Color and Colorimetry – Part 9

Systems intended to convey color images all need to have a defined white point for practical reasons. The white point is where the luminance axis passes through the plane of the chromaticity diagram on its way from black to white.

The white point can be defined absolutely as some combination of X and Y, which corresponds to some combination of R, G and B in a specific imaging format, ideally when they are equal. In television systems, the white point corresponds to the color difference signals having a value of zero. In a legacy composite system, the amplitude of the chroma signal would be zero at the white point.

If cameras creating the images and displays are not calibrated to the same white point, the reproduced colors will be incorrect and the picture will have a tint.

In a closed system where cameras and displays are under common supervision, the choice of white point doesn't make a whole lot of difference and it may be chosen for practical reasons. As a result there is no shortage of white points in use, and the attendant problem that material shot assuming one white point will take on a tint on displays assuming a different white point, unless some conversion takes place.

Although there is no absolute requirement, white points are traditionally chosen to fall on or near the curve, or locus, of a black body radiator, which means they can be defined either by their color temperature or by the CIE co-ordinates. Fig.1 shows the black body locus superimposed on CIE XY space.

Illuminant A, corresponding to the low color temperature of 3200 degrees K, is an obsolete white point dating from the days of tungsten incandescent lighting.

The white point of CIE XY is at least logical because it assumes equal energy presented to the standard observer and therefore appears at X = Y = Z = 0.333....... It is known as Illuminant E (for equal) and nearly corresponds to the spectrum of a black body at 5400 degrees K. The term nearly is used because the spectrum of a black body is a curve and so cannot actually produce equal energy over a range of wavelengths. To be precise, 5400 degrees is the correlated color temperature of illuminant E.

Fig.1. The locus of a black body radiator superimposed on the CIE XY diagram. Most white points are on the black body locus and so can be specified by temperature or by CIE coordinates. Illuminant E is shown at X = Y = 0.33.. corresponding to a CT of 5400K.

Fig.1. The locus of a black body radiator superimposed on the CIE XY diagram. Most white points are on the black body locus and so can be specified by temperature or by CIE coordinates. Illuminant E is shown at X = Y = 0.33.. corresponding to a CT of 5400K.

D 55 is a white point commonly used in photography and with a color temperature of 5500K, is so close to Illuminant E that it needs no justification. Both Illuminant E and D 55 provide spectra in which the color constancy of human vision appears to work best.

As has been seen, daylight is an elusive thing, because it changes with latitude, the seasons, the time of day and the amount of diffusion in the atmosphere. Illuminant D 65 replaces the earlier Illuminant C that was chosen as the original white point of NTSC back in 1953. D 65 corresponds more or less to the average appearance of white paper at midday somewhere in Europe illuminated by the north sky. It has a correlated color temperature of 6504 degrees K. It would have been 6500, but Planck's constant was redefined and the temperature of all the illuminants moved a bit.

D 65 has a hint of blue about it but it is used in most all television standards, including EBU Tech. 3213 for SDTV, SMPTE RP 145 for HDTV, ITU Rec. 709 for HDTV and Rec. 2020 for wide color gamut video.

Color images captured assuming one white point need to be processed before they can correctly be seen on a display that uses a different white point. The conversion process requires RGB values to be subject to a 3 x 3 matrix operation. One such process is the Bradford transformation matrix, named after the UK city where it was developed. Such processes are also related to the facility to change color temperature available in image processing software. When white points reside on the black body locus the conversion between white points and between color temperatures becomes the same thing.

Fig.2. The original color space of NTSC, shown by crosses, was abandoned when brighter phosphors were developed and the later space, shown by dots, was adopted and also used for PAL.

Fig.2. The original color space of NTSC, shown by crosses, was abandoned when brighter phosphors were developed and the later space, shown by dots, was adopted and also used for PAL.

The CIE XY space also allows color spaces used by particular image formats to be compared. The CIE horseshoe depicts the entire gamut of human vision and all practical color displays have a smaller gamut that forms a subset of the human visual space. These mostly rely on three primaries and therefore have a triangular color space that must be smaller than the human gamut.

For practical reasons, most color imaging signal formats provide a color space that is bigger than the space allowed by the three selected primaries but smaller than the human gamut. This means that some combinations of the signal can actually be illegal, a topic that will be considered in due course.

Back in 1953 the NTSC color television system was devised. The primaries selected were constrained totally by the availability of phosphors that could be used in cathode ray tubes. Fig.2 shows the primaries originally selected for NTSC as crosses. The color space was reasonably large, but the phosphors were not very bright and the red one suffered lag that somewhat smeared motion. The white point was Illuminant C.

It was not long before different phosphors were developed, shown as dots in Fig.2, that were more efficient, leading to brighter pictures, even though the color space became smaller and the white point was some way from the center of the triangle. The greater brightness was considered more important than the size of the color space. Attempts were sometimes made at the receiver to convert between the different color spaces, but this could not be completely successful because of the use of gamma.

Fig.3. Rec. 2020 color space compared with that of Rec. 709.

Fig.3. Rec. 2020 color space compared with that of Rec. 709.

The later NTSC color space was subsequently adopted for PAL although the white point was changed to D 65. Although there are slight differences, RP 145 and Rec 709 for HDTV use essentially the same color space as PAL and the later NTSC standard. The differences are so small that color information is essentially interchangeable, which simplifies standards conversion. The sRGB format, used in computers adopts the color space and white point of Rec.709.

Attempts to increase the size of the television color space, also known as "wide color gamut" led to Rec. 2020, which, amongst other things, defines new color primaries that are further apart than those of Rec. 709. Fig. 3 compares 2020 with 709. The D 65 white point is retained. It may be some time before TVs can actually display the entire gamut of Rec. 2020, but for now it acts as future proof container for wide gamut color material. Fig.3 also shows the original color gamut of NTSC adopted in 1953, which illustrates that the rate of progress in color spaces over 60 years is not very great.

It is important to appreciate that colors will only be displayed correctly if the source and the display have assumed the same primaries and white point. In all other cases conversion between different color spaces is required. This is a non-trivial undertaking for two reasons. One is that it needs to be performed in the linear light RGB domain for best results, so any color difference encoding and gamma encoding in the signals needs to be removed first and put back afterwards. The second reason is that a legal color in one space may be out of gamut in another. 

Fig.4.  To convert to a smaller color gamut, clipping, a), will work best for a picture naturally having low saturation, but will cause contouring on saturated material. Desaturation, or compression, b), will avoid clipping but will further de-saturate a picture that is naturally low in saturation.

Fig.4. To convert to a smaller color gamut, clipping, a), will work best for a picture naturally having low saturation, but will cause contouring on saturated material. Desaturation, or compression, b), will avoid clipping but will further de-saturate a picture that is naturally low in saturation.

In television, the biggest problem is in converting between wide color gamut and 709 color gamut. However in the wider use of color, converting from television or computer formats to CMYK printing formats may also present difficulties.

All color spaces have a white point, and these points tend to be in similar places. The result is that out of gamut colors tend to be found some way from the white point, and by definition are saturated. The simplest way of dealing with out-of-gamut values is simply to maintain the direction of the vector from the white point to the original color, which keeps the hue correct, and to clip the illegal saturation value to the biggest legal one.

The difficulty with such a simple system is that the use of clipping can introduce a visible contour, where all of formerly illegal codes have been forced to the same legal clip value.

Another approach is that, instead of clipping, the source color space is proportionately reduced by desaturating everything until it fits in the target gamut. Whilst this eliminates contouring, it does result in a desaturated picture.

Fig. 4 compares the two possibilities when going from a larger gamut to a smaller one. When the picture is already desaturated, because the subject matter does not explore the full gamut of the source, it may be better not to further reduce the saturation but to accept a small amount of clipping. Where the source picture has fully saturated areas, it may be better to desaturate to avoid contouring. Clipping, of course, is not reversible, whereas desaturation could be reversed.

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