Rochester Institute of Technology RIT Scholar Works Theses 5-1-2009 Color difference formula and uniform color space modeling and evaluation Shizhe Shen Follow this and additional works at: https://scholarworks.rit.edu/theses Recommended Citation Shen, Shizhe, "Color difference formula and uniform color space modeling and evaluation" (2009). Thesis. Rochester Institute of Technology. Accessed from This Thesis is brought to you for free and open access by RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. Color Difference Formula and Uniform Color Space Modeling and Evaluation by Shizhe Shen B.S. Zhejiang University, Hangzhou, CHINA (2002) M.S. Zhejiang University, Hangzhou, CHINA (2005) A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Color Science in the Center for Imaging Science, Rochester Institute of Technology May, 2009 Signature of the Author Accepted by Dr. Mark D. Fairchild, Coordinator, M.S. Degree Program i CHESTER F. CARLSON CENTER FOR IMAGING SCIENCE COLLEGE OF SCIENCE ROCHESTER INSTITUTE OF TECHNOLOGY ROCHESTER, NY CERTIFICATE OF APPROVAL M.S. DEGREE THESIS The M.S. Degree Thesis of Shizhe Shen has been examined and approved by two members of the Color Science faculty as satisfactory for the thesis requirement for the Master of Science degree Dr. Roy S. Berns, Thesis Advisor Dr. Mark D. Fairchild ii Color Difference Formula and Uniform Color Space Modeling and Evaluation Shizhe Shen A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Color Science in the Center for Imaging Science, Rochester Institute of Technology Abstract: Defining color tolerances numerically continues to be a topic of intense interest in colorimetry. A technique was developed to evaluate formula performance that incorporated visual uncertainty. In this technique, visual uncertainty was represented by randomized equal color-difference ellipsoids or randomized visual color differences. STRESS, a multivariate statistical tool, was employed to quantify these randomized equal color- difference ellipsoids or visual color differences. The STRESS clouds were composed of the STRESS values between the randomized equal color-difference ellipsoids and T50 equal color-difference ellipsoids, or between the randomized visual color differences and T50 visual color differences where T50 represented visually determined tolerances equivalent to an anchor-pair stimulus. These STRESS values clouds were taken as rulers to evaluate whether one color-difference formula over-, under- or well-fitted a specified color-difference dataset, based on an F-test. This technique is a necessary addition to the current deviation evaluation metrics, e.g., PF/3. In follow-on research, a Euclidean color space was developed with the color-difference formula based on IPT color space for supra-threshold color differences. The color-difference formula has similar chromatic modeling to CIE94. A lightness transformation function was applied to model color difference along lightness. A rotation matrix on the chromatic plane was also applied to achieve better characteristics of the color space. A step-wise optimization was performed to achieve better consistency and remove conflicts between different color-difference datasets. The evaluations include STRESS, F-test, hue constancy and equal color-difference ellipsoid shape. It was shown by the evaluation results that the Euclidean color space could be a potential candidate of a future color model useful for defining industrial color tolerances. iii i. DEDICATION THIS THESIS IS DEDICATED TO MY FAMILY FOR THEIR LOVE AND SUPPORT. iv ii. ACKNOWLEDGEMENTS I would like to thank the following people for their help with and support for my thesis and my study in color science: Roy S. Berns, my thesis advisor, for providing me the opportunity to study in Munsell Color Science Laboratory, finding my advantages and weaknesses, sharing his knowledge and vision on color science and guiding me exploring the amazing color world, Mark D. Fairchild, for sharing his knowledge in color appearance models, extending the concept of color space in my brain from three-dimension to more dimensions, Dave R. Wyble, for sharing his knowledge of photometry and spending time around ping-pong table with me, Lawrence Taplin, for leading me into the wonderful Matlab world, helping me on all kinds of computer and programming questions and bringing old fashion pizza, Mitchell R. Rosen, for introducing me the real world color management and advising me on several important periods, Rod Heckaman, for his optimism and encouragement on me, Val Hemink, for her hospitality and continuous help, the Munsell Color Science Laboratory faculties, staffs and students, for teaching me many interesting things and giving me another warm family, the DuPont Color Science Fellowship for their financial support of my research, my friends and family, for their love and support, and Ying, for her love, support and patience. v iii. TABLE OF CONTENTS i. Dedication iv ii. Acknowledgement v iii. Table of Contents vi iv. List of Figures ix v. List of Tables xi 1. INTRODUCTION ................................................................................................................ 1 2. BACKGROUND ................................................................................................................... 8 2.1. SMALL COLOR -DIFFERENCE DATASETS ................................................................................... 8 2.2. EVALUATION METRICS FOR COLOR -DIFFERENCE FORMULAS AND COLOR SPACES .............. 11 2.2.1. PF/3 ...................................................................................................................................................................... 11 2.2.2. STRESS (STandardized REsidual Sum of Squares) ............................................................................ 12 2.2.3. Hue constant datasets ................................................................................................................................... 14 2.3. EQUAL COLOR -DIFFERENCE ELLIPSOIDS .............................................................................. 17 2.4. COLOR SPACES , COLOR -DIFFERENCE FORMULAS AND COLOR APPEARANCE MODELS ..... 18 2.4.1. IPT ......................................................................................................................................................................... 18 2.4.2. CIEDE2000......................................................................................................................................................... 20 2.4.3. CAM02 SCD LCD and UCS ............................................................................................................................ 21 2.4.4. CIECAM02 series .............................................................................................................................................. 22 2.4.5. DIN99, DIN99d, DIN99o ............................................................................................................................... 24 2.4.6. OSA UCS GP and OSA UCS E ........................................................................................................................ 27 vi 2.5. COLOR -DIFFERENCE SPACES BASED ON MULTI -STAGE COLOR VISION THEORY AND LINE INTEGRATION ........................................................................................................................................ 29 2.6. DERIVATION OF EUCLIDEAN COLOR SPACES FROM COLOR -DIFFERENCE FORMULAS WITH ANALYTICAL METHOD .......................................................................................................................... 33 3. EVALUATING COLOR DIFFERENCE EQUATION PERFORMANCE INCORPORATING VISUAL UNCERTAINTY .......................................................................................................... 36 3.1. ABSTRACT ................................................................................................................................ 36 3.2. INTRODUCTION ....................................................................................................................... 37 3.3. ELLIPSOIDS FITTING PROCEDURES ....................................................................................... 38 3.4. GENERATING ELLIPSOIDS CONSIDERING VISUAL UNCERTAINTY ........................................ 45 3.5. EVALUATION OF ELLIPSOID VARIABILITY ............................................................................. 53 3.5.1. Shape Variance ................................................................................................................................................ 53 3.5.2. Orientation Variance ..................................................................................................................................... 54 3.6. USING THE RANDOMIZED ELLIPSOIDS FOR PERFORMANCE EVALUATION ......................... 55 3.6.1. Deviation between the RIT-DuPont Visual Color-Difference Data and Numerical Color-Difference Data 57 3.7. METHODS FOR OTHER DATASETS ......................................................................................... 62 3.7.1. Non-Ellipsoid Method .................................................................................................................................... 62 3.7.2 Average