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Saturation in RGB space is wrong[edit]

The first formula gives sqrt(2/3) for r=1,g=0,b=0 -- not 1 as one would expect. It can be reduced to sqrt(2/3*(rr+gg+bb-rg-rb-bg)). Note that by using this formula yellow, cyan and magenta are never fully saturated. They all have values of sqrt(2/3). It appears the intent was to give the distance from the 0,0,0 to 1,1,1 line, which would be sqrt(2*(rr+gg+bb-rg-rb-bg)). Normalizing this yields sqrt(rr+gg+bb-rg-rb-bg), and fully saturated red, green, blue, yellow, cyan and magenta all return 1. Both pure white (1,1,1) and pure black (0,0,0) return 0.

In any case the second formula of (max(r,g,b)-min(r,g,b))/3(R+G+B) is what all software I have ever seen uses. Red, green, and blue have a saturation value of 1/3. Yellow, cyan and magenta have a saturation value of 1/6. Again, white and black both have a saturation value of 0.

—Preceding unsigned comment added by Spitzak (talkcontribs) but heavily modified by Wm 04:37, 4 September 2007 (UTC), which he shouldn't have done

Correct formula[edit]

If no values of R,G,B = 0, then saturation = Sqrt[(R-1)^2+(G-1)^2+(B-1)^2]/Sqrt[3]. This is the distance from white(RGB(1,1,1)).

If one value of R,G,B = 0, the problem becomes finding the distance to white in the relevent plane (e.g. if B=0, then saturation = Sqrt[(R-1)^2+(G-1)^2]/Sqrt[2]).

If two values are zero, then saturation equals the value present minus one.

Note that all values pass the test: Red, green, blue, yellow, cyan, magenta, and black all equal 1. White yields 0. This algorithm works because of the way we desaturate a specific color in RGB, namely, we manipulate only nonzero values. R,G,B values of zero mean that the corresponding primary is fully desaturated and will stay that way as we move toward the fully unsaturated RGB value of that particular color (white). In other words, if B=0, then moving R and G proportionally toward 0 desaturates yellow.

Wm 04:37, 4 September 2007 (UTC)

A "correct formula" without a source is worthless. This one is worthless anyway, since it's so discontinuous at the gamut edges. Dicklyon 05:31, 4 September 2007 (UTC)

Correct formula, part 2[edit]

I'm getting a little frustrated by Wiki.

Anyway, the source is in the derivation above. It uses the following three definitions of saturation, which actually agree. Give me some time and I'll find in Wiki where the three definitions are actually equivalent:

1. Vividness of hue; degree of difference from a gray of the same lightness or brightness. Also called intensity.

2. The vividness of a color's hue. Saturation measures the degree to which a color differs from a gray of the same darkness or lightness.

3. In optics, the degree which colors of the same wavelength are differentiated from one another on the basis of purity which correlates with the amount of white present, such as red from pink.

Here's some Mathematica code, if you're interested:

f3[r_, g_, b_] := Module[{num = 3, ret = 0, r1 = r, g1 = g, b1 = b},

     num = num - If[r == 0, 1, 0];
     If[r == 0, r1 = 1];
     num = num - If[g == 0, 1, 0];
     If[g == 0, g1 = 1];
     num = num - If[b == 0, 1, 0];
     If[b == 0, b1 = 1];
     If[num == 0, Return[1],
       Return[Sqrt[(r1 - 1)^2 + (g1 - 1)^2 + (b1 - 1)^2]/Sqrt[num]]

Anyway, this is consistent with the definition of saturation. If it's not useful, well, sorry. Anything else needs to be called something other than saturation.

Sorry about the trouble I've caused. This is my first experience with Wiki.

Wm 08:04, 4 September 2007 (UTC)

A source is an independent book or article, not your derivation. Without a citation, the information cannot be persuasive. The reason I say it's worthless is that it gives very different answers for the saturation of for example (1,.5,epsilon) and (1,.5,0), for epsilon near zero, which get saturations of approximately .5/Sqrt[3] and .5/Sqrt[2] respectively. A usable formula would not have such discontinuities at gamut edges. I have a hard time interpreting this as anything but your own WP:OR. Dicklyon 15:22, 4 September 2007 (UTC)

moved to colorfulness[edit]

I've moved this article to "colorfulness", and will try in the next few days to put some better explanations up of the similarities and differences between saturation, chroma, and colorfulness. Maybe it would be worth emailing Mark Fairchild to ask for advice/diagrams/etc. This article could really generally use some better sourcing. --jacobolus (t) 20:50, 19 September 2007 (UTC)

What is the justification for this? Of the three terms (colorfulness, chroma, saturation), you used the least known. Google gives their ratios as 46:5100:27000. I myself had never heard of the term and I thought I knew something about color science. What do other people think?--Adoniscik (talk) 16:21, 18 January 2008 (UTC)
Well, I put it here for a couple of reasons. First, chroma and saturation are both frequently used very sloppily, for a wide variety of (not-so-) similar concepts, by different authors and different models (for instance, HSL, HSV, and CIECAM02 have 3 wildly different understandings of saturation). These are terms with centuries of contradictory baggage hanging from them. Second, I expect is for precisely this reason that the CIECAM02 model chooses the word colorfulness, rather than chroma, to describe the most “obvious” measure of color intensity. Ideally written, this article would more fully explain what colorfulness means in that context. Third, the general meaning of the word colorfulness is immediately obvious to readers, so those who are redirected from one of the other two is least disoriented, in my opinion, by leaving “colorfulness” as the title. Finally, both saturation and chroma are terms in wide use outside color science, and as their main articles are disambiguation pages, with the color science titles requiring parenthetical disambiguation (“saturation (color theory)” or whatever). This title lacks that aesthetic flaw. --jacobolus (t) 16:48, 18 January 2008 (UTC)
I think the main problem is not the name, but that the article is not currently well organized or comprehensive enough, to explain the full range of meanings of all these terms as used in various contexts. Once that is done, I think the title will be fine. To be honest, I don't care that strongly about it; any reasonably accurate title is fine, and I don't think it's an issue worth arguing over too much. Improving the article should be a much higher priority. --jacobolus (t) 16:59, 18 January 2008 (UTC)
My curiosity piqued, I looked it up in "Introduction to Color Imaging Science": Colorfulness is an absolute measure of hue intensity which increases with illumination level. This does not appear to agree with our definition, which claims it is a color measure relative to gray.--Adoniscik (talk) 17:10, 18 January 2008 (UTC)
I think we should email Mark Fairchild for advice, seeing as he is both the foremost expert, and very open to answering questions. But I don't have time to do that today. --jacobolus (t) 17:20, 18 January 2008 (UTC)

Excitation Purity[edit]

There is no explanation of the qmax function in the above section. It would be great if someone that knows how to compute this would add either the formula or a reference. I tried google and didn't find anything. Dhoerl 13:26, 5 October 2007 (UTC)

I provided an explanation and uploaded an image, but it looked ugly so I did not embed it. Can anybody send me a message to tell me why the colors spill outside the triangle? The image I derived it from just does not look the same in Inkscape as it does on the Web. Or you can upload a better picture yourself. --Adoniscik (talk) 22:44, 30 January 2008 (UTC)
tell me why the colors spill outside the triangle? — because SVG implementations are universally buggy and incomplete, and the bugs/missing parts of Inkscape's version differ from those in other implementations. --jacobolus (t) 01:02, 31 January 2008 (UTC)
So much for vector graphics hehe. Is Illustrator any better? If not I will just do it in PNG. --Adoniscik (talk) 02:14, 31 January 2008 (UTC)

Saturation is not lightness[edit]

According to the hsl/hsv-system the graphic can't be write. By only(!) reducing saturation you will go from red to white, not black. What the graphic shows is a reduction of lightness. —Preceding unsigned comment added by DeeJay Antoine (talkcontribs) 21:29, 5 June 2009 (UTC)

Terrible lede[edit]

Starting with sentence 2, the lede says:

"Colorfulness is the difference between a color against gray. Chroma is the colorfulness relative to the brightness of another color which appears white under similar viewing conditions. Saturation is the colorfulness of a color relative to its own brightness."

Huh?? (1) Colorfulness is "the difference between a color against gray"?? Is this supposed to mean the difference between a color and gray? -- But what would that mean? Does "gray" here refer to relatively bright gray (near white), or to relatively dark gray (near black), or to some mid-gray? Is "difference between" supposed to have some quantitative meaning? (2) According the the above quote from the article, "chroma" is 'the difference between a color against gray' 'relative to the brightness of another color....' "The difference between...relative to..." makes no sense. (3) According to the above, saturation is 'the difference between a color against gray' 'relative to [the color's] own brightness'. Again, makes no sense. And saturation has nothing to do with brightness -- it refers to (a transformation of) the ratio of a single-frequency hue to an equal-intensity mixture of all frequencies, that will generate the given color.

The first sentence of the lede says that the title term "colorfulness" occurs "[i]n colorimetry and color theory". Yet I can't find the word "colorfulness" in either one of those articles.

Hypothesis: The word "colorfulness" does not in fact appear in colorimetry or in color theory. The term was just made up by someone who wrote this article.

Therefore I suggest two things:

  • This article should be moved to Saturation (color theory). I know there has been movement back in forth in the past between these titles, with admonitions to discuss before moving. The reason people suggest moving it to saturation is that that's a real term.
  • Whether or not the article is moved, could someone who knows precisely what is meant in the literature by the distinctions among saturation, chroma, and (if it exists) colorfulness, please clarify the intro? Thanks. Duoduoduo (talk) 16:11, 10 June 2011 (UTC)

I was surprised to be redirected to an article titled "Colorfulness" when I looked up "saturation". "Colorfulness" is an awkward word used mainly, I suspect, by color scientists, when speaking about color science to a lay audience. It is the type of word that usually is preceded by a pause, and then followed by the phrase "if you will", or "for want of a better term". It is useful only as a "word" that everyone knows the meaning of (because it is made up of a well known and often used adjective, "colorful", turned into a noun by adding "ness" to it). Without it, it would be impossible to define saturation, chroma, and other terms in color science. It is not suitable as the title of an encyclopedia article, any more than "hotness" would be a suitable title for an article about heat. (talk) 13:39, 5 December 2011 (UTC)

Just to make that clear, „colorfulness“ is a well-defined technical term in colorimetry, just as (but different from) “chroma” and “saturation”. See Fairchild, Mark D. (2013). Color Appearance Models. Wiley-IS&T Series in Imaging Science and Technology (3 ed.). Hoboken: John Wiley & Sons. ISBN 978-1-119-96703-3.  --Uli Zappe (talk) 17:26, 15 April 2015 (UTC)

Formula Problem[edit]

There's a problem with the saturation formula right after reference 4. According to that formula, to be fully saturated, Luminance must equal zero. That can't be right. (talk) 18:52, 19 November 2014 (UTC)


The article was moved to Saturation (color theory) without discussion (that's where it came from a year ago if memory serves), and then moved back again (thanks for moving it back, Jacobolus). Let's don't repeat that. If there's a move desired, make a proposal here and we can talk about it. Dicklyon (talk) 05:32, 22 August 2008 (UTC)

Hi, Dicklyon. Just came across this interesting article during a random walk.
I'd like to propose a move for this article to "Colo[u]r intensity". As currently written, the article discusses "colourfulness", "chroma" and "saturation" as related but distinct concepts. It therefore seems wrong to name the article after just one of these concepts. "Colour intensity" on the other hand, seems to be a good catch all term. In the long run, assuming the article is correct that these three concepts are different, I see this article being split.
Of course, I came here to learn about colour theory, not to teach it. If I am wrong (because the article I've just read is misleading me) that these three concepts are different, then the article might need rewriting instead! GDallimore (Talk) 11:10, 2 February 2009 (UTC)
Where's this article you refer to? My impression is that "color intensity" is a relatively little-used term for this concept. Dicklyon (talk) 18:44, 2 February 2009 (UTC)
First sentence of this one "colorfulness, chroma, and saturation are related but distinct concepts referring to the perceived intensity of a specific color." Intensity being the only word used as a catch-all for all three terms. GDallimore (Talk) 10:17, 3 February 2009 (UTC)

Requested move December 2011[edit]

The following discussion is an archived discussion of the proposal. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

The result of the proposal was no move. Turns out that no one seems very interested in this requested move. I suggest that if another editor wants to move the page they start a fresh RM as the initial date of this request was back in December 2011, and this request is stale. -- PBS (talk) 14:20, 15 September 2012 (UTC)

ColorfulnessSaturation (color theory) – Request made by user:Trevj on 28 December 2011 using template:movenotice on the article page. First reason given "No consensus for previous move to Colorfulness, which seems to have proved controversial" -- PBS (talk) 14:43, 7 September 2012 (UTC)

-- Trevj (talk) 14:29, 28 December 2011 (UTC)
  • Comment – I'm kind of neutral on these two marginal titles. I think "Color saturation" might be better. Dicklyon (talk) 19:42, 7 September 2012 (UTC)
  • Comment I don’t understand your reasons. (1) this doesn’t seem to be an argument/reason – maybe you mean something more specific? (2) HSL and HSV are entirely non-scientific models created by computer programmers with poor understanding of color science, to match the constraints of 1970s hardware; the dimensions they call “saturation” are substantially unrelated to any human-perceived attribute, and entirely different from each-other; the two should not be taken as inspiration for anything. (3) Not sure what you’re saying. Maybe you think the text should be expanded? (4) Saturation refers to reflective objects, mostly, because it is a quantity which remains relatively unchanged under different lighting, but not exclusively; this also doesn’t seem like a reason or argument, but just a side note. Can you explain why you think Saturation (color theory) is a better title? –jacobolus (t) 20:00, 7 September 2012 (UTC)
By the way, I’ve been meaning to expand this article for years, but just haven’t gotten around to it. Sorry ’bout that. –jacobolus (t) 20:02, 7 September 2012 (UTC)
Sorry but I only have a vague recollection now of even placing this suggestion. Thanks PBS for the reminder, after correctly reformatting the proposal. Anyway, I think my rationale was that there didn't seem to be previous consensus (and consensus can change). Just looking at the article again now I see that chroma and saturation have their own headings and I think I was confused by the lack of further details for colorfulness itself. However, I'm far from being an expert (or even a layperson) in this area and so don't have overly strong feelings about the issue. Thanks for reading. -- Trevj (talk) 11:57, 11 September 2012 (UTC)
The above discussion is preserved as an archive of the proposal. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Assessment comment[edit]

The comment(s) below were originally left at Talk:Colorfulness/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

merge with chromaticity

Last edited at 01:51, 1 January 2012 (UTC). Substituted at 12:04, 29 April 2016 (UTC)