Activity 9: Binary Operations

In this activity, we're going to obtain the best estimate of cell area (pixel count) by using all the morphological and binary operations we have learned. Below is the image of the "simulated" cells that we're going to measure, punched papers imaged using a flatbed scanner.

Image of simulated cells, punched paper digitize using a scanner.

A quick look at the image tells us that we need to analyze several ROI (region of interest) in order to obtain the best estimate. Ofcourse, we could opt to obtain an isolated cell and perform area measurement but this will not always apply especially when the cells have areas that deviate slightly from one another. Also, the cells shape may not always be uniform. In order to obtain our region of interest, we could do thresholding and binarized our image for easier area measurements later on.

Below is the histogram of our image:

Histogram of the simulated cells.

We can see that most of the information in our image is roughly between 0.5 and 0.85. Base on this value, we could binarize our image using a treshold of around 0.85.

Statistically, if we can obtain several measurements of different cells, we can plot the histogram of our measurement and base from this histogram, we can obtain our best estimate for area measurement. This is precisely what we're going to do. We obtain several subimages (256 x256) from the original image and perform area measurement on each image. We do this by thresholding the image and perform morphological operations like opening and closing to separate nearly touching cells and to remove isolated spots. A literature on opening and closing operation is available in source [2].

In this activity, we obtain 20 subimages of sizes (256x256) randomly on the image.

Subimages of size 256 x 256.

The above image was thresholded at around 0.820 resulting to the image below:

Thresholded subimages.

Observe the presence of nearly touching cells and isolated spots on the subimages. We can futher clean this image by performing morphological operations. In this activity, we perform opening operation on the above image using a circle as structuring element having diameter = 8 pixels. Note that we have to be careful when choosing our structuring element for this could affect the sizes of the cells drastically.

Below is the resulting image after the opening operation.

Comparing to the "unopened image" above, we can see that the images are relatively clean and we are able to separate several nearly touching cells. Although, this separation is not 100% successful, we are somehow able to enhance our image for area measurement.

After performing morphological operations on our image, we are now in the position to obtain area measurement by labeling all contiguous blobs and couting their areas (pixel count). We can do this in scilab using the function bwlabel which labels all contiguous blobs and tabulates them in an array. Below is the resulting images after applying bwlabel.

Labeled subimages using scilabs bwlabel.

By looping on all the subimages and counting the area of each contiguous blobs, we can obtain a frequency distribution of the area of the cell. In our measurement, we disregarded area measurements greater than 800, since by visual investigation, the cells' pixel area is clearly below this value. Below is the histogram of the obtained cell areas.

Histogram of cell measurement

From the above histogram, we obtain an estimate of area = 530 pixels plus or minus 10 pixels since we use bins of spacing 20 pixels in our histogram. In the above histogram the number of cells having areas between 520-540 is 87, significantly higher than the other measured area.

Since our approach is statistical, the higher the number of subimages, the better. Although, we could perform morphological operations on nearly touching cells, it must be stressed that the approximation is much easier if we can obtain images of cells that are relatively sparse. We must think of this when we obtain images of cells in our experiment.

In this activity, I give myself a grade of 10 for performing the required measurement.

Acknowledgement
I would like to thank Irene for very useful conversations.

References

[1] AP 186 Activity 9 manual
[2] http://en.wikipedia.org/wiki/Mathematical_morphology#Opening_and_Closing