Alexander D. Logvinenko - Foundations of Colour Science: From Colorimetry to Perception

1. Chapter 3
2. Chapter 7
3. Chapter 17

1. Chapter 3
2. Chapter 4
3. Chapter 5
4. Chapter 7
5. Chapter 8
6. Chapter 11
7. Chapter 13
8. Chapter 15
9. Chapter 16
10. Chapter 17
11. Chapter 18
12. Chapter 19
13. Chapter 20
14. Chapter 21
15. Part 1

This edition first published 2023
2023 John Wiley & Sons Ltd

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Library of Congress CataloginginPublication Data

Names: Logvinenko, Alexander D., author. | Levin, Vladimir L., author.
Title: Foundations of colour science : from colorimetry to perception /
Alexander D. Logvinenko, Glasgow Caledonian University, UK, Vladimir L.
Levin, Central Economics and Mathematics Institute of the Russian
Academy of Sciences, Russia.
Description: First edition. | Chichester, UK : Wiley, 2023. | Includes
bibliographical references and index.
Identifiers: LCCN 2021060391 (print) | LCCN 2021060392 (ebook) | ISBN
9781119885917 (cloth) | ISBN 9781119885900 (adobe pdf) | ISBN
9781119885948 (epub)
Subjects: LCSH: Color. | Colorimetry. | Color vision.
Classification: LCC QC495 .L55 2022 (print) | LCC QC495 (ebook) | DDC
535.6dc23/eng20220215
LC record available at https://lccn.loc.gov/2021060391
LC ebook record available at https://lccn.loc.gov/2021060392

Cover Design: Wiley

The trigger for writing this book was, for me, the realisation that Grassmann's lawsthe cornerstone of colorimetry (which is the basis of colour science)seemed not to be quite correct. True, it has been reported from time to time before that Grassmann's laws get violated under some special circumstances such as high light intensity and/or at the far periphery in the retina. However, I realised that one of the most important aspects of Grassmann's lawsthe transitivity lawjust could not be possibly true for colour matching even under normal condition of viewing. Intransitivity of colour matching undermines the major achievement of colorimetry: the definition of colour as a class of equivalence (i.e., a class of visually indiscriminable lights) since in this case colour matching cannot be conceptualised as an equivalence relation. The problem, as I saw it, was not only that the whole grand construction of colorimetry, it turned out, was built on sand, but that, despite this, colour television, the very idea of which would have been impossible without colorimetry, still successfully worked.

In the end, resolving this apparent paradox proved to be rather easy (). However, in doing this I had been becoming more and more confident in the opinion that the very foundations of colour science should be reconsidered. Furthermore, it should be done on quite different grounds, involving rather different mathematics.

It so happened that thus far the basic mathematical tool of colour science has been linear algebra. There is good reason for this. Many modern ideas in linear algebraespecially the concept of linear functional and the resulting distinction between a linear space and its dual spaceseem to be specially designed to clarify thinking about colour theory (, p. 283).

Really, lights can be mixed together. Formally, this translates into the statement that there is an algebraic operation on the set of lights. Although colour is a mental, not physical attribute of light, a similar algebraic operation can be defined on the set of colours, namely, colour mixing. As known, the colour of the mixture of two lights depends on the colour of each light rather than their individual spectral compositions. Grassmann was, perhaps, the first to realise that this implies there being an algebraic structure of colour, which is relatively independent of that of light ().

It is the algebraic structure of colours that enables us to represent colours as vectors in the linear space. Also it allows us to use matrix algebra to perform colour computation, that has been widely used in colour science and its applications (e.g., colorimetry, colour imaging, computer graphics). Formally, the algebraic structure of colour is defined as that of the classes of visually equivalent (i.e., subjectively indistinguishable) lights. The vector representation of colours results from mapping the lights onto the classes of visual equivalence (the colour stimulus map). The vector representation of colour, empirically based on colour matching, puts colorimetry and its methods on par with the physical sciences, which has been acknowledged by the inclusion of colorimetry by Richard Feynman in his celebrated lectures on physics (, Ch. 35).