Talk:Dither

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Noise[edit]

Some scientists/engineers define dither broadly enough to include forms that have little or no noise content. In the examples given, the WWII bomb trajectory calculator, tapping on the cookie sheet, etc., the dithering signals are not particularly noisy. As long as the signal is large enough to overcome the slip-stick friction of the calculator's moving parts, or of the tater tots, but not so large as to introduce significant error, or send the tots across the kitchen, it will be an effective dither source. The "colored" and "psychoacoustic" dither used in digital audio is a step away from randomness, and indeed, some audio manufacturers (e.g. Lexicon) experimented with narrowband dither (at the Nyquist rate) which cannot really be described as noise.

So more broadly, dither can be defined as a signal which is injected into a system to overcome low-level non-linearity, be it quantization error or slip-stick friction. With this broad definition, it becomes practically synonymous with "stochastic resonance", which is the term the scientific -- especially the neurophysiological -- community uses to describe, well, dither. Not surprisingly, the transfer function of a neuron is not particularly linear. Therefore, not surprisingly, injecting a random (stochastic) signal into a neurological system increases its sensitivity. -Jim MacArthur, Chief Engineer, Harvard Electronic Instrument Design Lab Squinto 20:37, 6 September 2005 (UTC)

4 bit example pictures[edit]

Would be interesting to see not dithered and dithered pictures with an unoptimized 16 colour vga standard palette. Sure, the first one will look terrible and the second on not really good, but they'll serve as good comparisons to the other pictures and show what's possible with very few colours.

Modern image dithering[edit]

Image dithering is a much wider field of research that what is presented here. Most modern algorithms are not presented (Hey, FS is 35 years old !). Pseudo-random, stochastic dithering, blue-noise matrices, work by Ulichney and Ostromoukhov, etc. are all missing. See here for example : http://www.iro.umontreal.ca/~ostrom/publications/research.html#halftoning —Preceding unsigned comment added by Eforler (talkcontribs) 08:56, 24 June 2010 (UTC)

Noise in image dithering?[edit]

The explanations of the uses of dithering in both audio och image processing are excellent. However, I fail to see how the techniques are related. How does the "noise" fit into the picture when dithering an image? It would be great if someone could elaborate on this. MEMark 11:54, 27 October 2005 (UTC)

Audio is 1-dimensional, images are 2-dimensional. But otherwise what is happening is identical - noise is added to the signal to spread the quantization error over a number of samples. If you examine a dithered image closely, you'll see it looks noisy - the noise is actually visible as pixels of slightly variable colour which from further away (averaged by the eye) look like a single solid colour. Graham 10:34, 21 December 2005 (UTC)

Quantization error[edit]

"Another plausible solution would be to take 4.8 and round it so that four times out of five it rounded up to 5, and the other time it rounded to 4. This would average out to exactly 4.8 over the long term. Unfortunately, however, it still results in repeatable and determinable errors, and those errors still manifest themselves as distortion to the ear."

Is this only in practice? Why do these errors occur? Does oversamplng realy average this?

203.214.75.127

4, 4, 4, 4, 5, 4, 4, 4, 4, 5 does not create the same waveform as 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8... even though mathematically speaking they average to the same value over the long run. The ear will pick this up quite easily as a nasty sort of low-level scratchiness (distortion). By adding dither the error is spread randomly which is far more acceptable to the ear - it sounds like a quiet hiss instead of distortion. The brain is wired to detect patterns in the sounds it hears, so a systematic attempt to eliminate the rounding error will create a detectable pattern (called correlation) whereas simply randomising it makes it 'invisible' to the brain (uncorrelated). Graham 10:30, 21 December 2005 (UTC)

Frequency domain[edit]

I deleted the sentence about the ear being more sensitive in the frequency domain. I'm an electrical engineer and this statement makes no sense. Frequency and time domain are two ways of representing the SAME signal. — (unsigned comment by 195.243.189.189, 2005-12-21 01:41:21)

Split into multiple articles?[edit]

I think I originally advocated combining the general dither article and the image dither article (I think it used to be dithering), but now this article is very big and deals with some rather specialized stuff, so maybe we should split out the audio and image content, so that we have three articles:

Hmmm, I'm not so sure. The processes are the same - not just analogous, but identical. It's just that one type of data is 1-dimensional audio, the other 2-dimensional images. I think having them in one article makes this much clearer, and I don't think the article's THAT long. Graham 11:39, 23 January 2006 (UTC)
Ok. It is pretty long, but it would probably be fine to just rearrange it. It currently looks like two articles glued together, which, actually, I think I'm responsible for.  :-) — Omegatron 14:32, 23 January 2006 (UTC)
My concern is that audio dither is given much more coverage than digital imagry. For example, the article only goes into (a few sentences of) Floyd-Steinberg dither and neglects other forms of dithering, like Bayer ordered dithers or halftoning. --Trixter 22:07, 9 February 2006 (UTC)
I agree, except that I would call the articles audio dithering and image dithering. I think this split is a good idea because many readers will only care about one particular type of dithering (for example, a web graphic artist would only really care about image dithering, while a sound engineer would only care about audio dithering). Also, this will give the articles more room for much-needed expansion and lots of illustrative images. Deco 22:12, 28 April 2006 (UTC)

It would be nice if some text were introduced into the article at the transition to talking about image dithering to indicate that image dithering is the two dimensional equivalent of audio noise dithering. Jonabbey (talk) 04:12, 27 June 2008 (UTC)

Photography[edit]

So I guess the random placement of grains in regular photographic film is a form of dither? — Omegatron 15:43, 24 January 2006 (UTC)

I guess you're right... since a photographic emulsion molecule can really only be in one of two states - either "on", changed to silver, or "off", as silver halide - then smooth tones must be made from particles having a random distribution but a probability of being in one or the other state proportional to the grayscale of the image at that point. This is very similar to a dithered 1-bit image which are common on computers (especially older ones such as 80s-era Macs), though the "grain size" there is relatively enormous.Graham 22:04, 24 January 2006 (UTC)
Now that I rethink about it, I was thinking about anti-aliasing, not dither. But I guess it does both. — Omegatron 00:44, 13 February 2006 (UTC)

Why minimize quantization error?[edit]

Can somebody explain how dither minimizes the quantization error compared to simply rounding to the nearest quantization level?

It doesn't, really. It removes systematic error, such as if you're repeatedly rounding by the same amount, which can cause "new" signals to appear. When dithering, the quatization error manifests itself as noise rather than a signal. europrobe 19:56, 29 May 2006 (UTC)
I should have made myself clearer. I was actually addressing the very first sentence of the page: "Dither is a form of noise, or 'erroneous' signal or data which is added to sample data for the purpose of minimizing quantization error.". This sentence is not correct since quantization error is not minimized ( at least by any reasonable measure that I can think of ).
So change it. europrobe 17:26, 30 May 2006 (UTC)

Good article[edit]

Interesting stuff. Has anyone considered nominating this for Good Article status? Tpth 04:32, 2 August 2006 (UTC) I agree. This is a really informative and well-written article.216.107.192.114 18:00, 5 November 2006 (UTC) And I agree too. This is one of the best technical articles I have read. The examples given are excellent. Is there some way to replace the sound pieces with something that doesn't require a software download? —Preceding unsigned comment added by 162.129.251.22 (talk) 15:42, 11 December 2008 (UTC)

Optimised Palette[edit]

With regard to dithering images, what is the technique used to determine an optimised palette? Is it part of the dithering process, or can it be done independently? More specifically, would the optimised palette be the same regardless of which dithering process is to be used? --Malcohol 12:57, 29 August 2006 (UTC)

Aha! The Color quantization article discusses this issue. A quote: "Color quantization is frequently combined with dithering, which can eliminate unpleasant artifacts such as banding that appear when quantizing smooth gradients and give the appearance of a larger number of colors. Some modern schemes for color quantization attempt to combine palette selection with dithering in one stage, rather than perform them independently."--Malcohol 10:24, 31 August 2006 (UTC)

Dither & Bombsights[edit]

Norden bombsight currently states:

In combat, this accuracy was never achieved - because the Norden had been tested under "artificial conditions" at the US proving grounds, for example in the absence of anti-aircraft fire and/or adverse weather.

This seems to partially contradict this page which states:

Airplane bombers used mechanical computers to perform navigation and bomb trajectory calculations. Curiously, these computers (boxes filled with hundreds of gears and cogs) performed more accurately when flying on board the aircraft, and less well on ground. Engineers realized that the vibration from the aircraft reduced the error from sticky moving parts.

Ewlyahoocom 14:28, 6 September 2006 (UTC)

(This issue has been addressed - there is no contradiction. 82.139.85.81 04:28, 16 October 2007 (UTC))

This article shouldn't require cleanup[edit]

I am an electronics engineer and needed to review some theory behind decibel calculations. I found a link to this article on dithering. I was quite surprised to see that someone had placed a 'Cleanup' tag on this article, implying that it needed work. That is ridiculous - the discussion of dithering in this article and the examples of the usage of dithering in making digital photographs clearer, make this article one of the best written I have ever come across in Wikipedia. This subject could not be discussed and illustrated any more clearly, or reduced to anything more elemental without compromising the subject matter.--70.142.9.33 08:45, 3 September 2007 (UTC)

Cleanup tag removed on Sept. 3, 2007--70.142.9.33 09:11, 3 September 2007 (UTC)

I think that audio section is still a bit of a mess; seems to be someone's personal essay, not very well wikified, and completely unsourced. So I added an unsourced section tag. If we get a good source or two that will make it easier to work on. Dicklyon 16:33, 3 September 2007 (UTC)
I am actually doing an investigation on audio mastering and came across this great book by Bob Katz, "Mastering Audio: the art and the science", which explains in great detail the purpose of dithering in digital audio not only when converting between wordlengths, but when recording analong input through an Analog/Digital converter. I am planning to add some quotes and references to this book on the Digital Audio section, since I think it lacks the explanation of some purposes of dithering in digital audio.--Tevex 06:36, 18 September 2007 (UTC)

Sierra's filter light[edit]

Sierra may think his "filter light" is pretty good, but in images with slow gradients and such I think I'm seeing more vertical and diagonal banding than with Floyd-Steinberg. Is anyone else experiencing this issue? Shinobu 10:03, 2 December 2007 (UTC)


Images[edit]

Really nice article. Could we maybe add some more relevant images at the start? The original dictionary definitions are interesting, but could we have something a bit more appealing to the eye? Hate to be a wikifairy...

on the images ... isnt it kinda strange that Dithering_example_dithered_256color.png, contains 607 distinct colors ? (acording to Irfan view) 83.25.83.82 (talk) 23:17, 26 January 2008 (UTC)

Sure enough, someone boned it. I tried to fix, but some of the pixels needed to fix the inset are missing, and the magnification of pixels is by a non-integer, so it's hard to fix right. Dicklyon (talk) 00:02, 27 January 2008 (UTC)

This is an error, right?[edit]

"If we reduce our waveform by, say, 20% then we end up with the following values:"

then

"If any waveform, comprising the original values, were to be processed by multiplying each value by 0.8, the result would contain errors."

note that if you get 1, reduce it by 0.2, you'll have 0.8 . If you multiply 0.8 for 1-(0.2) (he meant, to try to get the original values again) , we get 0.64. The right value should be (0.8)-1 which is 1,25. I've changed so in the page, so if I'm wrong please say and Ill restore to 0.8 . —Preceding unsigned comment added by 189.33.159.46 (talk) 21:40, 7 March 2008 (UTC)

Dithering and compression[edit]

This is my original research so can't go in the article. I did some tests in GIMP of different image file formats (the image used being a screenshot of a web browser), and found that dithering in GIF and (palleted) PNG images substantially increases the compressed file size (by a factor of 2-3) compared to an undithered image, whether using optimized or pre-defined pallets. Presumably this arises as a result of the compression algorithms handling large areas of predictable solid colour far better than the randomness that dithering by definition creates. If anyone can find other studies to back these results up, it would be worth including. 128.232.228.174 (talk) 01:09, 3 April 2008 (UTC)

Yes, it's well known]. Dicklyon (talk) 04:20, 3 April 2008 (UTC)

is dithered really better than rounded? or is it just an oppinion[edit]

I just listened to all three audio samples, and I don't find neither two better than the other. I beleive it is only an opinion. Everybody has different ears decoding sound frequencies differently. —Preceding unsigned comment added by 76.203.38.243 (talk) 23:51, 12 September 2008 (UTC)

The Basic Central Idea First![edit]

The article is good for somebody who knows the basic idea first. Some of the links at the article's end are especially good for the person already familiar with the basic concept. But this article virtually leaves out the fundamental central idea and leaves the complete novice out of the explanatory process. Moreover, by focusing on applications first and getting into technical issues, the concept is lost -- the proverbial have no idea where the forest is because I'm examining all the individual trees and leaves.

Good pedagogy should make good concrete definitions and use an analogy if one is available that is itself very much concrete and one that the learner is likely to know quite well. Both of these I can do.

The central concept of dithering is to "ask the same question" repeatedly or measure the same output repeatedly on the exact same topic or exact same signal (or measure so quickly that the signal hadn't had the chance to change). However, before getting the answer to the question, or measuring the signal, one adds noise (random values much smaller than the signal). Then one says, "NOW tell me the answer once you added that random amount" (the random amount could be plus or negative). But this procedure is of no benefit unless you get to ask the question several times on the same topic, or measure the signal several times (quickly before it changes). One then collects all the answers and averages over the collection. This brings us to our oh-so-concrete analogy.

Pretend that a bank is not allowed to tell you over the phone your balance beyond rounding to the nearest dollar; let's say the policy is because the "cents" will confuse people or take more time for the talking computer. You ask "what's my balance?" and are told "$173". No matter how many times you ask, you will get the answer "$173". Now suppose you said instead, "add 20 cents to my balance, now what's my balance?" The answer still comes back "$173". Again though, no matter how many times you ask "add 20 cents to my real balance, now tell me the result", the answer will be "$173" every time. But what if you are allowed to ask your balance twelve times and each time you make a NEW (or potentially new) question: "add _____ cents, now what's my balance?". For the "_____" you use any number of cents from -50 (negative fifty) to +50 (positive 50) randomly. When the response comes back (we're saying bank ROUNDS to nearest dollar, that's why the ± 50¢) you record the various $173 and $174 answers to the twelve questions. Add them up and divide by twelve. That average will get you close to the balance in dollars and cents.

Dithering in the central concept as described above is not that mysterious at all. Just think: in my example, had I said "add a penny, now what's my balance?; add two cents, now what's my balance?; add three cents, now what's my balance?; add four cents, now what's my balance?..." and so on up to 100 questions (99 would suffice and if bank rounded you could either fix afterward or ask from -50 to +49 instead of from 0 to 99), you would know your exact true balance amount. If limited to say sixteen questions though (16 times oversampling), you cannot step thru every penny. A uniform random variable between -50 and +50 could be used as the "noise" in cents to add to the true balance before you get the "quantized" balance to the whole dollar only, but you'd add the 16 whole dollar amounts given as the answeres, divide by 16 and be very close to the right number of cents for your real balance. This is the central concept of fixing quantization error by dithering.199.196.144.13 (talk) 00:15, 4 November 2008 (UTC)


Dictionary Snippets[edit]

I removed screen shots of old dictionary definitions of "dither", but they were added back. I removed them for several reasons. First and foremost, Wikipedia is not a dictionary; etymology is not the main goal of the article, and these images are very prominently displayed at the top. Second, the definition listed in those images is unrelated to what the article is about, which is the modern signal-processing definition of dithering. Third, the images are distracting because they may appear, at first, to illustrate what dithering is. And finally, the images just contain text; we could just transcribe them into the article (at which point they would be mostly off-topic anyway). Rm999 (talk) 23:52, 5 July 2009 (UTC)

Obviously these would be inappropriate in a dictionary; but as you note, this is not a dictionary. While etymology is not the main goal, and not every topic needs to include discussion of the etymology of its name, dither as used in the sense of this article is a word whose etymology has actually been discussed a non-trivial amount in sources in the relevant technical field; so it's fair game. The point of these discussions is that the etymology is NOT unrelated to the modern signal processing use, and it clarifies what that relationship is. I personally like the dictionary snippets as they give a nice visual way to see how the word has been regarded over time, going back hundreds of years. For things in that time frame, public-domain book page images are very effective, more so than just copying text, in my opinion. Dicklyon (talk) 04:25, 6 July 2009 (UTC)
I think we'll need a third opinion, I don't think you addressed my points. I find these images inappropriate; the article states that the first applications of dithering came after WWII, so a definition from 1788 is obviously unrelated. Also, you cast off my argument that this is not a dictionary, so why do we need definitions? Rm999 (talk) 06:22, 6 July 2009 (UTC)

Third opinion here: I tend to think the pictures are not appropriate here and basically agree with Rm999's arguments above; however, I also think it makes sense to include some historical discussion of the word, since it is an old word with a definition which has changed significantly --- and, in fact, the old definition is clearly the one which inspired the modern technical use. I think the best solution here would be to add some text in the section marked "origins" which is basically a transcription of what is currently in the pictures. Deville (Talk) 00:52, 8 July 2009 (UTC)

Um, oh dear, I think I've just stumbled into the party. I have just deleted the second dictionary image (didder rather than dither). I agree with Rm999 that they distract from the main point of the article, although must admit I left one image in place because I like the visual! Also problematic, I think, is the large block quote from Ken Pohlmann. What it says is interesting, but we should rephrase and reference, rather than quote verbatim. Dickylon - if you think we need more discussion then feel free to revert my edit, but I think we're heading towards consensus. Sorry all for bumbling in without checking history/talk! GyroMagician (talk) 22:50, 27 October 2009 (UTC)
And I reverted before seeing your comment. As my summary says, I find it interesting to see the evolution of terminology, form the Middle English didderen that Pohlmann mentions, through the forms in the early and late 18th century dictionaries. That's just me, though. Dicklyon (talk) 23:05, 27 October 2009 (UTC)
Keep evolution history of didder . I am sure it was used in naval guns before ww2 but have not found a ref on line. I have used some dither in computer programs . Wdl1961 (talk) 23:38, 27 October 2009 (UTC)
But the evolution of the word has got nothing to do with the article. I think a direct link can be made (as the Pohlmann quote shows) from dither as in shake to dither as deliberately injected noise. But we don't need to go back earlier than that - we're talking WWII, not 18th Century! GyroMagician (talk) 09:00, 28 October 2009 (UTC)
Personally, I think the etymology of modern terminology provides an interesting insight into the related thinking over the ages. Nothing wrong with including some concrete connection to the evolution of the term through the 18th c. I also find it interesting that it's treated as a "provincialism" of Yorkshire, even in it's modern form in late 18th c; not worth talking about, but OK for a figure and caption. Dicklyon (talk) 15:29, 28 October 2009 (UTC)
I think that the main point of this article should be about the technical aspects of dithering, not the etymology, yes we can have an image (singular) of a dictionary clipping but the first image should be relevant to dithering itself, not the origins of the word. --Blacklemon67 (talk) 19:57, 3 July 2011 (UTC)

I think it is tremendously silly to include what amounts to a copy-paste of a dictionary entry in an encyclopedic article. Following the reasoning that has been given above, we could include such images in every single article on Wikipedia! It's redundant and certainly does not belong in the lede:

Lead images should be images that are natural and appropriate visual representations of the topic; they not only should be illustrating the topic specifically, but should also be the type of image that is used for similar purposes in high-quality reference works, and therefore what our readers will expect to see.

--90.184.154.70 (talk) 14:48, 6 July 2012 (UTC)

and other errors correlated to the main signal[edit]

""Dither is an intentionally applied form of noise used to randomize quantization error, [ and other errors correlated to the main signal] , preventing large-scale patterns such as "banding" (stepwise rendering of smooth gradations in brightness or hue) in images"" it does not seem to belong there. pls discuss. Wdl1961 (talk) 15:51, 28 October 2009 (UTC)

Sounds plausible, but unclear what it refers to. GyroMagician should tell us; and where he got it. Dicklyon (talk) 18:48, 28 October 2009 (UTC)

Sound files need explanation[edit]

The two sample sound files are an excellent addition but need more explanatory text. Has dithering been added to the second sample? If so, what kind of dithering? It would be ideal if there were three samples: 16 bit original, 6 bit without dithering, 6 bit with dithering. Ross Fraser (talk) 21:32, 21 July 2010 (UTC)

Strange Choice of Image For Intro Paragraph?[edit]

I find it a little odd that the first few images (most annoyingly the first image) is a picture of an entry in a dictionary defining the word 'dither'. Considering this article seems to be more focused on electronic dithering itself rather than the origins of the word ('dither'), in my mind it makes more sense to start the article off with an example of image dithering, and under that an ogg clip containing an example of audio dithering. LiamSP (talk) 03:24, 27 December 2010 (UTC)

Good idea; I put that old dictionary image because there wasn't much else. Make one? Dicklyon (talk) 05:27, 27 December 2010 (UTC)

Removal of original research[edit]

I removed mention of Riemersma (Hilbert-Peano) and Scolorq dithering. Riemersma dithering is either a joke or a disgrace for dithering algorithm designers. It gives pathetic results, performs irregularly depending on the image dimensions, offers no demonstrated performance gain and breaks cache efficiency. Scolorq is original research that hasn't been quoted in reliable papers as far as I know.

Also, I removed mention of the Stevenson-Arce dithering. The person quoting its "large matrix", the person who implemented it, and the person who generated the image apparently did not understand what they were talking about. Stevenson-Arce is designed to work on hexagonal arrays and will obviously give ugly results on regular square pixel images.

Finally, none of the statue pictures were dithered using gamma correction and are thus all wrong, but I understand it would be inconvenient to remove them all. At least the worst ones are gone. Sam Hocevar (talk) 12:35, 23 March 2011 (UTC)


I disagree about the comment about Riemersma dithering, though I do not know why it was made the default method in Imagemagick. But I strongly agree about the point regarding gamma that you made, and to that effect, I rendered a new set of images, below. (Not embedded, because I couldn't figure out how to do that in Wikipedia without uploading them, which I did not do because it's pointless to upload them if someone deems them unacceptable.) Since you seem to have strong opinions regarding the matter, I'll leave it up to you to either use or to not use them. I used gamma 2.0, and did so with animmerger, software I have created myself. Since it does nothing special but use well known algorithms, I don't think using my custom software counts as original research, but I'll leave it to the wikipedia quality control enthusiasists (for a lack of better term) to decide what's what and not. Only thing is that the Bayer version was created by a different algorithm (Yliluoma-2) that only happens to use a Bayer 16x16 ordered dithering matrix, as I did not have at hand a program that uses genuine ordered dithering with gamma support. Bisqwit (talk) 10:32, 24 May 2011 (UTC)

Floyd-Steinberg Jarvis-Judice-Ninke Stucki Burkes Sierra-3
http://bisqwit.iki.fi/kala/mich-floyd.png http://bisqwit.iki.fi/kala/mich-jjn.png http://bisqwit.iki.fi/kala/mich-stucki.png http://bisqwit.iki.fi/kala/mich-burkes.png http://bisqwit.iki.fi/kala/mich-s3.png
Sierra-2 Sierra-2-4A Stevenson-Arce Atkinson Bayer
http://bisqwit.iki.fi/kala/mich-s2.png http://bisqwit.iki.fi/kala/mich-s24a.png http://bisqwit.iki.fi/kala/mich-sa.png http://bisqwit.iki.fi/kala/mich-atkinson.png http://bisqwit.iki.fi/kala/mich-bayer.png

Audio Spectra wrong[edit]

Sorry, but the Audio spectrum is wrong, if the 500 Hz sine would be correctly dithered, no harmonics will be seen. Nothing. Only the added noise will remain. — Preceding unsigned comment added by 91.51.96.47 (talk) 16:51, 21 July 2012 (UTC)