Comments on: Explaining the JPEG Algorithm

Explaining the JPEG Algorithm

cgc373 — Tue, 11 Sep 2007 18:35:36 -0800

Algorithm. JPEG compression explained.

By: zsazsa

zsazsa — Tue, 11 Sep 2007 18:45:09 -0800

This article doesn't really show you what the DCT coefficients actually look like. Imagine this image laid over the matrix right before the "Quantization" section. That image is what made me "get" how JPEG worked: the DCT "figures out" how each block can be expressed by adding up each of those blocks in varying amounts. If you're familiar with JPEG artifacts, you'll definitely recognize those patterns.

By: growabrain

growabrain — Tue, 11 Sep 2007 18:47:15 -0800

wow

By: nasreddin

nasreddin — Tue, 11 Sep 2007 18:52:14 -0800

It was interesting and then there was math and I ran away ps: I'm pretty sure that's not a 256 color image, so shouldn't one pixel be represented by 2 or 4 bytes?

By: StickyCarpet

StickyCarpet — Tue, 11 Sep 2007 18:56:46 -0800

There's still a few bugs to be worked out.

By: klanawa

klanawa — Tue, 11 Sep 2007 18:59:45 -0800

nasreddin, each colour of every pixel has 255 possible variations. that's 16581375 colours... or something.

By: Gary

Gary — Tue, 11 Sep 2007 19:18:45 -0800

It was interesting and then there was math and I ran away That's why image compression articles are supposed to use a picture of Lena to keep everyone interested (previously discussed here).

By: tss

tss — Tue, 11 Sep 2007 19:18:53 -0800

Good post, and zsazsa's postscript is nice too.

By: weapons-grade pandemonium

weapons-grade pandemonium — Tue, 11 Sep 2007 19:20:45 -0800

From StickyCarpet's link: These noises are desirable for us to remove. Best deletion reason ever.

By: eriko

eriko — Tue, 11 Sep 2007 19:41:37 -0800

Sigh. jpeg, j2k, gif -- and not an img tag to be seen.

By: odinsdream

odinsdream — Tue, 11 Sep 2007 19:41:47 -0800

Don't worry about the factor of 1/2 in front or the constants Cw (Cw = 1 for all w except C0 = 1/Sqrt(2)). Oh, I wont.

By: Rhomboid

Rhomboid — Tue, 11 Sep 2007 19:48:05 -0800

Sigh. An article about jpeg and why it has artifacts that itself includes a screenshot of a program in jpeg format -- the very thing that jpeg should not be used for.

By: b1tr0t

b1tr0t — Tue, 11 Sep 2007 20:02:01 -0800

16,777,216, actually.

By: about_time

about_time — Tue, 11 Sep 2007 20:04:30 -0800

Similarly, AES block cipher flash animated.

By: TheOnlyCoolTim

TheOnlyCoolTim — Tue, 11 Sep 2007 20:42:12 -0800

Don't worry about the factor of 1/2 in front or the constants Cw (Cw = 1 for all w except C0 = 1/Sqrt(2)). Oh, I wont. As someone who maybe actually slightly knows what's going on in this area, those numbers actually are not all that important. Just scaling. Really, the discrete transforms like this always have a ton of mess in the actual formulas that's just bookkeeping and obscures the actual meaning. Basically, to consider the one dimensional case you multiply your data function d(x) by a cos(w*x) function* that has a certain frequency w. You do this multiplication at each point x and add all the results: so d(0)cos(w*0) + d(1)cos(w*1) and so on. The result is that the more your data resembles the cosine function with that frequency w the larger the frequency domain coefficient D(w) will come out. You do this for several frequencies and get the whole D(w) function. All the other numbers are just there to make it actually work right. Sometimes some of those numbers are seriously called "twiddle factors." This technique and similar ones are very extremely important to all the electronic stuff you enjoy every day. This is actually a sort of easier one because it doesn't deal with complex numbers and complex exponentials, which are like a super version of the cosine function. (*a cosine function is basically the shape of ripples in water or holding the end of a rope and shaking it up and down)

By: cerebus19

cerebus19 — Tue, 11 Sep 2007 20:45:00 -0800

Is this something I would have to be a software engineer to be interested in? Hang on a second. I am a software engineer, and I still don't want to read it. Thanks anyway.

By: jefflowrey

jefflowrey — Tue, 11 Sep 2007 20:52:02 -0800

TheOnlyCoolTim... Every time I hold the end of a rope and shake it up and down, I get something basically the shape of a sine function... What am I doing wrong?

By: Dataphage

Dataphage — Tue, 11 Sep 2007 20:57:50 -0800

Jefflowery: Start shaking the rope at eye lovel, not at navel level. Duh.

By: intermod

intermod — Tue, 11 Sep 2007 21:22:51 -0800

Digital cinema projection is standardized on JPEG2000. Note that that is NOT "Motion JPEG". Which means that each frame is an individually decompressed image that stands on its own, with no previous frame info needed unlike in MPEG video encoding (i.e. no temporal encoding). 24 frames of 8 megapixel JPEG2000 images rendered every second? Yeah, that's some seriously expensive computing horsepower.

By: spiderskull

spiderskull — Wed, 12 Sep 2007 01:33:57 -0800

Disregard the anti-nerd comments above -- I thought this was a great link. Thanks.

By: rpn

rpn — Wed, 12 Sep 2007 01:38:35 -0800

intermod: Motion JPEG is the same thing (apart from using JPEG instead of JPEG2000), just individual JPEGs for each frame. Don't confuse MJPEG and MPEG, although MPEG can function in a similar mode by just using I-frames (i.e. no inter-frame prediction).

By: kid ichorous

kid ichorous — Wed, 12 Sep 2007 05:39:41 -0800

TheOnlyCoolTim... Every time I hold the end of a rope and shake it up and down, I get something basically the shape of a sine function... What am I doing wrong? Aaaaa! You're out of phase! Quick, lock yourself in a closet before you screw up spacetime.

By: delmoi

delmoi — Wed, 12 Sep 2007 06:21:28 -0800

ZOMG MATH = SCARY. Er, wait...

By: cgc373

cgc373 — Wed, 12 Sep 2007 07:02:33 -0800

Oh, yeah, I meant to post a via Danny Yee (who got it from Robot Wisdom).

By: DarkForest

DarkForest — Wed, 12 Sep 2007 07:20:00 -0800

Is this something I would have to be a software engineer to be interested in? Probably, or at least a mathematician of some sort. 10 years ago I had to implement jpeg decoding on a low powered device, and I was using the jpeg group's decoding library and it was slow as crap. So some manager type comes by and tells me I should be able to optimize it. Fuck. This was about a day before a major demo and there was no way I was going to understand the math behind it or write it more efficiently than the jpeg group did. (sorry, just venting some 10 year old steam). Maybe I could have used this article then. I've bookmarked it, but I doubt I'll ever read it.

By: Potsy

Potsy — Wed, 12 Sep 2007 08:12:56 -0800

intermod: Heh, I wish digital cinema was "8 megapixel". Unless you're looking at one of those new LCOS projectors from Sony or somebody else, the de-facto standard DLP setup is actually around 2 megapixel, or even less if you're talking about the "scope" aspect ratio.

By: ROU_Xenophobe

ROU_Xenophobe — Wed, 12 Sep 2007 09:28:19 -0800

Potsy: I read that as referring to digital projectors in movie theaters, not home stuff.

By: MythMaker

MythMaker — Wed, 12 Sep 2007 11:45:57 -0800

And, actually, digital cinema (movie theaters) is 12 megapixel - it's 4K across.

By: Joakim Ziegler

Joakim Ziegler — Wed, 12 Sep 2007 12:22:01 -0800

Basically, everyone realizes that the digital cinema consortium is just wanking when they specify 4k resolution. In fact, that's the maximum resolution, and if you supply 2k, according to the standard, you're required to supply 2k as well, since very little hardware will be able to use 4k. The specification of 4k JPEG2000 is "old cinema" trying to assert itself as still much better quality than "new cinema", the people who are saying that hey, HD resolution is really better than film anyway for delivery, and probably for other stuff too, if you go all-digital, since you're eliminating grain. I think fewer and fewer people believe the old cinema folks now, though. My guess is 2k is going to be the standard and pretty much no one will use 4k.

By: MythMaker

MythMaker — Wed, 12 Sep 2007 14:21:17 -0800

Well, considering that cameras like the RED ONE actually SHOOT in 4.5K, I'm not so sure that's true. As hard drives continue downward in price, and processors and busses continue downward in price, the digital pipeline certainly becomes easy enough for 4K. Right now it's at the limits of technology, but with Moore's Law, what' difficult now is trivial in a decade.

By: Joakim Ziegler

Joakim Ziegler — Wed, 12 Sep 2007 15:29:59 -0800

MythMaker: Yeah, the Red One can shoot at 4.5k, but I'm involved in a couple of feature projects that are considering using the Red One, and most are thinking they'll actually use 2k. 2k is used a lot for scanning 35mm film too, and there, it actually has to reproduce the grain from the film. Pristine 2k without grain is more than enough. As a comparison, there's the Kodak test where they showed that the resolution of typical distribution copies in 35mm isn't more than 750-800 lines. Given that that's 1.85:1, that's 1480 lines horizontal, quite a bit less than 2k's 2048. The main reason people are using 4k in post today is to extremely faithfully reproduce the grain in 35mm negatives. Once we start capturing on something that has pixels instead of grain, we'll need a lot less for the same subjective viewing experience.

By: StickyCarpet

StickyCarpet — Wed, 12 Sep 2007 16:56:07 -0800

the Red One can shoot at 4.5k ... most are thinking they'll actually use 2k Special effects master shots were often done in 65 millimeter to hide the artifacts, then transfered to 35 for final viewing.

By: MythMaker

MythMaker — Wed, 12 Sep 2007 22:16:45 -0800

Sure, 2K is good enough. But 4K will blow people's minds. The grain in a 35mm film scan shows that film resolution is effectively less than 4K. But claiming that the future, say a decade down the road, won't use 4K is like someone in 1987 proclaiming "Oh my God! A 20 Megabyte Hard Drive! I will never be able to fill it all!" It seems a bit shortsighted. As the technology gets cheaper and hard drives get bigger and cheaper, there will eventually be no reason at all not to work in 4K. In addition, there are reasons to shoot oversampled, in 4K, and then downconvert at the end to 2K. The downconversion will smooth out small imperfections (say, from pulling keys) in the final master. Frankly, I think we'll see video and cinema go *way* beyond 4K. UHDV is 7,680 × 4,320, and they've already done demonstrations of the technology. Do the productions you're working with have definite access to a RED? There are only 25 in circulation at the moment, you know... You'll have to let me know how the RED works out.