How do We Define ‘Accurate’ Colour?

How do We Define ‘Accurate’ Colour? How we could quantify colour in an ‘accurate’ fashion? Before jumping into this topic, let’s talk a little bit more about why the quantification of colour is important to photographers, designers, imaging professionals, people in textile industries and more.

When we try to describe a colour, the most common way of doing it is to refer to an object with the colour in mind. For example, when we describe the colour ‘red’, people will usually use ‘apple’ to describe ‘red’. But what kind of apple are we talking about? Are we thinking about the same apple? Look at Figure 1, there are at least seven different shades of ‘red’ among different varieties of apple. Not to mention the last one; it’s not even red! Therefore, there are discrepancies when we use objects to describe colours. And we need to find a way to reduce the discrepancies in communication.

Figure 1: Different varieties of apples

Humans tend to use ‘numbers’ to express an accurate measurement. For example, we use numbers to describe length, weight and etc. Therefore, we need a way to express colours in numeric forms, so we could say colour A and colour B are the same because they have the same numeric values. Back in 1913, CIE (Commission Internationale de l´Eclairage) defined Tristimulus Values (XYZ values) for quantifying the colours humans can perceive. The XYZ values are constructed by multiplying the following three attributes: the spectral power distribution of the light source, the reflectance of the object and the Standard Observer functions to describe the characteristics of the human visual system. As a result, when colour A and colour B have the same XYZ values, we could say colour A and colour B look the same.

Figure 2: Formula for calculating XYZ values

Another advantage of defining colours in numeric values is that we could easily express colours in a diagram with a coordinate system. And this forms a colour space. Figure 3 shows the 1931 CIE xy chromaticity diagram, which represents all the colours that humans could perceive. However, this diagram does not truly reflect the sensitivity of the human visual system. Take blue and green, for example. Humans are very sensitive to blue and less sensitive to green: a little bit more of red we recognise as purple and a little bit of green we recognise as cyan. This phenomenon is not reflected in Figure 3, a CIE 1931 xy chromaticity diagram. As a result, in 1976, the u’ v’ chromaticity diagram was proposed to reflect the sensation of the human visual system.

Figure 3: CIE 1931 xy chromaticity diagram

Figure 4: CIE 1976 u’v’ chromaticity diagram

Now, we have defined a system to describe colours in numeric form.

The next question is, how do we measure colours?

We could use a ruler to measure length and a scale to measure weight. When we measure colours, we need to measure light first. Measuring light is not as easy as using a ruler or scale, but there are instruments out there to help. For example, we could use a spectroradiometer to measure the spectral power distribution of the light.

However, these instruments are bulky and expensive, and they are not easy to carry around. Therefore, a more simplified device called ‘colorimeter’ was developed. A colorimeter measures light through a set of XYZ filters, so the speed is faster than spectroradiometer, but with less accuracy.

*XYZ filters: Optical filters to mimic the optical characteristics of XYZ values (tristimulus values) in terms of transmittance per wavelength.

As stated earlier, when we have a set of XYZ values with the same numbers, we could say these colours look the same. But there are occasions when the XYZ values are not the same, but they still look very similar. For example, when we see a bright light in a bright room versus a dimmer light in a dim room, the measured XYZ values are not the same (due to different light intensities, but we still perceive the same colour of light. This is due to the adaptation of our visual system. Another scenario is to compare the colours from different media. For example, one from the monitor and one from the printed paper. Hence, we need another metric to quantify this adaptation phenomenon. L*a*b* colour space (shown in Figure 5) was then proposed and built for this ‘normalisation’ purpose. It defines the brightest level of light in a scene or a media (e.g. paper) as 100 and normalises all other colours in the scene or media according to the brightest light. As a result, now we can compare light with different intensities or colours from different media.

Figure 5: L*a*b* Colour Space

When we look at two similar, but slightly different colours, we will wonder how close these colours are? Without using numeric values to represent colours, we could say ‘it’s close’. But how close? And what is the definition of ‘close’ since the perception of colours vary from person to person. With the XYZ colour space or L*a*b* colour space, we can quantify the difference between colours. By calculating the distance between two colours in a particular colour space (L*a*b* colour space is usually used), a difference value can be obtained. This difference value is called ‘Colour Difference’. We usually use delta E* for designating ‘Colour Difference’.

The simplest version of the colour difference formula is called delta E* 76 (delta E*ab).

A more complex formula is used in the textile and graphic arts industry. It was announced in 1994, hence it is called delta E* 94.

In 2000, researchers developed a newer version of the colour difference formula to truly reflect what the human visual system perceives. It is called delta E*2000 (delta E*00). Due to large amount of research studies to achieve high correlation between the calculated values and human perception, delta E*00 has now become International Standard and is recommended for use in all scientific research work.

As we have seen in the formulas above, two sets of L*a*b* values are required. If we need to judge the accuracy of a particular colour, then a set of measured L*a*b* values and a set of defined L*a*b* values are required. We could obtain the measured values using the instruments mentioned earlier, but how do we obtain ‘defined’ or ‘standard’ values? The ‘defined’ or ‘standard’ values can be obtained by using standard charts (Figure 6). These colour charts have defined L*a*b* values for all the colours in the chart and every chart is produced very carefully to meet the tolerance. Hence, these charts could be used as a reference since the values will not change.

To judge the accuracy of a colour, delta E*00 is often used. Delta E*00 < 1.00 means there is no perceivable difference for experts when comparing two colours side-by-side. Delta E*00 < 3.00 means there is no significant difference for typical person. (The experts mean colour science professionals or experienced photographers, designers, imaging professionals, etc.)

In summary, we have learned about how to use numbers to define colours and the reason behind it. We have also identified the differences between each colour space, such as XYZ and L*a*b*. And lastly, we learned ways to measure colour and how to define colour differences. Using delta E*00 values, we can judge if the colour is accurate or not.

Figure 6-1: X-rite Classic ColorChecker Chart

Figure 6-2: X-rite Digital ColorChecker SG Chart

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How do We Define ‘Accurate’ Colour?