Table of Contents

Acknowledgements

About the Authors

1. Introduction 1

1.1 Preface 1

1.2 Why Base this Book on MATLAB? 2

1.3 A Brief Review of the CIE System of Colorimetry 4

2. Linear Algebra for Beginners 13

2.1 Some Basic Definitions 13

2.2 Solving Systems of Simultaneous Equations 14

2.3 Function Approximation 16

3. A Short Introduction to MATLAB 19

3.1 Matrices 19

3.2 Matrix Operations 21

3.3 Solving Linear Systems 23

3.4 M-Files 25

3.5 Using Functions in MATLAB 25

4. Computing CIE Tristimulus Values 27

4.1 Introduction 27

4.2 Colour-Matching Functions 28

4.3 Interpolation Methods 29

4.4 Extrapolation Methods 38

4.5 Correction for Spectral Bandpass 38

4.6 Tristimulus Values 39

4.7 Chromaticity Diagrams 43

5. CIELAB and Colour Difference 49

5.1 Introduction 49

5.2 ACIELAB and CIELUV Colour Space 50

5.2.1 A Representation of CIELAB Using MATLAB 56

5.3 CIELAB Colour Difference 60

5.4 Optimised Colour-Difference Formulae 64

5.4.1 CMC (l:c) 64

5.4.2 CIE 94 67

5.4.3 CIEDE 2000 68

6. Chromatic-Adaptation Transforms and Colour Appearance 75

6.1 Introduction 75

6.2 Chromatic-Adaptation Transforms (CATs) 76

6.2.1 A Brief History of CATs 80

6.2.2 CMCCAT97 80

6.2.3 CMCCAT2000 83

6.3 Colour-Appearance Models (CAMs) 86

6.3.1 CIECAM02 88

7. Physiological Colour Spaces 93

7.1 Introduction 93

7.2 Colour Vision 94

7.3 Cone-Excitation Space 96

7.4 MacLeod and Boynton Chromaticity Diagram 101

7.5 DKL Colour Space 106

8. Colour Management 119

8.1 The Need for Colour Management 119

8.1.1 Using MATLAB to Create Representations of Gamuts 121

8.2 RGB Colour Spaces 122

8.2.1 sRGB 123

8.2.2 Adobe RGB (1998) 125

8.3 The International Color Consortium 126

8.4 Characterisation and Calibration 127

8.4.1 Approaches to Characterisation 128

9. Display Characterisation 131

9.1 Introduction 131

9.2 Gamma 131

9.3 The GOG Model 132

9.4 Device-Independent Transformation 133

9.5 Example Characterisation of CRT Display 134

9.6 Beyond CRT Displays 140

10. Characterisation of Cameras 143

10.1 Introduction 143

10.2 Correction for Nonlinearity 144

10.3 Correction for Lack of Spatial Uniformity 146

10.4 Characterisation 146

10.5 Example Characterisation of a Digital Camera 149

11. Characterisation of Printers 159

11.1 Introduction 159

11.1.1 Physical Models 160

11.1.2 Neural Networks 161

11.2 Characterisation of Half-Tone Printers 162

11.2.1 Correction for Nonlinearity 162

11.2.2 Neugebauer Models 163

11.2.3 Example Characterisation of a Half-Tone Printer 165

11.3 Characterisation of Continuous-Tone Printers 169

11.3.1 Kubelka-Munk Models 169

11.3.2 Interpolation of 3D Look-Up Tables 172

11.3.3 General Linear and Nonlinear Transforms 173

11.3.4 Example Characterisation of a Half-Tone Printer 173

12. Multispectral Imaging 179

12.1 Introduction 179

12.2 Computational Colour Constancy and Linear Models 180

12.2.1 Example Using MATLAB 181

12.3 Properties of Reflectance Spectra 182

12.3.1 PCA and SVD 183

12.3.2 SVD Using MATLAB

12.4 Application of SVD to Reflectance Recovery 189

12.5 Techniques for Multispectral Imaging 191

12.5.1 Maloney-Wandell Method 191

12.5.2 Imai-Berns Method 192

12.5.3 Shi-Healey Method 192

12.5.4 Methods Based on Maximum Smoothness 193

12.5.5 Device Characterisation Revisited 193

12.5.6 Spectral Recovery Using Low-Dimensional Linear Models in MATLAB 193

12.6 Fourier Operations on Reflectance Spectra 193

A. Table of White Points of Illuminants used in r2xyz and Other Functions 197

B. Colour Toolbox 199

B.1 Where to Find the Toolbox 199

B.2 How to Install the Toolbox 199

B.3 Summary of Toolbox Files 199

B.3.1 Computing CIE Tristimulus Values 199

B.3.2 CIELAB and Colour Difference 200

B.3.3 Chromatic-Adaptation Transforms and Colour

Appearance 200

B.3.4 Physiological Colour Spaces 200

B.3.5 Colour Management 200

B.3.6 Display Characterisation 200

B.3.7 Characterisation of Cameras 201

B.3.8 Characterisation of Printers 201

References 203

Index 213

About the Author

Stephen Westland was awarded his BSc and PhD from the University of Leeds. In 1986 he joined Courtaulds Research as a Colour Physicist before returning to academia in 1990 to work at the University of Keele. He worked as a post-doctoral researcher and lecturer in the Department of Communication and Neuroscience where he taught and researched colour measurement, human colour vision, computational imaging and image processing. In 1990 he was appointed as a Reader in Colour Imaging at the Colour Imaging Institute of the University of Derby. He was appointed as Professor of Colour Science and Technology in the School of Design at the University of Leeds in 2003 where he currently teaches and researches. He has published more than 100 refereed papers in the areas of colour imaging, colour management, colour physics and colour design. He has been active in professional bodies that are concerned with colour. He is an active participant in conferences organised by the Society of Imaging Society and Technology (IS&T) and served on several organizational and technical committees. In 2008 he was awarded a Fellowship of the Society of Dyers and Colourists and the Davies Medal from the Royal Photographic Society for his research on digital colour imaging.