Activity 9: Binary Operations

In this activity, we are to measure the individual areas of a number of punched paper. It is assumed that the areas of the punched paper are uniform. The image I used is Circles001.jpg shown below:
For faster calculations, I subdivided the images into 10, 256x256pixel images. A typical subdivision is shown below:
Closing and Opening operators are necessary to be able to separate nearly touching circles and to clean the edges of broken circles. In general opening and closing operators are "mixtures" of dilation and erosion operator from the previous activity. Opening operations is achieved by dilating an eroded image. That is we are to perform erosion on an image then perform dilation on the resulting image. On the other hand, Closing is achieved in the opposite manner, in this case, performing erosion on a dilated image. Since erosion and dilation requires binary images, I binarized the subimages using 0.8 as a threshold. The code I used for the whole process is given below:

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I = imread("C:\Users\RAFAEL JACULBIA\Documents\subjects\186\activity9\C1_10.bmp");
se = imread("C:\Users\RAFAEL JACULBIA\Documents\subjects\186\activity9\disk.bmp");
bw = im2bw(I,0.8);

OC = erode(dilate(dilate(erode(bw,se),se),se),se);
L = bwlabel(OC);
imshow(L,[]);

imwrite(L/max(L), "C:\Users\RAFAEL JACULBIA\Documents\subjects\186\activity9\C1_10_labeled.bmp");
//imwrite(CO/max(CO), "C:\Users\RAFAEL JACULBIA\Documents\subjects\186\activity9\c2\C2_01_labeled2.bmp");
//imwrite(OC/max(OC), "C:\Users\RAFAEL JACULBIA\Documents\subjects\186\activity9\c2\C2_01_labeled3.bmp");
//imwrite(clos/max(clos), "C:\Users\RAFAEL JACULBIA\Documents\subjects\186\activity9\c2\C2_01_labeled4.bmp");
scircle = [];
for i=1:max(L)
circle = size(find(L==i));
scircle(i) = circle(2);
end

scircle

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The structuring element I used was a 5x5 pixel "circle" which actually looks more like a cross than a circle drawn using GIMP. I performed opening and then closing operations on the images. In the code I displayed the resulting image with different circles "labeled" a typical image is shown below:
The areas of all subimages were tallied and a histogram of the values were obtained:

I selected only areas between 300 and 800, since I believe areas out of this range are either circles grouped together or small pixels which are the result of dividing the images or is an artifact of binarizing the images. The value with largest occurence was found at 547 pixels. To confirm if this value is correct, I measured the diameter of one circle and found it to be 26 pixels corresponding to an area of 530 pixels, hence the obtained areas was near the calculated values. Another method I used to confirm the area is isolating a single circle, binarizing it and counting the number of pixels. Using this method I was able to obtain an area equal to 536 pixels which is still near the calculated value.

I also tried entering the whole image into scilab. It is interesting to note that limiting the values for area is not neccessary if we performed the operation on the whole image. I was able to obtain an area of 557.8 which is near the value obtained if I subdivided the images. The histogram is given below:




For this activity I will give myself a grade of 10 since I believe I have performed the activity correctly.

Eduardo David Helped me in this activity.