Color science

Our color science is what makes the output of the digital imaging system produce faithful and accurate color images. The science of calibrating computer input and output devices (scanners, displays, printers) and of image processing has been an important topic of research for our group. The following paragraphs give a brief overview of some of the fundamental principles of color.

Introduction

The sensation of color is evoked by the physical stimulation of light-sensitive elements in the human retina. The stimulation consists of electromagnetic radiation in the visible spectrum comprising wavelengths between 380 and 780 nm. The light-sensitive elements, known as cones, can be separated into three classes, each class being sensitive to a different spectral distribution of radiation. This trichromacy of color sensation means that many different spectral distributions can produce the same perceived color. Such equivalent stimuli, even though they have physically different spectral distributions, are called metamers and the phenomena metamerism. Metamerism is fundamental to the science of color measurement, and without it, viewing a continuous variation of color from a color CRT display could not exist. In fact, nearly all colors seen on a color CRT are metamers.

Color matching

Because of the phenomenon of trichromacy, any color stimulus can be matched by a mixture of three primary stimuli, so long as none of the three can be matched by a mixture of the other two. Color matching can be expressed as:
equation 1

which should be read as "color stimulus C is matched by R units of primary stimulus R mixed with G units of primary stimulus G and B units of primary stimulus B." All colors having the same tristimulus values R, G, and B are metamers; they will match color stimulus C and will appear to be the same color.

Experimental results have shown that for most practical purposes color matches obey the rules of linearity and additivity. This principle, as applied to color, is known as Grassmann's law. What this means, as a practical matter, is that if two color stimuli

are mixed, the resulting stimulus will be
equation 3

The consequence of Grassmann's law is that if the tristimulus values of every monochromatic stimulus of unit radiance are known, the tristimulus values of any other stimulus can be calculated by integration. Thus, if the tristimulus values of all monochromatic stimuli are denoted as formula 1 per unit radiance, then the tristimulus values of a stimulus having a spectral radiant distribution of formula 2 are

Experimental measurements of color matching have been carried out using a significnt sample of people with normal color vision. A set of three functions, formula 3 , derived from these experiments have been used by the Commission International de L'Éclairage (CIE) in 1931 as the basis of an international standard. The three functions, known as color-matching functions, are shown below.

Figure: Color-matching functions of the CIE Standard Observer based on matching stimuli of wavelengths 700.0, 546.1, and 435.8 nm.

At the same time these color-matching functions were adopted as a standard, the CIE adopted another set of cleverly designed primary stimuli that have special properties; they are designated as X, Y, and Z, with corresponding tristimulus values X, Y, and Z and color-matching functions formula 4 Although X, Y and Z are linearly related to R, G and B, they are imaginary (non physical) primaries chosen so all luminance information in any mixture of the three is contributed by Y. Another condition of their choice makes the three color-matching functions have non-negative values at all wavelengths. The color-matching functions shown below are normalized to have equal valued integrals over the visible spectrum.

Figure: CIE 1931 color-matching functions

Standard illuminants and illumination sources

For secondary light sources (either reflecting or transmitting objects), the stimulus formula 5

is replaced by either formula 6

, where

is the spectral reflectance factor, formula 9

is the spectral transmittance factor and formula 10

is the spectral distribution of the illuminant. Thus, formula 11

is a perfect white-reflecting diffuser and formula 12

is a clear transmitting filter. The perceived color of any transmitting or reflecting object is a funciton of the illuminant, formula 10

. In 1964, the CIE defined the spectral distribution functions of standard illuminants and their correlated color temperatures (expressed in degrees Kelvin). These illuminants, though mathematically defined as standards, are not precisely realizable as physical sources. The illuminant chosen for our viewing conditions is Illuminant D(50)

, having a correlated color temperature of 5000° Kelvin. Illuminant D(50)

, is approximately equivalent to natural noon-day sunlight on a bright but slightly overcast day. The light source chosen for illuminating both reflective and transmissive objects to be scanned in one configuration of our digital imaging system is a tungsten-halogen bulb having a correlated color temperature of 3250° Kelvin. The spectral distributions of the chosen viewing illuminant and illuminating source are shown here.

Figure: Relative spectral power distributions of a tungsten-halogen source and the CIE Standard Illuminant

The above is based on the IBM Research Report RC19240 "Color Calibration for the TDI Pro Scanner" by Gordon W. Braudaway and Hon-Sum P. Wong.

Additional reading

More extensive treatments of the theory of color may be found in the following references:

G. Wyszecki and W. S. Styles, Color Science: Concepts and Methods, Quantitative Data and Formulae (2nd ed.), John Wiley & Sons, Inc., New York, 1982.
D. B. Judd and G. Wyszecki, Color in Business, Science, and Industry (3rd ed.), John Wiley & Sons, Inc., New York, 1975.
C. A. Poynton, Poynton's Color Technology Page, an on-line site with some good information.

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