Activity 10: Binary Operations

When an image is binarized it is split into two components, the background and the foreground. The background, in binary values, carries the zeros. It is often the part of the image that is ignored and disregarded. The foreground, on the other hand, is the the one that is valued with ones and it is often the region of interest in the image.

However, binarizing an image does not guarantee that the outcome will be noiseless since noise may be of the same gray level of the region of interest. This is where morphological operations such as opening and closing comes into play. Opening is a morphological operator that involves two steps, the first step is to erode the image with a specific structuring element and then dilate it the same structuring element used for erosion. The effect of this operation is that certain part of the foreground are removed and the preservation of the foreground that has the same shape as the structuring element. The other useful morphological operation is the Closing operator. Like the opening operator, the closing operator also involves two step, however, it first dilate the image with a specific structuring element and then erode it with same structuring element used. The effect of this operation is that the background that has the same shape as the structuring element used is preserved while eliminating other background pixels.

Now that we have the tools, we now must define the goal. In this activity, an image of scattered punched paper, shown in figure 1 will represent a normal human cell. Area of these cells must be obtained and averaged using techniques that were discussed/used in the previous activities.

Figure 1. An image of the scattered punched papers that represents the normal human cell.

Now let us try to separate the foreground from the background by binarizing the image to a certain threshold.

Figure 2. Binarized image at threshold equals 0.8 a.u.

But from the binarized image, we can see that noises are still present as predicted. So now, we apply one of the discussed operations, the Opening operator.

Figure 3. Opening operator applied to the image of the scattered punch paper.

Now to get the average pixel area of the cells, we apply the technique learned from Activity 4: Area estimation of images with defined edges by using the follow function and then apply Green's theorem after. But before doing so, we first cut up the image into 256x256 pixel subimages and then use bwlabel to label each blob in each of the subimages to measure each of the blobs area independently.

The calculated area was then kept in a list and then was plotted for a histogram to observe where is the mean of the histogram is.

Figure 4. Histogram of the cell area computed from the subimages.

But to confirm the mean area of the cell observed in the histogram, statistics was applied to mathematically obtain the mean and standard deviation of the cell area. The histogram data was first cropped area values greater than 1000 pixel area. This range was considered as an outlier since it is an overshoot produced by cells that are clumped together. The mean area and the standard deviation computed is,

Mean cell area: 428.21

Standard deviation: 174.05

So now that we obtained the average area of a single cell, let us find an application for this. Consider the image in figure 5.

Figure 5. Image of cancer cells together with normal cells.

The image above was again made of punched paper but this time larger shaped punch paper was included. This large punched paper represents a cancer cell. So now, that we know the average area of a normal cell, the goal is to implement a way to isolate these cancer cells from the normal cells. The image in figure 5 was also binarized to a certain threshold and then was cleaned by using the Opening operator.

Figure 6. (Top) Binarized image with a threshold of 0.8 and (Bottom) Resulting image after Opening operator was applied with a circular structuring element with a radius of 5 pixels.

Now to isolate the cancer cell, we will use again the opening operator but this time with a circular structuring element with radius equal to

The reason for this is that we consider the maximum deviation from mean is still an area of a normal cell and by knowing that the cancer cells are much larger than the normal cells. The resulting image after the Opening operator was applied is shown in the image below.

Figure 7. Isolated cancer cells.

In the image above, we can see that we successfully isolated the cancer cells from the normal cells by just using morphological operations and the techniques learned from the previous activity. Because of this success, I will give myself a grade of 10. I find this application very interesting since my research is about porous materials and so I can see that this technique is very useful in the field of my research.

References:

• Dr. Soriano. Applied Physics 186 Activity manual, Activity 10: Binary Operations. 2010.
• Morphology - Opening
• Morphology - Closing
• Opening Operator
• Closing Operator