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Color theory and design

2011, Wiley Interdisciplinary Reviews: Computational Statistics

In this article, we discuss color theory and design with emphasis on use in statistical, scientific, and data visualization. Color theory is inextricably linked to the physiology of the human visual system, and color design is similarly inextricably linked to human perception. We discuss color perception in the human visual system. We then quantify color perception in terms of the Munsell System and the International Commission on Illumination (CIE) color space. We continue to discuss color design with a perspective on individuals with defective color perception and finally conclude with a discussion of color design for the use of color in presentations. 

Overview Color theory and design Edward Wegman∗ and Yasmin Said In this article, we discuss color theory and design with emphasis on use in statistical, scientific, and data visualization. Color theory is inextricably linked to the physiology of the human visual system, and color design is similarly inextricably linked to human perception. We discuss color perception in the human visual system. We then quantify color perception in terms of the Munsell System and the International Commission on Illumination (CIE) color space. We continue to discuss color design with a perspective on individuals with defective color perception and finally conclude with a discussion of color design for the use of color in presentations.  2011 John Wiley & Sons, Inc. WIREs Comp Stat 2011 3 104–118 DOI: 10.1002/wics.146 HUMAN VISUAL SYSTEM T he perception of color has at least two major components. On the one hand, color can be discussed simply as a phenomenon of certain wavelengths of electromagnetic radiation. On the other hand, most electromagnetic radiation cannot be perceived by human beings. It is the very narrow band of electromagnetic radiation that can be perceived by humans that we call light and which leads to an incredible sensory experience that we call vision. It is this marvelous confluence of, in some sense, absolute wavelengths of electromagnetic radiation and psychophysical decoding of these wavelengths in the human visual system that gives rise to the perception of color. Human vision relies on light sensitive cells in the retina of the eye. There are two basic kinds of sensors. These are rods and cones. Rods are cells which can work at very low light intensity (scotopic), but cannot resolve sharp images or color. The rods contain a pigment, rhodopsin, also called visual purple, which saturates at higher levels of light. Cones are cells that can resolve sharp images and color, but require much higher light levels to work. Figure 1 illustrates the major components of the human eye. Both the rod cells and the cone cells are located on the retina. The central part of the retina is called the fovea, which is where cells responsible for vision are most densely located. There are about 107 foveal cones. The combined information from these sensors is sent to the brain and enables human vision. There are three types of cones. A somewhat simplistic interpretation is that red cones are sensitive to red light, green cones are sensitive to green light, and blue cones are sensitive to blue light. More precisely, the cones are sensitive to long, medium, and short wavelengths of light. The peak response of the cones do not actually occur precisely in the red, green, and blue color bands, but the perception of color depends on contrast among the stimulation levels of the different cell types. With the simplification of red, green, and blue cones in mind, when red light hits the eye, the cones sensitive to red are excited, causing a particular sensation in the brain. That is what we call ‘red.’ This is what physically happens when we observe, say a tomato in neutral daylight: the sunlight, composed of electromagnetic waves with wavelengths from 380 to 780 nm, shines on the tomato. The tomato absorbs the light from 380 to 580 nm and reflects the light from 580 to 780 nm. This light reaches the eyes, where it excites the cones that have their sensitivity centered on 570 nm. The signals from these cones are finally processed by our brain. We are taught that this particular sensation is called ‘red.’ The relationship between wavelength and actual hue is roughly: • 620–730 nm: red • 590–610 nm: orange • 550–580 nm: yellow ∗ Correspondence to: ewegman@gmail.com Center for Computational Data Sciences, George Mason University, Fairfax, VA, USA • 490–540 nm: green DOI: 10.1002/wics.146 • 380–440 nm: violet. 104 • 450–480 nm: blue  2011 Jo h n Wiley & So n s, In c. Vo lu me 3, March/April 2011 WIREs Computational Statistics Color theory and design Pupil Iris Cornea Posterior chamber Anterior chamber (aqueous humour) Zonular fibres Ciliary muscle Lens Suspensory ligament Retina Choroid Sclera Vitreous humour Hyaloid canal Optic disc Optic nerve Fovea Retinal blood vessels FIGURE 1 | Schematic diagram of the human eye. This image is used under the Creative Commons Attribution-Share Alike 3.0 License. Details are at http://creativecommons.org/licenses/by-sa/3.0/legalcode. The colors we see are affected by the intensity of light and by its spectral content. At low levels of illumination, objects are less colorful because rods are dominant. In bright daylight, we see more color, contrast, and saturation because cones dominate. Figures 2 and 3 illustrate these effects. COLOR THEORY Based on the notion that all color perception in humans can be reconstructed using the three so-called primary colors, red, green, and blue, a theory of color perception can be developed. It should be noted that other animals may have more or less color perception or no color perception at all. Indeed, the pigments in the eyes can vary from one animal group to another and can be used to tell the evolutionary distance between animal groups.1 Thus color theory based on red, green, and blue applies to human color perception and not necessarily to any other animal groups. Additive color processes, such as television, work by having the capability to generate an image Vo lu me 3, March/April 2011 composed of red, green, and blue light. Because the intensity information for each of the three colors is preserved, the image color is preserved as well. The spectral distribution of the image will probably be wrong, but if the degree of intensity for each of the primary colors is correct, the image will appear to be the right color. Red, green, and blue are the additive primary colors because they correspond to the red, green, and blue cones in the eye. Subtractive color processes work by blocking out parts of the spectrum. The idea of subtractive color is to reduce the amount of undesired color reaching the eye. If, for example, one had a yellow image, one would want to have a dye that would let red and green reach the eye, and block out blue. The additive secondaries become the subtractive primaries, because each of the additive secondaries will reflect two of the additive primaries, and absorb one of the additive primaries (Figures 4 and 5). See also Table 1. With this information, in a subtractive color system, such as printed documents that reflect light, if we wanted red, we would mix magenta and yellow. Magenta would absorb green, and yellow would  2011 Jo h n Wiley & So n s, In c. 105 www.wiley.com/wires/compstats Overview FIGURE 2 | Image at low level of illumination so that it is less colorful. Rods would dominate. Photo by Yasmin Said. FIGURE 3 | Image at high level of illumination in open air market. Cones would dominate. Photo by Edward Wegman. absorb blue, leaving only red to be reflected back to the eye. For black, a combination of all three would be used, which should, in principle, block out all light. In practice, printers use black as well, because the dyes used in printing are not perfect, and 106 some light from other parts of the spectrum still is reflected. A useful observation in an additive color system is that because magenta is made of red and blue in equal intensities, that mixing magenta and green is,  2011 Jo h n Wiley & So n s, In c. Vo lu me 3, March/April 2011 WIREs Computational Statistics Color theory and design TABLE 1 Additive Secondaries/Subtractive Primaries Absorption Chart Color Reflects Absorbs Yellow Red and green Blue Magenta Red and blue Green Cyan Green and blue Red FIGURE 4 | Additive secondaries are derived by combining primary colors. FIGURE 5 | Subtractive primaries mixing chart. in effect mixing red, blue, and green, which should give us pure white. Thus in an additive color system, magenta and green are complementary colors. In the same way, red and cyan are complementary colors and yellow and blue are complementary colors. Figure 6, which is a somewhat doctored black and white photograph of the late Professor Sam Wilks illustrates the complementary nature of these color pairs. One can take advantage of these complementary pairs in data visualization as well as anaglyph stereo. In the data visualization context, if one has two clusters, it is useful to brush one with, say, red and the other with, say, cyan. These colors together make white, so where the clusters overlap, the mixing of colors will yield white. Plotted against a black background, it becomes evident where the clusters overlap. Similarly Vo lu me 3, March/April 2011 FIGURE 6 | Professor Sam Wilks illustrating additive complementary colors. This photo is used with permission of the Army Conference on Applied Statistics. Professor Wilks proposed the Army Design of Experiments Conference. The first such conference was held in October 1955 and was chaired by Professor Wilks. with anaglyph stereoscopic displays, it is useful to make one eye peer through a red filter and the other through a cyan filter. Thus the overall impression is a white background. Often, the anaglyph glasses are red and green giving a background color of yellow, or red and blue, giving a background color of magenta. Color can be defined by three properties: hue, saturation, and lightness or brightness. When we call an object ‘red,’ we are referring to its hue. Hue is determined by the dominant wavelength. The saturation of a color ranges from neutral to brilliant. Colors are desaturated by mixing in white or gray or black. Lightness or brightness refers to the amount of light the color reflects or transmits. The Munsell System Color ordering systems, such as the Munsell System, use the three properties of color to identify unique colors. Notice that colors are distributed in three dimensions: hue, chroma (saturation), and value (lightness). We commonly see colors arrayed in two dimensions. This is a useful, but incomplete representation. Value is the third dimension that is not shown in two-dimensional color wheels, but is often used in image editing software. Professor Albert Munsell’s (1885–1918) description of the color system was published in Refs 2,3. Munsell’s system was based on rigorous experimental research with careful measurements of human visual responses  2011 Jo h n Wiley & So n s, In c. 107 www.wiley.com/wires/compstats Overview FIGURE 7 | Illustration of the Munsell color system. The vertical direction represents value or lightness. The radial direction represents Chroma or Saturation. The angular direction represents Hue. This image is used under the Creative Commons Attribution-Share Alike 3.0 License. Details are at http://creativecommons.org/licenses/by-sa/3.0/legalcode. to color (Figure 7). It persisted for many decades, eventually being superseded by systems such as the CIE (in French, Commission Internationale de l’Eclairage). 2.0 x(l) y(l) z(l) 1.5 1.0 CIE Models If the Munsell system established the threedimensional nature of color perception, the CIE models attempt to establish numerical values.4,5 To measure and predict the appearance of a particular color, we need a way to link perception to numbers and formulas. Scientific color values were established earlier this century by the CIE group. CIE models for defining color space all rely on the same basic numbers. There are basically two variants of the CIE color space known respectively as CIE XYZ and CIE xyY. As mentioned earlier, the cones within a human eye have stimulus response to different wavelengths, long, medium, and short wavelengths. These, we mentioned, are frequently designated as Red, Green, and Blue although the peak sensitivity of each type of cell does not correspond exactly to these colors. These are designated in the CIE system as CIE XYZ (Figure 8). The ability of the human eye to respond to three different wavelengths is called tristimulus. It is, of course, possible for two sources of light with distinctly different spectral distributions to combine to present a tristimulus value to the eye and be recorded as a certain color. It is possible for another two sources of light with different spectral distributions from the first two to combine and present the same 108 0.5 0.0 400 500 600 700 l/nm FIGURE 8 | XYZ Color matching functions as described in the text.4 This image is used under the Creative Commons Attribution-Share Alike 3.0 License. Details are at http://creativecommons.org/licenses/by-sa/ 3.0/legalcode. tristimulus value to the eye, which would therefore be recorded as the same color even though the combined spectrums are distinctly different. This effect is called metamerism. Because of the distribution of cone cells on the retina, color perception depends on the field of view with each individual having different distribution and different field of view. The CIE sought to eliminate this variability be defining a standard colorimetric observer. With the belief that most cones are located within 2◦ of the fovea, the chromatic response of the standard colorimetric observer was taken to be the response of the average human within 2◦ . Based on extensive experimentation,6,7 the standard  2011 Jo h n Wiley & So n s, In c. Vo lu me 3, March/April 2011 WIREs Computational Statistics Color theory and design colorimetric observer is characterized by three color matching functions. The color matching functions are a numerical description of the chromatic response of the standard colorimetric observer, which is, of course, the average chromatic response of a number of humans. The CIE defines the color matching functions as x(λ), y(λ), and z(λ) where λ is the wavelength in nanometers. The tristimulus values X, Y, and Z for a color with spectral power distribution f (λ) are given in terms of the standard colormetric observer as  ∞ f (λ)x(λ)dλ X= The CIE xyY color space is a derived color space. The Y value was designed to reflect the overall luminance (brightness, lightness). The remaining two dimensions are characterized by the x and y and are used to specify colors. Here the normalized values are given by X X+Y+Z Y y= X+Y+Z Z z= . X+Y+Z x= 0 Y=  ∞ f (λ)y(λ)dλ 0 Z=  ∞ f (λ)z(λ)dλ. 0 The values x and y specify the chromaticity diagram, independent of luminance. This diagram is illustrated in Figure 9. In the CIE XYZ color space, the saturation (chroma in Munsell, purity in CIE) is the Euclidean 0.9 520 0.8 540 0.7 560 0.6 500 580 0.5 y 0.4 600 620 0.3 490 700 0.2 480 0.1 470 460 0.0 0.0 0.1 380 0.2 0.3 0.4 0.5 0.6 0.7 0.8 x FIGURE 9 | CIE xyY Chromaticity Diagram as a function of x and y. The range 380 to 700 nm represents the range of perception of visible light for humans. Saturation as well as chroma are represented in this diagram. This image is used under the Creative Commons Attribution-Share Alike 3.0 License. Details are at http://creativecommons.org/licenses/by-sa/3.0/legalcode. Vo lu me 3, March/April 2011  2011 Jo h n Wiley & So n s, In c. 109 www.wiley.com/wires/compstats Overview distance between the position of one color (x, y) and the illuminant’s reference white (xw , yw ), i.e. that set of three chromaticity values that determines the reference white in the xy plane divided by the same distance for a pure (monochromatic) color with the same hue (xc , yc ) = ρmax (x − xw , y − yw ) + (xw , yw ) where ρmax is the maximum in the chromaticity diagram. Then purity is defined as (x − xw )2 + (y − yw )2 . p=  (x − xc )2 + (y − yc )2 (R − µ)2 + (G − µ)2 + (B − µ)2 . 3 While Figure 9 represents the experimentally derived range of colors that a human being can see, mechanical reproduction of these colors typically occupy a much smaller range of available colors. This range of colors that are reproducible by a given technology is called the gamut. Measuring color allows us to compare the color gamut, or range of colors produced by different methods (Ref 8, Section 18.7). Color transparency film produces a wide range of colors including some a monitor cannot display. Color printers and printing presses have different color gamuts. Roughly speaking in the order of decreasing gamut range the technologies are: color transparency film, color monitors and HDTV systems, NTSC systems, color printers, and printing presses. These systems can never capture all the colors that the eye can see, but they can simulate the appearance very successfully if color reproduction is understood and controlled. Another important characteristic of each component in the color production system is its gamma (γ ). It is a number that indicates the relationship between the signal values at input and output of a particular device. A γ of 1 indicates a linear behavior. This means that the device’s output is directly proportional to its input. A color display may have a nonlinear color behavior. If the video signal at the input contains a value of 60% of full-scale red, the image on the screen may be only 30% of full-scale red (thus dark-red). This is why a scanned image normally looks darker when it is shown on a display. This behavior can be graphically displayed in a γ curve (Figures 10 and 11). 110 0.8 γ correction 1/2.2 0.7 0.6 0.5 0.5 0.4 In an RGB space, saturation can be thought of as the standard deviation, σ , of the color coordinates R (red), G (green), and B (blue). Letting µ be the luminance, then σ = 0.9 0.5   1 CRT γ 2.2 0.3 0.218 0.2 0.218 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 FIGURE 10 | A typical γ curve for a CRT. In order to correct for the nonlinearity in the display device, a complementary γ correction curve must be introduced. Note that near one and near zero the γ curve is close to the idea linear response. This means respectively whites are white and blacks are black. This image is used under the Creative Commons Attribution-Share Alike 3.0 License. Details are at http://creativecommons.org/licenses/by-sa/3.0/legalcode. To summarize the color concepts: Hue: color with no black, white or gray added Tint: hue + white Shade: hue + black Tone: hue + gray or hue + varying degrees of its complementary color • Value or Lightness or Brightness or Luminosity: how light or dark a color appears • Intensity or Purity: how bright or dull a color appears, also called saturation and/or chromaticity. Basically, how much of the hue is identifiable. Grays are achromatic, meaning no hue/color. • • • • Digital Colors Although the CIE and Munsell color systems assume a continuous range of colors, in fact, when reproduced digitally, there are only a finite number of distinct colors available. Many of us from childhood would be familiar with the idea of a finite number of colors. Crayola crayons for beginners came in a box with 8 colors (23 ). More advanced color choices could be had in boxes of 16 colors (24 ), or 32 colors (25 ), or even 64 colors (26 ). The Crayola website9 gives an interesting  2011 Jo h n Wiley & So n s, In c. Vo lu me 3, March/April 2011 WIREs Computational Statistics Color theory and design (a) (b) (c) FIGURE 11 | Illustration of the effect of γ adjustments. Notice that the whites remain white (T-shirt) and the blacks remain black (shadow). The middle image was what came from the digital camera. The left image is with γ adjusted down, the right with γ adjusted up. This illustration is courtesy of Edward Wegman. chronology of the development of the Crayola colors, including some interesting name changes reflecting political correctness. For example, Prussian blue was changed to midnight blue, flesh was changed to peach, and Indian red was renamed chestnut. There are currently 120 Crayola colors available close to the next power of 2, 27 = 128. Typically, digital colors are represented at the hinted-at powers of 2. Depending on the application, the color resolution can range from 28 to 264 . The GIF image file format uses 28 , i.e. 8 bit color or 256 distinct colors. This is far from the range of colors the human eye can distinguish, so it is poor at representation of continuous tone images. The GIF file format compresses images in color space so that all colors are mapped into only one of the 256 colors available. The usual recommendation is to use GIF file format only if the image has a small range of colors, e.g., in line drawings. The JPG (or JPEG) file format has a 24 bit color space, i.e., 224 = 16,777,216. This amounts to 8 bits for each of red, green, and blue. JPG files are compressed spatially rather than in color space. Thus neighboring pixels may be somewhat averaged. However, because JPG is normally used for continuous tone images such as photographs, this spatial compression is not usually noticed. It is however detectable when JPG compression is used for line drawings. TIFF format files also employ 24 bit color and need not have any compression. Thus, if space is not of consideration, TIFF files are preferred. More recently, another image file format has emerged, the PNG format. This was created when the developers, Unisys, of the GIF format decided to enforce the patent on LZW compression on which the GIF file format is based. PNG format also is capable of millions of colors. The human Vo lu me 3, March/April 2011 eye is generally thought to be unable to distinguish 224 distinct colors, so that for purposes of rendering images for human perception, 24 bit color is more than adequate. For scientific purposes, however, a higher color resolution is desirable. The HDF file format is used for the earth observing system (EOS), which has the capability of 264 , or 64 bit color. Most computer-based color schemes use a 24 bit color scale, 8 bits in each of red, green, and blue, or equivalently 256 levels for each of the colors. Thus (0,0,0) would represent black, (255,255,255) would represent white, (255,0,0) would represent pure red, etc. Color in a webpage can be specified by specifying the intensity of each of the RGB components. This is typically done in hexadecimal notation, where 0 , . . . , 9 represent those numbers and A, B, C, D, E, F represent the numbers 10, 11, 12, 13, 14, 15, respectively. Thus the code FF in hexadecimal is 255 in decimal notation. Thus the code for pure white in HTML would be %FFFFFF. COLOR DEFICIENCIES IN HUMAN VISION Deficiencies in human color vision can result from a number of causes. Perhaps the most frequent deficiency is caused by changes due to aging of the individual. Other deficiencies can result from defective performance of certain types of cones even if all three are present, missing types of cones, from altogether missing cones, or from trauma to the brain. Most of color theory is based on the notion of tristimulus meaning that there are three types of cones in the human eye, which have photopigment receptors that are sensitive to light in different wavelength ranges. Individuals with all three cone type are called trichromats. There is some indication  2011 Jo h n Wiley & So n s, In c. 111 www.wiley.com/wires/compstats Overview that some individuals may have a fourth type of photopigment so that they, indeed, might have four different types of cones and hence have an even richer color experience.10 The Elderly Because the general population is aging, the majority of difficulties with color perception is among the elderly. One of us defines elderly as elderly = max(65, age of EJW+10). The 2000 census indicated that 12.4% of the US population was over 65 years old, and estimates by Hayutin11 from the Stanford Center on Longevity indicate that by 2030 some 22% of the US population will be over 65. Indeed more than 20% of residents of most developed economies will be older than 65. Deficiency of vision in the elderly is a result of yellowing and darkening of the lens and the shrinking of pupil size. Yellowing of the lens has the result of blocking short wavelength (blue) light so that the intensity of bluish colors is diminished. Of course, colors that have a blue component will shift in the perception of the elderly so that cyan, blue-gray, light blue, magenta will be affected and more difficult to distinguish. Because of the shrinking of the pupil size, less light will reach the photoreceptors in the eye so that colors generally appear darker that they would for younger individuals with similar illumination. For example, yellows may appear brown and blues may appear black. Of course, when considering color design for the elderly, these effects must be considered. More saturated primary colors are thus recommended. Color Blindness There are three basic types of color impaired vision, what might be called color blindness. People with normal color vision, as mentioned before, are called trichromats. One less severe form of color impaired vision occurs when there is an overabundance or marked deficiency in cone cells with one of the three photopigments or when one of the photopigments responds to an unusual wavelength. The individuals are called anomalous trichromats. Basically, anomalous trichromats can match color in the complete range of hues, but require extra stimulation of certain primaries. They are not technically color blind, but, in general, have difficulty in distinguishing certain colors that a normal trichromat would easily distinguish. Depending on which primary requires extra stimulus, anomalous trichromats fall into one of three categories: protoanomalous, deuteranomalous, or tritananomalous. The proportions of the anomalous trichromats are outlined in Table 2. 112 TABLE 2 Types and Percentages of Anomalous Trichromats. (Reprinted with permission from Ref 12. Copyright 2004) Type Cone % Male % Female Protoanomalous Red 1.0 .02 Deuteranomalous Green 4.9 .38 Tritananomalous Blue ∼0 ∼0 TABLE 3 Types and Percentages of Dichromats. (Reprinted with permission from Ref 12. Copyright 2004) Type Cone %Male %Female Protanope Red 1.0 Deuteranope Green 1.1 0.01 Tritanope Blue 0.002 0.002 0.02 While anomalous trichromats have color vision, and so are not technically color blind, there is a definite impairment of color vision. Truly color blind individuals have either one, two or three deficient photopigments, i.e. they have only two types of cones, dichromats, one or no type of cones, monochromats. The encoding of the protein necessary for color recognition resides on the X chromosome. Because males have only one X chromosome, whereas females have two X chromosomes, color blindness is much more likely to occur in males. The effect is masked in females even if there is a defect in one X chromosome, the other will compensate. Table 2 reflects this effect because of the reduced production of one of the photopigments. For dichromats, there are some hues which they simply cannot perceive. Colors that would appear completely different for trichromats, would appear to be the same color (metamers) for the dichromat. As with the anomalous trichromats, the dichromats fall into one of three classes depending on which color photopigment they are missing. Table 3 outlines the types and percentages of dichromats. Again, because of absence of the protein necessary to produce photopigments, the prevalence of color blindness in males is substantially higher than in females as reflected in Table 3. Protonopes and deuteranopes are red-green color blind and generally see only blues and yellows. Analogously, tritanopes are blue-yellow color blind and see only reds and greens. When the stimulus to the two types of photoreceptors is equal, the dichromat will perceive the color as gray. This is the so-called neutral point. For protonopes and deuteranopes, the neutral point are almost the same. For the protonope the neutral point is approximately 495 nm and for  2011 Jo h n Wiley & So n s, In c. Vo lu me 3, March/April 2011 WIREs Computational Statistics Color theory and design the deuteranope, the neutral point is approximately 500 nm. These would appear to be a slightly bluish green to a trichromat individual. At wavelengths lower than the neutral point, these dichromats would see a rapidly saturated blue and wavelengths higher than the neutral point they would see a rapidly saturated yellow. Thus they can easily distinguish these colors. Of course, while protonopes and deuteronopes are deficient in the range of hues, they are not deficient in the range of lightness and saturation. Unless a color is pure or saturated, dichromats will still have some perception of the deficient color. For example, a protonope will have no red receptors. However, the green photopigment is still slightly responsive a long wavelengths and the rods also will also be receptive, so some perception of the red color can be made, although the protonope may not recognize it as ‘red’ (see Figure 8). Similarly, for the deuteranope. The neutral point for the tritanope is about 570 nm, which would appear yellow to a normal trichromat. Higher wavelengths would appear red and lower ones green. ‘The description of dichromatic color perception comes from both theory and from studies of a few people who were dichromatic only in one eye. However, it’s not absolutely conclusive. First, there is no guarantee that the normal eye of a unilateral dichromatic is really normal. Second, studies often find that dichromatic color vision is much better than that predicted by theory. The best guess is that rods activate the red component red-green opponent process to give dichromats a weak three-dimensional color space.’ (Ref 12) Monochromats are a most interesting case. They may have only one photopigment for their cones or as is often the case they have no cones, only rods. Monochromats are truly color blind. Those with rods only generally have poor vision. They can match any color only in the sense of gray scale and so saturation and brightness are difficult to distinguish. Green12 reports that monochromats are exceedingly rare occurring in 1 case in 10,000,000. Finally, brain damage can create a very rare condition called achromatopsia, individual who are also monochromats. One interesting situation is the case of albinism, lack of the pigment melanin. This is a genetic disorder called oculocutaneous albinism. In order to exhibit albinism, one must inherit a mutant allele from both the mother and the father, thus males and females are affected equally for autosomal disorders. The disease is characterized either by the failure to synthesize pigment proteins or the failure of integratory proteins to implement them into tissue. The pigment may be missing from skin, hair, and eyes. People affected Vo lu me 3, March/April 2011 with albinism frequently have difficulty with vision, although it is not a given that they will be color blind. Both albinism and color blindness have to do with the failure to synthesize pigment proteins, but they can and often are independent conditions. COLOR DESIGN The use of color as a design element entails both a physiological response from the viewer as well as a response based in a cultural context. For example, while many Western brides wear white dresses as a symbol of purity, Chinese brides usually wear red, a color that is a symbol of good luck. The use of color symbolism varies tremendously from culture to culture. However, there are still certain physiological responses that are products of the human visual system combined with experience common to all humans. For example, distant objects often appear as bluish and somewhat indistinct as, for example, viewing mountains or forests from a distance. This is a consequence the greater refractive index for shorter wavelength of light. This bluish hazing effect is known as aerial perspective and is an experience common to all cultures. This is why the sky appears blue. Similarly, this same refractive index effect is why the moon appears reddish when low in the sky. From the perspective of data visualization, it is fruitful to understand the distinction between a cultural understanding of color and a physiological response to color. From a physiological perspective, color perception is a nearly automated function of the brain. Color perception has evolved with human beings over several hundred million years. As Green12 points out ‘. . .color perception is fast, accurate, automatic, and effortless. On the other hand, thinking is a relatively recent evolutionary advance, and we are not yet very good at it. Thinking means reading text, attaching meaning to an icon, searching memory, etc. These activities are relatively slow, error-prone, require mental resources and effort and take learning.’ It is unlikely, even if an individual is a dichromat, that he would confuse orange with blue, but even an individual with completely normal vision can easily misread a word in a paragraph. This is why proofreading is a difficult task. The brain interprets what it expects to see and the thinking process required for careful reading is relatively slow and error prone. There are certain physiological reactions that are in essence hard-wired, such as grouping, linking, and depth perception. There are also color  2011 Jo h n Wiley & So n s, In c. 113 www.wiley.com/wires/compstats Overview VISUALIZATION VI SU AL I ZATION FIGURE 12 | The word, VISUALIZATION, when rendered all in green is much easier to read compared with the same word in multiple colors. The all green word is naturally grouped because of the common color, whereas that effect is not found in the multi-colored word. design principles that are common and are interpreted as harmonious or garish color combinations. These principles are frequently used by artists and graphic designers. Finally there are elements in the use of color, which are interpreted in the context of culture. Hard-Wired Perception Several features of color perception are hardwired into the human brain. As mentioned in the previous paragraph, one of these is grouping and linking. If groups are rendered in distinct colors, then color associates groups together even if they are physically separated in space. Figure 12 illustrates the effect of color grouping by associating letters that have the same color. This effect can be used in data visualization by brushing clusters in a data display with distinct colors to associate elements of the cluster. A second related illustration is found in Figure 13. In this figure, we illustrate the use of color for spatial association. The point of Figure 13 is that not only does the color provide a visual linking, but also that this linking is enhanced with very distinctive hues. In our CrystalVision software,13 we provide the three primary additive colors and the three secondary additive colors as the default brushing colors, i.e., red, green, blue, cyan, magenta, and yellow. These six colors provide, in some sense, the maximal separation of hues. Figure 14 is a screen shot of CrystalVision illustrating these grouping and linking effects. Use of hue for grouping and linking is natural for certain data visualization tasks. We have already seen the effect for clustering. Hue is also good for showing categorical (nominal scale) variable. People naturally break the hues into categories, which they quickly and easily judge as being the same or different. This makes color an ideal way to indicate that objects have similar or different meaning, function, or importance. One can easily distinguish 12 or so colors: red, green, blue, yellow, orange, magenta, pink, brown, cyan, black, gray, white. On the other hand, hue is poor for showing quantitative (continuous) variables, i.e. more/less, bigger/smaller, because there is no natural ordering. Some advocate use of the ‘rainbow scale,’ red–orange–yellow–green–blue–violet, as a natural ordered representation with blue as less and red as more. People may have learned this order to an extent, but it is not a very powerful innate perception. If it works at all, it is probably because it approximates a brightness scale: blue is dark, green is middle brightness, and yellow is high brightness. Figure 15 illustrates another effect of color contrast. The left panel of the figure has a dark foreground and a yellow background. On the right-hand panel the background color is yellow and the foreground color is the dark blue–green. These panels illustrate a perceptual the impact of foreground–background contrast. Most printed materials use black or colored ink on white paper, which makes the darker color appear to pop out of the background. Indeed, astronomers historically have printed black and white sky photos as negatives in order to see fine detail. On the other hand, the light against a dark background, such as illustrated in Figure 14, allows a much more detailed comparison of hues. Both cyan and yellow tend to be considerably less prominent against a white background which is why we typically prefer to use a black background. In FIGURE 13 | The figure on the left is composed of all blue tones, whereas the same pattern on the right has bright (primary) contrasting colors. It is considerably easier to distinguish the two groups on the right-hand side because of the color contrast. 114  2011 Jo h n Wiley & So n s, In c. Vo lu me 3, March/April 2011 WIREs Computational Statistics Color theory and design FIGURE 14 | Screen shot of CrystalVision parallel coordinate display illustrating the grouping and linking effects. The color bars on the upper left-hand side are the six default brushing colors. Notice that the axes are colored red while the axes labels are cyan. These are complementary colors which are in some sense maximally different, and which add to white. TEXT TEXT FIGURE 15 | Foreground–background separation. general, achromatic background are preferred in order to have maximal use of color in data visualization. Color Design Based on the Color Wheel As we have indicated in the Color Theory Section, the modern view of color perception depends on the Vo lu me 3, March/April 2011 notion of tristimulus and the experimental results that the normal human eye has three photopigments in its cones, which roughly correspond to red, green, and blue. These three hues are taken to be the primary colors. Historically, the artistic view was that red, yellow, and blue were the primaries. This has led to the fact that some color wheels begin with these as primaries and mixing these yield secondary and tertiary hues which are usually characterized as RYB color wheels. A color wheel which is based on RGB as the primaries is usually known as HSV (hue, saturation, and value) color wheel. A simplification showing only fully saturated hues can be used in for purposes of color design. Figure 16 illustrates the RYB color wheel. The RYB color wheel was originally described by Isaac Newton in his 1704 treatise on Opticks.14 The 18th century understanding of color vision was predicated on the idea that red, yellow, and blue were the primary colors. The use of the RYB color wheel as a model for complementary colors and as a basic tool for art and printing became well established. Two documents, Goethe15 and Chevreul,16 became the handbooks for color theory. Even today the RYB color wheel is  2011 Jo h n Wiley & So n s, In c. 115 www.wiley.com/wires/compstats Overview (a) (b) Red Redviolet Redorange Orange Violet Blueviolet Yelloworange Yellow Blue Bluegreen Yellowgreen Green FIGURE 16 | The RYB color wheel. These images are used under GNU Free Documentation License. (a) (b) H Red Orange Rose Magenta Yellow Chartreuse green Violet Blue Green Azure Cyan Spring green FIGURE 17 | HSV color wheel based on RGB primaries. The left image shows primary, secondary and tertiary hues. The right image show a more continuous version of the hues. These images are used under GNU Free Documentation License. used to describe complementary colors in art and photography.17 In general, color design principles suggest a number of different strategies for using color. The simplest strategy would be to choose a monotone achromatic scheme. Such a scheme would not employ any color at all, but use black, white, and shades of gray. This kind of color scheme is sometimes used by interior designers, but while it can be dramatic, it also risks being boring. A related scheme is a monotone chromatic scheme. Here, a single hue is chosen, which is varied in lightness and saturation. Again, this type of scheme can be boring. Another scheme is an analogous hues scheme. In such a use of color, two or three hues close together in color space are used. For example, shades of green or blue greens can be used effectively. A more daring use of color is 116 a complementary color scheme. Here complementary colors on the color wheel are used. An example using the RYB color wheel would be blue and orange or the Christmas colors of red and green. Another color scheme is the split complementary color scheme. Instead of choosing the exact complementary color, choose colors that are adjacent to the complementary color. So that opposite to orange would be blue, but a split complementary scheme might choose blue–green and blue–violet. Usually one would want the split complementary hues to be also different in brightness and somewhat desaturated. A final strategy is a triad color scheme. Here one can choose three colors equally spaced around the color wheel. As with the split complementary scheme, two of the hues should be desaturated.  2011 Jo h n Wiley & So n s, In c. Vo lu me 3, March/April 2011 WIREs Computational Statistics Color theory and design Examples of these schemes are found in US postage stamps. These stamps are often design with the color principles in mind. The 2010 Katherine Hepburn stamp is an example of the monotone achromatic scheme. The 2010 Holiday Evergreens Forever stamp is a good example of the monotone chromatic scheme. The 2010 Love stamp is a good example of an analogous hues scheme. The 2008 Winter Holidays stamp has four different designs which illustrate the complementary color scheme. The 2010 Lunar New Year stamp is a good example of the triad color scheme. While we cannot reproduce these stamps here, their images are easily found on the web. Figure 17 illustrates the HSV color wheel with only the fully saturated colors indicated. The use of this color wheel for color design has also been used, although we do not pursue that idea for this article. • black: death, rebellion, strength, evil • white: purity, cleanliness, lightness, emptiness • yellow: warmth, cowardice, brightness • green: nature, health, cheerfulness, environment, money, vegetation. These, of course, are based primarily on impressions from a Western culture. We do not discuss this dimension of color at any length except to note that there can be an emotional response to color so that the use of color in data and scientific visualization should be approached with these possible responses in mind. CONCLUSIONS Color as a Cultural Expression Color, of course, also evokes emotion, which, to a large extent, is culturally based. Green12 makes suggestions of these responses: • red: urgency, passion, heat, love, blood • purple: wealth, royalty, sophistication, intelligence • blue: truth, dignity, power, coolness, melancholy, heaviness We have all experienced color to some extent, even those who have limited color vision. In this article, we have tried to systematically lay out principle of color theory and design with the goal of making sense in the development of scientific and data visualization software. By understanding color theory, the functioning of the human visual system, and basic color design principles, we hope that the reader will appreciate good usage of color when he or she sees it and will employ these principles when designing displays. ACKNOWLEDGEMENTS This article is based on lectures given by one of us (E.J.W.) in graduate courses in Statistical Data Mining and in Scientific and Statistical Visualization. Much of the discussion in the Section on Color Deficiencies in Human Vision and the Subsection on Hard-Wired Perception is based on material in Green (2004). The inspiration of Marc Green is hereby gratefully acknowledged. REFERENCES 1. Goldsmith TH. Optimization, constraint, and history in the evolution of eyes. Q Rev Biol 1990, 65:281–322. 2. Munsell AH. A Color Notation. Boston, MA: G. H. Ellis Co; 1905. 6. Wright WD. A re-determination of the trichromatic coefficients of the spectral colours. Trans Opt Soc 1928, 30: 141–164. doi:10.1088/1475-4878/30/4/301 7. 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How Population Aging Differs Across Countries: A Briefing on Global Demographics. Stanford, CA: Stanford Center on Longevity; 2007. 14. Newton I. Opticks. London: The Royal Society; 1704. 12. Green M. 2004. http://www.visualexpert.com/. (Accessed November 30, 2010). 16. Chevreul M-E. De la Loi du Contraste Simultané des Couleurs et de l’assortiment des Objets Colorés, 1839. 13. Luo Q, Wegman E, Fu X. CrystalVision, a Visual Data Mining package for Windows, 2000. 17. Mante H. Color Design in Photography. New York: Van Nostrand Reinhold; 1972. 15. Goethe JWv. Zur Farbenlehre. Dortmund: Harenberg Kommunikation; 1810 (Republished 1979). FURTHER READING Eddy WF. An introduction to color systems, Stat Comput Stat Graph Newslett 1990, 1:7–10. Editors of Time-Life Books. Color. New York: Time Life Books; 1970. Mante H. Photo Design: Picture Composition for Black and White Photography. New York: Van Nostrand Reinhold; 1971. 118  2011 Jo h n Wiley & So n s, In c. Vo lu me 3, March/April 2011