by the sum of the RGB values in that pixel. Afterwards, the chromaticity can easily be represented by two color channels r and g since b = 1-r+g. The image used and the test image is shown below:

OBJECT

TEST IMAGE

Two methods are used in this activity, non-parametric and parametric. Parametric segmentation is done by determining the probability that a region belongs to the region of interest. In particular, a gaussian probability distribution function is assumed. For non-parametric segmentation, the frequency value of the pixel in the histogram itself is used to backproject the value for that pixel. The two dimensional histogram of the original image test image is shown below:
The x-axis corresponds to the R channel, the y-axis corresponds to the G channel and the z axis corresponds to the frequency. From the figure, it can be seen that the region where the frequency is highest is at the blue region as expected.

The following are the results of the color segmentation:

It can be seen from the images that parametric segmentation looks better as it was able to approximate the general shape of the blue parts of the lamp are well separated from the other colors. However, the non-parametric segmentation is very accurate in the sense that slight changes in the shade of blue in the image is no longer considered blue. This is easily observed in the post of the lamp since in this part the shade is darker than the top parts.

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Scilab Codes:
Parametric
I = imread("lamp_section.jpg");
orig = imread("lamp_orig.jpg");
av = I(:,:,1)+I(:,:,2)+I(:,:,3);
r = I(:,:,1)./av;
g = I(:,:,2)./av;
b = I(:,:,3)./av;

av2 = orig(:,:,1)+orig(:,:,2)+orig(:,:,3);
r2 = orig(:,:,1)./av2;
g2 = orig(:,:,2)./av2;
b2 = orig(:,:,3)./av2;

r = r*255;
g = g*255;
frequency = zeros(256,256);
sizer = size(r);
for i=1:sizer(1)
for j=1:sizer(2)
x = abs(round(r(i,j)))+1;
y = abs(round(g(i,j)))+1;
frequency(x,y) = frequency(x,y)+1;
end
end
//imshow(log(frequency+0.0000000001));

r = r/255;
g = r/255;

mr = mean(r);
devr = stdev(r);
mg = mean(g);
devg = stdev(g);

pr = (1/(devr*sqrt(2*%pi)))*exp(-((r2-mr).^2)/2*devr);
pg = (1/(devg*sqrt(2*%pi)))*exp(-((g2-mg).^2)/2*devg);

prob = pr.*pg;
prob = prob/max(prob);
scf(0);imshow(orig);
scf(1);imshow(prob,[]);
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Non Parametric:
I = imread("lamp_section.jpg");
orig = imread("lamp_orig.jpg");
sizeO = size(orig)
av = I(:,:,1)+I(:,:,2)+I(:,:,3);
r = I(:,:,1)./av;
g = I(:,:,2)./av;
b = I(:,:,3)./av;

av2 = orig(:,:,1)+orig(:,:,2)+orig(:,:,3);
r2 = orig(:,:,1)./av2;
g2 = orig(:,:,2)./av2;
b2 = orig(:,:,3)./av2;

r = r*255;
g = g*255;
frequency = zeros(256,256);
sizer = size(r);
for i=1:sizer(1)
for j=1:sizer(2)
x = abs(round(r(i,j)))+1;
y = round(g(i,j))+1;
frequency(x,y) = frequency(x,y)+1;
end
end
scf(0);imshow(log(frequency+0.0000000001));

r2 = r2*255;
g2 = g2*255;
seg = zeros(sizeO(1),sizeO(2));
sizer2 = size(r2);

for i = 1:sizer2(1)
for j = 1:sizer2(2)
x = abs(round(r2(i,j)))+1;
y = round(g2(i,j))+1;
seg(i,j) = frequency(x,y);
end
end

scf(1);imshow(log(seg+0.000000000001),[]);
scf(2);imshow(orig);
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I will give myself a grade of 10 for this activity since the objectives were met and the results are interesting.
Collaborator:
Ed David