Ch.7 - Color Systems

 

There are many possible ways to specify the color of an object. Here we will look at 3 such methods, each differing from the other in some minor and some major ways. All provide a way to “quantify” the concepts of hue, saturation, and brightness.

 

Munsell System

 

Devised by Munsell in 1905 (and later revised), this system relies on a system like that of Newton’s color wheel to locate hue and saturation on a disk using circular coordinates. Hue is determined along the edge of the disk, and saturation the distance from the center. Brightness is measured along the axis running perpendicular to the disk, creating a cylindrical coordinate system.

 

 

It was designed to allow the viewer to describe and compare colors of objects. They must be viewed under the same illumination, however. The illumination used is north skylight (the one usually favored by painters).

 

Hue: 10 hues, each subdivided into 10 subdivisions, for 100 equally-spaced subhues

Chroma (Saturation): 0 (gray) to 10-18 (full color), depending on the hue

Value (Brightness): 0 (black) to 10 (white)

 

Designations: H V/C

 

The actual 3D shape of the system is somewhat irregular, as it is set by how well the average human eye can distinguish the various combinations of HVC.

 

 

Advantages: A relatively simple system for comparing colors of objects by assigning them a set of numbers based on standard samples. Widely used in practical applications such as painting and textiles.

 

Disadvantages: Complementary colors are not on opposite sides, so that one cannot predict the results of color mixing very well.

 

Ostwald System

 

Here, the color-space is essentially defined by a double cone. The hue is specified by the direction away from the central axis, as it was in both Newton’s color wheel and the Munsell system. In the Ostwald system, the hue is set by the dominant wavelength of the reflectance curve for each color. In a manner similar to the other two systems, saturation is determined by the distance from the central axis, and brightness the location along this axis. So here we have

 

Dominant Wavelength (Hue)

Purity (Saturation)

Luminance (Brightness)

 

The actual numerical values assigned to the purity and luminance of a color are set by using “temporal mixing” of the human eye. A spinning disk with wedges of “pure” color, white, and black is used. The “color” of a stationary uniform test patch that matches a spinning disk containing X% pure color, Y% white and Z% black would be C=X, W=Y and B=Z, or X Y Z for short. (Note that because X+Y+Z MUST equal 100, it really only requires TWO numbers to specify the purity and luminance.) Thus, the dominant wavelength, and XYZ (or CWB) specify the overall color.

 

 

If the “pure (or full) color” is at the “equator” of the color-space, going toward the “north pole” gives the effect of adding white at the expense of the color while keeping black fixed.  Going toward the “south pole” gives the effect of adding black at the expense of the pure color while keeping the white fixed.

 

Description of Processes:

 

Tinting: adding white to the full color

Toning: adding gray to the full color

Shading: adding black to the full color

 

 

Note that these “definitions” are not precise  where do you draw the line between tinting and toning (i.e. how bright is your gray?)

 

Application to Printing

 

Because the purity & luminance is set by the fraction of white and black sitting “along side” the pure color on the spinning disk that the eye temporally blends into a color, this system is very useful in the printing industry, where the eye spatially blends black and colored inks on white paper.

 

The C.I.E. (Commission Internationale d’Eclairage) System

 

This is the real standard used most widely today, as it is based on quantitative colorimetry. It uses:

 

Luminance (Brightness)

Chromaticity (Hue & Saturation) as a combination of 2 coordinates (x,y)

 

Graphically, it resembles Newton’s Color Circle, but its shape is determined by the properties of how true spectral sources are perceived when colors are combined, and there is a discontinuity between violet and red that contains the non-spectral purples.

 

Important locations:

 

Perimeter: the “dominant wavelength” of the SPD of the source/object

(x,y) = (1/3,1/3): achromatic point (white & grays) = “equal power point”

 

Purity: relative displacement of the object/source from the achromatic point (no color) to the perimeter (pure saturated color).

 

 

Addition of 2 Colors: On a line joining the two dominant wavelengths, weighted by their respective luminances (closer to the brighter one, of course!)

 

Addition of N colors: weighted sum, as was the case for 2 sources. For RGB, anything within the triangle with these at the corners can be produced. NOTE: many colors lie outside this region, and cannot be produced with RGB addition!! Also note that one can get saturated colors between R and G but not G and B!

 

Color printing also has its region of chromaticity it can produce.

 

 

Practical applications in displays:

 

For any 3-color emitting device, the possible combinations of (x,y) that can be produced depends on the (x,y) values of the 3 individual colors. This will be true for CRT displays (thick computer monitors & standard color TVs), LCDs (laptop displays & flat-panel LCD TVs), or plasma displays (etc.). Pure RGB displays, therefore, cannot produce highly saturated yellows & greens.

 

 

In principle, the chromaticity in the CIE system can be done on any colored surface, including the standards in the Munsell and Ostwald systems. Hence it is possible to convert between these systems (see Fig. 3-19 of the textbook to see how the Munsell system “maps” onto the CIE plane).

 

Tristimulus Values

 

Thomas Young discovered in 1802 that the human eye seemed to have 3 separate color receptors. In fact, the human eye’s main color receptors under good lighting conditions, the cones, do behave this way. But their actual operation is more complex than would occur with three simple independent light meters (more on this later). But given this fact, he reasoned that all perceived colors could be obtained with the appropriate mixes of “output” from these 3 sensors.

 

More experiments by Maxwell indicated that these 3 “primary colors” were not unique in being able to produce a perceived “white”. Many combinations can do this, as you can see by looking at the CIE color diagram. Furthermore, some saturated colors cannot be produced from just 3 other ‘primaries”.

 

Color Matching

 

To uncover how the human eye detects color quantitatively, color-matching experiments are performed. On adjacent regions of a reflective surface the “sample” color and an RGB (or other combination) mix is projected. The RGB outputs are adjusted until the two regions match in hue, saturation, and brightness. The individual outputs of each RGB source provides a quantitative set of numbers. Usually these are specific monochromatic sources:

 

B is 436 nm

G is 546 nm

R is 700 nm

 

In REAL units, white requires 0.014 B + 0.0189 G + 1.000 R (note the insensitivity of the eye to 700 nm!!) but these are usually “renormalized” to 1B + 1G + 1R giving “white”.

 

Maxwell also found that to get some perceived colors from RGB, a little bit of R (usually) or G or B has to fall on the “sample” to get a match. Mathematically, this would be the same as having a negative contribution of R, G, or B, since it has to be “added to the other side”.

 

Using mixes of the above-listed wavelengths, it was possible to match virtually any monochromatic sample. The amount of each required is given by the color matching functions:

 

 

 

 

For example, to reproduce the eye’s response to a monochromatic sample with a wavelength of 600 nm, requires green and red in the relative amounts 0.06246 and 0.34429, or a ratio G/R = 0.1814. The total amounts are not critical, as the chromatic sensitivity of the eye is not very dependent on the total luminance.

 

Another example: To reproduce a 500 nm sample requires 0.04776 B, 0.08536 G and 0.07173 R. Here, one would have to shine a small amount of R onto the sample, in order to match the B+G next to it.

 

Non-monochromatic Sources

 

Most real objects are not monochromatic. They have broad SPDs. What combinations of RGB are needed to reproduce real objects illuminated by white light? This is what to do:

 

Get the SPD of the object illuminated by a white light source

 

Calculate the product of SPD_λ and the color matching function for R, G, and B at each λ.

 

For each of R, G, and B, add up these products over all of the values of λ.

 

(The mathematically astute will recognize this as the product integrated over wavelength λ).Using the example from your textbook, let’s do this for butter:

 

 

 

 

 

 

CIE xyz System

 

In principle, we could use 3 sources other than the RGB ones used earlier. The CIE system, in fact, has defined another set of 3 called xyz that “mathematically” can produce any real value, and a number of ‘unreal” ones. They are defined by positive and negative contributions of RGB, and are thus not truly “physical” sources.

 

We will not do much on this, but still utilize the xy coordinates to calculate the effects of real light sources.

 

Light Sources on the CIE Diagram

 

The colors we perceive from real light sources can be located on the CIE chromaticity diagram. The CIE has 3 common non-chromatic light sources: a 2800 K incandescent lamp (“A”), direct sunlight (“B”), and overcast skylight (“C”). Other sources, such as neon and argon lasers, produce a series of monochromatic emission lines, which are located on the periphery of the CIE curve.

 

 

Color Addition on the CIE Diagram

 

Given the (x,y) coordinates of 2 sources, the chromaticity of their sum can be found by calculating the weighted sum of the two individual components.

 

Let’s use the example from the textbook (page 76) to see this in action. Suppose we had 2 light sources with coordinates (x,y) of:

 

(x₁,y₁) = (0.12,0.33) a blue-green color  position “P” below

(x₂,y₂)=(0.45,0.51) a yellowish color  position “Q” below

 

If the blue-green source 1 is 2 times brighter than the yellowish source 2, then obviously the combination will be weighted closer to the former than the latter. Mathematically:

 

The result would be found at (x₃,y₃) = (0.23,0.39), indicated by position “T”:

 

 

Note that “E: is the nonchromatic “white light” location.

 

Location T could also be produced using a monochromatic source of wavelength 500 nm mixed with white light, mixed with the proper weights. Also note that mixing P and Q will give a hue equal to a 500 nm monochromatic source, but it will not achieve a saturated color.

 

In reality, the situation is not quite so simple (see Appendix 3 if you want to know more). Human judgement of mixtures of “white” and monochromatic light are not always precise straight lines (see Fig. 3-19 of the textbook to see how this translates to the Munsell system).

 

A similar “problem” occurs in color matching a sample, as described earlier:

 

 

In the diagram above, B and G of the correct relative brightnesses will give a 500 nm hue, but it will not be saturated. One cannot add more RGB colors to get better saturation, either. The only way to match a saturated 500 nm hue with an adjacent region illuminated by RGB would be to let some R shine on the “monochromatic”  sample.