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3. Make some changes to this page, and then hit preview on the right. You can always preview any post or edit it before you share it to the world.

First call, it was a recording of downtime at areas such as Ortigas, Pasig, etc. Not hearing our area in the list, I called them again so I could speak to one of their agents.

Finally an agent answered. Before he could ask for my name I asked why we had no internet at our area, Loyola Heights. He didn’t answer the question, but instead, went for protocol and asked for my name. I gave it, and I also gave the name that was attached to our subscription. He then asked me where I was located despite me telling him that a few minutes ago.

He asked me to hold for a while, as he would be checking with their technicians to see where Internet would be down.

It was a good five minutes before he came back. The first thing he said? He told me to reset our router.

I said I’ll do that later since our router is upstairs.

He said try connecting the laptop to the router.

Again, I said I can only do that later.

Furious, I asked him if I did all those, if my Internet come back.

He said no, he wasn’t sure if those solutions would work.

It was then when I started ranting and rambling about how much precious time and money we wasted because one they couldn’t provide what we paid for, and second, because they won’t tell us straight if there was a problem.

I mean, if you’re the provider, and you know something is wrong, you should tell the user straight to the point that something is wrong, not blaming it on the user’s hardware.

He should have said, “sir we’ve been having problems” not “sir you should do this and this and that and shit” while covering up what has been happening.

GAHD.

30 minutes later the Internet was back up. Yes I restarted our router, but that was long before our connection came back up.

Dear Sky Internet Philippines, do your job. Quit bullshitting your users. Please deliver.

For other Sky Internet users, Internet at midnight to morning apparently has been erratic since Feb 7. WTF.

From sunset to sunrise, and sunrise to sunset, you have always been there for me.

Whether it was bright or dark, you always held my hand.

I’m holding on tight.

I told her that I plan on getting a few things done before I turn 30.

Why 30?

30 years old is an age that I think is somewhat feasible for goals I have set for myself. By that age, I won’t be too young to lack maturity, and I also won’t be too old to be too late.

And then I remember, around 2 years ago, I wrote a blog entry on how I planned to live my life for the next 8 years. Two years after writing that, I immediately looked it up and read it.

In that blog entry I laid out different things. First I wrote about accepting the difficulty of my current situation. Next is I wrote about alternative paths. Then I zeroed in on specifics on what I want or what I can actually do to reach my goals. And finally I even set a time limit: I gave myself 8 years.

So now what I’d be doing is I’ll be addressing each point I wrote so I can realize where am I right now in my life.

—

First I would have to accept the fact that I am not going to graduate on time. Whatever happens, pass or fail, I would not try anymore to fast forward my academic life. I will be doing things my pace while adhering to the maximum residency rule of the university (maximum time you can stay in UP = [years of academic program] + [years of academic program]/2 ). If I pass most of my subjects this semester, I’d only be taking an extra semester, if not, an extra year. Consequently, I won’t be taking up summer classes next summer. I’d be taking that time to finally take a break that I truly deserve. After all that hype before and after shifting, I think it would be time for me to sit down for a while, regroup, and recharge. Maybe I could even do some part-time work.

Do you know what’s surprising? Even if I was already surrendering two years ago telling myself, “no BA, accept it, you won’t graduate on time,” I have a high chance of graduating April next year. Four summers I toiled and took classes instead of vacations (yes I didn’t follow my own road map). Also for a few semesters I almost maximized my allowable units. The result? I have 13 units (plus PE and CWTS) left for the next semester. That means I can actually take up an extra subject!

Second, I would have to find alternative laboratories that I could do research in for my future thesis. Let’s face it, competition in the laboratories in National Institute of Physics is tough (in the Instrumentation Physics lab for example, out of 27 applicants they would only be accepting 13). So, I would be needing a back up plan if ever I don’t get in one. Surely, there are other laboratories around in the Philippines and it’s possible that I could do some research in them for my future thesis. I would just need to find out where these are and whom I could contact. And also, this is the hard part, I would need to find a thesis adviser who would take me in whatever academic state I’m in and wherever lab I’m from. Research areas I’m thinking of include meteorology, environmental science research, or possibly even geology.

Do you know what’s surprising again? I got in the Instrumentation Physics Lab. So this part I didn’t have to worry about too much. Unfortunately my current research topic doesn’t deal with the research areas I had interest in. But still, I’m (somewhat) enjoying my stay in the laboratory.

Coincidentally, an offer came up this afternoon concerning a new and different research topic of interest. I’ll be looking more into it tomorrow.

Third, I would take up a graduate course in any of these three fields: meteorology, environmental science, or geology. Yes, those are the three fields I mentioned in the previous paragraph. Why do I want to get into one of them, you ask? Because in the future, I really don’t want to be stuck in a jail cell more commonly referred to as an office cubicle. I want to go out in the world and explore, to learn things first hand. I want my job to be something that entails travel and field work and discovering and working with other people. And of course, having an Applied Physics degree would I guess be very much helpful in those fields.

Yes. This still holds. I kept on mentioning that I won’t be kept in a box, and that’s because I want to explore the world. I can’t learn about the world by bolstering myself inside an office.

I will learn about the world by plunging myself into the world.

Actually I have already zeroed in on what graduate course I’d be taking. God please let this be the right choice.

Fourth, if God and the Jesuits permit, I would get a job as a Physics teacher in the Ateneo de Manila High School. While taking up one of the Master’s courses that I have mentioned, I guess it wouldn’t hurt to be earning a few extra cash while teaching kids the hardest subject in their fourth year lives in the process. There is a lack of Physics teachers (or just teachers for that matter) in high schools and I guess it wouldn’t be bad to help out for a while in one school until I finish my Master’s degree.

Actually I forgot about this part. For a year I was really bent on wanting to be a teacher in the Ateneo High School. I even told my past teachers in the Ateneo about it (and they even said they’d already be writing recommendation forms for me). But then now I’m not so sure if I can actually stay in such an institution.

I have new principles and beliefs right now, and I’m not really sure if I would be passing on the right lessons to these Catholic school boys.

Also, I noticed that these kids are becoming richer and richer and at the same time brattier and brattier, so, I’m not really sure. Hahaha.

Finally, if things work out the way I planned them to be, I want to settle down when I reach 28. Yeap, have a family and all that chorva. When I was a kid what I wanted to do was to get rich first, and then get married when I already have a lot of money. But with the recent hard times, if I’d continue with that in mind, I might end up settling down after I turn 50. Hahahaha. But seriously, rich or poor, as long as I have a stable source of income, by 28 I hope I’d already be starting a family.

With regards to this goal, I just realized that if I’d be getting a PhD, I’d be getting it in around 6 or more years from now. So by the time I turn 28, I’ll just be fresh out of grad school. But yes, I think it’s still achievable.

After a few conversations with some friends I have actually made peace with not being ultra-rich in finances as long as I’m ultra-rich in intellect and spirit. What good is money, when you’re not happy right?

—

So that’s where I am right now.

With this entry I was able to disprove and prove myself at the same time. Also a few plans from the blue-print are getting ready to be set on concrete. And finally, I have realized that I have 6 fucking years left before I turn 28.

Would I still be keeping my goal of 28 years old?

Oh God help me.

To properly follow the series of blog entries, please click on the Category: AP186 located all over the blog (in each entry, in the right sidebar). But for convenience, I linked it here: Category: AP186. This is to avoid confusion from reading personal blog entries sandwiched between the image processing entries.

I hope you enjoyed and learned a lot from my blog entries. I’ve put a lot of effort in trying to keep my entries entertaining for my readers to not lose interest. Anyways. If you want to use them for reference, go ahead, just give credit where it’s due. I believe that in the near future I myself would be using my entries for reference

‘Til next time.

PS If I will have fun in my project I’ll be posting a blog entry about it. Hehehe. We’ll see.

Back in 2002, my siblings and I had a relatively high-end computer. It had specs (500Ghz, 80gig hard drive and 512mb RAM, a good video card) that were optimal for playing the newest game at that time, which was the graphics and memory intensive Warcraft 3. Making my setup wicked still is that it had two monitors, enabling me to chat and surf the web while at the same time playing Counter-Strike.

This set-up lasted for quite a few years. In fact, I’ve been using this computer until first year college. Through the years I pushed my use of its hard drive to the limit: I’ve reinstalled/changed its OS many times (Windows, Ubuntu, both), I partitioned the hard drive for different set-ups (for dual-booting, for media organization) and then I filled it with lots of stuff.

As I installed different games, captured more pictures, pirated more music (hehehe), downloaded more movies, the 80gig hard drive, I realized, was not enough with the demand for more storage. Even now that I own a 3 year old Macbook Pro with a hard drive of 160gig, I sometimes find this storage is not enough (as of now I only have 11.42 gigs left).

Of course, this demand was obvious to the computing community, and that is why different programmers developed different ways of compressing files. Zip, tar, rar, and all were basic solutions to compression of multiple files.

Another compression technique of interest is image compression.

Cameras are evolving rapidly: from pinholes to higher grade lenses, from film to memory card storage. In the next few years we expect that cameras can capture images of higher and higher resolution. But problem is, higher resolution also means more space occupied. To be able to optimize your storage, images must be compressed, though not at the expense of losing quality.

That is why the Joint Photographic Experts Group conceived the JPEG image format.

The JPEG compression algorithm is quite complicated and too technical, but one part of the algorithm catches our physicists’ eye for pattens. An image can be reconstructed with the help of the combination of patterns obtained from a Discrete Cosine Transform (DCT).

“The DCT transforms an 8×8 block of input values to a linear combination of these 64 patterns. The patterns are
referred to as the two-dimensional DCT basis functions, and the output values are referred to as transform
coefficients. The horizontal index is u and the vertical index is v.” [2]

As physicists, besides learning the DCT, we also learned Principal Components Analysis (PCA) to represent different sets of data. PCA basically decomposes our data into eigenvalues, eigenvectors, and principal components. Similar to DCT, these broken down information can be used to reconstruct the original dataset. What we do is simply combine some of these components to able to reconstruct the original image. I say “some” because yes, it is possible that we can use only a few components to represent the original data without significant loss.

And that is where the beauty of DCT and PCA lies. From these methods we can choose to use different combinations basis functions to reconstruct our original image. Along these combinations you can choose to use less basis functions to reconstruct. Less basis functions for reconstruction means less memory used.

Now we are ready to compress an image using PCA.

We first get an image that we want to compress and then convert it to grayscale. Upon conversion, we chop up the image into 10×10 regions. The chopped up images were then sampled using PCA, and then resulted to 100 basis functions, aka eigenimages representing the original image.

Notice that the components that the PCA method produced are similar to the components in the DCT method.

After obtaining our eigenimages, we use different combinations of the eigenimages multiplied to the principal components to get our reconstruction.

Above is the reconstruction using different numbers of eigenimages (the numbers are embedded on the photo as white text). Notice that even if we just used only 7 eigenimages, an accurate reconstruction is still produced. Quality then starts to decrease when we only used 4 eigenimages. Using 2 eigenimages for reconstruction, the quality then dramatically drops. But as seen in the last block, even 1 eigenimage can be used to reconstruct the image, though at low very quality (try squinting your eye, the image may still look like of high quality, hehe).

In theory, the image is already compressed because less eigenimages, meaning less information was needed to reconstruct the image.

I cannot make an analysis with regards to file size. Apparently, as you save your PCA compressed image using Scilab, it goes through another compression to make it JPG, effectively disregarding the previous compression we made.

Conclusion
Principal Components Analysis instead of Discrete Cosine Transform was used to compress an image. An image can be reconstructed using small basis functions called eigenimages. It is possible that 7 eigenimages may already be enough to compress the image without a significant loss in quality.

I give myself a grade of 10/10 for demonstrating knowledge of the subject and producing the needed results.

Acknowledgments

• Brian for helping me code.
• Joseph for also helping me code and the discussions about eigenimages.
• Dennis for insightful discussions and for sharing the frustration.
• Troy for the Adobe Photoshop tips.

References
1. M Soriano, “A14 – Image Compression”
2. http://en.wikipedia.org/wiki/JPEG
3. http://en.wikipedia.org/wiki/Principal_component_analysis

‘TIS DONE!

One of my favorite scenes in the Matrix (besides the spoon bending, bullet evading, reality warping scenes) is the scene wherein Neo is being taught the basics of the Matrix. Neo and Morpheus were walking along a bustling street of seemingly hostile and preoccupied people clad in black. Morpheus was explaining something to Neo when a lady in a red dress walks by and catches Neo’s attention. And then we realize that the woman in red was just to test how cautious Neo, or even the viewer is with respect to his surroundings. Morpheus calls Neo’s attention and tells him to “look again,” only to find a gun point-blank towards his head.

Of course, this was just a simulation to test our hero, so Neo is still well and alive.

But you can’t blame Neo. In a sea of black coats, black ties and black socks (even black sunglasses) a beautiful woman wearing red is a very welcome distraction. If I were him I’d also be turning my head in admiration.

We human beings can easily distinguish prominent colors such as the red of the woman’s dress with the help of our eyes and brains. In a sea of black and white, it is easy to point out which is red. But how about our computers? How can we teach them to automatically isolate different colors?

Today we learn about color image segmentation using two different methods: parametric image segmentation and non-parametric image segmentation.

But before we start isolating the colors, we first talk about brightness and chromaticity. A 3-dimensional object illuminated at a direction can have different colors at its different parts due to differing brightness along the object. That is why we just want to get the normalized chromaticity coordinates to help us in further segmentation. Getting the normalized chromaticity coordinates eliminates the effects of differing brightness, allowing us to analyze the object based on its color alone.

To get the normalized chromaticity coordinates, we first get the sum of the values of the three red, green and blue channels. Next is we divide each channel with the sum. Mathematically it is explained by the following equation:

where R, G, B are the red, green, and blue channels, I is the sum of these channels, and r, g, and b are the normalized chromaticities.

Notice that r+g+b = 1. We can then simply represent b as b=1-r-g to simplify our dimensions into 2.

Representing this in 2D space, we get

where the x-axis represents the normalized red chromaticity, while the y-axis represents the normalized green chromaticity. Notice that when we get equal parts of red, green and blue (values of 33, 33, and 33 each), we get the color white.

Now that we are ready to segment our images using the two different methods.

To segment based on color, from the image we first get a region of interest (ROI) containing the color that we want to segment. This ROI we convert to normalized chromaticity coordinates for processing. Now we can choose what kind of segmentation we want.

Parametric
Parametric segmentation is basically assuming that the color of interest we want is a Gaussian probability along the r and g axes of the normalized chromaticity coordinates. Thus, what we do is get the mean and the standard deviations along the r and g coordinates to get two different Gaussians along each axes. These Gaussians we multiply to get a probability distribution along the normalized chromaticity coordinates to get a Gaussian function containing similar colors.

In layman’s terms, what this does is it projects a Gaussian probability distribution in the normalized chromaticity coordinate plane, with mean and standard deviations coming from the ROI. This denotes the colors similar to our ROI.

This method effectively eliminates pixels of color not in the Gaussian probability distribution from the original image.

Non-parametric
Non-parametric segmentation on the other hand, utilizes the ROI’s histogram along the normalized chromaticity coordinates. It takes values of the colors from the ROI and stores it in a histogram. This method stores the color information specific to the ROI. This means that it does not project different points in the normalized chromaticity coordinates. The advantage of this method is that it does not encapsulate colors that are not present in the ROI.

The obtained histogram is then projected back to the image. Each pixel is scanned and if the r,g, and b values of this pixel are within the histogram, the value of this coordinate is projected on to the image.

Both image segmentation methods are demonstrated in the image below.

From the image, we can see that the parametric method segmented the whole iPod very cleanly, selecting the whole iPod on the process. On the other hand the non-parametric method segmented only points near the region of interest, and looked dirty compared to the parametric segmentation.

People may say that they prefer the parametric method due to its cleanliness, segmenting the whole object of interest. But sometimes this is not the case, when in the image there are other, err, uninteresting objects of similar color of our region of interest.

Pictured above is the segmentation of the pink iPod along a laptop screen with a picture of an aurora. Since the aurora exhibits colors that are similar to the iPod, it too is segmented when we segment the image using the parametric method.

What if we want to segment the iPod only, not the screen?

With non-parametric segmentation, we can isolate the colors truly belonging to the iPod since we fill the histograms with the values found only in the ROI. We don’t overestimate some values, as the parametric segmentation sometimes does. Because we get only the colors inside the ROI, we can separate the iPod from the screen.

More interesting is that different ROIs yield different segmentations. At first glance of the unprocessed image the iPod’s color seems to be similar all throughout. Checking the histograms and the backprojections of different ROIs says otherwise.

So when do we choose one over the other?
It depends on the application on which type of segmentation we would use. If we want to get the whole object, say, for applications of area counting, we can use the parametric segmentation since we can isolate the whole object using only a small patch. Though this process is in danger of segmenting from other parts of the image, you can still get the whole object through segmentation.

On the other hand if you strictly want just the color in or around the ROI, we can use the non-parametric image segmentation. As we see above, the pink iPod was separated from the pink aurora. Also, another application of this method is you can use multiple patches and store them in the same histogram to isolate objects of different colors at the same time (say you want to isolate a yellow ball at the same time with an orange ball).

Conclusion
We have demonstrated image segmentation through two different methods: parametric and non-parametric segmentation. Advantages and disadvantages of each method were discussed. Applications for each method were also presented. For this activity, I give myself a grade of 11/10 12/10. for thoroughly demonstrating knowledge about the subject and for giving the required output. Plus 1 for discussing and demonstrating when one method is more advantageous compared to the other. Another plus 1 for demonstrating both masking and NCC in the comment below.

Acknowledgments

• Miss Loren Tusara, for teaching me how to segment images 2 years ago. She greatly helped me in determining how to code the histogram backprojection method which I use for research up to this day.
• Ma’am Jing for teaching me how to vectorize the backprojection code in an RM late last year.

References
M. Soriano, “Activity 13 – Color Image Segmentation”

In the previous entry, I mentioned that I am a musician, though informally trained. It’s one hobby that I pursue because I just want to enjoy it, so I don’t need to make it more complicated than what it really is for me.

Another hobby that I pursue is photography, a field in which yet again, I am informally trained. I do not own professional grade cameras and equipment, nor have I attended any workshop on teaching me how to capture the perfect images. I just capture memories (yes, that’s what I think of my photos) on the go without any forethought on how to optimize the end product.

But one aspect in photography that I always am conscious of are the white balance settings.

This setting allows the modification, or more of adaptation of the camera to compensate for the light present in the scene. For example, you have a yellowish light illuminating the object, a white balance setting would negate the yellow effect on the object, allowing the capturing of the object’s true color.

So how do these white balance settings work?

Our memory machine, err, our camera basically stores color information by storing intensities of three different colors: red green and blue.

To illustrate mathematically, we have the following equations from our lab manual [1]

where S(λ) is the spectral power distribution of the incident light source, ρ(λ) is the surface reflectance and η(λ) is the spectral sensitivity of the camera. Note that all these values are different for the red, green and blue plane. K is the balancing constant for the capturing process.

So now that we know how the camera captures images, we now look into how to balance our images. We look at two white balancing algorithms: the white patch algorithm and the gray world algorithm.

White Patch Algorithm
In the white patch algorithm, what we do is simply select a true white patch from a wrongly balanced image. We want this white patch’s value to be 1 for all color planes (when R=G=B=1, we get the color white), so what we do is we get the values of red, green and blue from that white patch. After we obtained these values, we divide it from the whole image to get our balanced image.

Gray World Algorithm
The gray world algorithm on the other hand utilizes the whole image rather than a patch of white. We get the average the values of each pixel from red, green and blue, and then divide the obtained value from their respective color plane. In using this algorithm, we assume that the mean color of the world is gray.

Above is an application of both the white patch algorithm and gray world algorithm on wrongly balanced images.

Notice that both algorithms worked properly, as we can distinguish each color properly.

So now we have two algorithms, when would we know when to choose one over the other?

Say in our image, each of the colors red, green and blue are not well represented, ie we have a set of similar colored objects. Invoking the white patch algorithm as seen above, we can be able to distinguish the different tones of red. However, invoking the gray world algorithm, the balancing goes awry.

How is this so?

Since the gray world algorithm requires the average value for each of the colors, we need to make sure that each color (or also the color white which is the combination of all colors) is well represented to avoid overbalancing (is there such a term?) of the image. This occurs when we divide the planes of the image wrong constants derived from getting the mean.

So now that we learned about white balancing, we try to apply it to real life.

Pictured above is our favorite seatmate, Jhona Rhaye who is coincidentally wearing white. Obviously, the image at first is wrongly balanced as Jonats seems like to be suffering from carotenosis (his skin is yellow-orangish). Using his shirt on the white patch algorithm we balance his photo. Also since the photo is mostly white from the CSRC environment and since white represents R, G and B equally, we can also use the gray world algorithm.

Conclusion
We were able to automatically balance images through 2 algorithms, white patch algorithm and gray world algorithm. Since we were able to produce visually pleasing results, we give BA a grade of 10/10

Acknowledgments

• Dennis for collaborating with me on taking the photos.
• May Ann and Tisza for their materials.
• And Jonathan for his face.

[1] Soriano, “A12 – Color Image Processing”

As a post-script
At the top of this entry is a photo of the beautiful Mucci taken using a Nikon D3000. It was an inviting bright, warm and sunny morning and Mucci was unusually behaved and sweetly affectionate. To preserve the warmness of the memory, I chose a white balance that would enhance the warm colors (yellow and orange). For me, it was effective because I feel warm and comfortable every time I see this photo.

I am a musician.

I am a musician in the sense that one, I can sing in tune, and two, I can play music using an instrument of choice, which is the guitar.

But if you want to be very strict with your terms, I am not a formal musician. I sing and play music by ear. I base my music skills on what I hear. If you give me a musical piece to read and play (you know, with the staff and the notes), my brain automatically presses the pause button. I can’t read notes as fast as a formally trained musician can.

Who needs notes anyway? I know that I can play and sing from my heart and soul, so, I don’t care much about formality.

That was what I thought until I joined the glee club back in high school.

In the club, since I was a late addition, the conductor wasn’t able to let me listen through the whole song first. Instead, he gave me a score sheet to work with. Me being the informally trained musician, had a hard time deciphering which note is which. I had to do painstaking visual inspection. I stopped at every note and manually counted the lines or spaces needed to get to that note. Knowing which line it was, I recite the letters one by one. Knowing the letter, I *try* finding it on the piano. And then I finally sing.

Slow eh?

This is now where technology comes in.

Since note reading is simply visual inspection (wait did I say simply?), we can use different image processing techniques to teach a computer to read a musical score sheet for us.

So how do we go about this? We do it through the following steps:

First we get an image of the score that we want to read. For the purposes of this activity, we want to read Beethoven’s Symphony No. 9 due to it’s simplicity and familiarity.

Second is we binarize the image through thresholding. After binarizing, we invert it by subtracting 1 from the whole image and then getting the absolute value.

Next is we extract the different notes with the help of template matching. We get the templates of the quarter note and the half note pictured above. These notes we also binarize and invert.

Then we get the Fourier transform of the note template, multiply it to the conjugate of the Fourier transform of the whole score, and then get the Fourier transform of the product. Once we get the points of highest correlation, we binarize by thresholding, and then apply morphological operations to clean up the image.

In this part of the coding, a little tweaking was done. The template matching for the quarter notes detected only the quarter notes while on the other hand, the template matching for the half notes detected BOTH the quarter and half notes. To account for this, the matched templates for the quarter notes were subtracted for the matched templates in the half notes. This leaves us with only the blobs of the half notes.

A visual summary of the steps for comparison.

Now that we know the location and the type of the notes, we simply use these values to see what kind of notes they are. And with the help of Scilab’s sound function, we play the music.

http://static.photobucket.com/player.swf

I’ve uploaded the music video (yes, I made a music video) to Photobucket. I don’t know if it’s streaming. If it’s not, I’ll try posting it to Youtube.

Conclusion
A computer can be taught how to read musical score sheets encoded as images. This can be achieved through template matching, binary operations (thresholding, eroding, dilating, opening, closing) and point location. For this activity, I give myself a grade of 10/10. Though I was able to post it very late, I know I did a well enough job. I understood and applied the concepts very well and produced the needed output.

MUCH THANKS

• Arvin Mabilangan for providing initial ideas on how to go about this activity.
• Dennis Diaz, Tisza Trono, Andy Polinar, Aivin Solatorio, Joseph Bunao, for the discussions and sharing the frustration of writing this code.
• Andy Polinar for giving me the idea on how to sort the notes
• And most especially, Troy Gonzalez the musician for scoring the music. If it were not for you I wouldn’t be able to play this song.

References
1. Soriano, M. ” Activity 11 – Playing Notes by Image Processing”
2. http://www.phy.mtu.edu/~suits/notefreqs.html

As a kid, I used to be fascinated with outer space. Mainly, I guess, because of how my sister always exclaimed that she would be an astronaut when she grew up (although she never pursued this dream, as she became an attorney instead). I used to look at photos of stars in the net back then. In more recent years, I was giddy when I found out that Mac OSXs featured an image of an aurora with stars behind it as its initial wallpaper (see here).

When looking up in the sky with your bare eyes, the stars nearly look the same in terms of size, most of them simply bright white dots. But looking closer with the help of telescopes, as in the image pictured above, you would notice that other heavenly objects such as nebulae and supernova are present. You may also notice the differently sized stars.

In terms of research, it would be very interesting to be able to teach the computer to automatically differentiate these different objects from each other. It’s possible that you may have thousands of images of stars in your database and manually sorting and labeling them by size would be a great pain.

That is why there are different image pre-processing steps available. Binarizing the image by thresholding is one of them.

But even though binarizing by thresholding your images may be of great help, sometimes it is not enough. What about in cases when even in careful thresholding, different artifacts are still present?

Simulation of normal cells and binarizing using a threshold

For example I have a simulation of different “normal” cells pictured above. I would want to know what the area of a normal cell is by labeling each cell and then counting the pixels that each cell contains. However, the labeling process goes awry because of the extra pixels that were not eliminated by our initial thresholding. The calculation for area by pixel counting would then be erroneous.

This is the reason why morphological operations were invented. Morphological operations are preprocessing steps to help us enhance our images for easier and more advanced processing.

If you remember in the previous entry, I mentioned the operations open (erode dilate) and close (dilate erode). These operations are very useful in cleaning up an image for preprocessing. Opening cleans up the image of blobs smaller than the structuring element, while close eliminates holes in the blobs in the image.

So how could these operations help us in our processing? First, by applying open our binarized image above, we eliminate the extra salt and pepper pixels on the right. And then by closing, we eliminate the holes inside the cell blob. Take note that since you reverse the initial operation applied (eroding after dilating, or dilating after eroding), you effectively restore the original size of the object after cleaning up the extra pixels or holes.

Having cleaned up the area and closed up the cell while maintaining its original area, we can now count the pixels of our normal cell to get the the relevant values in calculating our area.

mean area = 523.77778 px
stdev = 25.034421 px
minimum = 478 px
maximum = 615 px

Now that we know this information, we can use it to isolate the normal cells from the abnormal cells.

Pictured above is another simulation of cells. but this time, rather than having all normal cells, mixed in are “cancer cells” distinguishable by their larger size. In this photo, there are at least 5 cancer cells mixed in.

So what we want to do is to automatically isolate these larger cells by using the information we have obtained beforehand. Remember that the opening operator erases objects that are smaller than the structuring element. What we can do then is create a structuring element with the same shape and size of the average normal cell. Applying the opening operator on the image using this structuring element effectively erases the normal cells, leaving the cancer cells behind.

In the case of our image, we shall make a circular structuring element very similar to the normal cells. Since we know the geometry of the cell, we use this information to create that structuring element. We use the maximum cell size to ensure deletion of smaller cells (615 pixels of are, so more or less a radius of 15 pixels will be used).

Also note that the opening operator erases objects with respect to shape, not with respect to area. So even larger clumps of normal cells are erased due to their contiguous shape being close to the structuring element.

Conclusion
In this activity we have applied two different preprocessing binary operations, namely thresholding and morphological operations. These operations are very helpful in enhancing our images for processing, such as in the case of this activity, isolation of cells by their area.

I give myself a grade of 10/10 for producing the needed output, and showing understanding of how to use different binary operations.

Acknowledgements
As usual, I thank Dennis, Joseph, Mabi, Tisza, and ma’am Jing. I also thank Andy for adding a few insights.

References
[1] http://www.outerspacesite.com/supernova.html
[2] Maricor Soriano, “A10 – Binary Operations”