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Separation of 'Colour' and 'Brightness'

Since the human eye has three types of colour sensors, a full plot of all visible colours would be a three-dimensional figure. However, the concept of colour can be divided into two parts: 'brightness' (or luminance) and 'chromaticity', which is a specification of the quality of a colour, regardless of its brightness.  The chromaticity of a particular colour can be expressed by two quantities, r and g, which are defined as the R(red) value of the colour matching function, at a specific wavelength, divided by the sum of R+G+B (representing overall brightness), and G (green) divided by R+G+B.  The third colour component B can be derived by subtraction of the other two, since they must add up to the overall brightness. Mathematically, this can be expressed in two equations:

 

 
 

 and

 
 

 

By following this procedure, a two-dimensional plot of chromaticity can be produced.  For single-wavelength colours of the spectrum, the result is shown in Figure 2, below, where the wavelengths are indicated in nanometres along the horse-shoe shaped path of the spectral colours.

 

Figure 2 - Chromaticity Diagram in CIE rg Chromaticity Space
Notice that the path of the spectral colours passes through rg=(0,0) at 435.8 nm, through rg=(0,1) at 546.1 nm and through rg=(1,0) at 700 nm, since these are the defined primaries.  Also, the equal energy point (E) is at rg=(1/3,1/3).

 

Because of Grassman's law, described above, any colour that can be perceived by the human eye can be represented by r and g values that lie inside the path of the spectral colours.  All the colours achieved by mixing single-wavelength spectral colours lie along a line joining the two wavelengths on the spectral path.  The mixtures include colours made by mixing spectral colours at opposite ends of the spectrum (Red and Blue), which are known as 'Purples' and do not have any equivalents in the monochromatic spectrum.  The line joining the two ends of the spectral path is called the 'line of purples'.

 

The CIE XYZ Colour Space

 

For various technical and convenience reasons, the CIE went on to define a new colour space, with the aim of providing colour matching functions that are always positive numbers. The new colour matching functions, were called , , and .

 

Because of the linearity of human colour perception, it was possible to achieve the desired aim through linear mathematical transformations of the RGB data shown in Figure 2.  The procedure is shown diagrammatically in Figure 3 below:

 

 

Figure 3 - Construction of the triangle specifying the CIE XYZ color space.
The triangle Cb-Cg-Cr is  the xy=(0,0),(0,1),(1,0) triangle
in CIE xy chromaticity space.

 

Figure 3 shows the CIE xy chromaticity axes as red lines. These lines enclose the entire spread of colours that can be seen by the standard observer.  This is called the ‘gamut’ of human colour perception.  The line connecting Cr and Cb is the line of zero luminance, along which the human eye has no spectral sensitivity, and is called the 'alychne' (pronounced al-ik-knee). 

 

After applying the necessary linear mathematical transformations, the chromaticity plane xy of the new XYZ colour space is as shown in Figure 4, below. 

 

Note: When looking at Figures 3 and 4 on your monitor, the colours you see depend on the colour space of the device, and no device has a gamut large enough to present an accurate representation of the chromaticity at every position on the diagrams.

 

 

 Figure 4 - The CIE 1931 xy color space chromaticity diagram.

 

The curved edge of the gamut is called the ‘spectral locus’ and corresponds to monochromatic light, with wavelengths indicated in nanometers. The straight edge on the lower part of the gamut is the line of purples. Less saturated colours appear in the interior of the figure, with white at the centre, where x=y=1/3.

 

Practical Colour Spaces

 

For any two points within the chromaticity diagram shown in Figure 4, then all those colours, which can be formed by mixing the colours at these points, lie on a straight line connecting the points.  Similarly, all colours that can be formed by mixing three sources are found inside the triangle formed by the source points on the chromaticity diagram (and so on for multiple sources).  Unfortunately, the ability of the human eye to perceive differences in colour is not uniform as one travels along one of these lines.  In some parts of the chromaticity diagram, quite small movements result in significant difference in colour perception whereas, in other places, the x and y values can change by relatively large amounts before a human observer notices a significant difference.

 

The perception of changes in chromaticity becomes important in digital photography because 'digitisation' limits the number of values of x and y that can be used.  For an 8-bit system, there are 256 possible different values of each of the three tristimulus values, and it is important to ensure that the digitisation steps are used as effectively as possible within the overall colour space.

 

The very wide gamut of the CIE colour space, where the primaries are at the limits of human vision, makes it unsuitable for work with 8-bit channels, because visible steps between colours (known as posterisation) will inevitably result.

 

The sRGB Colour Space

 

The sRGB (standard RGB) colour space was proposed by Hewlett-Packard and Microsoft, with the digitisation constraints in mind, to display colour in a consistent and reproducible way on a computer monitor.  sRGB defines the chromaticities of red, green, and blue ‘primaries’, defined as those colours where two out of the three channels are zero. The gamut of chromaticities that can be represented in sRGB is the colour triangle enclosed by these primaries. The sRGB's color gamut encompasses only about 35% of the visible colours specified by the CIE but was carefully chosen to provide an adequate representation of colour within the constraints of an 8-bit system.  The sRGB triangle is shown in Figure 5.

 

 

Figure 5 - The colour triangle of the sRGB colour space and location of the primaries.
The white point (D65) is shown in the centre.
Note that areas of the CIE XYZ colour space outside the triangle cannot be accurately coloured,
because they are out of the gamut of computer displays.

 

Th numbers in parentheses are the Red, Green,and Blue 8-bit values stored in the sRGB data file of the image. As one moves along one of the sides of the triangle, the numbers for the farther primary increase, becoming equal at the points shown on the diagram. The third value increases as one moves towards the primary on the opposite side of the diagram. At the 'white point' in the centre, all three values are (255,255,255). This 'white point' is chosen to be equivalent to overcast daylight with a colour temperature of 6500K, hence the term 'D65'. The 8-bit 'numbers' corresponding to any given point within the colour space are contained in the file that is passed from camera to display device. The colours that you see are then generated by the phosphors in the monitor or the inks in the printer. If your display interprets the numbers differently, through not being set to the same colour space, it will not reproduce the colours in the same way as they were interpreted by the camera.

 

The sRGB colour space also defines a non-linear transformation between the intensities of the primaries and the actual numbers stored. This curve is designed to replicate the brightness response of a computer display, known as the ‘gamma’ of the display. It is very important to reproduce this curve accurately, in order to get the correct display of an sRGB image. The form of the Gamma curve is shown in Figure 6.

 

Figure 6 - Non-linear Response of Computer Display (gamma).

 

This non-linear conversion means that sRGB provides a reasonably efficient use of the values in an integer-based (8-bit) image file. More detailed information on the sRGB colour space and the Gamma response function can be found at http://en.wikipedia.org/wiki/SRGB .

 

Since sRGB serves as a "best guess" for how another person's monitor produces colour, it has become the standard colour space for displaying images on the internet.  The relatively small gamut provided by sRGB is still considered broad enough for most colour applications.

 

The Adobe RGB Colour Space

 

The sRGB colour space is sometimes avoided by high-end print publishing professionals because its colour gamut is not large enough, especially in the blue-green colours, to include all the colours that can be reproduced in printing.  Printers use ‘subtractive’ colours of cyan, magenta, and yellow, together with black ink (‘CMYK’) and these inks have significantly different properties from the ‘additive’ red/green/blue elements of luminescent displays.

 

The ‘Adobe RGB 1998’ colour space was designed by Adobe Systems, Inc. to encompass most of the colours achievable on CMYK printers, but by using only the RGB primary colours that can be shown on a computer display.  This colour space, shown in Figure 7, encompasses roughly 50% of the visible colours specified by CIE, improving upon the sRGB gamut primarily in cyan-greens.

 

 

Figure 7 - The colour triangle of the Adobe RGB 1998 colour space
and location of the primaries.
The white point (D65) is shown in the centre.
Note that areas of the CIE XYZ colour space outside the triangle cannot be accurately coloured,
because they are out of the gamut of computer displays.

 

Although Adobe RGB can reproduce more saturated cyan-greens, the converse is that less saturated colours are represented by lower numbers than in sRGB. For example, the green primary (0,255,0) in the Adobe colour space is further from the white point, so the green 8-bit value will be smaller when the location of the primary in sRGB colour space is reached. The result is that if a file of Adobe RGB data is mistakenly displayed it as if it were sRGB, it looks unsaturated and washed out. This is precisely what happens in almost all web browsers and other common programs that are not ‘colour space’ aware.

 

Within the limitations of 8-bit encoding, Adobe RGB colours are further apart from one another than are those in sRGB, since the number of distinct colour values available is the same as in sRGB but they have to cover a wider gamut.  Because the colour values are more widely spaced, working in Adobe RGB can reveal more visible steps in a colour gradient than in the case of  sRGB.  The solution is to use a higher resolution than an 8-bit representation can provide and, under these conditions, Adobe RGB can provide a better colour response because of its wider gamut.

 

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