## Wednesday, October 10, 2012

### How many colors are there - Addendum

I am reminded today of a line from the song "Alice's Restaurant Masacree" by Arlo Guthrie. He and his friends were off to the garbage dump on Thanksgiving day, when they found the dump closed. Here Arlo takes over the narrative

... we drove off into the sunset looking for another place to put the garbage. We didn't find one. Until we came to a side road, and off the side of the side road there was another fifteen foot cliff and at the bottom of the cliff there was another pile of garbage. And we decided that one big pile is better than two little piles, and rather than bring that one up we decided to throw our's down.

I am quite happy about all the responses I have had to my post on counting the number of colors, ranging from the highly technical to the downright flippant. These responses were posted in a variety of places, and I have decided that one big list of comments is better than five different small lists of comments.

Here's how others answered the question of how many colors there are.

My co-worker Parker Will, who always cracks me up, sent me a link to one person's very imaginative answer. 512 cubic inches. This book simply contains all the colors that are fit to print. It reminds me of a book that may still be in my basement... a book which is a times table from 1 to 999 by 1 to 999.

The RGB Colorspace Atlas

Nancy Eagan ...as much as there is sunlight ..?

Wei Ji • I think the ultimate question is: how to define "a" colour? the unit that enables us to count how many colours are there.

[Me - Excellent point!]

Mark Taylor • Very thoughtful article. You missed "4" - which is the answer an inkjet printer would give you ;-)

By the way I've also wondered about what the limits of CIELAB space were, and just assumed as a self-taught color scientist I hadn't yet read the right book!

Gary FieldResearch on the number of colors issue usually starts with reference to the Dorothy Nickerson and Sidney Newhall paper of 1943 (JOSA, pp. 419-422). They conclude that there are about 7,500,000 surface colors at "supraliminal" viewing conditions, and 1,875,000 colors when viewing conditions approximate those used for color matching work.

Some experimental work of mine (1996 TAGA Proceedings, pp. 14-25) from a printing industry perspective suggested that the offset lithographic process could produce about 1,200,000 colors, while the gravure process could achieve about 1,500,000. A later estimate by Andreas Paul of FOGRA was about 1,000,000 colors for 4-color offset lithography, and around 1,400,000 for seven-color lithography.

Mike Pointer and Geoff Attridge concluded that there were about 2,280,000 discernible colors in their 1998 CR&A article (pp. 52-54).

A "color" could be said to exist when an observer indicates that the perceived new sensation differs from a previous sensation. The "16.7 million colors" touted for color monitors means, in my opinion, that there are 16.7 million different combinations of RGB radiation, but because many of these combinations are visually identical, they are not distinct colors from a human perspective. The estimates reported in previous paragraphs are based upon color difference equations of one type or other. Different equations will produce different results, and the illumination level exerts a powerful influence upon the visual color discrimination task.

A TAGA essay of mine, with more detail and some extra references, entitled "The number of printable colors" appears in a collection published under the title of "Color Essentials - Volume 2" that was published by the Printing Industries of America.

http://store.piworld.com/store/p/120-Color-Essentials-Volume-2.aspx

[Me - I am honored to have you comment, Gary. I have one of your books in my bookcase! I have read through your paper, Gary. If I understand correctly, the number is more or less based on the original deltaE formula? Better estimates could be arrived at through DE2000, although this would be a lot of work. I agree with your assessment of the 16.7 million number.]

David Albrecht - There are 4 million colors, give or take a few. This is based on the observations and surveys done over the years for a trained human eye and what it can observe. As Gary points out, a monitor may be able to display more combinations of RGB, but we will only be able to see about 1/4 of the combinations. And according to the rules of observation, if we can't observe them, they do not exist. The "if a tree falls in the woods" concept.

From this 4M or so we drop to untrained human eye, to "compromised" human eye (color blind/deficient), printable colors, etc. It's still amazing that we can reproduce those 1M colors with just 4!

[Me - Nice to have a comment from an old friend.  If a color falls in the woods, will someone walk by and return it to the box?]

Gary Field • Adding to David's comment, color discrimination capability for those with normal color vision peaks between the late teens and early 20s. This brings to mind Keith McLaren's observation concerning "correct" color vision; it is "... always that of the observer having the power to accept the batch as a good commercial match".

So, the young do indeed have a more colorful world, but the older people who usually wield the 'OK' stamp of approval, establish the color boundaries.

Alessandro Rizzi • Let me suggest an interesting paper about the impossibility of counting the number of colors:
"Why we don’t know how many colors there are"
by Ján Morovic, Vien Cheung, and Peter Morovic
presented at CGIV 2012 conference this year
http://www.slideshare.net/jmorovic/why-we-dont-know-how-many-colors-there-are

Gary Field • @Alessandro: Thank you for that link to the CGIV paper about why we don't know how many colors there are; I found the authors' slide presentation online. Except for very constrained conditions (observer, viewing source; or, if computed, the formula), a definitive, universal number is not likely. I will be happy when claims of "billions" or "a few thousand" colors no longer appear in print (yes, a low bar!).

Arnaud Fabre • Everybody agrees on the fact that the conditions to compute the number of colors are :
- a well defined set of observation conditions
- a perceptually homogeneous colorimetric space
I did not read the paper of CGIV, but I assume that it only ask how we can do serious science with at the basis a vision test applied to 30 persons more or less. And of course Lab is not so perceptually homogeneous, and even with the dE2000 patch, the parameters and the threshold are not so obvious to set.
But it is the only thing we have, right ? and it did not work so bad most of the time. So the basic idea is more :
"how can we compute the number of color that are available with those assumptions ?"

Paul Lindström • John – on DE2000 – What is commonly repeated is that a DE of 1 when using the DE Lab formula from 1976, is a reasonable threshold for where humans with reasonable colour vision see a difference between hue shades (colours). When using DE2000 my guess is that the threshold should be somewhere be between 0.5 and 0.75. Might not sound much of a difference, but using 0.5 would double the number of colours (if my layman use of math is correct).

[Me - Math Guy time... if 0.5 DE were to be used instead of 1.0 DE, the number of colors would go up by a factor of 8, since there would be twice as many in all three directions.]

Ryan Stanley • John,

I noticed that in this question vs. your blog you phrase the question two ways:
1: How many colors are there?
2: How many colors are in your rainbow?
The way you interpret those questions can give different answers. Further I think this is where confusion in the industry comes; from laymen to scientist.
I say this because the first question is more scientific; how many colors are there…actually?
For this discussion, let’s look at the “reflectance curve” of light or what “makes” our color as a guide.
If we use what has been defined as the “visible spectrum” of electromagnetic radiation, we find ourselves roughly between 380nm-700nm. Over the years we’ve had spectrophotometers break this down for us with % reflectance across this band. Leaving out fluorescents for this exercise and saying that 0% reflectance is absolute Black (absence of light) and 100% is absolute White (all light). The earlier models commercially available could read every 20nm; now we have models widely available that ready every 10nm; newer models becoming available that can read every 5nm. But let’s just say every 1nm; for if there is a difference in reflectance then there is a difference in color (were not talking about perceivable color just yet).
That’s means from 380 to 700 we have 321 distinct points available for our reflectance curve across the visible spectrum.
Each point has the potential to reflect all light 100% or no light 0%, as well as all points in-between; leaving out decimals for simplicity’s sake (we should measure out to at least two however 000.00) that gives us at least 101 points to choose from.
So we find our % reflectance or “n” is the number of things to choose from, and we choose 321 of them or “r”. With order not being important, and repetition allowing, we have our formula for “how many colors are there?”:
(n+r-1)!/r!(n-1)!
The answer is striking, so I’ll give the short one: 7.83532204e+98
-This is roughly (we only used 0%-100% as whole values) how many colors are available in the visible spectrum for us “to be able” to perceive.

The next question is ambiguous; “how many color are in your rainbow”, or how I read it; how many colors can you see?
You showed a chromaticity diagram in your blog, with that as a reference;
The way humans perceive light can be compared to how we engineer color as well. We have rods, cones, and available “opsins” (light sensitive chemicals) in our eyes that allow us to perceive shades. This is inverse but still comparable to the Red, Green, and Blue LED’s that make up our computer monitors, or the CMYK pigments in our printers. In the diagram you show what we can see vs. what we can produce or what’s in or out of gamut.
Similar to how you mention “it is impossible to build a computer monitor with three fixed lights that will display all possible colors” , it is additionally impossible for the opsins in our eyes to “perceive” all colors that are available to “receive”.
So depending on who you are, how old you are, your gender, race, which eye you use and even what species you are we all “perceive” color differently. This is what makes color so hotly debated and unique! There are even tetrachromats, or women who can see FOUR distinct ranges of color; making their world much more rich I can imagine.
This is the number where no one really has the right answer and as you state in your blog: “Pick a number between 3 and 16,777,216” .

I would be curious to know if anyone has performed a study or has information on the ability of the opsins to receive light at various levels?
This would allow us to create a similar chromaticity diagram for what we “should” be able to perceive vs. what is available to receive.
Interesting topic; I look forward to other responses.
-Ryan Stanley

[Me - I am going to disagree a little bit, Ryan, on a semantic basis, with your scientific answer. It comes down to what the word "color" means. I think the definition that you have given is something like "unique spectral stimulus". If you go down this path, then I think the number you should come up with is a zillion to the zillionth power, since each of the zillion photons received by the eye could have any of the zillion available wavelengths. But, I don't think it's fair to call each unique spectra a "color". Color does not occur at least until the photons enter the eye. This is, of course, semantics.]

Amrit Bindra • There are as many colors as one could perceive or as a community we all could jointly perceive.

Gary Reif • This is all a reminder that we live in an analog world.

George Dubois If you go by the L,a*,b* color sphere where virtually all colors go from a= -60 to +60 and b=-60 to +60 and L goes from 0 to 100 then you have a color space of 1.13 E 6 (1,130,000). If taking a Delta E for most people of 1.0 being distinguishable then there are 1.13 million colors. If you prefer to say that good people can see to .5 Delta E then the number would be 4.5 m.
[Me - This is a quite reasonable "back of the napkin" estimation. You have assumed a cylinder with average radius of 60... ehhh... sounds good. The choice between cube, cylinder and ellipsoid would give a range between 0.7 and 1.4 million. The assumption that 1 deltaE (or 0.5 deltaE) is the limit of human perceptibility is a bit more iffy, I think. A change of 5 delta E in the chroma of bright yellow is barely perceptible, whereas a change od 0.5 deltaE near gray is barely perceptible.]

Ryan Stanley As with all topics concerning color or colour, it can be debated to include a greater portion of the UV and IR portion of the spectrum (why i stated roughly) as 380-700 is more universally accepted. To your point however, if we expand it out further and add 20nm on each end, we only find ourselves with an even larger number of potential colors available to receive.
In reference to "how many NM are there between viable differences" I would ask;
what is the definition of viable in this case, or what are you looking to achieve?
Further to the point, "do we get too complex abou how we look at colour?" And bringing both topics together, I would say;

Color and the science of color or more succinctly the interaction between matter and radiated energy is so much more than just what we can see. From instruments that can tell us what metals we have in seconds to unlocking the composition of the atmosphere on a planet in another solar system. We've even been able to identify the expanse of the universe through Doppler or the red/blue shift of distant stars. All through our understanding of "Light".
Armed with the knowledge of color, we begin to use it and shine that light back on the mysteries of the universe. Only through a complex walk can we arrive at simplicities door.
To quote Albert Einstein:
"A man should look for what is, and not for what he thinks should be",
"The most beautiful thing we can experience is the mysterious. It is the source of all true art and science."

Interesting topic; I look forward to other responses.
-Ryan Stanley

[Me - Here are the other responses, Ryan! Thanks for the suggestion.]

John Wells But if you are colour blind, how many colours can you see? I have seen colours matched to less than 0.5 dE and would say they do not match! The colour matchers eye is critical. The analog version is merely a tool to aid those with less critical vision and to overcome the human foibles. For instance put two similar colours side by side, after about 30 seconds the brain, which does not like differences, will try and merge the colours, hence some colour matches are worse than others. The human eye is king (So long as you are not colour blind) and all following analog based matchings, should be based on the total conditions observed at the time the eye passed the colour.

[Me - If someone is colorblind, the number drops appreciably, since color space is two dimensional or one dimensional. As for discerning changes of 0.5 deltaE, that points out a problem with deltaE 76.]
[Me - This one below was my favorite. It was posted on the blog itself. Anyone who knew me in my previous incarnation as John the Revelator knows that music has always been a big part of my life.]

Steve Fowler
we need look no further than Joseph and the amazing technicolor dreamcoat.
the answer is clearly 29 (or maybe 27, or 26 if you're an art teacher).
red and yellow and green and brown and
Scarlet and black and ochre and peach
And ruby and olive and violet and fawn
And lilac and gold and chocolate and mauve
And cream and crimson and silver and rose
And azure and lemon and russet and grey
And purple and white and pink and orange
And blue
Newton, phah...Tim Rice and Andrew Lloyd Webber have the answers (except for silver and gold.....oh yeah, and black)

#### 1 comment:

1. When you talk about Color Blindness you need to specify what type of color blindness you are referring to. There are types of color blindness that are tri-chromatic except the sensitivity of the cones are shifted or otherwise significantly differnt than the standard observer. In this case the dimensionality is still 3.