Activity 9: Binary Operations

In this activity, we are to estimate the size of one punched paper by examining an ensemble. By applying the closing and opening operators in Scilab, we tried to separate nearly touching circles and clean the edges of circles. From here, we plotted the obtained areas and the peak which corresponds to more frequent areas within the ensemble is taken as the area of an individual circle.

The figure below is the image of the ensemble of punched papers. This image is further subdivided into 256x256 subimages. For our discussion, we will refer only to one subimage. All subimages undergone the same morphological operations.

ORIGINAL

SUBIMAGE

The subimage is binarized. The proper threshold value is obtained from its histogram. In depth discussion of which is found in the previous activities. If we are to consider a subimage with only one circle, thresholding is enough. However, an ensemble of circles needs further operations since overlapping of circles may occur. Another reason for further operation is that the area of each circle may vary. The opening and closing operators were implemented on the subimages. Bwlabel in scilab renders a particular color to a blob. A blob is anything white in the binarized image. So long as one circle is connected even with only 1 pixel, bwlabel reads that as one blob. Note that the structuring element used is a circle with a diameter of 4 pixels.

After the subimage undergone the operation it looked like the one below. The subimage (original and binarized) was also posted for comparison.
In the binarized image we can see that the circles were well separated from the background. However, there are still circles that are overlapping. After applying the operator we could see that we were able to separate one circle as one blob which corresponds to a particular area. Note that the extracted areas were the areas of blobs. By tallying the areas we obtained the most occuring area for each subimage. This was done for all 13 subimages. The resulting histogram (below) shows that the most occuring area is at around 541 pixels. To verify this area, I isolated one circle and measured its diameter. The diameter obtained was 26 which orresponds to an area of 530. This is near the value extracted from the histogram.

HISTOGRAM

For this activity I give myself an 8/10 since I am not sure if the operation I used is enough.
Collaborators:
neil, gary, gilbert