Color matching calculations

Kubelka-Munk theory n. A theory describing the optical behavior of materials containing small particles, which scatter and absorb radiant energy. It is widely used for color matching calculations. The mathematical equation describes the reflectance or transmittance in terms of an absorption coefficient, K, and a scattering coefficient, S. The K-M theory is based on the assumption of... 

Today, the speed of the Pentium processors has allowed for much more complicated algorithms written on the Windows platform, such as computing many-flux calculations and spectral matching routines. New color-matching technology provides sophisticated and intuitive color formulation that is easily learned and used by the expert as well as the novice color matcher. 

The database is an integral part of a computer color-matching system. It is the characterization of all pigments and resins from which formulas will be calculated. Creating a database involves producing samples of pigments, resins, and known mixtures of each. Once database samples are measured and saved to the database, the database is calibrated. 

Contemporary color-matching systems enable sample additions to the calibration database for increased performance. In addition, the sample set is variable for each individual colorant. An application may require only 5 samples for a yellow colorant but 12 samples for a reflex blue to achieve optimum performance. Note that additional samples, are used in the calculation of the absolute K and S data. These samples are not a function in a search-and-correct calculations. 

Because basic pigment properties are calculated using absolute units, how they are applied in the matching algorithm add versatility to contemporary color-matching... 

Both reflectance and transmittance measurements can be applied to the same database. For plastics and translucent liquids and for printing or coating on nonopaque substrates, this is a very important feature. In these applications it is not sufficient to match a standard in reflectance only a transmission match is equally important. Contemporary color-matching systems can combine both types of matches in one calculation using only one database. To use this capability, it is necessary that the spectrophotometer measure both the reflectance and total transmittance of the sample. 

X n. Special color matching functions of the CIE standard observer used for calculating the X tristimulus value. McDonald R (ed) (1997) Colour physics for industry, 2nd edn. Society of Dyers and Colourists, West Yorkshire, England. 

Y n. Special color matching function of the CIE standard observed used for calculating... 

Beside visual assessment, the color of an object can be characterized more precisely in terms of mathematical models, which are based on the remission and transmission spectra in the visible light area [6]. The most common CIELAB system, defines a color space and allows one to describe a specific color in terms of L (lightness) and the color coordinates a and b, and color differences or tolerances by related AL, A Ab and a combined AE value. L, a, b, values can be transformed into the probably more convenient terms of L (lightness), h (hue) and c (chroma). Today, colorimetry software is used for color matching and allows very precise calculations of pigment formulations. 

The tables incorporated into color calculating routines by spectrophotometer manufacturers can be found in the ASTM publication Standard Test Method for Computing the Color of Objects by Using the CIE System (90). This ASTM standard is a compilation of calculated product tables for various illuminants with the two standard observers for color matching. Both standard observers are used in various industries to specify color. The operator must choose which observer is to be incorporated into the color calculations for the measured specimens. The overall difference in the color of an object observed by the 10° CIE 1964 Supplementary Observer or the 2° CIE 1931 Observer is usually small but noticeable. This is due to an uneven distribution of cone receptors in the retina of the standard eye. At a solid acceptance (cone) angle of 2°, light from the object activates the cones around the fovea, which are relatively close together and allow maximum... 

The difficult task of expressing our everyday experiences of color matching often cannot be adequately defined in a color space. Extended light sources, flicker, stroboscopic effects, variable contrast backgrounds and surrounds, matte surfaces, and polished top layers such as a leaf (107) and others cannot be properly defined mathematically. Calculations that involve such parameters are only approximations of the situations they represent. Try to imagine how dull a scene would be if you only perceived instrument measured color information. 

Fig. 8 Top variation of the average surface charge a) = Q)/A with potential, for a supercapacitor composed of a l-butyl-3-methylimidazolium hexafluorophosphate ionic liquid electrolyte and graphite electrodes. The points are raw data extracted from CGMD simulations while the lines are different polynomial fits of the data. Bottom Surfacic differential capacitance, which is either calculated by differentiating a = f(A ) (the colors match with the top panel plots), or from the fluctuations of the charge, using importance sampling methods (WHAM). °...

The cone spectral sensitivities may be regarded as colormatching functions based on primaries that are said to be imaginary in the sense that, although calculations of color matches based on them are possible, they are not physically realizable. To exist physically, each such primary would uniquely excite only one type of cone, whereas real primaries always excite at least two types. 

The calculated value of A has the right units, and the numerical value matches the values found in Table 20-5. The color is right, as shown by the photo in the margin of page 885. 

The proper implementation of the CIE system requires use of a standard illumination source for calculation of the tristimulus values. Three standard sources were recommended in the 1931 CIE system, and these may be presented in terms of color temperatures (the temperature at which the color of a black-body radiator matches that of the illuminant). The, simplest source is an incandescent lamp, operating at a color temperature of 2856 K. The other two sources are combinations of lamps and solution filters designed to provide the equivalent of sunlight at noon, or the daylight associated with an overcast sky. The latter two sources are equivalent to color temperatures of 5000 K and 6800 K, respectively. 

Fig. 5. Structural superposition of binding sites using Med-Sumo . The Surface Chemical Features (SCF) are used to superimpose the protein binding sites (toppanel).The SCF are represented in color code bar (bottom panel) and the SUMO score measure the quality of the 3D structural superimposition that is calculated using a bit-wise matching algorithm of the color code-bar fingerprint (bottom panel).

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