The color of a bunch of dots, Part 5

It's about time!  People have been banging on my door, tackling me in parking lots, and calling me at 3:00 AM to demand that I finish my series of blog posts about halftones. Well, maybe the part about being tackled in the parking lot is a bit of a hyperbole. But, there were two comments on the previous blog post in this series.

Picture taken from out of my window

In the first four parts of this series, I described four different mathematical models that allow one to estimate the color of a halftone.

1. Murray-Davies equation

The Murray-Davies equation estimates the spectrum of a halftone from three pieces of information: the spectra of the paper and of the solid, and the percentage of area that is covered by the halftone. The model assumes that the halftone area has either the reflectance of the solid, or the reflectance of the paper, and that the ratio between them is the halftone area on the plate or in the digital file.

2. Murray-Davies equation with dot gain correction

In this model, the straight Murray-Davies equation is augmented with a further assumption - that the halftone dots grew somewhere between the plate (or file) and the substrate. Note that I didn't have to change much in the equation. I just changed Ain (the input dot area in the file) to Aout, which is the effective dot area on the substrate.

3. Yule-Nielsen equation

The Yule-Nielsen equation assumes that there is a leakage of color from the halftone dots to the substrate between the dots. This acts to boost the color beyond what the Murray-Davies formula predicts. There is a parameter, called the n-factor, which is used to adjust the amount of leakage. In the equation below, n is used to characterize the richness of the halftone.

4. Noffke-Seymour

The Noffke-Seymour equation assumes that the volume of ink is equal to the halftone area on the plate or in the digital file. That amount of ink is squished out to some greater or lesser degree. The ink film of the dots is smaller, but the dots cover more area. Beer's law is used to predict the reflectance of the dots. In the equation below, Aout is used to characterize the richness of the halftone.

Assessment of the equations

In part 3 of the series I pointed out that the two Murray-Davies formulas provide a poor prediction of the color of a halftone. (Parents, please cover your children's ears. I am about to spew some apostasy.) It is unfortunate, but Murray-Davies remains the predominant mindset. It has been enshrined even in ISO 12647-2, which provides us with curves for what the TVI should be, despite the fact that the predictions from this are just plain lousy. Yes, I said it. ISO 12647-2 promulgates a dumb idea.

OK, so maybe that's an over-statement? The idea of TVI is good in principle. Using Murray-Davies, you get one number from which to assess how rich the color of a halftone is. Having one number is great for process control. But there are much better alternatives: either equation 3 or 4. Either of these equations have a single parameter to express the richness at which a halftone is printing. The benefit is that they both provide a reasonably accurate estimate of the spectrum of that halftone. Given the spectra or paper and solid, along with one number to describe the richness, you can reconstruct the spectrum of the halftone.

Why does this matter?

Maybe it doesn't matter that we use TVI, which is based on a poor model of reality. Everything is working, right? Well... I would beg to differ.

You really think your TVI formula is working?

First problem: If I compute the TVI of AM and FM tone ramps, TVI would lead me to believe that a simple plate curve can make one look like the other. Or that I could make a magenta tone ramp printed offset look like a magenta tone ramp that was printed gravure or ink jet. Getting the proper TVI is a necessary, but not sufficient, condition to get a color match.

Second problem: If you compute TVI in one region of the spectrum, you won't necessarily get the same TVI from another region. This problem led to the SCHMOO initiative. (SCHMOO stands for Spot Color Halftone Metric Optimization Organization.)

Third problem: How do you compute the spectrum of a halftone? You can't accurately estimate the spectrum (or color) of a halftone using TVI and Murray-Davies.

Which is better?

So, the natural question is, which equation is more better? Yule-Nielsen or Noffke-Seymour?

First, I need to acknowledge my own affiliations. Many of you may be under the impression that my last name is "Math Guy". This is not quite correct. My middle name is "the Math Guy", and my last name is Seymour. Yes... the Seymour of the Noffke-Seymour equation.

Second, I will make a totally impartial statement which can be proved with algebra. At the extremes, the two equations (YN and NS) are identical. At the end of minimum richness, they both simplify to the Murray-Davies equation. At the other end (maximum richness) they both simplify to Beer's law.

Beer is my law

Both equations are based on verifiable assumptions about the underlying physics. Light spreads in the paper, and that causes halftones to be richer. Halftones dots squish out and that causes halftones to be richer. Which one is the predominant effect?

I will make another totally impartial statement. It doesn't really much matter which physical effect is larger. It has been demonstrated through looking at a bunch of data that numerically, the effects are very similar. In between the two extremes, the two equations act very similarly. I suppose some math guy could figger some way to figger just how close the two equations are. But, experience says they are close.

In short, it doesn't much matter which equation (YN or NS) is used. I prefer mine, of course, because. Just "because".

Call to action

What to do about this? To be honest, I don't know. But, the first step to recovery is a trip to the bookstore to buy a shelf full of self-help books. (While you are there, ask about my latest book, How I Recovered from My Addiction to Self-Help Books.)

Part of the problem is that Murray-Davies is such a wonderfully simple equation. You can easily solve it going forward. As it is written above, you can plug in the spectrum of the solid, the substrate and a dot area, and it will give you an estimate of the spectrum of that halftone. But (and here is the cool part) anyone who remembers some of their high school algebra can solve the Murray-Davies equation for the dot area. Plug in the three spectra (solid, substrate, and halftone) and you can solve for the apparent dot area. You can poke this into one cell of a spreadsheet even after a whole evening of experimenting with Beer's law.

This does not hold true for the YN or NS equations. :( These are both "trap door" equations. You can go one way easily, but going the other way requires a bunch more cells, maybe even a whole page. They both require an iterative approach to solving.

If only I knew a math guy who could figger this out!

The color of a bunch of dots, part 2

In the color of a bunch of dots, part 1, I focused on one simple equation for the prediction of the reflectance of a halftone, the Murray-Davies equation. This equation is reasonable and readily understood, but it does not do such a good job at predicting what happens when ink meets paper. The Murray-Davies  equation does such a poor job of predicting reflectance that the prediction error has become one of the most common standard process control parameters for printing.

Dot gain in the headlines

That comment is important enough to repeat. Please read this slowly, carefully articulating every word: The Murray-Davies  equation does such a poor job of predicting reflectance that the prediction error has become one of the most common standard process control parameters for printing. It is called "dot gain" by old pressmen, and "tone value increase" or "TVI" by the intellectual elite. Feel free to decide which group you belong to and use the appropriate phrase.

Of course, we knew one source of error in the Murray-Davies approximation. Halftone dots are bigger in real life than they were in the image file. Ink squishes out between the plate and the blanket and then again when it transfers from blanket to paper, so the dots on the paper are bigger [1]. To be fair to those using the Murray-Davies equation to compute TVI, the degree to which the dots spread is a valid control parameter indicative of how dots squish out.

But, to be fair to people who make brash, negative comments about the Murray-Davies equation (and then have the gall to repeat them in italics), how much the dots squish is only part of the prediction error.

Optical dot gain

The Murray-Davies equation was published in 1936. It was known at least by 1943 that it did not work well for halftone dots on paper. I quote from Yule: "Experimental results do not agree exactly with the theoretical relationships except for screen negatives and positives with sharp dots."

Enter John A.C. Yule and W. J. Neilsen. They presented a paper at the 1951 TAGA conference [2] entitled "The Penetration of Light into Paper and Its Effect on Halftone Reproduction", where they described another reason for the discrepancy. [3]

Yul Brynner, Leslie Nielsen, and Dodd Gayne
(from The King and I in the Cockpit) [4]

The Murray-Davies formula makes the assumption that light either hits a halftone dot or paper. Furthermore - and this is the critical part - that the dots of ink don't effect the color of the paper. Yule and Neilsen point out that this is just not the case. Anyone who says otherwise is itching for a fight.

The diagram below shows the Yule-Neilsen effect. When we look at a halftone, some of the light follows path #1. It passes through the ink once, reflects from inside the paper, and then exits for us to behold its marvelous hue. The ink acts like a filter, so two passes make it a richer color.

Some of the light, however, passes through the ink once and then scatters within the paper. This hapless light then exits from between halftone dots. Since it has only passed through the filter (the ink) once, it will not take on quite as rich a hue.

Dramatization of the  Yule-Neilsen effect

The next diagram illustrates what the result looks like. The paper between halftone dots takes on a richer hue as a result. The magnitude of the effect depends on a few factors. First, obviously upon the amount that the paper scatters light. This is related to the opacity of the paper. A paper that is translucent will tend to scatter light further, enhancing the Yule-Neilsen effect. 

Second, and perhaps not so obvious, is the screen ruling. If the dots are closer together, the light doesn't have to scatter as far to infuse the whole area between halftone dots.

Equally dramatic demonstration of the effect of the Yule-Neilsen effect

These gentlemen, Mr. Yule and Mr. Neilsen, were pretty sharp guys. They knew some math. The graph below shows the equation that they came up with to model this effect. From this equation, it was now possible to predict the reflectance (or density as in the graph) of a halftone from the dot area on the paper and the densities of the paper and solid.

The celebrated Yule-Neilsen equation as it originally appeared

The equation above is written in terms of density and not reflectance. This makes it a bit hard to relate to the Murray-Davies equation. Here is the equation written in a way that makes the correspondence obvious.

Yule-Neilsen equation

Comparing this back to the Murray-Davies equation, we see that the only difference is that in the Yule-Neilsen equation, all the reflectance values are raised to the power of 1/n. The Murray-Davies equation is a special case of the Yule-Neilsen equation with n = 1.

Murray-Davies equation

The appropriate value for "n" depends on the translucency of the paper. One researcher (Pearson) said that it should be between 1.4 and 1.8. Another set of researchers (Qian et al.) had it at 1.3 for their substrate.

Now it gets complicated

This thing that has become known as "tone value increase" thus is comprised of two parts: 

1) The dots on the paper are richer in color than expected because the dots squish out to cover more paper. This is known as physical dot gain.

2) The light spreads between the dots to make the paper take on a tint of the color. In doing so, they also make the color of a halftone richer than expected. This is known as optical dot gain.

That was the easy part. Now for the complicated part. 

Optical dot gain is not as easy to measure as physical dot gain. You need to take a picture of the dots, and assign each pixel to either dot or paper. This isn't all that hard, but it can't be done with a standard spectrophotometer. A second instrument is used, called a planimeter. For "hard" dots - dots that have crisp, well defined edges, the assignment of each pixel isn't that hard. You simply set a threshold gray value somewhere around half way between "paper" and "dot". But for softer dots, the measurement you get depends a lot on how the threshold is chosen.

So, basically, no one in a production environment ever measures physical dot gain. The two types of dot gain get rolled into one. The combination of the two, TVI has become the process control parameter of choice. Any difference between the tone value in the file and the tone value on the paper is undifferentiated.

But researchers generally use the Yule-Neilsen equation to model the relationship between CMYK tone values and reflectance. I have a short list of such papers below [5]. The Holy Grail for these folks is to find a formula that will allow them to compute the whole shooting match. CMYK tone values, along with some press parameters, go into the magic black box. CIELAB values come out.

The Yule-Neilsen equation (and the n value that go with it) are kind of a one-way street. It can be used in prepress to predict what a halftone will look like, but you can't use it in the press room to verify that the print is correct. 

So, for the time being we are stuck with the Murray-Davies equation. Maybe that's not so bad? I will address this issue in the next post in this series. Maybe the current way of measuring halftones is not the panacea that we think it is.

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[1]  I am taking a very web-offset-centric view of this. The same principles apply to other types of printing.

[2]  TAGA (Technical Association of the Graphic Arts) has been running an annual conference since the ten commandments were inscribed via a lithographic process without the help of Yule Brynner. The 2014 call for papers is out. Submissions dues by July 19th, 2013.

[3]  I missed this conference and hence the landmark paper, but I don't quite recall why.

[4] Seriously for the moment. Yule is the print scientist. Yul is the actor who my wife has a crush on. Someday I will shave my head to compete. Neilsen is another print scientist.The actor's last name is spelled "Nielsen". My wife does not have a crush on him, but regardless, I will someday grow my hair white.

The insidious misspelling of Neilsen's name is so pervasive that Google's patent search returns 11,400 results searching on "Yule Nielsen factor" and only 88 on the correct spelling. This just ticks me off.

Scan from the 1951 TAGA Journal, showing correct spelling

[5] Here is a list (incomplete) of papers where the Yule-Neilsen formula is featured as a way to predict the color of a halftone.

Pearson, M. (1980). N-value for general conditions. In TAGA Proceedings, (pp. 415–425).

Viggiano, J. A. S. (1985). The color of halftone tints. In TAGA Proceedings, (pp. 647–663).

Pope, W. (1989). A practical approach to N-value. In TAGA Proceedings, (pp. 142–151).

Rolleston, R., & Balasubramanian, R. (1993). Accuracy of various types of Neugebauer model. In IS&T and SID’s Color Imaging Conference: Transforms and Transportability of Color, (pp. 32–37).

Arney, J. S., Arney, C. D., & Engeldrum, P. G. (1996). Modeling the yule-nielsen halftone effect. Journal of Imaging Science and Technology, 40(3), 233–238.

Hersch, R. D., & Crt, F. (2005). Improving the Yule-Nielsen modified spectral Neugebauer model by dot surface coverages depending on the ink superposition conditions. In IS&T Electronic Imaging Symposium, Conf. Imaging X: Processing, Hardcopy and Applications, SPIE, vol. 5667, (pp. 434–445).

Gooran, S., Namedanian, M., & Hedman, H. (2009). A new approach to calculate colour values of halftone prints. In IARAGAI.

Rossier, R., & Hersch, R. D. (2010). Ink-dependent n-factors for the Yule-Nielsen modified spectral Neugebauer model. In CGIV – Fifth European Conference on Colour in Graphics, Imaging, and MCS/10 Vision 12th International Symposium on Multispectral Colour Science.

Qian, Yiming, Nawar Mahfooth, and Mathew Kyan, (2013) Improving the Yule-Nielsen modified spectral Neugebauer model using Genetic Algorithms, 45th Annual Conference of the International Circle

The color of a bunch of dots, part 1

First off, most printing today is done with dots. Halftone dots. Oh, you knew that already? Just in case you didn't, have a look at magazine with a magnifying glass. You'll see that highlight areas are made of tiny dots, and shadows are made of dots that are so big they run all together.

Scan from a catalog showing halftoning

A formula to predict the reflectance of a halftone

Way back in 1936, a fellow by the name of A. Murray of Eastman Kodak [1] was pondering the measurement of halftones. Murray sought out his friend, E.R. Davies [2] to ask if there were a simple formula. Davies gave him such a good enough answer that Murray decided to publish the results. Naturally, by Stigler's law,  the resulting equation isn't known as the Davies equation, but rather, as the Murray-Davies equation.

  

Contrary to popular belief, the Murray-Davies formula
was not developed by Bill Murray and Geena Davis

Suppose that you have an area that is halftone dots that cover 20% of the area, something like the area below. Of the light shining on this area, 20% will hit ink, and the remaining 80% will hit paper. If there are 100 photons playing this game, 20 will hit the ink. Suppose further that the ink will reflect 5% of the light that hits it. That means that, of the initial 100 photons in the game, only 1 will reflect back from the ink, since 5% of 20 is 1. 

Now, let's look at the fate of the other 80 photons. Suppose that the paper has a reflectance of 80%. That means that 80% of those 80 photons (64) will reflect. All told, 1 + 64 = 65 of the original 100 photons will reflect.   

The pattern on my jammy bottoms

Did that all make sense?  If so, then congratulations! You understand the Murray-Davies equation. If the various R's in this equation stand for the reflectance of the various things, and A stands for the dot Area, then this simple formula will give an approximation for the reflectance of the halftone:

The celebrated Murray-Davies equation

You may have seen an uglier version of this equation, one involving logarithms or 10 raised to some power.  Trust me. IT's all the same equation. People put that kind of complication in just to make themselves sound smart. Sometimes they are actually smart. Especially when I do it. But the point is, the simple equation above is the basic Murray-Davies equation.

Trouble in Paradise

It didn't take long to see that the formula does not do a fabulous job of estimating the reflectance of a halftone. And it didn't take long to find an explanation. If one compares the size of the dots on the plate with the size of the dots on the paper, it is obvious that the dots get bigger when you print. There is dot gain. And if the dots are bigger, then one would expect the reflectance to go up as well.

Clearly if one would like midtones to be the right color, dot gain must be measured and ultimately controlled. The Murray-Davies equation provides a way to measure the dot gain. First, you solve the Murray-Davies equation for the area term, A. This revision of the Murray-Davies equation (shown below) answers the question "How big must the dots be in order to get a certain reflectance?" 

You measure the reflectance of the paper, the solid, and the halftone, plug them into the equation below, and you have an  indirect measurement of the size of the dots. The difference between this indirectly measured dot area and the area on the printing plate (or the area requested in the digital file) is called the dot gain.

Aside from changing the name from "dot gain" to "tone value increase", this basic formula has survived to this day as a control metric. The image below is a screenshot from the most recent (unpublished, as yet) version of the main ISO standard for printing, ISO 12647-2. The horizontal axis is the tone value (dot area) going from 0% (paper) to 100% (solid ink). The vertical axis is the expected amount of increase in tone value for each of five different types of printing. For printing type A, a 50% tone value in the image file is supposed to print like a 66% halftone.

One of the jobs of the printer is to maintain the press so that these are the tone value increases that are seen on a daily basis. If the press is printing differently (maybe the 50% tone value measures as a 64% rather than a 66%) a look up table (known as a plate curve) is introduced between the digital file and the plate manufacture so that the combined system has the proper tone value increase. As a result, a contact proof can be printed or displayed on a calibrated monitor that accurately predicts what the press will print.

So, it would appear that all is well with the world. The printer has a tool to monitor the way that halftones are printed, and can digitally adjust this to a value that ISO has prescribed. By keeping this constant, the printed product will always be the correct color. 

Or so it would appear. Stay tuned for the next installment, where I show that this simplistic view of tone value increase is lacking, particularly when we go beyond the borders of conventional web offset printing with CMYK inks.

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[1] Almost no one knows this guy's first name. It is ironic that his last name has gone down in the history of printing without a first name. Note to the historians: When you put my name down in the history books, please make sure my first name is there. And if you have enough space, I wouldn't mind having my middle name, "the Math Guy" included. I said, "almost no one" because I have found exactly one person, Dr. J. A. S. Viggiano, who has preserved the first name: Alexander. Alexander has that first name on at least 22 patents.

[2] Guess what? I don't know this guy's first name.

"Density is ink film thickness"

I've heard it said thousands of times. Solid ink density tells you how thick the ink is, and CIELAB tells you the color. Along with this goes the converse: solid ink density does not tell you color, and CIELAB doesn't tell you the amount of ink. I'm writing this post to set the record straight. There is nothing fundamentally different between density and CIELAB, except that there is less information in density.

The start of the scandal

I admit to my own little contribution to this scandal. I have talked about Beer's law. Incessantly. I even wrote a blog about Beer's law. In hindsight, I realize that I should have just stuck with Wien's Law [1]. But there it is, I ordered the Beer.

Beer's law, or Wien's law?

I didn't mention ink in that particular blog, but it wasn't long before I started having a little ink with my Beer. In one post, I used Beer's law to explain why ink sometimes changes in hue when you slather it on. As if that wasn't enough, I pulled out another six-pack to describe how to reach a CIELAB target when all you have control of is ink film thickness or pigment concentration.

Image from the world famous perifarbe blog post

Let's have a look at each of the four myths and see how they stand up.

Myth #1 - Solid ink density is ink film thickness

Now, if there were laws about truth in blogging, I woulda probably shoulda mentioned that Beer's law is a decent approximation, but there are some other things going on that limits it a bit when we are talking about ink.

Beer's law (when applied to ink) assumes that light enters the ink, reflects from the paper underneath the ink, and then goes back through the ink. The more distance it travels in the ink, the more likely it is to be absorbed. Those are the two fates of a photon: it gets caught, or it makes it out of the ink. The thicker the ink, the higher the probability of getting caught. Beer's law puts no limit on this. Given a thick enough ink, the density could be a zillion. (This would correspond, of course, to a reflectance of one in ten to the zillionth. My densitometer doesn't quite go that high.)

There are, however, two other potential fates for a hapless photon. A photon without much hap could bounce off the top of the ink, never having a chance to see the ink at all. This is called specular reflection. Another fate has to do with transparency. Photons could bounce around inside the ink and eventually find their way back out before even seeing the paper.

These two effects guarantee that there will be at least a few wayward photons that wind their way back to the detector. Thus, this puts a limit to the density, so all good proportionality must eventually come to an end. Buy me a beer some day, and I'll tell you everything you want to know about the Tollenaar-Ernst equation [2].

One of my favorite equations, the Tollenaar-Ernst equation

The T-E equation in action

Conclusion? Myth partly busted. 

Myth #2 - CIELAB does not measure ink film thickness

I presented a paper at the 2008 TAGA conference entitled "Building a bridge from Dense City to Colorimetropolis". The paper was dreck, but I am quite proud of the clever title [3].

Photo-realistic drawing of the San Francisco bridge 

In this paper I showed that the color difference between paper and the solid (in deltaE values) correlates reasonably well with (paper relative) density when measuring cyan, magenta, and yellow inks. My conclusion is that CIELAB values contain all the information that density values do.

It is incorrect to say that CIELAB does anything really any different from density. The only issue is that of the software catching up. If spectrophotometers and offline software packages reported the right numbers in a way that could be readily understood by press crews, then the myth would just plain go away.

Myth busted! Here is the correct statement to replace the first two myths: "Both density and CIELAB are indicative of ink film thickness, but neither is completely true, especially when you get to high density." [4]

Myth #3 - CIELAB tells you the color of the ink

Well, duh. CIELAB is color, right?

Some pedantics might argue that CIELAB is not color, but that CIELAB is a good enough approximation to work for many industries. CIELAB tells you a lot about the appearance of an object, but it doesn't take a lot of things into account, like

1. The effect of adjacent colors on our perception of an object
2. The effect of out perception of a white point in our field of view.
3. Goniophotometric effects such as glossiness, opalescence, and metallic luster
4. Eye fatigue
5. Differences  in color vision between people, even among people who are not color-blind

Setting all this sophisticated stuff aside, I'm gonna say that CIELAB is a good measure of what we perceive as color. Myth Confirmed!

Myth #4 - Solid ink density does not tell you the color

All I gotta say is "orange". An orange ink may have exactly the same density as a yellow ink. The blue filter in a densitometer may see exactly the same density on an orange and a yellow ink. But, the orange ink is a different color.

The issue is, solid ink density is only one number, so it can't possibly tell you what the color is. Color is three-dimensional. Well... what if I look at all three density filters, red, green, and blue? A densitometer can report all three of these, right? That gives me three dimensions, so there you go. We have defined the color, right?

I'm gonna say "no". The three filters in a densitometer are different than the three filters in my eye.

Once again, myth confirmed!

My (perhaps unpopular) conclusion

There is nothing magical about density that allows it to put a micrometer on an ink film. Inherently, density and CIELAB are sewn from the same cloth. They are both measures of the reflectance, as measured through specific spectral filters. In one case the filters were selected so as to capture the richest part of the spectrum for specific inks. In the other case, the filters were selected so as to mimic the human eye. Other than that, the only difference is in the math.

If there were just a bit more math applied to CIELAB values to serve as a proxy for ink film thickness, then density would no longer be necessary.

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[1] I'm not kidding. Not only is there a law of physics called Beer's law, but there is a law of physics called Wien's law. It says that if you know one black body radiation curve, you know them all. In some sense, they all look alike no matter what the temperature. This is also known as the Wine-goggles effect. After enough wine, all bodies look the same, no matter how hot they really are.

[2] Tollenaar, D. and Ernst, P.A.H., “Optical density and ink layer thickness,” Adv. Print. Sci. Techn., 1962, Bol. 2, pp. 214-233.

[3] I was also proud of the really ornate and detailed drawing, which was my depiction of the San Francisco bridge. The TAGA conference that year was held in San Francisco.

[4] I have an article in the upcoming IDEAlliance bulletin that looks at the traditional Murray-Davies formula for computing dot gain, which is based on the science that went into density measurement. In the article, I show rather conclusively that this paradigm does not work for determining dot gain of spot colors. The density of a 70% for example, is nearly identical to the density of the solid, when it is clear that the 70% and the solid have different CIELAB values.

I don't yet have the data to come to any conclusion about the relationship between density and ink film thickness for spot colors, but I suspect that the same sort of thing applies. If one looks at the density/ink film relationship at the wavelengths with highest density, I suspect that these too will reach a saturation point long before the color stops changing.

Red is the color of....

I ran across an interesting blog today. Jeff Yurek writes a blog called "dot color". If you like my blog, you will like his. It's good stuff.

Jeff's blog

I found his blog because he wrote a blog post about one of my blog posts. Jeff, you have become my instant buddy. (Please take note of this, any of you who wish to become my buddy! I can be had that cheap.)

As I read through his posts (all very interesting), I came across one post that got me thinking. The blog was about the psychological effect of colors, specifically about whether color can have an effect on our buying habits. We would all like to think that we are ultimately in charge of whether we open up our wallet, but maybe the subconscious brain reacts emotionally to colors and clouds our thinking. I like this idea because it is such a good excuse for me to give to my wife when I return from a business trip. Any rationalization that keeps me for accepting responsibility for my bad behavior is a good thing.

Jeff's blog pointed out one bit of research that showed that red is an auspicious color for Olympic wrestlers. Similar research showed that a red background is a good thing for eBay auctioneers as well. People bid higher when there is a red background. Paradoxically, a red background will also lead people to try to negotiate better prices.

Number 316 is clearly excited about bidding because his hair is red

Jeff explains the paradox this way:
"Why? The exact mechanism remains a mystery but researchers see some evidence that aggressive colors like red may actually cause a spike in testosterone levels."

This all got me thinking. There are a lot of designers who will tell you how to use color to manipulate mood. Should I put all this advice into the same bucket where I store advice from palm readers, astrologists, political candidates, and psychotherapist who seem to have this psychological need to make me into a better person? Or is there some science behind the effect of color on mood?  If there is a general consensus on the effect of colors, then perhaps there is some underlying psycho-physical basis.

Moody colors

To answer this, I looked at three books for designers and three websites (see list at the end). Do they basically agree on the psychological effect of seeing red?

"Reds are bright and warm, cheerful and inviting." (Kobayashu)

"Red is passionate, the color of hearts and flames; it attracts our attention, and actually speeds up the body's metabolism." (Chijiiwa)

"[If red is your color] you crave excitement and live for the moment. Easily bored, you also enjoy having the power to get things done quickly. Red lovers are passionate about life." (Sutton and Whelan)

True Red was chosen as the 2002 Pantone color of the year. They had this to say about red in their press release: "This red is a deep shade and is a meaningful and patriotic hue. Red is known as a color of power and/or passion and is thus associated with love."

And here are the comments from from color consultant Kate Smith:

"Recognized as a stimulant, red is inherently exciting and the amount of red is directly related to the level of energy perceived. Red draws attention and a keen use of red as an accent can immediately focus attention on a particular element.

Increases enthusiasm

Stimulates energy and can increase the blood pressure, respiration, heartbeat, and pulse rate

Encourages action and confidence

Provides a sense of protection from fears and anxiety" (Smith)

Kate Smith, not to be confused with Kate Smith

Kate, incidentally, has an active blog on color with 1.32 zillion posts.

Here is what another color consultant, Angela Wright, has to say about red:

"Physical, Positive: Physical courage, strength, warmth, energy, basic survival, 'fight or flight', stimulation, masculinity, excitement. Negative: Defiance, aggression, visual impact, strain." (Wright)

Angela Wright, not to be confused with Angela Cartwright

Do these descriptions of the effect of red all agree? 

One could easily just read through them and say, "yeah, they match". This is a bit problematic though, because of the Forer effect. Bertram Forer was a psychologist who gave his students a personality test, and then handed each one a sheet of paper allegedly being a description of their personality. The students overwhelmingly felt that the descriptions fit them. Unbeknownst to the students, however, each one received the same evaluation, which was a compilation of vague statements from horoscopes. So, it could be that the descriptions of red sound harmonious because they are vague and general enough to sound like they agree.

My opinions on astrology are colored by the fact that I am a Scorpio,
and scorpios don't believe in astrology

Here is a simple test, though, that might even be considered somewhat objective, provided you are not being terribly critical, and have low standards for scientific, un-peer-reviewed research. And provided you are cool with my scientific process of selection of these six references as random, uncorrelated, and authoritative. And, of course, if you are not particularly demanding about doing actual science.

The original premise from Jeff's blog was that red revs people up. How about we look through the descriptions for phrases that say red excites, and phrases that say that red mellows. Scanning through the descriptions of red, I find the following words or phrases that are consonant with revving up:

   

"passion or passionate" (three times)

"speeds up metabolism"

"exciting or excitement" (three times)

"energy" (three times)

"fight or flight"

"stimulant or stimulation" (twice)

"aggression"

"enthusiasm"

"increase bodily functions"

"encourages action"

I see no words that suggest that red will mellow one out. 

This research is incomplete. Ideally, I would identify three or four dimensions (like exciting/relaxing, happy/sad, and fattening/slimming) that colors can be described in. Each color would be given a position in this three or four dimensional space, as well as a tolerance range. If the tolerance ranges overlap a lot, then this is all mumbo-jumbo. If not, then there might be something to the idea that colors elicit emotions.

In an ideal world, of course, the National Institute of Giving Money to Brilliant Applied Mathematicians would knock on my door and give me an embarrassing amount of cash to research this question that is absolutely vital to sustaining our economy. And I would work hard to sustain the economy by throwing elaborate gala events for a hundred or so of my favorite color consultants.

Until I get that know on my door, the tentative conclusion is that red is a color that revs people up. Or, maybe I should say that, based on this research, I can't reject the hypothesis that people believe that the color red revs people up.

-------------  References ---------------

Shigenobu Kobayashi, A Book of Colors, 1987, Nippon Color 

Hideaki Chijiiwa, Color Harmony, a Guide to Creative Color Combinations, 1987, Rockport Publishers

Tina Sutton and Bride M. Whelan, Complete Color Harmony, 2004, Rockport Publishers

Pantone, http://pantone.wikia.com/wiki/True_Red

Angela Wright, Colour Affects website

Kate Smith of Sensational Color, http://sensationalcolor.com/color-messages-meanings/color-meaning-symbolism-psychology/all-about-the-color-red.html

   

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

Here are some answers from various LinkedIn groups. I have added some of my own snarky comments.

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 Field - Research 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)