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Analysis of Umberger's Theory for Subtractive Color Reproduction

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Analysis of Umberger's Theory for Subtractive Color Reproduction Rochester Institute of Technology RIT Scholar Works Theses 11-1-1990 Analysis of Umberger's theory for subtractive color reproduction Paul R. Bartel Follow this and additional works at: https://scholarworks.rit.edu/theses Recommended Citation Bartel, Paul R., "Analysis of Umberger's theory for subtractive color reproduction" (1990). 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]. ANALYSIS OF UMBERGER'S THEORY FOR SUBTRACTIVE COLOR REPRODUCTION by PAUL R. BARTEL B.S. Warsaw Polytechnic (1981) A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Center for Imaging Science in the College of Graphic Arts and Photography of the Rochester Institute of Technology November 1990 Signature of the Author_P_a_u_I_R_"_B_a_rt_e_I _ Center for Imaging Science Accepted by ---'--'M..:.:e::..:n..:.:d:..:.;i'-'V:...:a;;..:eo;::z:....-R:..;.a:::..v.:..;a:..:.;n...:.;iC-.- __ Coordinator, M.S. Degree Program COLLEGE OF GRAPHIC ARTS AND PHOTOGRAPHY ROCHESTER INSTITUTE OF TECHNOLOGY ROCHESTER, NEW YORK CERTIFICATE OF APPROVAL M.S. DEGREE THESIS The M.S. Degree Thesis of Paul R. Bartel has been examined and approved by the thesis committee as satisfactory for the thesis requirement for the Master of Science degree Peter G. Engeldrum, Thesis Advisor Leonard M. Carreira Dr. Roy S. Berns Date ii THESIS RELEASE PERMISSION ROCHESTER INSTITUTE OF TECHNOLOGY CENTER OF GRAPHIC ARTS AND PHOTOGRAPHY Title of Thesis ANALYSIS OF UMBERGER'S THEORY FOR SUBTRACTIVE COLOR REPRODUCTION I, PAUL R. BARTEL , hereby grant permission to the Wallace Memorial Library of R.I.T. to reproduce my thesis in whole or in part. Any reproduction will not be for commercial use or profit. Da te : _---'-O_3=-----~O-'-I_---""9~!__- iii ANALYSIS OF UMBERGER'S THEORY FOR SUBTRACTIVE COLOR REPRODUCTION by PAUL R. BARTEL Submitted to the Center for Imaging Science in partial fulfillment of the requirements for the Master of Science degree at the Rochester Institute of Technology ABSTRACT A method, proposed by Umberger, for the identification of additive stimuli representative of the red, green, and blue primaries controlled by dyes obeying Beer's law was examined. The primary stability study suggests that for a set of colors created of various dye concentrations, the pattern of Umberger 's primary distribution is a translation of the original colors on a chromaticity diagram. Results of a theoretical color reproduction study where the color- matching functions of Umberger 's primaries were assumed as the color reproduction system's spectral sensitivities indicate an increase in metric chroma of reproduced colors. Color reproduction errors for a large number of colors were minimized for spectral sensitivities corresponding to Umberger 's primaries controlled by dye concentrations resulting in an 18% transmittance gray color- A technique was proposed for optimizing the system's spectral sensitivities to colors constituting the reproduced scene. IV ACKNOWLEDGMENTS Successful completion of this thesis owes recognition to support from many sources. Valuable and timely assistance and advice was particularly appreciated from the following: Peter G. Engeldrum of the R.I.T. Center for Imaging Science who kindly consented to act as thesis advisor and gave much of his time and encouragement in its supervision; Dr. Roy Berns of the R.I.T. Color Science Department ; Mr. Leonard M. Carreira, Senior Technical Specialist at the Xerox Corporation; Edwin J. Breneman and Jerry LeBlanc of Kodak Research Laboratories, Rochester, N.Y. TABLE OF CONTENTS 1 . INTRODUCTION 1 1.1. Relationship between primaries and spectral sensitivities in a color reproduction system 1 1.2. Primaries of additive color reproduction systems.... 6 1.3. Stability of primaries of subtractive dyes 10 method" 1.4. MacAdam's analysis - "stable primaries 14 1.5. Umberger 's Primaries 15 1.6. Objectives 21 2. PRIMARY CHROMATICITY AND SPECTRAL RESPONSE DETERMINATION 2 4 2.1. EXPERIMENTAL PROCEDURE 24 2.1.1. Intro4uction 24 2.1.2. Computation of Umberger's primaries 25 2.1.3. Computation of the spectral responses 29 2.1.4. Description of experimental colors 30 2.1.5. Film dye ( colorant ) set 36 2.1.6. Description of experiments 36 2.2. RESULTS 39 2.2.1. Chromaticity range of Umberger's primaries 39 2.2.2. Color-matching functions of Umberger's primaries 48 2.2.3. Discussion - Summary, optimum color for primary determination 54 3 . COLOR REPRODUCTION STUDY 59 3.1. EXPERIMENTAL PROCEDURE 59 3.1.1. Introduction 59 3.1.2. The subtractive color reproduction system computer model 61 3.1.3. Steps involved in color reproduction 62 3.1.4. Color error analysis 66 3.1.5. Description of experiment I 68 3.1.6. Description of experiment II 70 3.2. RESULTS 75 3.2.1. RESULT OF EXPERIMENT I 75 3.2.1.1. The most appropriate primary reference color for primary determination 75 3.2.1.1.1. Reproduction of a scene containing a variety of colors 75 3.2.1.1.2. Reproduction of a scene containing colors from a limited hue region 81 3.2.1.2. Character of color reproduction errors 82 3.2.1.3. Investigation into the cause of the large increase in metric chroma 94 3.2.1.4. Character of the spectral sensitivities of the color reproduction system 99 3.2.1.5. Grass green primary reference color as an exception 106 vi 3.2.2. RESULTS OF EXPERIMENT II 114 4. DISCUSSION 122 5. CONCLUDING REMARKS 133 6 . REFERENCES 138 7 . APPENDIXES 140 1. FORMULAS FOR THE L*a*b* COLOR SPACE 140 2 . THE NEWTON-RAPHSON METHOD 142 3. COMPUTER PROGRAMMING FOR PRIMARY STABILITY STUDY... 145 4. THE COLOR REPRODUCTION PROGRAM 155 5. Dmax SUBSTITUTION FOR RELATIVE CONCENTRATIONS WHEN NEGATIVE SPECTRAL RESPONSES ARE OBTAINED 164 6. COLOR REPRODUCTION WITH ALL POSITIVE SPECTRAL SENSITIVITIES 178 7. GRAY SCALE REPRODUCTION WITH UMBERGER'S PRIMARIES 195 8 . FORTAN CODE LISTING 205 vn LIST OF TABLES Table 1 Experimental colors used in the two studies. p. 35 Table 2 CIE L* a* b* coordinates of the primary reference color followed by Umberger's primaries for film A, illuminant C. p. 71 Table 3 Results of color reproduction using various primary reference colors for identification of Umberger's primaries. Color-matching functions of Umberger's primaries are the spectral sensitivities of the color reproduction system. p. 76 Table 4 Results of the paired-sample T test of color reproduction of a set of colors using various spectral sensitivities. Color-matching functions of Umberger's primaries are the spectral sensitivities of the color reproduction system. The random variable is the difference in color error for a given color reproduced using two different spectral sensitivities. p. 80 Table 5 Results of the paired-sample T test of color reproduction of ten sets of Munsell colors using two sets of spectral sensitivities. Color-matching functions of Umberger's primaries are the spectral sensitivities of the color reproduction system. The random variable is the difference in color error for a given color reproduced using two different spectral sensitivities. The two primary reference colors are: 18% transmittance gray color and the color of northern sky- p. 83 Table 6 CIE L* a* b* coordinates of the dyes of film A at unit concentration and illuminant C. p. 86 Table 7 Discrepancies between metameric concentration values and concentration values obtained through the subtractive color reproduction system computer model for a variety of reproduced colors. Spectral sensitivities of the color Umberger' reproduction system correspond to primaries computed for the primary reference color of northern sky. p. 98 vm Table 8 The maxima of the spectral sensitivities corresponding to Umberger's primaries and the average color error <Delta E> of color reproduction. Colors from the Colorset, Film A, illuminant C. p. 100 Table 9 Results of color reproduction using various primary reference colors for identification of Umberger's primaries. p. 116 Table 10 Results of the paired-sample T test of color reproduction of a set of colors using various spectral sensitivities. Color-matching functions of Umberger's primaries are the spectral sensitivities of the color reproduction system. The random variable is the difference in color error for a given color reproduced using two different spectral sensitivities. p. 120 APPENDIXES Table 5.1 Results of color reproduction using Dmax substitution for concentrations when negative spectral responses of the image sensors are obtained. Film A and colors from the Colorset, illuminant C. p. 173 Table 6.1 Results of color reproduction using various primary reference colors for identification of Umberger's primaries. The image sensors have only positive spectral sensitivities. Film A and colors of the Colorset, illuminant C. p. 185 Table 7 . 1 Results of color reproduction for flat gray colors using various primary reference colors. p. 201 Table 7.2 Color error delta E for 14 flat gray colors. Primary reference color: Caucasian skin, Y=29.24, x=0.377, y=0.336. Film A, and Illuminant C p. 202 IX LIST OF FIGURES Figure 1 Diagram of a color reproduction system. p. 3 Figure 2 Intensity vs. wavelength of additive primaries. p. 8 Figure 3 Primaries controlled by dye concentration. p. 11 Figure 4 Transmittance vs. wavelength of a green unstable primary realized by magenta dye of film A. The dye obeys Beer's law. Transmittance changes are given for the following three concentrations: cl= 0.1, c2=0.5, and c3=1.0. p. 13 Figure 5 Extinction coefficients (spectral densities) modulated by transmittance of the color of dark lemon peel (SPSE Handbook colors).
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