I finished my paper and presentation on Friday; at some point I'll get around to updating this blog with some more neat info I learned during my project. It was just so very hectic these past couple of months.

Anyhow, throughout the duration of getting this degree, and more towards the end, I have been confronted again and again by the notion that math = arithmetic. It does not. I've also been asked over and over again what I can do with this degree, usually with assumptions stated by the questioner. Sure, adding and subtracting are useful things, but no, I'm not only qualified to balance my checkbook; I'm not qualified to be an accountant (as those people deal more with law than even with arithmetic); I'm not (according to the state) qualified to teach, as I have no education degree or coursework. I usually sigh and give the "it gives me a clear and logical way of thinking, so that I can succeed at anything I want to do" answer.

Today, I found a much, much better answer. Go read it: Lockhart's Lament. It's kind of a long pdf, but the first 7 pages answer the topic I'm speaking of today; the rest bemoans the educational system, the "math" curriculum we have in place today.

But I think it should be shared anyways...

It snowed -- HERE -- on Friday!

I've learned something cool I thought I'd share.

A few weeks ago, I was with friends in a store, and I got mesmerized by a TV there. Not from what it was showing, but from the quality. That wasn't TV - those people were right there in the box, I'm telling you! So was all the natural scenery they showed. Somehow.

Of course, I've seen HDTV before, but that was before I dealt with broadcast television for any length of time. After looking at the few snowy news casts I've caught over the past several months, this HDTV was even more astoundingly clear.

But why is it so crystal clear? What have they fundamentally done to change it? I found out at least one thing recently.

You might have heard the terms "progressive scan" or "interlaced scan" bandied about in all this hubbub about HDTV. I think I have. Of course, I had no clue what they meant, so I didn't focus on them very much. Now I do know what they mean; let me explain them to you.

See, regular TV will send you the same 30 frames per second that HD TV sends you. But with regular TV, every other frame only sends you half the frame -- say, the even-numbered lines of the image. Then the frames in between are the odd-numbered lines of the image. Now, 30 frames per second is really fast, and sufficiently fast for this method of transmission to fool your brain into seeing the whole picture. But the edges aren't clearly defined, going about it this way.

In fact, rimspace was kind enough to create this animation for me to put here, showing yall what I mean by the every-other-line thing. It shows you right now one frame; clicky on it to see the next frame. Click as much as you want, as fast as you can, to see a slowed-down version of what happens on your TV.





Cool, huh? Thanks, rimspace! *huggles*

And that's what's called an interlaced scan. But HDTV uses a progressive scan; that is, it'll send you the *whole* frame, every time. Not just half. Hence, you're getting those edges defined in each frame, instead of some operation your brain does as a difference between successive frames. This is certainly going to yield crisper images. So, HD for the win! :-)

In case you're curious why they didn't do it this way from the get-go, the math wasn't there. Now we have the algorithms to compress the data sufficiently to keep within the FCC's and hardware's limitations on bandwidth, so they can send double the data now (with the progressive scans) as they did before (with the interlaced scans).

Cool, huh? :-D

Alright, Part One was the "how it works"; Part Two is the "why it works." Or at least, some theories to that end. This I couldn't really tone down the mathese on as much as I'd like. If you're less interested in this part, fret not. I shall bring you more "how it works" stuff at later dates.

So, without further ado...

( Click here to read more -- Warning: Lots of images! (Mostly math stuff, though) )

I am sorry for my long hiatus; I have been in data-gathering mode. I have decided to focus, at least for a few weeks, on sharpening of digital images, a seemingly limitless topic.


I have put together some of that information and submitted a paper to a conference; I will be presenting it there in one and a half weeks or so. I shall reproduce it here for all of you interested folks. I will be adding some explanatory remarks throughout; if you're interested in seeing the original paper, let me know, and I'll get it to you.

Sharpening Digital Images

Abstract

This paper explains one method of sharpening digital images, a convolution operation on the matrix comprising the digital image. It then motivates the operation with a theoretical example and with a numerical approximation. (The latter part of this will be done in my "Part Two" post here).


There are many different ways computers sharpen digital images; it depends in part what specific problems you have with the original. For instance, if it was simply captured at a lower resolution than what you need or want, then what you'd want to do is get the computer to guess at what's not there; that delves into statistics (what's the most probable value of the in-between pixels, based on the surrounding pixels?).


But for this paper, I focused on something done when the resolution is just fine, or perhaps even higher than needed. The method discussed below manipulates the values in the image to create a sharper appearance, rather than increasing resolution.


( Click here to read more -- Warning: Lots of images! (Mostly math stuff, though) )

... And I'm going to cut this off here for now, and post the motivation and the numerical approximation another time. Translating this into Plain English is almost more difficult than writing the paper to begin with!

Do you have any distorted digital images you'd be willing to pass along to me? I'm hoping to have some examples of the various methods of digital processing, and of course many peoples' reasons for doing anything to a digital image is because they didn't like how it looked originally: perhaps the camera was angled funny (not vertical), perhaps it was blurry, whatever.

Please email them to me, if you have any such! Thanks!

This project will be a (very large) expansion on my talk I gave in November. Thought I'd start this blog (this record of my project) off with this online version of my talk there as a basis, to get everyone on the same page. Some of you have already been exposed to this talk, of course, either in person or where I posted this to begin with; just as a heads up, I haven't changed anything, so you'll probably want to skip over this entry if it sounds familiar.

I think this subject is neat :-)

( Click this link for the presentation; I'll warn you, there are lots of pictures and it may take a bit to load )

This is my blog about my senior seminar project, a semester-long affair with weekly updates and a formal presentation and paper at the end.

My topic will be Mathematics Behind Digital Image Enhancements.

It is my intent to make much of the material here accessible to non-mathies; in fact, I'm creating this as a separate blog so that I can share it with my friends and family who might wonder what I'm up to over here with my odd equations and arcane symbols. I intend to update at least weekly, in order to prepare what I'll say at seminar that week, and perhaps more often, as the urge strikes me.