Principles of Colour Reproduction in Digital Images Notes: Colour Reproduction and Gamut

WYSIWYG (ˈwɪziwɪɡ)

What You See Is What You Get

The last few chapters of this book feel a bit unrestrained, with few references provided, making them difficult to understand. However, to maintain the integrity of the content (and because I’ve already renewed this book three times), I’ll push through and finish writing this.

“Attributes”

First, a series of “attributes” for colour reproduction are defined:

• Scope: Divided into “related to the colour reproduction itself” and “related to the relationship between the colour reproduction and the original colour”. I didn’t quite grasp this; most fall into the latter category, while those related to preferred colours belong to the former.

This probably refers to whether the goal of colour reproduction is to restore the original colour to varying degrees (be it in terms of spectrum, tristimulus values, or colour appearance) or if it has other objectives. For example, when photographing a colour chart under low colour rendering light, should the reproduction show the inaccurate colours, or the colours of the chart under a standard illuminant.

• Application: Divided into application-dependent or application-independent. I didn’t understand this either; most are in the latter category, with only creative colour reproduction being in the former.

This is likely more “radical” than the previous case. Although preferred or memory colours also involve adjustments that deviate from an “accurate” state, they still align with psychophysical phenomena (memory colour is also considered a type of colour appearance phenomenon). Application-dependent might refer to more creative and exaggerated processing for specific application scenarios, such as converting to black and white or artistic colourisation.

• Nature: Divided into deterministically describable (where the colour reproduction is known to have such properties) and “ideal state reproduction”. I didn’t quite get this either. The general idea seems to be that the former can be determined (described using relationships like “equal” or “relative”), while the latter is more ambiguous (like memory colours, preferred colours, etc.).

• Expression: Divided into what can be quantitatively measured by physical methods and what can be qualitatively measured by psychovisual methods. This is easy to understand. The book mentions that “quantitatively measurable” and “related to the original colour” always appear together, but this seems neither sufficient nor necessary. For example, a colour reproduction with equal colour appearance is related to the original colour but cannot be quantitatively measured.

These attributes also have their own codes (a capital letter), but I can’t see any relationship between them. The codes don’t even match the examples that follow, and I can’t find any literature that mentions these things.

Hunt’s Classification

Hunt divides the goals of colour reproduction into several categories, from Chapter 11 of his book The Reproduction of Colour.

Spectral Colour Reproduction: The spectra of the original and the reproduction are identical. An example is Lippmann photography (a 1908 Nobel Prize winner), which is achieved through interference. The Swiss Federal Institute of Technology Lausanne (EPFL) replicated and analysed this in detail in 2021 ¹.

Exact Colour Reproduction: The tristimulus values (in absolute terms) of the original and the reproduction are identical. This means that under the same viewing conditions, the absolute colour appearance attributes (lightness and colourfulness) are identical.

Colorimetric Colour Reproduction: The colour coordinates (tristimulus values normalised to the corresponding white) of the original and the reproduction are identical. This means that under the same viewing conditions, the relative colour appearance attributes (lightness and chroma) are identical.

The three types above are physically measurable, but it is important to note that good colour reproduction results can only be achieved under identical viewing conditions, as they do not account for the influence of viewing conditions on colour perception. A good example is reproducing a white sheet of paper under incandescent light on a self-luminous display. If the tristimulus values or colour coordinates are identical, the colour on the display will appear more yellow. This is possibly because a self-luminous display does not induce the discounting-the-illuminant phenomenon, leading to a lower degree of chromatic adaptation than in an incandescent lighting environment.

Equivalent Colour Reproduction: Under their respective viewing conditions, the absolute quantities of the colour appearance attributes are the same, but the tristimulus values are different. This takes into account the effects of viewing conditions on colour perception, including chromatic adaptation.

Corresponding Colour Reproduction: Under their respective viewing conditions, the relative quantities of the colour appearance attributes are the same, but the colour coordinates are different. The ideal colour reproduction for a camera should fall into this category.

These two types are the counterparts of the first two types mentioned above, but they take colour appearance into account. Ignoring the problem of metamerism, it is theoretically possible to achieve a “What you see is what you get” effect. The original text mentions that in equivalent colour reproduction, although the absolute luminances are different, they should be relatively close. However, in reality, due to the high non-linearity of lightness perception at high brightness levels, the absolute luminances can differ significantly.

Preferred Colour Reproduction: Colours are adjusted to satisfy preference. For example, making blue skies bluer, skin tones rosier, or increasing lightness to meet people’s preferences for pictures. This can be understood as image retouching, and a large part of a camera’s colour reproduction falls into this category.

ICC’s Four Rendering Intents

The goal of colour reproduction in the ICC colour management system is called Rendering Intent, and it is divided into four types:

• Perceptual: Preserves the overall colour appearance of the image. When gamut sizes do not match, it will compress or expand the gamut to fit the target gamut. It changes the hue and saturation of all colours in the image but maintains the overall visual relationship between the colours.
• Saturation: Aims to make the saturation of the target image as high as possible. When compressing or expanding the gamut, it does not prioritise matching the overall colour appearance. Generally, the target gamut is larger than that of the perceptual intent.
• Absolute Colorimetric: Matches the colorimetry as accurately as possible. The parts of the source and target gamuts that overlap remain unchanged. Colours outside the target gamut are mapped to the closest possible position while preserving their hue.
• Relative Colorimetric: The difference from the absolute colorimetric rendering intent is that it first transforms the white point and black point of the original image to the white point and black point of the target gamut. Then, colours that are out of gamut after this transformation are mapped to the nearest position while preserving their hue.

Here, the white point and black point refer only to luminance. Both absolute and relative colorimetric intents involve chromatic adaptation. The absolute luminance in the absolute colorimetric rendering intent also remains largely unchanged, even if the target gamut has a brighter white point.

Gamut

A gamut refers to the range of colours that a device or system can reproduce. A gamut has different shapes in different spaces. For an additive system like a display, the RGB gamut is a cube. After applying a non-linearity (Gamma) to RGB, it remains a cube because R, G, and B are linearly independent. By using a transformation matrix from RGB to XYZ, the cube is mapped into the XYZ space, where the gamut becomes a parallelepiped.

When we mention “closest”, “minimum difference”, or “hue”, we are referring to these concepts within a uniform colour space. The transformation from XYZ to a uniform colour space includes a non-linear step. Even simple uniform colour spaces like IPT or sUCS consist of two linear transformations with a non-linear transformation sandwiched between them.

This non-linear transformation turns the parallelepiped into a very complex shape containing curved surfaces and lines, and it is non-convex in most cases. To describe such a complex boundary, a convex hull or an $\alpha$-shape can be used as an approximation.

Once the shape of the gamut in the uniform colour space is determined, out-of-gamut colours are moved into the gamut along different “paths” (e.g., lines of constant lightness, constant hue, or other oblique lines). The distance of the move can be determined by a distance parameter. The simplest and most direct method is clipping, where any colour outside the gamut is moved directly to the gamut boundary.

That’s a Wrap!

This concludes the notes on this book. More content on the last two chapters regarding colour management, displays, and capture devices will be introduced in other works (as they are covered too hastily in this book).

Procrastinating from the winter break to the summer break, I’ve managed to re-learn colour science. I hope both you and I have made new discoveries and gains.