Colour Representation

[Hill: 672-688. Foley & van Dam: p. 574-604]

Light

Visible light consists of a spectral distribution of electromagnetic energy having wavelengths in the range 400-700 nm. The perceived colour of visible light is to some extent a subjective experience.

The electromagetic spectrum

ROY G BIV acronym

The following is a potential spectral energy distribution of light reflecting from a green wall.


The Retina

The retina has both rods and cones, as shown below. It is the cones which are responsible for colour perception.

There are three types of cones, referred to either as B, G, and R, or equivalently as S, M, and L, respectively. Their peak sensitivities are located at approximately 430nm, 560nm, and 610nm for the "average" observer. Animals exist with both fewer and more types of cones. The photopigments in rods and cones are stimulated by absorbed light, yielding a change in the cell membrane potential. The different types of cells have different spectral sensitivies:

Mapping from Reality to Perception

Different spectra can be perceptually identical to the eye. Such spectra are called metamers. Our perception of colour is related only to the stimulation of three types of cones. If two different spectra stimulate the three cone types in the same way, they will be perceptually indistinguishable.

Colour Matching

In order to define the perceptual 3D space in a "standard" way, a set of experiments can (and have been) carried by having observers try and match colour of a given wavelength, lambda, by mixing three other pure wavelengths, such as R=700nm, G=546nm, and B=436nm in the following example. Note that the phosphours of colour TVs and other CRTs do not emit pure red, green, or blue light of a single wavelength, as is the case for this experiment.

The above scheme can tell us what mix of R,G,B is needed to reproduce the perceptual equivalent of any wavelength. A problem exists, however, because sometimes the red light needs to be added to the target before a match can be achieved. This is shown on the graph by having its intensity, R, take on a negative value.

In order to achieve a representation which uses only positive mixing coefficients, he CIE ("Commission Internationale d'Eclairage") defined three new hypothetical light sources, x, y, and z, which yield positive matching curves:

If we are given a spectrum and wish to find the corresponding X, Y, and Z quantities, we can do so by integrating the product of the spectral power and each of the three matching curves over all wavelengths. The weights X,Y,Z form the three-dimensional CIE XYZ space, as shown below.

Often it is convenient to work in a 2D colour space. This is commonly done by projecting the 3D colour space onto the plane X+Y+Z=1, yielding a CIE chromaticity diagram. The projection is defined as:

The chromaticity diagram looks as follows. 



A few definitions: 


  
spectroradiometer 
  
A device to measure the spectral energy distribution. It can therefore 
  also provide the CIE xyz tristimulus values. 
  
illuminant C 
  
A standard for white light that approximates sunlight. It is defined by a 
  colour temperature of 6774 K. 
  
complementary colours 
  
Colours which can be mixed together to yield white light. For example, 
  colours on segment CD are complementary to the colours on segment CB.

  


  

  
dominant wavelength 
  
The spectral colour which can be mixed with white light in order to 
  reproduce the desired colour. Colour B in the above figure is the dominant 
  wavelength for colour A. 
  
non-spectral colours 
  
Colours not having a dominant wavelength. For example, colour E in the 
  above figure. 
  
perceptually uniform colour space 
  
A colour space in which the distance between two colours is always 
  proportional to the perceived distance. The CIE XYZ colour space and the CIE 
  chromaticity diagram are not perceptually uniform, as the following 
  figure illustrates. The CIE LUV colour space is designed with perceptual 
  uniformity in mind.

  
 

  


Colour Gamuts
The chromaticity diagram can be used to compare the 
"gamuts" of various possible output devices (i.e., monitors and printers). Note 
that a colour printer cannot reproduce all the colours visible on a colour 
monitor.







The RGB Colour Cube
The additive colour model used for computer graphics 
is represented by the RGB colour cube, where R, G, and B represent the colours 
produced by red, green and blue phosphours, respectively.





The colour cube sits within the CIE XYZ colour space as follows.







Colour Printing
Green paper is green because it reflects green and 
absorbs other wavelengths. The following table summarizes the properties of the 
four primary types of printing ink. 




  
  

    dye colour
    absorbs
    reflects

  

    cyan
    red
    blue and green

  

    magenta
    green
    blue and red

  

    yellow
    blue
    red and green

  

    black
    all
    none


To produce blue, one would mix cyan and magenta inks, as they both reflect 
blue while each absorbing one of green and red. Unfortunately, inks also 
interact in non-linear ways. This makes the process of converting a given 
monitor colour to an equivalent printer colour a challenging problem. 

Black ink is used to ensure that a high quality black can always be printed, 
and is often referred to as to K. Printers thus use a CMYK colour model. 

Colour Conversion
Monitors are not all manufactured with identical 
phosphours. To convert from one colour gamut to another is a relatively simple 
procedure (with the exception of a few complicating factors!). Each phosphour 
colour can be represented by a combination of the CIE XYZ primaries, yielding 
the following transformation from RGB to CIE XYZ:


 

The transformation 
 yields the colour on monitor 2 which is 
equivalent to a given colour on monitor 1. Quality conversion to-and-from 
printer gamuts is difficult. A first approximation is shown on the left. A 
fourth colour, K, can be used to replace equal amounts of CMY, as shown on the 
right. 
                   K = min(C,M,Y)
  C = 1 - R        C' = C - K
  M = 1 - G        M' = M - K
  Y = 1 - B        Y' = Y - K



Other Colour Systems
Several other colour models also exist. Models such 
as HSV (hue, saturation, value) and HLS (hue, luminosity, saturation) are 
designed for intuitive understanding. Using these colour models, the user of a 
paint program would quickly be able to select a desired colour.