Madeline Krajewski

I’ll admit, April 1st made quite the splash. I was suddenly and horrendously confronted with the realization that Capstone presentations are a month away–in fact, less than that, depending on who gets assigned which day. I am quite concerned, as I believe I’m at the halfway mark, yet over half of the way through the semester. All the progress I thought I’d been making on Algorithm 2 crumbled before my feet, and I have not been able to get a clear answer on what, exactly, I need to do instead. I’ve reread Doug Stinson’s paper on the algorithmic approach I need to take for my second algorithm, and I’m no closer to understanding it on my fifth reading of it as I was after the first two. As of right now, I believe I am doomed.

What is Algorithm 2 (besides a heart-stopper)? In this Algorithm, the goal is to take the secret image and bash it into unrecognizability. It will take a perfectly happy photo of a bird (or whatever the user desires), and break it into k number of fragments, or “shares.” Each fragment has double the number of pixels as the original image (a puzzling fact), and should look like television static. (I am old enough to remember such things, to the surprise of some.)

Then, each share gets distributed to a person, hereafter dubbed a “spy” (though not by Doug Stinson, but by me). The total number of shares which must be present to reassemble the secret image is t. If t < k, then some spies can die or get captured by the enemy without compromising the “mission.”

Now, back to being doomed.

The math part (ie, the Linear Algebra) is the easy part, which should alarm most anyone. Math is rarely the easy part. In fact, it is usually the most difficult part. It has been about four years since I took Linear Algebra, and I remember being quite content to abandon matrices and vectors from then on. So for me to now recognize it as a long lost love in the face of these other, stranger parts of this Algorithm is… not exactly inspiring my confidence.

Here are my list of questions (and therefore, woes):

• If we’re doubling the number of pixels (as opposed to squaring), won’t the image get distorted?

My professor informed me we must double the amount of pixels, and reiterated this many times upon my questions. However, I don’t understand why that’s the case. To preserve a pixel’s (square, 1 by 1) dimensions, we would need to turn it into a 2 by 2 grid. This makes four pixels, however, not two. I’m rather confused on how an image doesn’t become terribly mangled through this process if we aren’t preserving the pixel’s square dimension. However, since my professor was adamant, I figure I must be missing a larger share (ha) of the puzzle. Therefore, my next question:

• Is there a method of compressing all the duplicated pixels down into one which isn’t detailed in this paper?

In Stinson’s paper, the images of the shares, secret image, and generated result appear to be the same size and dimensions as one another in the diagram. Is this due to formatting and visibility instead of accuracy? Still, that would make overlay an odd word choice on Stinson’s part, and I doubt this is the case. I’m sure the confusion is on my end, not his. Speaking of overlaying,

• When overlaying, why would I not simply set any gray pixels to white? Wouldn’t that remove any degradation, so long as those changes only occur after all image shares have been assembled for that pixel?
• How does overlaying work?
• How is the number of pixel expansions determined?

The number of pixel expansions isn’t double the number of shares, nor double the number of people needed to reconstruct the image (as seen in the example with 2 out of 4 shares; the number of pixel expansions is six. Is it due to addition, somehow, or is that also by chance? Elsewhere, matrices have square dimensions).

• Why does a weight (w) exist, and what is its function?

It seems to relate to the number of pixel expansions we must do, yet I don’t know why. Additionally, it’s not a square of either of those number options, either.

Doug Stinson, if you happen to be reading this, please help me.

Now, on Algorithm 1:

I finished writing the encoder, yay! The only thing left to do is the decoder, which should not be as intense. I’ve had to dedicate time this week towards planning my next project presentation to my Capstone class, and to driving myself mad over Algorithm 2. Also, it was brought to my attention that I needed more birds in my testing pool, so here are some new images to enjoy!

Sources

“Puffin Talk on Saltee Island Great” by Wynand van Poortvliet on Unsplash

“California Quail” by Richard Lee on Unsplash

“Black-Capped Chickadee” by Patrice Bouchard on Unsplash

“Blue-Winged Kookaburra” by Peter Scholten on Unsplash

“A Peacock in the Helsinki Zoo” by Julius Jansson on Unsplash

“Stork-Billed Kingfisher Perching on Brown Wooden Stand” by Thomas Maximilian Lener on Unsplash

“Pink Pelican” by Maksim Samsonov on Unsplash

“Ruby Throated Hummingbird” Photo by Candi Foltz on Unsplash

“The Raven” by Daniel Shapiro on Unsplash

“UK Seagull Portrait” Photo by Peter F. Wolf on Unsplash

“Bee Hummingbird, Cuba” by Anne and Saturnino Miranda from Pixabay