Computing Chromatic Adaptation Sabine S¨usstrunk A thesis submitted for the Degree of Doctor of Philosophy in the School of Computing Sciences, University of East Anglia, Norwich. July 2005 c This copy of the thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with the author and that no quotation from the thesis, nor any information derived therefrom, may be published without the author’s prior written consent. ii Abstract Most of today’s chromatic adaptation transforms (CATs) are based on a modified form of the von Kries chromatic adaptation model, which states that chromatic adaptation is an independent gain regulation of the three photoreceptors in the human visual system. However, modern CATs apply the scaling not in cone space, but use “sharper” sensors, i.e. sensors that have a narrower shape than cones. The recommended transforms currently in use are derived by minimizing perceptual error over experimentally obtained corresponding color data sets. We show that these sensors are still not optimally sharp. Using different com- putational approaches, we obtain sensors that are even more narrowband. In a first experiment, we derive a CAT by using spectral sharpening on Lam’s corresponding color data set. The resulting Sharp CAT, which minimizes XYZ errors, performs as well as the current most popular CATs when tested on several corresponding color data sets and evaluating perceptual error. Designing a spherical sampling technique, we can indeed show that these CAT sensors are not unique, and that there exist a large number of sensors that perform just as well as CAT02, the chromatic adap- tation transform used in CIECAM02 and the ICC color management framework. We speculate that in order to make a final decision on a single CAT, we should consider secondary factors, such as their applicability in a color imaging workflow. We show that sharp sensors are very appropriate for color encodings, as they pro- vide excellent gamut coverage and hue constancy. Finally, we derive sensors for a CAT that provide stable color ratios over different illuminants, i.e. that only model physical responses, which still can predict experimentally obtained appearance data. The resulting sensors are sharp. iii iv ABSTRACT Contents Abstract iii List of figures xiii List of tables xvi Publications xvii Acknowledgements xix 1 Introduction 1 1.1 ImageFormation ............................. 7 1.1.1 Illuminants ............................ 7 1.1.2 Reflectance ............................ 9 1.1.3 Sensors............................... 9 1.1.4 Physical Image Formation . 10 1.2 SensorsoftheHumanVisualSystem . 11 1.2.1 Trichromatic Theory of Color Vision . 14 1.2.2 Opponent Color Modulations . 19 1.3 CIEColorimetry ............................. 21 1.4 Conclusions ................................ 24 2 Chromatic Adaptation 25 2.1 PerformanceMeasure. 26 2.2 VonKriesChromaticAdaptationModel . 27 2.3 ScalingCoefficients ............................ 30 v vi CONTENTS 2.4 StrongvonKriesCoefficientModel . 33 2.4.1 Retinex .............................. 35 2.5 GeneralChromaticAdaptationModels . 36 2.5.1 Linear Chromatic Adaptation Models . 36 2.5.2 Non-linear Chromatic Adaptation Models . 39 2.6 Relational Color Constancy . 40 2.7 SpectralSharpening ........................... 42 2.7.1 Sensor-basedSharpening . 43 2.7.2 Applications of Spectral Sharpening . 44 2.8 CorrespondingColors. 46 2.8.1 ExperimentalMethods . 46 2.9 Conclusions ................................ 48 3 Spectral Sharpening 49 3.1 Introduction................................ 49 3.2 Lam’sExperiment ............................ 50 3.3 Linear Chromatic Adaptation Transforms . 53 3.4 TheSharpAdaptationTransform . 56 3.5 Comparison of the Sharp CAT with other linear CATs . 60 3.6 Discussion................................. 62 3.7 Conclusions ................................ 64 4 Spherical Sampling 67 4.1 Introduction................................ 67 4.2 SphericalSampling ............................ 69 4.3 SamplingExperiment. 72 4.4 StatisticalEvaluation. 80 4.5 Conclusions ................................ 83 CONTENTS vii 5 White-Point Independent RGB Sensors 85 5.1 Introduction................................ 85 5.2 White-pointIndependence . 87 5.3 GamutCoverageOptimization. 88 5.3.1 Experiment ............................ 90 5.3.2 Results............................... 92 5.4 HueOptimization............................. 95 5.4.1 Brightness and Gamma Invariant Hue . 98 5.4.2 Experiment ............................ 99 5.4.3 Results...............................102 5.5 White-point independence, Gamut coverage, and Hue constancy . 104 5.6 Conclusions ................................105 6 Stable Color Ratios 111 6.1 Introduction................................111 6.2 Experiment ................................113 6.3 ComparisonwithCAT02 . .115 6.4 AbsoluteversusRatioErrors. .117 6.5 Conclusions ................................119 7 Conclusions 121 7.1 FutureWork................................123 Bibliography 125 Appendix 144 A Land’s Experiments 145 B Color Constancy of Corresponding Colors 149 C Prediction Errors of linear CATs 153 viii CONTENTS D Color Spaces and Color Encodings 169 D.1 ColorSpaces................................169 D.2 ColorSpaceEncodings . .171 D.3 ColorImageEncodings. .173 E Linear transforms for color encodings 175 F Hue Constancy Plots 179 G Visual Examples 183 List of Figures 1.1 An example of chromatic adaptation. See text for explanation. 1 1.2 Left: An object imaged under a tungsten illuminant. Right: The same image transformed to appear correctly under monitor viewing conditions.................................. 2 1.3 A graphical illustration of color constancy: If the human visual sys- tem is perfectly color constant, the effect of the illuminant could be discounted by simply modeling illumination change. However, most colors exhibit some degree of color inconstancy. The corresponding color of the sample under the reference illuminant (ABC)1, i.e. the color coordinates that best describe its appearance under the test illuminant, are given by (ABC)3. .................... 3 1.4 Relative spectral power distributions (SPD) of CIE daylight illumi- nants and standard colorimetry illuminants A and D65. 8 1.5 Left: the Macbeth ColorChecker. Right: reflectance spectra of color patches13(blue),14(green),and15(red). 9 1.6 Left: cross-section of the human eye. Right: a close-up of the reti- nal cell layers (note that the light enters from the bottom). Both illustrations are taken from [KFN01]. 12 1.7 Typical colorimeter set-up for color matching experiments. ...... 16 1.8 CIE 1931 2◦ r, g, b color matching functions. 16 1.9 CIE 1931 2◦ x, y, z CMFs (solid line) and Judd-Vos modified 2◦ x, y, z CMFs(dottedline). .. .. .. ... .. .. .. .. .. ... .. 17 ix x LIST OF FIGURES 1.10 The normalized cone fundamentals of Stockman and Sharpe (solid line), Smith and Pokorny (dashed line), and Vos and Walraven (dot- tedline)................................... 18 1.11 The normalized opponent sensitivities of Poirson and Wandell [PW93]. 20 ′ ′ 1.12 Equal color differences in the x, y (left) and u ,v (right) chromaticity diagrams. The illustration is taken from [Hun98]. 23 2.1 A simple asymmetric matching experiment. See text for explanation. 28 2.2 Strong and week von Kries coefficient models. Left: The strong von Kries model assumes that the gain is dependent only on signals from the same cone class. Right: The weak von Kries model assumes that the gain is dependent on signals from all cone classes. The illustrations are taken from [BW92]. 33 2.3 Original Vos and Walraven cone fundamentals (dotted line) and sensor- basedsharpenedsensors(solidline).. 45 3.1 Distribution of Lam’s 58 samples in CIE a∗, b∗, measured under D65. 51 3.2 The normalized Bradford sensors (dash) compared to the normalized LMS(HPE)conefundamentals(solid). 54 3.3 The normalized sensors resulting from different chromatic adaptation transforms: HPE (solid color), Bradford (dash), Fairchild (dotted), CAT02(dash-dot). ............................ 56 3.4 The Sharp sensors (solid color) compared to the other CAT sensors: HPE (solid), Bradford (dash), Fairchild (dotted), CAT02 (dash-dot). 59 4.1 Evenly distributed points on a sphere (N = 700), using the general- izedspiralsetmethod. .......................... 70 4.2 The corresponding spectral sensor sensitivities of two neighboring sur- face point vectors that are 3 degrees apart. 72 4.3 All sample points within a 20 degree radius of Bradford, Sharp and CAT02 (for N = 5, 000). ......................... 73 4.4 All sample points that result in sensor combinations with a RMS CIE ∆E 4predictionerror. 74 94 ≤ LIST OF FIGURES xi 4.5 All RGB sensors that result in 14,025 different combinations with a RMS CIE ∆E 4predictionerror. 76 94 ≤ 4.6 Isometric surfaces projected on a plane for different RMS CIE ∆E94 thresholds.................................. 77 4.7 Close-up of the 4.6. See text for explanation. 78 4.8 The best sensors found through spherical sampling (solid lines) com- paredtotheCAT02sensors(dottedlines). 79 4.9 All sample points that result in sensor combinations that are not statistically significantly different from CAT02 at 95 percent confidence. 81 4.10 All RGB sensors (59 red, 31 green, and 3 blue for a total of 1,056 combinations) that are not statistically significantly different from CAT02 at 95 percent confidence. For comparison, the Sharp sensors, the Bradford sensors and the CAT02 sensors are also plotted. 82 ′ ′ 5.1 The x, y and