Quirks in Blue

Tenth in a series of blog entries about color theory with live help from the ColorTheory (Step 10) .  First_post,  Prev_post, Next_post

One of the annoying things I discovered as I explored the various color options (several of which are in the Color Theory application), was that the color “blue” always kept popping up as a problem.

For example, in trying to map the hues in the color wheel according to the CAM02 model, the math started to fail right around hue angle = 240, pure blue in the sRGB model. In the color wheel you can see a definite strong edge right at that point.

CAM02 hue as a function of sRGB Hue

We can look directly at the hue angles in the figure to the left- the RGB hue angle is across the bottom, and we see that the CAM02 hue angle not just stops, it reverse as we approach RGB blue.

Rim of RGB gamut in CAM02 Oppoenent Processes

We can plot this in terms of the red/green, yellow/blue opponent processes as used by CAM02 as well. We can plot the rim of the RGB color wheel (which is better described as a hexagon). As we see in the figure to the left, there is a definite “horn” right at that corner of the RGB.

Of course, CAM02 is not the only uniform perception model, and maybe this is just a “quirk” in that specific model. So let’s look at another unform color space, the Uniform Color System developed by the Optical Society of America (OSA-UCS). This is an interesting model in that it was specifically developed for the purpose of determining a perceptually uniform distribution of the colors. Unfortunately for my use here, it’s got two quirks that make it more difficult to use that the CAM02 model- it uses a different set of fundamental color observers (the 1961 10 deg CIS observer models) so that it can’t be computed from the XYZ or the RGB color models without reference to the actual paint chips involved, and it is difficult mathematically to invert it. But it makes for good test set to evaluate more standard models.

Rim of RGB gamut in extrapolated OSA UCS

At any rate, there is data on the RGB values for the colors used in the OCA UCS model, and between that and a least square fit to approximately map it to RGB space, we can look at the RGB colorwheel rim in its coordinates. And there we discover an even bigger “horn” than in the CAM02 model.

OSA UCS opponent color range

(This isn’t a completely fair graph- the actual colors used to define the OSA-UCS weren’t extended to the complete RGB gamut as seen in the following graph.)

Sharpman-Stock Cone Fundamentals

We can look at the fundamental cone response curves for an explanation. At “perfect” blue in the RGB model, the green and red “lamps” are completely off. As the hue shifts to either side, we turn on either the green or the red lamp. But it is a misnomer to consider these as pure red or green in the cone responses- the red and green responses are very close to each other. So the red light triggers green cone response, and the green light triggers some red cone response. The blue response is far from each. So the eye can detect that there is something other than blue being added, but it can’t tell if the added light is red, green, or grey.

palette, label, x, y, clr, note, ...
quirk, palette1pat1, 132, 41, #0401fc, "center", ...
quirk, palette1pat2, 132, 77, #2e2ee6, "below", ...
quirk, palette1pat3, 132, 173, #ecf005, "yell, center", ...
quirk, palette1pat4, 196, 77, #2b01fc, "right", ...
quirk, palette1pat5, 68, 77, #012bfc, "left", ...
quirk, palette1pat6, 68, 209, #fcd201, "yell left", ...
quirk, palette1pat7, 132, 209, #e6e62e, "yell below", ...
quirk, palette1pat8, 196, 209, #c9f005, "yell, right", ...
quirk, palette1pat9, 260, 77, #5501fc, "far right", ...
quirk, palette1pat10, 4, 77, #0155fc, "far left", ...
quirk, palette1pat11, 132, 113, #5252cd, "far below", ...

The bottom shows a pure yellow, followed by a trio of yellow plus red, yellow plus white, and yellow plus green. The top shows the same for blue, but it also show the next step out as well, because it remains very difficult to tell which side is adding green, and which side is adding red.

Of Pats and Palettes, and Peaks

Ninth in a series of blog entries about color theory with live help from the ColorTheory (Step 9) .  First_post,  Prev_post, Next_post

This post will be a bit more dull, because we’re going to spend it introducing a new panel in the Color Theory application. Or, if you actually enjoy playuing with the application, it may make the application a little more interesting.

We’re adding the “Palette” panel, to allow us to stash and manipulate little pats of color.

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The Appearance Layer of Color Perception

Eighth in a series of blog entries about color theory with live help from the ColorTheory (Step 8) .  First_post,  Prev_post, Next_post

In the last two posts, we discussed how the eye perceives color, first through its red, green, and blue cone response, then through its black-white, red-greeen, and yellow-blue opponent responses. But that isn’t the end of the story.

In this post, we’ll discuss three dimensions of color appearance- hue, luminance or value, and colorfulness or saturation. These dimensions were first carefully worked out by Munsell, but we will look at the latest model, the CIE Color Appearance Model 2002 (CIECAM02, or simply CAM02).

For the RGB model, the appearance variables are the well-known HSV- Hue, Saturation, and Value. But these are only rough approximations to the real variables, chosen to be easy to compute.

For better models, we go to the CIECAM02 model. It defines variables JCH: J for Lightness which corresponds to Value, C for Chroma which the amount of color (where the Saturation is the fraction of color), and H for hue (but measured differently from the HSV hue)

Red and Unique Green

Equal Lightness

Equal Chroma

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The Neurological Layers of Color Perception

Seventh in a series of blog entries about color theory with live help from the ColorTheory (Step 7) .  First_post,  Prev_post,  Next_post

To summarize where we ended the last time, we showed the RGB wheel which represents the first layer of color processing by the eye, using the three cone cell responses. But there are several pieces of evidence that the optical system doesn’t stop there.

The opponent theory of color is based on the observation that there is considerable evidence that our eyes don’t think in terms of three quantities of red, green, and blue. Rather it thinks of three pairs of opposing colors: black vs. white, red vs. green, and blue vs. yellow.

Four Unique Colors

In analyzing the opposite colors, researchers were able to identify four unique colors of red, green, yellow, and blue. The four colors you see are the ones identified by Hurvich and Jameson where unique green is that green with the least amount of yellow or blue in it, (not the color with the most intense green).

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The Biological Layers of Color Perception

Sixth in a series of blog entries about color theory with live help from the ColorTheory (Step 6) .  First_post,  Prev_post,  Next_post

Colors are fun to investigate, because there are so many ways to look at them, all different. all seemingly contradicting each other, and yet all correct. There are a wide variety of different color wheels, each of which illustrates something different. And here we start to look at them.

As discussed in a previous post , this arrangement originated with Newton and his investigation of the spectrum. But it’s not quite what the spectrum really shows.

Color Wheel according to spectrum

The spectrum color wheel distributes the colors equally across the spectrusm. Note that blue and green make up much more of the spectrum than the traditional wheel allows.

We now see the wavelengths (in nanometers) of light equally across the wheel. But we also see two additional labels for the ends of the spectrum, ‘>660′ for the Infrared, and ‘<420′ for the Ultraviolet. This represents the ends of the rainbow. The magenta colors between them are “nonspectral”- they will not appear in a rainbow or a prism, and they can’t be represented by a single frequency of light. Yet we see them.

Because our eyes can see all the wavelengths, all at once.

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Reflected Heart Yin-Yang Symbol

Traditional Yin-Yang

I have long been fascinated by some of the more mathematical Chinese philosophical writings such as the binary complications of the I Ching and Tao duality. Specifically in this case, the Yin-Yang symbol of the cyclic dependence of dual principals- night to day to night; winter changing into summer, summer back to winter (my home in Minnesota is particularly prone to this cycle), and the basic notion of the Yin-Yang- when the dark is darkest and most triumphant, that only means that the ascension of the light has begun.

But the mathematical side of me has always been bothered, deep inside, by the symbol itself. Because it doesn’t really show what they say it shows. As we see in the next figure, while it may be 100% white at the top, it doesn’t start to change to black until almost one-quarter of the turn is complete. So even though there is a nice dot at the top center to show that there is always black even in brightest white, that promise is then broken for half of the turn to darkest black.

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Connecting the Math to the Wheel

Fifth in a series of blog entries about color theory with live help from the ColorTheory (Step 5) .  First_post,  Prev_post,  Next_post

We’ll show off the common HSV (Hue, Saturation, Value) system this time, but mostly we’re showing off more about ColorTheory application. HSV per se was developed in the 1970′s at the legendary PARC and NYIT research centers , but really they were just making the engineer’s RGB model friendlier with more painterly color models.

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Yes, There’s Math in Color Theory

Fourth in a series of blog entries about color theory with live help from the ColorTheory (Step 4) .  First_post,  Prev_post,  Next_post

The RBG model is a simple one. There are three lights, R, G, and B. There are three numbers, each ranging from 0 to 255, each saying how bright that light should be. The lights could be the three phosphers in a cathode ray monitory, or three laser diodes in an LED display.

But that is also the difficulty with RGB from a scientific viewpoint. Each new set of lights represent a new set of colors. There was the NTSC standard for TV in 1953, with PAL for the Europeans. Adobe has one, as does Apple. Wikipeida lists a sample of thirteen different RGB standards. CYMK is even worse, as every new printer has its own CYMK color separation model.

From a scientific viewpoint, a more stable viewpoint is to base the color model by matching the cone receptors of the eye. And the most venerable of these is the CIE XYZ model (with the 1931 two degree observer), developed in 1931 on the basis of color observation experiments. So venerable that even though CIE itself has offered alternate definitions based on more recent research , the one that all current popular non-proprietary color models, including the RGB models and the CYMK models, and the CIE’s own CIELAB and CIECAM02 color appearance models, all remain based on the 1931 version.

Of particular note is the standard color model for HTML color, the sRGB model, defined in 2002. It is defined by starting with XYZ with a matrix transformation plus a nonlinear luminance function .

And now let’s show off some of the math.

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The 90% Color Wheel

Third in a series of blog entries about color theory with live help from the ColorTheory (Step 3).  First_post,  Prev_post,  Next_post

The Yurmby (RGB, CYM) wheel is not the original color wheel, nor is it the most common color wheel. The most common is the one first proposed by Newton as part of his prism studies and refined from there. It defines three primary colors of Red, Blue, and Yellow, and secondary colors of Orange, Green, and Purple. Only 8% of the color wheels in Google image are Yurmby, 90% are the Traditional wheel, with 2% “other”.

The Traditional wheel has been in use for almost 250 years. The first three-color printing process developed in 1710 was based on RYB, with a four-color RYBK soon to follow.

There is no doubt that the Yurmby wheel is mathematically accurate as to how it represents RGB and CYMK colors. Why does the traditional wheel insist on being so useful that it has stayed in use for the last three centuries?

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The Simplest Way to Colors

Second in a series of blog entries about color theory with live help from the ColorTheory(Step 2) First_post,  Next_post

The first thing I want to illustrate what James Gurney calls the Yurmby wheel. It is a concise summary of the engineer’s answer to the question of color- what is the simplest way to make colors?

Additive colors

The modern engineer (for this discussion, anytime after color TV) was uses three lights to make color, one red light, one green light, and one blue light, to make up the RGB color system . This works because the eye in most people sees color through three types of cone cells, red-sensitive, green-sensitive, and blue-sensitive (there are exceptions, look here and here). It’s the basis of LED flat computer screens and it is the standard for defining color in HTML for the World Wide Web. It also goes by the name of the “additive color model” and is often illustrated by a figure like the one on the right.

But the engineers were preceded by the printers, who have been using three colors (plus black for a clean look) cyan, magenta, and yellow for full color printing since 1902 in the CYMK color system . It goes by the name of the “subtractive color model” and is often illustrated by a figure like the one to the left.

Subtractive Colors

Note that both figures cycle through the same six colors- red, yellow, green, cyan, blue, and magenta. So let’s show how they are just two views of the same color wheel.

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