Analysis of Umberger's Theory for Subtractive Color Reproduction

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11-1-1990

Analysis of Umberger's theory for subtractive color reproduction

Paul R. Bartel

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FOR

SUBTRACTIVE COLOR REPRODUCTION

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

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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

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iii ANALYSIS OF UMBERGER'S THEORY FOR SUBTRACTIVE COLOR REPRODUCTION

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 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). Film B, illuminant C. p. 28

Figure 6 Spectral densities for film A and film B. The higher cyan and yellow curves are for film B. The data are scaled to yield an END of 1.0 for a

5000K source for film A and 3200K source for film B. p. 37

Figure 7 Chromaticities of the Munsell colors. Illuminant C. p. 41

Figure 8 Chromaticities of Umberger's primaries of the Munsell Colors. Film A, illuminant C. p. 42

Figure 9 Chromaticities of colors of Breneman's

color-chart. Illuminanr C. p. 43

Figure 10 Chromaticities of Umberger's Primaries of colors of Breneman's color-chart. Film A, illuminant C. p. 44

Figure 11 Chromaticities of 5/4 Munsell Colors. Illuminant C. p. 45

Figure 12 Chromaticities of Umberger's Primaries of 5/4 Munsell Colors. Film A and B, and Chromaticities

as for illuminant C where Y=19.5. p. 46

Figure 13 Chromaticities of Blue Primaries of 5/4 Munsell Colors. Film A and B, x and y as for illuminant C Y=19.5. p. 47 Figure 14 Scaled red color-matching functions of Umberger's primaries found for the colors of photographic set papers. Film A, and illuminant C. p. 49

Figure 15 Scaled green color-matching functions of Umberger's primaries found for the colors of photographic set papers. Film A, and illuminant C. p. 50

Figure 16 Scaled blue color-matching functions of Umberger's primaries found for the colors of photographic set papers. Film A, and illuminant C. p. 51

Figure 17 Chromaticities of primaries of #13 dark blue MacBeth color from the color-checker. The dotted triangle represents the gamut of the primaries defined by the dark blue color of the MacBeth Color Checker. The illuminant is identified with a triangle. Film A, illuminant C. p. 53

Figure 18 Equivalent sensitometric characteristic used in

model. p. 65

Figure 19 A CIELAB a*, b* plot of the primary reference colors: a) Caucasian skin, b) northern sky, c) grass green, d) 18% gray, e) average tristimulus value of all colors matchable by dyes of film A (the Colorset), and f) average tristimulus value of the subset of colors

consisting of photographic set papers. p. 72

Figure 20 CIELAB a*, b* values of Umberger's primaries of the following colors: a) Caucasian skin, b) northern sky, c) grass green, d) 18% gray, e) average tristimulus value of all colors matchable by dyes of film A (the Colorset), and f) average tristimulus value of colors of the subset of photographic set papers. p. 73

Figure 21 Histogram of color reproduction error delta E for the set of colors reproduced by dyes of film A (the Colorset). Spectral sensitivities of the

color reproduction model correspond to Umberger's primaries found for the primary

reference color of average tristimulus value of

the colors of the Colorset. Illuminant C. p. 87

xi Figure 22 Color reproduction shifts obtained with spectral sensitivities corresponding to Umberger's primaries found for primary reference color of average tristimulus value for all the colors reproduced by dyes of film A (the Colorset). Color reproduction of all colors of the Colorset reproduced by dyes of film A. Illuminant C. [ R, G, B designate Umberger's primaries for the primary reference color. C, M, and Y are the unit concentrations of film A dyes (from

table 6) . ] p. 88

Figure 23 Color reproduction shifts obtained with spectral sensitivities corresponding to Umberger's primaries found for primary reference color of 18% gray. Color reproduction of all the colors of the Colorset reproduced by dyes of film A. Illuminant C. [ R, G, B designate Umberger's primaries of the primary reference color. C, M, and Y are the unit concentrations of film A dyes

(from table 6) . ] p. 89

Figure 24 Color reproduction shifts obtained with spectral sensitivities corresponding to Umberger's primaries found for primary reference color of Caucasian skin. Color reproduction of all the

colors of the Colorset reproduced with dyes of film A. Illuminant C. [ R, G, B designate Umberger's primaries of the primary reference color. C, M, and Y are the unit concentrations of film A dyes (from table 6).] p. 90

Figure 25 Color reproduction shifts obtained with spectral sensitivities corresponding to Umberger's primaries found for primary reference color of northern sky- Color reproduction of all the

Figure 26 Reproduction Lightness vs. Chroma Ratio for the set of colors reproduced by dyes of film A (the Colorset). The primary reference color, for which Umberger's primaries were determined, is the average tristimulus value of the set of

colors reproduced with dyes of film A. Illuminant C. p. 92

xn Figure 27 Reproduction Lightness vs. Original Lightness

for all colors reproduced with dyes of film A (the Colorset). The primary reference color, for which Umberger's primaries were determined, is the average tristimulus value of all colors reproduced with dyes of film A. illuminant C.

p. 93

Figure 28 Color-matching functions for primary reference color of Caucasian skin. Film A, illuminant C. p. 101

Figure 29 Color-matching functions for primary reference color of northern sky. Film A, illuminant C. p. 102 Figure 30 Color-matching functions for primary reference color of grass green. Film A, illuminant C. p. 103

Figure 31 Color-matching functions for primary reference color of 18% gray. Film A, illuminant C. p. 104

Figure 32 Color-matching functions for primary reference color of average tristimulus value for all

colors reproduced with the dyes of film A (the Colorset), illuminant C. p. 105

Figure 33 Histogram of color reproduction error delta E for the set of colors reproduced with dyes of film A (the Colorset). Spectral sensitivities

of the color reproduction model correspond to Umberger's primaries found for the primary

reference color of grass green. Illuminant C.

p. 108

Figure 34 Color reproduction shifts obtained with spectral sensitivities corresponding to Umberger's

primaries found for primary reference color of grass green. Color reproduction of all colors

reproduced with dyes of film A (the Colorset). Illuminant C. [ The three lines join the origin with the coordinates of the primaries. R, G, B designate Umberger's primaries of the primary reference color. C, M, and Y are the unit

concentrations of dyes of film A (from

p. table 6) . ] 109

Figure 35 Reproduction Lightness vs. Original Lightness for all the colors reproduced with dyes of film A (the Colorset). The primary reference color, for which Umberger's primaries were determined,

xm is grass green. Film A. Illuminant C. p. 110

Figure 36 Reproduction Lightness vs. Chroma Ratio for the set of colors reproduced with dyes of film A (the Colorset). The primary reference color, for which Umberger's primaries were determined, is grass green. Film A, illuminant C. p. 112

Figure 37 Color reproduction shifts for the colors of

photographic set papers. The colors were

reproduced with spectral sensitivities corresponding to Umberger's primaries found for the primary reference color of average tristimulus value of all the colors reproduced with dyes of film A (the Colorset). Illuminant C. [ R, G, B designate Umberger's primaries corresponding to the primary reference color. C, M, and Y are the unit concentrations of film A dyes (from table 6).] p. 117

Figure 38 Color reproduction shifts for the colors of photographic set papers. The colors were

reproduced with spectral sensitivities corresponding to Umberger's primaries found for the primary reference color of average tristimulus value of photographic set paper colors. Illuminant C, dyes of film A. [ R, G, B designate Umberger's primaries corresponding to the primary reference color. C, M, and Y are the unit concentrations of film A dyes (from

table 6) . ] p. 118

APPENDIXES

Figure 3.1 Flow chart diagram of the program MAIN. FOR for finding Umberger's Primaries. p. 146

Figure 4.1 Flow chart diagram of the color reproduction

program REP. FOR p. 156

Figure 5.1 Equivalent sensitometric characteristic used in

model. p- 167

Figure 5.2 Histogram of color reproduction error delta E for the set of colors reproduced by dyes of film A (the Colorset). Spectral sensitivities

of the color reproduction model correspond to Umberger's primaries found for the primary

reference color of the average tristimulus value

of the colors of the Colorset. For a negative

spectral response Dmax=3.5 was substituted for

concentration. Illuminant C. p. 174

xiv Figure 5.3 Color reproduction shifts obtained with spectral sensitivities corresponding to Umberger's primaries found for primary reference color of average tristimulus value of all the colors reproduced with dyes of film A (the Colorset).

Color reproduction of all colors of the Colorset reproduced with dyes of film A. Illuminant C. For negative spectral responses the concentration is substituted with Dmax=3.5. [ R, G, B designate Umberger's primaries of the primary reference color. C, M, and Y are the unit concentrations of film A dyes (from

table 6) . ] p. 175

Figure 5.4 Reproduction Lightness vs. Chroma Ratio for the set of colors reproduced by dyes of film A (the Colorset). The primary reference color, for which Umberger's primaries were determined, is the average tristimulus value of the set of colors reproduced with dyes of film A. For

negative spectral responses Dmax=3.5 was substituted for concentration. Illuminant C. p. 176

Figure 5.5 Reproduction Lightness vs. Original Lightness for all colors reproduced by dyes of film A (the Colorset). The primary reference color, for which Umberger's primaries were determined, is the average tristimulus value of the set of colors reproduced by dyes of film A. For negative spectral responses Dmax=3.5 was substituted for concentration. Illuminant C. p. 177 Figure 6.1 Flow chart diagram of the color reproduction

program modified to cut off negative spectral

sensitivities. p. 181

Figure 6.2 Histogram of color reproduction error delta E for the set of all colors reproduced with dyes of film A (the Colorset). Spectral sensitivities

of the color reproduction model correspond to

Umberger's primaries found for the large area primary reference color of average tristimulus value of all the colors of the Colorset.

Spectral sensitivities are without their

negative parts. Illuminant C. p. 186

Figure 6.3 Color reproduction shifts obtained with spectral

sensitivities corresponding to Umberger's

primaries found for primary reference color of

average tristimulus value of all the colors

xv reproduced with dyes of film A (the Colorset). Color reproduction of all colors of the Colorset reproduced with dyes of film A. Spectral

sensitivities are without their negative parts. Illuminant C. [ R, G, B designate Umberger's primaries of the primary reference color. C, M, and Y are the unit concentrations of film A dyes

( from table 4) . ] p. 188

Figure 6.4 Reproduction Lightness vs. Original Lightness for all colors reproduced by dyes of film A (the Colorset). The primary reference color is average tristimulus value for all colors of the

set. The spectral sensitivities are without the

negative parts. Film A. Illuminant C. p. 189

Figure 6.5 Reproduction Lightness vs. Chroma Ratio for the set of colors reproduced by dyes of film A (the Colorset). The primary reference color is the average tristimulus value of the set of colors

reproduced with dyes of film A. The spectral sensitivities have no negative parts. Film A, Illuminant C. p. 190

Figure 7.1 Histogram of color reproduction error delta E for the set of flat grays. The primary reference color is Caucasian skin, film A. Illuminant C. p. 203

Figure 7.2 Reproduction Lightness vs. Original Lightness for the set of flat grays. The primary reference color is Caucasian skin. Film A. Illuminant C.

p. 204

xvi 1 . INTRODUCTION

1.1. Relationship between primaries and spectral

sensitivities in a color reproduction system

Color reproduction has turned, over the years, from an art

form to an almost exact quantitative science. This

progress can be attributed to the continuing research of

the principles of color reproduction theory. In

particular, the understanding of how primary colors combine

to reproduce colors led to a formal definition of the

requirements that a given color reproduction system has to

fulfil in order to accurately reproduce colored images.

This thesis explores how those requirements apply to a

identification of theory, proposed by Umberger[l], for the

color film. the color of light controlled by dyes in

Generally there exist two methods of color reproduction.

where lights from One is based on additive color mixing

and the other is based different sources are superimposed

where the color results from on subtractive color mixing

"subtraction" through selective absorption of portions of

a color the incident white light. For convenience,

described as consisting of three reproduction system can be

image generators, and parts: 1) the image sensors, 2) 3) the computational subsystem whose purpose is to

transform the image sensor output into suitable image generator inputs [2], see figure 1.

The design of the image sensors and image generators must

reflect the trichromat icity of the human color vision [3].

Consequently, three kinds of image sensors with linearly

independent sensitivity curves and three kinds of image

generators with linearly independent spectral curves of the

primary colors are needed [2]. Let us consider the

requirements that have to be met by the spectral

sensitivities and by the primaries of a color reproduction

system to accurately reproduce colored images.

To ensure that the original and the reproduced colors shall

have the same visual appearance, or be metameric, Hardy and

Wurzburg[4] have imposed on the color reproduction system

the criteria of colorimetry, i.e. the science of color

measurement. Colorimetric color reproduction can be

obtained over a wide range of brightness levels if:

X' X Y* k * Y (D Z' Z

where :

k - is a proportionality constant,

- of the original X,Y,Z represent tristimulus values color, image sensors image generators

Rl CI

FIG. 1

A COLOR REPRODUCTION SYSTEM

Ri- SPECTRAL RESPONSES

A -TRANSFORMATION MATRIX

Ci - INPUTS TO THE IMAGE GENERATORS

i = 1,2,3. X',Y',Z' - represent tristimulus values of a mixture of

R,G,B primaries.

An arbitrary assignment, in equation (1), of a value of 100

Y' for Y and to a reference white renders the relative

luminances independent of overall changes in intensity of

either the original or reproduced scene. This kind of

color reproduction is defined as "colorimetric color

reproduction" for which the reproduced colors must have

chromaticities ( x=X/(X+Y+Z) and y=Y/(X+Y+Z) ) and relative

luminances (Y) equal to those of the original [5].

The application of colorimetric criteria to color

reproduction defines the requirements for the effective

spectral sensitivities of the color reproduction system.

the To satisfy equation (1) for all possible colors,

system spectral sensitivities of the color reproduction

functions must be linear transforms of the color matching

of the eye[4] :

r x = A * y (2) b z

where :

sensitivities of the color - represent the spectral

reproduction system, x,y,z - represent the CIE 1931 2 degree standard observer color-matching functions,

A - is a 3X3 with matrix coefficients dependent on the x,

z y, chromaticity coordinates of the RGB primaries of the color reproduction system. Thus we have:

Xr Xg Xb A-i = y- yg yb (3) Z r Zg Zb

Sensitivities obtained from equation (2) are proportional to the color-matching functions corresponding to the effective primaries of the system. Consequently, for every set of color matching functions there is a proprietary primary and vice versa. A straightforward color reproduction system transforms the exposure signals to the primaries through an identity matrix. In general, any set of color-matching functions can be used instead of the unique set corresponding to the primaries. In this case,

the color reproduction system has to be capable of supporting a linear transform which allows for the required cross-coupling between image sensors and image generators.

In deriving the requirements regarding the effective

spectral sensitivities of the system, Hardy and Wurzburg

assumed that the amounts of primaries produced by the image generators are directly proportional to the exposures of the image sensors. Such an assumption is sufficient as a

rough approximation and it simplifies the discussion of color systems which is the topic of succeeding sections.

1.2. Primaries of additive color reproduction systems

In an additive color system, mixtures of varying amounts of

three colored lights, or primaries, attempt to recreate the

colors of the original scene. Maxwell [ 6 ] , [ 7 ] was the first

to realized this system by making three red, green, and

blue photographic recordings of the intensity of a scene

each done through a different colored filter. An image was

then synthesized on a screen by simultaneously projecting

the separation positives through the same filters. In

Maxwell's experiment, the three different photographic

recordings modulate the mixtures of varying amounts of the

colored lights or primaries. See figure 2.

The requirements regarding the effective spectral

sensitivities of the color reproduction system, described

to additive in section 1.1, can be applied directly any

primaries can be color reproduction system. The RGB

the CIE XYZ tristimulus values of specified by computing

distributions of the primaries: the spectral power R(Xr,Yr,Zr), G(Xg,Yg,Zg), B(Xb,Yb,Zb).

The spectral power distribution (SPD) of the primary refers

to the spectral region of the viewing illuminant

transmitted by a given colored filter. See figure 2. For

example, the SPD of the red primary can be written:

SPDr(X) = Tr(X)*E(X) (4) where :

Tr(A) - spectral transmittance of the red colored filter,

E(A) - spectral energy distribution of the illuminant.

Consequently, the X tristimulus value of r units of the red

primary is computed as follows:

X = k / r * SPDr(X) * x(A) * dA (5)

where: X

x()\) - CIE 1931 2 degree observer function,

k - scaling constant.

"r" factor which modulates The quantity is a linear scaling

the amount of the red primary- In Maxwell's experiment

this factor represents the transmittance of some area of

white positive uniform density of the black and image;

color separation. Since otherwise referred to as the red

"r" is independent of wavelength it can be taken outside

the integral. Equation (5) becomes: ADDITIVE SYSTEM

1(A)

BLUE PRIMARY

1(A)

GREEN PRIMARY

KX) RED PRIMARY

400 700 nm

FIG. 2

PLOT SHOWING INTENSITY vs WAVELENGTH OF A SET OF ADDITIVE PRIMARIES

I.V.-.M INTENSITY CHANGES X = r * k / SPDr(A) * x(A) * dX- (6)

The integral in equation (6) represents the tristimulus

value Xr of the spectral power distribution of the red primary. The following expression is obtained for the

tristimulus value of r units of the red primary:

X = r * xr. (7)

Similar, computations can yield the remaining X, Y and Z tristimulus values of r, g, and b units of the red, green, and blue primaries respectively.

The chromaticity coordinates of r units of the red primary can be found from the following equations:

r*X,

xr - = constant; (8a) r*(Xr+Yr+Zr )

r*Yr yr = constant. (8b) r*(Xr+Yr+Zr )

Equations (8) indicate that chromaticity coordinates, x and

constant throughout the y, of additive primaries remain

reproduced scene independent of the relative amount of the

particular primary; i.e. the primaries are said to be

primaries remain stable because stable. Concluding, the

are modulated their spectral power distributions (SPD's) by

in equation (5). linear scaling factors, such as, "r",

matrix in equation (2). Stable primaries define the A 10

Summarizing, colorimetric theory dictates the spectral

sensitivities for additive color reproduction systems. Let

us now consider if this theory can also be applied to

subtractive color reproduction systems.

1 3 . Stability of primaries of subtractive dyes

Another tristimulus method of color reproduction involves

the use of dyes or colorants which subtract the blue,

green, and red portions of the visible spectrum to produce

the desired gamut of colors. In the particular case of

photographic transparencies, each of the three superimposed

layers contains a different absorbing dye whose

concentration is to be adjusted on a point-by-point basis.

In analogy to the additive process, the green, blue, and

red amounts of transmitted lights which the absorption

bands of the cyan, magenta, and yellow dyes control are

frequently referred to as subtractive primaries. See

figure 3 .

The dyes that are formed in a transparent color film can

absorbers. The usually be regarded as homogenous

transmittance of such materials as a function of various concentrations c, m, y of the three dyes is described by

Beer's law[8] : 11

LIGHT SOURCE

RED

GREEN

YELLOW DYE

BLUE

FIG. 3

PRIMARIES CONTROLLED BY DYE CONCENTRATION 12

= T(X) exp{-2.3[ci*ei(X) + c2*e2(X) +

C3*e3(X)]} (9)

where: i = 1,2,3,

= T(X) transmittance of the mixture of the dyes,

ci = relative concentration of the iTt. dye,

i(X) = spectral extinction coefficient of the im. dye

per unit concentration.

The X, tristimulus value of, for example, the green primary

controlled a by certain concentration m of the magenta dye

is computed as follows:

X = k /exp[-2.3 * m * * * * em(A)] E(X) x(A) dX , (10)

or, A

= k * * X(m) jSPDg(X,m) x(A) dX , (11)

where: A

SPDg(A,m) = exp[-2.3 * em(X)] * E(X), (12)

and represents the spectral power distribution of the green

primary modulated in a nonlinear manner by, m, the

concentration of magenta dye. Expressions can be found

also for the remaining tristimulus values: Y(m) and Z(m).

Figure 4 illustrates how the spectral transmittance of the

magenta dye undergoes nonlinear changes as a function of relative concentration, m, of the dye. According to chapter 1.2, chromaticities of primaries will remain stable 13

WAVELENGTH C = 0.5 C=1.0

FIG. 4

Transmittance vs. wavelength of a green unstable primary dye obeys Beer's realized by magenta dye of film A. The law. Transmittance changes are given for the following = three concentrations cl= 0.1, :0 and c3 l .0 14

only if their spectral power distributions are scaled

linearly. For tristimulus values X(m), Y(m) , and Z(m),

expressions and (8a) (8b) can not be equated to constants.

in a Beer's law Consequently, system the chromaticities of

the primaries vary as a function of the relative dye

concentration. The subtractive primaries are said to be

unstable .

Since the coefficients in equation (3) depend on the

chromaticity coordinates of subtractive primaries which

vary through the reproduced scene, there is no unique set

of spectral sensitivities which can be associated with the

dyes of a subtractive color system. Primary instability

prevents direct application of additive theory to

subtractive systems.

' method" 1.4. MacAdam s analysis - "stable primaries

In dealing with the problem of unstable primaries, an

approach was proposed by MacAdam [9] to establish colorimetrically rather than radiometrically the chromaticities of the primaries of real dyes. In analogy to laws for the addition of lights, MacAdam formulated a

law of subtractive color mixture which enabled him to 15

establish three subtractive primaries. MacAdam found, by

trial and error, mixtures of the three dyes which would

trace almost straight lines on the chromaticity diagram when the concentration of each such mixture is increased

from zero to some finite value. Since only relatively low concentrations were used, the chromaticities of the primaries were established by extrapolation of these lines with other lines found by adding these mixtures to different starting combinations of the three dyes. But

MacAdam' s primary identification method also has its

problems. The obtained loci would fall either inside or

outside of the spectral locus. Since no lines are absolutely straight, there is no good criterion for determining when a locus has been located. This method also requires the computation of large numbers of chromaticity values. MacAdam was able to optimize for chromaticity only, and the method is not generally

applicable to all dyes.

1.5. Umberger's Primaries

In an attempt to apply additive color theory to subtractive

suggested a to color systems, Hardy and Wurzburg[10] way determine the primaries of a subtractive color reproduction 16

system. If for some given starting combination of the

three dyes of the system the amount of one of the subtractive colorants is slightly varied, the difference in spectrophotometric curves, calculated as chromaticity, corresponds to the primary controlled by that particular

colorant .

Umbergerfl] expanded their method to photography. He employed differential calculus to compute the rate of change of the color of the starting concentrations of three dyes with respect to the concentration of one of the dyes.

This thesis proceeds with Umberger's approach to identify

the spectrophotometric curves of primaries of a color film.

The transmittance of a colored area of the film composed of

various concentrations c, m, y of three dyes obeying Beer's

law is given as:

T(X) = exp{-2.3[ci*ei(A) + c2*2(A) + c3*e3(A)]} (13)

where :

of the T(A) = transmittance of the mixture dyes,

iTh- c; = concentration of the dye,

iTh- coefficient of the dye Ei(^) = spectral extinction

per unit concentration. 17

When viewed the the by eye, transmitted light creates a

sensation of color C[X,Y,Z] which can be represented by

its tristimulus values:

X = k * J T(A) E(A) * x(A) * dA, 14a) A

Y = k jTtA) * E(A) * y(X) * dX, (14b) X

Z = k / T(X) * E(X) * 5(A) * dA. 14c) X

Beer's law suggests that a change in the amount of a primary, induced by a small change in concentration, c', of one of the component dyes, will be accompanied by a slightly different transmittance spectrum of the film:

T'(A) = exp{-2.3 [ci'*ei(X) + c2*e2(A) + c3*e3(A)]}. (15)

When the two transmittance spectra are combined with the illuminant they will produce two different spectral power distributions E(A)*T(A) and E(X)*T'(X) which correspond to two different colors, C and C'. The difference between the two spectral power distributions,

E(X)*T(X) - E(X)*T'(X), (16) 18

can be regarded as corresponding to an additive color stimulus modulated by the dye whose concentration has been

altered .

As the foregoing discussion suggests, for very small

changes in concentration dc i of one of the component dyes the spectral quality of the primary Pi controlled by its corresponding dye can be identified by partial differentiation with respect to concentration of the

initial dye concentration T(X):

= * = - * e * dT/dci -2.3 * i(A) T(X) 2.3 > (A )

exp{-2.3[ci*i(/) + c2*2(A) + c3*e3(A)]J (17)

Substitution of the expression, e ; (A ) * T(A), as an

back into estimate of the primary, P i [X i , Y i , Z j ] ,

the tristimulus equations (14) will identify the primary:

* * * * x(X) , (18a) Xi = -2.3 k JT(X) e;(X) E(A) dA X

* * * y(X) * dX, (18b; Yi = -2.3 k /t(A) i(X) E(X)

* * * z(A) * dA, ( 18c) Zi = -2.3 k / T(X) i(X) E(X)

= where: i=l, 2, 3, and T(^) 19

exp{-2.3[ci*e1(A) + c2*e2(X) + c3*e3(/X)]}

The tristimulus equations indicate that primary Pi is

linear in spectral density function ej(A). However,

is not a T(X), linear multiplier of, ti(A), as a function

of relative dye concentration, Ci. Since the spectral density function, i(A), is not linearly scaled the primaries are unstable. Moreover, the transmission

is c c function, T(A), actually T (X , i , 2 , c 3 ) , where the

concentrations d, c2, c3 can be regarded as random

variables, the spectral quality of a given subtractive primary is dependant upon the starting point and therefore

the primary will be unstable.

Umberger observed that for gray colors the transmission

function T(A) is approximately independent of wavelength and can be replaced by a constant, Tn= T(X), representing a spectrally flat gray color. Consequently,

the transmission function, Tn, becomes a linear

multiplier of the spectral power distribution of the primary, e;(A) * E(A), and it can be taken outside of the integration sign:

= * * * * (19a) Xi -2.3 Tr. Ui(\) E(X) x(X) d/,

A 20

Yi = "2-3 * Tn *ji(A) E(X) * y(A) * d/, (19b) A

z> = "2.3 T *ji(A) * E(A) * 5(A) * dA, 19b) A where: i = 1, 2, 3.

The spectral power distribution of the primary Pi is thus proportional to the spectral extinction coefficient

i(X) of the respective dye at unit concentration.

Umberger proposed a theory which states that for subtractive color reproduction systems in which Beer's law applies, the primaries are represented by i(X) or dye-extinction curves regarded as the transmission spectra

of additive filters. A more accurate determination of the primary may be necessary for nongray colors. In such cases, the primaries are computed by modulating the i(A) function with the transmission function, T(A), prior integration. The established additive theory can thus be

used to determine the appropriate spectral sensitivities of

the color reproduction system to achieve colorimetric color

reproduction . 21

1.6. Objectives

In past analysis conducted by those attempting to develop a linear model of a subtractive system, the system's spectral

sensitivities corresponded to either the chromaticities of

the primaries of hypothetical block dyes chosen to replace

real dyes[ll] or to the chromaticities of MacAdam's primaries. The disadvantage of the block dye method is

that they only approximately correspond to real dyes.

Also, MacAdam's method is not applicable to all sets of dyes and it can result in imaginary primaries.

This thesis uses Umberger's theoretical approach to

identify the primaries corresponding to the dyes in a

Beer's law color reproduction system. Umberger formulated

the primaries in terms of spectral density curves, ,(X)

(i=l,2,3,), regarded as transmission spectra of additive

filters :

* dT(A)/dci = -2.3 * T(X) Si(>) (20)

Umberger assumed that To ensure stability of the primaries

is a spectrally flat gray T(A) = constant, i.e. T(A)

quantitative analysis in color. Umberger did not conduct

Umberger's support of his assumption. Generally,

accurate. For example, real dyes assumption may not be 22

obeying Beer's law are usually capable of producing only a spectrally selective gray color. The consequences of

Umberger's assumption that T(A) is spectrally flat are not fully know. Therefore, this work explores the influence of various functions of T(A) on Umberger's theory.

This thesis explores, in detail, the consequences of modulating the spectrum of Umberger's primary, i(A), with various transmittance functions, T (A ) Since T(A)

influences the resultant chromaticities of the primary, it will be referred to as the spectrum of the primary

reference color.

Taking advantage of the power of modern computers which

Umberger's were not readily available at the time of

conduct two computer publication, I applied his theory to

studies :

the primary stability study and

the color reproduction study.

explores the influence of T(A) The primary stability study

Umberger's primaries. on chromaticity coordinates of

of were Generally, two classes of possible choices T(X)

investigated :

constant and, a) grays where: T (A ) 23

b) nongrays where: T (A ) /constant .

The objectives of the preliminary primary stability study were :

1. To estimate the chromaticity range of Umberger's primaries for T(A) corresponding to a variety of real

colors .

2. To determine if, on the basis of chromaticity plots

obtained for a number of Umberger's primaries, an optimum

primary reference color for primary determination can be

found .

3. To determine the color-matching functions of Umberger's

primaries .

The second part of the thesis, the color reproduction

Umberger's and study, is a more detailed analysis of theory

is based on findings obtained in the primary stability

different study. My work explores the effect of primary

of color reproduction reference colors T(A> on the accuracy

sensitivities of the subtractive color when the spectral

are derived from reproduction system computer model

reference Umberger's primaries computed for the primary

color T(X) 24

2. PRIMARY CHROMATICITY AND SPECTRAL RESPONSE DETERMINATION

2.1. EXPERIMENTAL PROCEDURE

2.1.1. Introduction

In subtractive color reproduction systems the amounts of red, green, and blue light are controlled by the absorption bands of the cyan, magenta, and yellow colorants. These colorants are frequently referred to as subtractive primaries. Color transparencies using absorptive dyes obeying Beer's Law, see equation (9), are an example of such a system. Nonlinear changes of the absorption spectra of the dyes, due to changes in concentration, alter the primaries of the system. The primaries of such systems are different for each color, or each mixture of three concentrations, in the image and they are said to be unstable. A primary is unstable when its chromaticity coordinates vary with the amount of the colorant.

According to additive color reproduction theory, there is a

primaries of the system and unique relationship between the

match. the spectral responses needed for a colorimetric

However, for a subtractive system the primaries are not

a large unique (not stable) and there are, consequently, 25

set of spectral responses. What primary set to select, under these circumstances, still remains as one of the

fundamental subtractive color reproduction problems.

A primary stability study of a subtractive color reproduction system, such as a color reversal film, was conducted to understand the magnitude of the primary instability. Additionally, the set of spectral responses associated with the primary was also calculated to garner a first order understanding of the range of variation.

2.1.2. Computation of Umberger's primaries

Umberger [1] has shown that for a given mixture of concentrations ci, c2, and c3 the spectral characteristics of the primary controlled by minute changes

in concentration of its corresponding dye, dc \ , can be determined from the following equation:

* * aT(X) = -2.3 * i(X) T(A) dci (21) where :

i = 1, 2, 3,

- the dT(A) spectral characteristics of primary

the two determined as the difference between 26

spectrophotometric transmittance curves before and

after the change in concentration,

- spectral e'(X) extinction coefficient of the dye

corresponding to the primary being investigated,

T(A) = T(X,cl,c2,c3) =

exp{-2.3[ci*(A) + c2*e(A) + c3*e(A)]} (22)

- spectral transmittance of the starting concentration

of the dyes according to Beer's law [8].

Equation (21) was used in a computer program [Appendix 3]

to obtain chromaticities of subtractive primaries for a

variety of real surface colors. The relative amounts of

the three starting concentrations of the dyes were chosen

to reproduce a specified original surface color- (The sets

of colors used in the experiment, are listed separately in

chapter 2.1.4). The problem of finding those

concentrations is equivalent to metameric color matching,

which in this case is the determination of concentrations

of the cyan, magenta, and yellow dyes that yield the same

X, Y, and Z tristimulus values as the original surface

color- The Newton-Raphson method [Appendix 2] was used in

calculating the matching concentrations. The colorimetric

matches of some colors required negative amounts of dye,

which is impossible to achieve. Therefore, all such colors

were declared as unmatchable within the gamut of a 27

particular film (dye set) and were dropped from further

analysis .

The transmittance curve, T(A), corresponding to the match,

was generated according to equation (22). This spectral

transmittance curve was substituted into equation (21).

The product of this spectral curve, T(A), and each

extinction coefficient, e*(A) where i=l, 2, 3, yielded

the primary spectral curves for some particular color. For

an example see figure 5. Thus the following primary

spectral curves were obtained:

T(A) * ei(A) ~ red primary spectral curve,

T(A) * e2

T(A) * e3(A) - blue primary spectral curve.

It is to be noted that the extinction coefficients are

treated here as transmittances ; i.e. Umberger's primaries.

Once the spectral characteristics of the the R, G, and B primaries were determined, their CIE Xi, Yi, Zi

(i=l,2,3) tristimulus values were computed according to the

following equation:

Xi = k*(-2.3) Z T(X)*ej(A)*x(A)*E(A) *^A> (23al A

* Yj = k*(-2.3) 2 T(A)*i(A)*y(X)*E(A) AA, (23b) A 28

; 7\y tc-\'3''';7T^'^i

-^r- ..-r T :~ " -,rr

' c --^ -i e- ? ^ / / S C < *" / ;S / /

, z' / \ / 5 - / V / / / / /\ ~ / / \ / / ' /

~^^- . 1

gas S( saiE TffiE

FIG. 5 Extinction coefficients (Spectral Densities) modulated by transmittance of the color of dark lemon peel (SPSE Handbook colors). Film B, illuminant C. 29

= Z, k*(-2.3) Z T(A)*i(A)*5(A)*E(A) * 4A, (23c)

and

k= z * l/[ E(A)*y(A) A A] . (24) *\

Chromaticity coordinates of the primaries were determined from the following equations:

x = X/(X+Y+Z), y = Y/(X+Y+Z), z = Z/(X+Y+Z) (25)

2.1.3. Computation of the spectral responses

The procedure of calculating the r(X), g(X)> and b(A) spectral responses, or color matching functions, can be described as finding a linear transformation between the

CIE 1931 2 degree standard observer color-matching functions x(A), y(A), and z(X) and the unknown r(X), 1(A),

values of the and b(A) spectral responses. The tristimulus

functions can be r(X), I(A)> and b(A) color-matching

and z the tristimulus calculated by substituting for x, y,

functions values of the x(A), y(X), and z(A) color-matching in the following relationship: 30

R x A' -i G = * y (26) B z

The transformation matrix, A', is based on the xj, yi} and zi chromaticities of the R, G, B primaries for i= 1,

2, 3 respectively.

xl x2 x3 cr 0 0 yl y2 y3 0 eg 0 (27 zl z2 z3 0 0 cb

The three proportionality coefficients cr, eg, and cb

serve to normalize the matrix so that tristimulus values of

CIE illuminant C (X=98.074, Y=100, Z=118.23) are obtained

for unit amounts of R, G, and B primaries.

For a description of the program, MAIN. FOR, written to find

Umberger's primaries and their corresponding spectral

sensitivities for a given input color and a dye set refer

to Appendix 3 .

2.1.4. Description of experimental colors

The sets of test colors were chosen to include a wide gamut of colors which are most likely to be found in a natural

scene under daylight illumination. It was intended that

a 3 the experimental colors were not to be dominated by 31

color process or commercial colorants. The test color data was used for both the primary stability study and for the color reproduction study. The test color data are

summarized in table 1.

The set of colors found in the SPSE-Handbook [12] includes colors of skin, foliage, sand and soil, colors of various construction materials like brick and cement, colors of wood, and colors of domestic and citrus fruits.

Parry Moon's [13,14,15] sets of colors describe colors of various materials used indoors. The data was initially collected in order to develop more thoroughly the engineering aspects of lighting and decoration (improved visual conditions and a more pleasing psychological effect). Daylight illumination corresponding to illuminant

C is assumed for viewing of those colors. This set of

colors consists of:

a) Colors of school room materials. This group

contains colors of school chalkboards of various kinds,

wall and ceiling paints, Venetian blinds and window

shades . b) Colors of ceramic tiles. Those are the tiles used

in rooms for floors and walls.

c) Colors of furniture; office and school furniture

made out of steel, linoleum, and wood in a variety of

finishes .

It was of interest to test the computer model of color reproduction using charts that are used for testing real films. Stability of Umberger's primaries for the colors of the charts could also be tested. Therefore, two color checkers, the Breneman's color-chart [ 16 ] and the MacBeth

Color-Checker [17] were also included. The checkers include the most important colors in evaluating the quality

of color reproduction. Both color-checkers attempt to

simulate the spectral reflectance of objects which are likely to present some problems or that are critical in color reproduction. For example, the critical colors are the color of human skin and that of foliage. Colors which

present some problems are the ones with high infrared or

a well ultra violet reflectance. Both color checkers have

white black. spaced gamut of achromatic colors from to

MacBeth color-checker- Two sets of data were used for the

was taken from One set of chromaticity coordinates

of spectral reflectance reference [17]. Also, measurements 33

were made of an actual color-checker using a Colorscan spectrophotometer instrument (Milton Roy Co.) with 45/0 geometry.

The Colorscan was also used to measure the spectral reflectance of 53 samples of colored set papers, Set

Shop/New York 3 West 20 Street New York, NY 10011, which are used by photographers.

The arrangement of the Munsell colors in the chromaticity diagram follows an organized geometrical figure, which can be useful in identifying certain trends in the results of primary stability study and color reproduction. The fact that it also is a uniformly spaced scale of color can be helpful in judging the magnitude of errors of the reproduction process. One hundred and forty Munsell colors were chosen randomly to include a wide variety of Munsell

Hue, Value, and Chroma.

Additionally, a separate set of 14 spectrally flat gray colors was generated ranging from 0.5 to 95 percent

reflectance . 34

All colors which were given as spectral reflectances, with

the exception of the 14 flat grays, were combined into one

file yielding 221 colors. See table IB. This set of

colors is referred throughout the text as The Colorset.

The Colorset is said to represent an average color scene

containing average subject matter. Each color in such a

scene can be treated as representing an element of an array

of square patches of equal surface area. In the actual

computations only those colors which were within the color

gamut of the dye set of the particular film were used. The

procedure for finding colors within the gamut of the three

dyes is explained in more detail in Appendix 2.

The computations were limited to only one illuminant. The

long established CIE illuminant C was chosen for doing the

calculations because the chromaticity coordinates of both

color-checkers and of the sets of colors measured by Parry

Moon [13,14,15] are based on this illuminant. Moreover,

form a colors of the Munsell system are designed to

under illuminant C. perceptually uniform color space 35

A) Colors given as chromaticities:

1. SPSE-Handbook colors [12],

2. MacBeth color-checker [17],

3. Breneman's color-chart [16],

4. Parry Moon's sets of colors:

a) colors of school room materials [13],

b) colors of ceramic tiles [14],

c) colors of furniture [15],

B) colors given as spectral reflectances:

1. 140 Munsell colors [18],

2. 53 colors of set papers,

3. Caucasian skin [12],

4. northern sky [12],

5. grass green [12],

6. green leaf [12]

7. MacBeth color-checker.

8. 14 Flat grays.

TABLE 1

Experimental colors used in the two studies 36

2.1.5. Film dye (colorant) set

It is not usually possible to specify the colorant set of photographic film in terms of its actual extinction coefficients. Densities that relate to dye amounts, or concentrations of dyes in the film, are often useful in specifying the colorant set. The spectral densities are

normalized to make equal amounts of the densities appear

neutral. The normalization assures that a combination of

unit amounts of the three dyes together forms a neutral of

1.0 density under some given viewing illuminant. Such spectral densities scaled in this manner are referred to as

equivalent neutral densities (END's).

Two sets of Spectral Density data were used in the experiment, and are shown in figure 6. In the text they

are referred to as dye sets of Film A and Film B.

2.1-6. Description of experiments

Chromaticities of Umberger's primaries were calculated for

listed in a variety of different sets of colors separately

when a smaller set of section 2.1.4. On certain occasions,

limited number of colors would colors was preferred, only a 37

cyan

yellow magenta

WAWHILIIK] fern])

FIG. 6

Spectral Densities for film A and Film B. The higher cyan and yellow curves are for film B. The data are scaled to yield an END of 1.0 for a 5000K source for film A and 3200K source for film B. 38

be chosen from some given set of colors. The results

showing chromaticities of the red, green, and blue

primaries to corresponding various sets of colors were

plotted on the chromaticity diagram. Chromaticity of the

illuminant was also included in the plots to provide

additional reference. The chromaticity range of primaries

was then determined visually by inspecting the plots. It

was assumed that the plots can be helpful in revealing the

position of the average set of primaries corresponding to

the average color of a given set of colors.

The influence of the colorants on the chromaticity range of

primaries was investigated. In the experiment two sets of

colorants were used corresponding to Film A and Film B.

Chromaticities of primaries of one set of colors were

calculated using two sets of colorants and the results were

plotted on the chromaticity diagram.

For a given set of colors, whose primaries had been

determined, plots were made, one for each of the primaries,

showing the r(A), g(A) and b(X) spectral responses.

Throughout the experiment CIE illuminant C was used. This was selected, instead of the modern equivalent D65, because a significant colorimetric data base of real surface colors gathered from the literature used this illuminant. 39

2.2. RESULTS

2.2.1. Chromaticity range of Umberger's primaries

The chromaticity coordinates for the 140 Munsell colors are

'B' shown in figure 7. Figure 8, shows the 'R', 'G', and

primaries of the 140 colors. It is easy to notice that the

patterns of the red and green primaries are similar to one

another and to the original distribution of colors.

Likewise, for the colors of Breneman's color-chart,

figure 9 and figure 10, as well as, for any other set of

experimental colors a similar observation can be made. The blue primaries, on the other hand, bear no apparent

resemblance to the original distribution of colors. In all

of the plots the blue primaries continue to plot in a

similar manner i.e. the blue cluster shows mainly vertical

spread, compare figure 8 and figure 10.

A closer investigation of the chromaticities of the blue primaries was conducted using both films. It was decided that the chromaticity distribution of the original colors

as well as their corresponding primaries should distribute in an easily identifiable pattern. For this purpose,

Munsell colors having value = 5 and chroma = 4 (5/4) were

chosen. Their chromaticities plot as an ellipse on the 40

chromaticity diagram, see figure 11. As expected, the red and green primaries repeated this pattern in their respective regions in the chromaticity diagram, figure 12.

Plotting only the chromaticities of the blue primaries revealed a pattern resembling an ellipse with high

in eccentricity the case of film A and one bearing a close resemblance to a circle for film B, see figure 13. The ellipses representing the primaries are shifted relative to one another and this reveals itself the most for the blue

primaries .

This observation suggests that the type of film, i.e. the dye set, plays a role in determining where the center of primaries will be located. In addition, it is assumed that the patterns are to some degree deformed by the characteristics of the chromaticity diagram. In the plot of the blue primaries this becomes especially evident.

In summary, the results indicate that, for a given set of colors, the pattern of primary distribution shows a translation of the basic arrangement of the original colors on the chromaticity diagram. 41

~~FIG. 7 Chromaticities of the Munsell colors. Illuminant C 42~~

~~> :~~

~~FIG. 8 Chromaticities of Umberger's primaries of the Munsell colors. Film A, illuminant C. 43~~

~~FIG. 9~~

~~Chromaticities of colors of Brenenam's color-chart Illuminant C. 44~~

~~I I I I I II I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I~~

~~. >.~~

~~FIG. 10~~

~~Chromaticities of Umberger's primaries of colors of Brenenam's color-chart. Film A, illuminant C. 45~~

~~.0 .l~~

~~FIG. 11~~

~~Chromaticities of 5/4 Munsell colors. Illuminant C 46~~

~~FILM B~~

~~e- s!~~

~~' '' I I i i l i i i i i ' ' I I | | | ; i l | M | | I I I | l l I | I !>.H , =S A .g a ? @=~~

~~FIG. 12 Chromaticities of Umberger's primaries of 5/4 Munsell colors. Film A and B, and chromaticities as for illuminant C where Y=19.5. 47~~

~~Hi FILM A~~

~~^ FILM B a D e o~~

~~aft IK 5~~

~~iff (S.HSgg.USS .137 .H .IMJI .MS .157 .US 2S~~

~~FIG. 13~~

~~Chromaticities of blue primaries of 5/4 Munsell colors Film A and B, x and y as for illuminant C Y=19.5. 48~~

~~2.2.2. Color-matching functions of Umberger's primaries~~

For each of the Umberger's primaries three separate plots of corresponding color-matching functions were made. Each family of the color-matching functions was scaled so it would have a maximum value of one, see figures 14, 15, and

~~16. After the scaling the plotted curves showed a~~

~~spectrum. The similarity in shape in certain parts of the~~

~~positive best similarity was typically observed for the~~

~~worst was part of the blue color-matching curves and the~~

~~which the for the green. It appears that the degree to~~

~~parts of rescaled curves show dispersion in the remaining~~

~~on the input color set. the visible spectrum is dependent~~

~~affects The choice of Umberger's primaries strongly~~

~~negative portions of the magnitudes and boundaries of the~~

~~spectral sensitivities.~~

~~functions revealed the Graphs of the color-matching~~

~~certain color-matching functions for existence of inverted~~

~~the 14. A closer examination of colors, see figure~~

~~distributions of the primaries for primary chromaticity~~

~~inverted color matching reference colors producing~~

~~examination revealed that for functions was conducted. The~~

~~the sides of the color bounded by such colors the gamut,~~

~~excludes the of the primaries, chromaticity triangle~~

~~as shown in figure 17. chromaticity of the illuminant, 49~~

~~ot w~~

~~2 t i E- OT i i~~

~~mWiyiK]^ dffQKTDD~~

~~FIG. 14~~

~~Scaled red color-matching functions of Umberger's primaries found for the colors of photographic set papers. Film A, illuminant C. 50~~

~~co w~~

~~< >~~

~~J X> s M E-i OT hH OS H~~

~~wBIU1K1TO CketuD~~

~~FIG. 15 functions of Umberger's Scaled green color-matching papers colors of photographic set primaries found for the Film A, illuminant C. 51~~

~~/ \~~

~~. " / \ / \ co ffi - w ~ / \ X~~

~~< \ > 5- / \ CO X ?J X s J M \ Eh OT II a ffl"~~

~~OS 0 " Eh~~

~~> . , , , , , , , ! 1 1 1 1 1 1 1 1 1 , 1 1 1 0 , | j I, 1 410 WMIILIIMQTM tooMD~~

~~FIG. 16~~

~~Scaled Blue color-matching functions of Umberger's primaries found for the colors of photographic set papers. Film A, illuminant C. 52~~

In the computation of the spectral sensitivities the values of the proportionality coefficients are chosen by imposing the condition that CIE illuminant C is obtained for unit amounts of Red, Green, and Blue primaries, see equation

~~(27) in the thesis. If the chromaticity of the illuminant~~

~~falls outside the gamut, one or two negative tristimulus~~

~~values are required to specify such color yielding inverted~~

~~color-matching functions.~~

~~The number of obtained inverted color-matching functions is~~

~~also dependent on the type of colorants used. For example,~~

~~colorants from when MacBeth checker was reproduced using~~

~~behavior red film A only three colors showed this ( 13,~~

~~green 14, and blue 15; the inverted color-matching~~

~~). When functions were: blue, green, and red respectively~~

~~added to the list film B was used, four more colors were~~

~~magenta yellow green yellow 16, 17; ( moderate red 9, 11,~~

~~functions were: green, the inverted color-matching red,~~

~~green, and red respectively )~~

~~function of Umberger's Summarizing, the color-matching~~

~~of similar for a wide variety primary primaries are very~~

~~inverted color-matching reference colors. Occasionally,~~

~~illuminant lies outside the color functions result when the~~

~~gamut of the primaries. 53~~

~~i i i I i i i 'i | i i i i | i i i 1 1 1 1 1 1 1 1 1 1 1 1 i 1 1 1 1 1 i ii.ti .s @.a 1.4 @.s @.~~

~~FIG. 17~~

Chromaticities of primaries of #13 dark blue MacBeth color from the color-checker. The dotted triangle represents the gamut of the primaries defined by the dark blue color of MacBeth Color Checker. The illuminant is identified with a triangle. Film A, illuminant C. 54

~~2.2.3. Discussion - Summary~~

~~optimum color for primary determination~~

Application of the additive color reproduction theory for subtractive films is complicated by the fact that the primaries are unstable and there is no unique set of spectral sensitivities which can be associated with the

dyes. Solution to this problem of unstable primaries can be reached statistically by optimizing spectral sensitivities to the average set of primaries. According to Umberger[l], such primaries correspond to the color of the average

~~spectral transmission over the area of the dye image which in the text is also referred to as the primary reference~~

~~color - Consequently, it remains of interest to estimate the average color over the area of a color reproduction.~~

~~For example, Ralph Evans [19] proposed that integration over the total area of all possible scenes would assure complete statistical sampling and the resultant color would be gray.~~

~~Evans attempted to utilize integrated transmittance as~~

~~exposure and color-balance determination criterion [19],~~

~~[20]. His approach has been used successfully in practice.~~

~~systems which For instance, many commercial color printing~~

~~measure for exposure utilize integrated transmittance as a~~

~~calibrated and color-balance determination are by finding 55~~

~~their best average adjustment using a standard reference~~

~~negative, containing average subject matter. It can be~~

~~assumed that the standard reference negative will integrate~~

~~to gray or a hue near gray. In the past, some of the~~

~~systems were calibrated using a reproduction of an 18% gray~~

~~card instead of a standard negative.~~

~~Results of the primary stability study indicate that~~

~~primaries found for constant hue lines of the Munsell~~

~~colors, see figure 8, seem to converge towards some central~~

~~point of the pattern. This point of convergence, is not~~

~~easily defined since even chromaticities of primaries of~~

~~the gray colors have unstable primaries which tend to form~~

~~clusters. This is observed, for example, in figure 10~~

~~where the chromaticities that cluster the most in the green~~

~~and red regions correspond to the various gray reference~~

~~colors. In addition each pattern of primary distribution is~~

~~deformed by the nonuniformity of the color space.~~

~~The points of convergence reside in an area which is~~

~~colors around the occupied by the primaries of lying~~

~~Munsell value scale. This can imply that the color~~

~~chromaticities such primaries is corresponding to the of~~

~~it is possible that not very saturated. On the other hand,~~

~~average out to a color a set of 140 Munsell colors would 56~~

~~lying close to the neutral value scale. Hence, the~~

~~chromaticities of the points to which the patterns of~~

~~primaries have translated can be assumed as representing~~

~~the average primaries corresponding to an average color of~~

~~the scene area.~~

~~Thus it seems plausible to say that a gray primary~~

~~reference color can be satisfactory for a color process~~

~~statistically designed to reproduce a wide variety of~~

~~colors over a wide variety of scenes.~~

~~Obviously, there exist a diversity of scenes which~~

~~integrate out to a color other than gray. A critical color~~

~~such as the flesh tone can dominate the scene (color~~

~~identification, ID, photography) and it may be important to~~

~~optimize the primaries for that particular color. A~~

~~general method for finding the primaries for a nongray~~

~~integrated scene consisting of an arbitrary set of colors~~

~~remains to be determined. Different ways for locating the~~

~~"optimum" or average primary reference color need to be~~

~~tested for such an array of colors. The method should~~

~~account for the observation that the patterns of primary~~

~~distributions approximately look like translations of the basic arrangement of original colors to the chromaticities~~

~~of the primaries of the average color of a given set of 57~~

~~colors. Such a method could be based on finding the centroid of distribution of tristimulus values or~~

chromaticities of the original colors. This average color can, for example, be defined as the average tristimulus values for the entire color set. This procedure can be thought of as finding the average length of the component

~~vectors of some resultant color vector-~~

~~Concluding remarks~~

According to Umbergerfl], identification of primaries which correspond to the color of the average spectral transmission over the area of the dye image enables the application of additive theory to subtractive films.

~~Umberger's theory was tested in a color reproduction system~~

~~computer model. The model uses spectral sensitivities~~

~~which correspond to Umberger's primaries.~~

~~An experiment was conducted, in the second part of the thesis, to find the best estimate of the large area primary~~

~~reference color for the identification of Umberger's~~

~~color reproduction of primaries that are to be utilized for~~

~~real surface a scene containing a certain number of~~

~~best reference colors. A color is defined as the primary 58~~

~~color, for a given set of colors, if it can reproduce this~~

~~set of colors with the smallest average color error-~~

~~The primary stability study suggested the testing of the~~

~~average tristimulus value of a color set as the primary~~

~~reference color with along other primary reference colors,~~

~~color" as an "optimum in the color reproduction study- Due~~

~~to their frequent occcurrence in real life, the following~~

~~additional primary reference colors were utilized to~~

~~determine the primaries of the reproduction system:~~

~~1. Caucasian skin,~~

~~2. northern sky,~~

~~3 . grass green .~~

~~The first color, the flesh tone, is an example of a~~

~~critical color. In the case of, for instance, color ID~~

~~photos, the flesh tone dominates the scene and it can be~~

~~important to optimize the primaries for that particular~~

~~color. Also, many scenes can be dominated by the other two colors, foliage or grass green and blue sky. In addition, an 18% gray color was used in the test. Historically, an~~

~~18% gray color has been successful in the color calibration~~

~~of color reproduction systems.~~

~~The test, its procedures, and its results are described in the second part of the thesis. 59~~

~~3. COLOR REPRODUCTION STUDY~~

~~3.1. EXPERIMENTAL PROCEDURE~~

~~3.1.1. Introduction~~

According to additive color reproduction theory, there is a unique relationship between the primaries of the system and the spectral responses needed for a colorimetric match. On the other hand, the primaries of a subtractive color reproduction dye system are different for each color in the

~~image and are said to be unstable. According to~~

~~Umberger[l], identification of primaries corresponding to~~

~~the color of the average spectral transmission over the~~

~~area of the dye image is necessary for the application of additive theory to subtractive films.~~

~~of a In part one of the thesis, primary stability study~~

~~system was conducted for subtractive color reproduction dye~~

~~can be found in a typical a wide variety of colors that~~

~~was to estimate an area scene. One objective of the study~~

~~scene - the average color of the reproduced primary~~

~~average - set of reference color for which a corresponding~~

~~found. As a result of the (Umberger's) primaries can be~~

~~candidates of an average color have study, several possible 60~~

~~emerged for a scene containing a number of real surface~~

~~colors .~~

~~A study was conducted to test Umberger's theory and to~~

~~explore the effect of different primary reference colors,~~

~~on the T(A), accuracy of color reproduction when spectral~~

~~sensitivities of the subtractive color reproduction system~~

~~are derived from Umberger's primaries computed for the~~

~~primary reference color T(A). The spectral sensitivities~~

~~of the system correspond to the color-matching functions of~~

~~Umberger's primaries established for primary reference~~

~~colors selected as a result of the primary stability study~~

~~described in the first part of the thesis. The experiment~~

~~involved a simulated imaging of real surface colors, using~~

~~a subtractive color reproduction system computer model.~~

~~The model is representative of a color reversal film. It~~

~~can reproduce a given color by providing a corresponding~~

~~spectral transmittance curve of the superimposed three dye~~

~~layers of the film.~~

~~It was of interest to identify the most suitable primary reference color for the reproduction of a scene containing~~

~~a certain number of real surface colors. A color is defined as the best primary reference color, for a set of colors representing the scene, if it can reproduce this set 61~~

of colors with the smallest average color error. Also, with regard to individual colors, the color error was broken down into its component of metric chroma, metric hue, and lightness to determine which attribute had the

~~greatest contribution to the color error.~~

~~3.1.2. The subtractive color reproduction system~~

~~computer model~~

~~In accordance with additive color reproduction theory the~~

~~subtractive color reproduction system computer model~~

~~consists of: the image sensors, image generators, and the~~

~~computational subsystem whose purpose is to transform the~~

~~image sensor output into suitable image generator inputs,~~

~~see figure 1. The three sensitivity layers of the film~~

~~constitute the image sensors. The spectral sensitivities~~

~~of the layers correspond to the color-matching functions of~~

~~average Umberger's primaries obtained for a given primary~~

~~reference color. The image generators consist of the three~~

~~dye layers of the developed film. It is additionally~~

~~layer assumed that, in color films, each sensitivity~~

~~matrix relates controls only one dye layer. An identity~~

~~layers to the inputs of the responses of the sensitivity~~

~~assumed that no the image generators since it is~~

~~place. cross-mixing of signals can take 62~~

~~For a description of the program, REP. FOR, representing the subtractive color reproduction system computer model refer~~

~~to Appendix 4 .~~

~~3.1.3. Steps involved in color reproduction~~

~~Initially, the spectral responses of the color reproduction~~

~~system computer model have to be defined. For a chosen primary reference color Umberger's primaries have to be computed together with a corresponding set of spectral~~

~~sensitivities. For a description of this calculation refer to the primary stability study in section 2.1.2. and 2.1.3~~

~~respectively -~~

~~In this experiment the image sensors have theoretical~~

~~spectral sensitivities which can produce both positive and negative spectral responses. However, such sensitivities are not possible to realize with real photographic~~

~~systems. For a description of an experiment in which the image sensors of the color reproduction system have only the positive portions of the theoretical spectral~~

~~sensitivities computed on the basis of Umberger's primaries~~

~~refer to Appendix 6. 63~~

~~The original color is given in terms of its spectral~~

~~T0(A). The transmittance, R, G, B responses of the image~~

~~sensors to a given object-color stimulus are described by~~

~~the formulas :~~

~~R = k Z * T0(A) E(X) * T(A) *&\, (28a)~~

~~G = k * Z To(A) E(A) * g(X) *AA, (28bl~~

~~= B k Z To(A) * E(A) * t.(A) *AA, (28c) A~~

~~where :~~

~~_ To (A) the spectral reflectance factor of the object-~~

~~color stimulus,~~

~~k is chosen such that R=G=B for To = 1,~~

~~E(A) - the relative spectral power distribution of the~~

~~illuminant [21], CIE Illuminant 'C,~~

~~- r(A ) , g (A ) ,b(A ) spectral sensitivities of the color~~

~~reproduction system.~~

~~The R, G, B spectral responses are regarded as inputs to~~

~~the computational subsystem. They are used to determine the dye concentrations ci, c2, c3 of the reproduced color in the transparency. 64~~

~~The amount of dye in each of the three dye layers of the~~

~~film required for the reproduction of some given color was determined using the following constraints:~~

~~1. If R, G, B > 1.0 then ci = 0, i = 1,2,3, (29)~~

~~2. If 10-ax < R, G, B <. 1.0 then~~

~~ci = -log R,~~

~~c2 = -log G, (30)~~

~~c3 = -log B,~~

~~10-Dmax 3. If R, G, B <_ then the color is declared as~~

~~unreproducible and it is rejected from further~~

~~computations. This is equivalent to a color photographic~~

~~process with the sensitometric characteristics shown in~~

~~figure 18. Note that Ci can not be computed using the~~

~~logarithm function for negative exposures. A method of~~

~~resolving this problem has been examined and is explained~~

~~in Appendix 5 .~~

~~The last constraint not only checks for negative exposures~~

~~but it also prevents the density from becoming infinite for~~

~~positive exposure values approaching zero. Maximum density~~

~~was assumed to be equal to 3.5. of the dye, Dmax , Equivalent Neutral Density~~

~~FIG. 18 model Equivalent sensitometric characteristic used in 66~~

~~The spectral transmittance, Tr(A), of the three~~

~~superimposed dye layers of the reproduced color was~~

~~synthesized according to the formula for Beer's law.~~

~~= Tr(A) exp{-2.3[ci*e!(A) + c2*e2(A) + c3*e3(A)]} (31)~~

~~The extinction e coefficients, i (\) , were the same as the~~

~~spectral densities for a particular film. (See~~

~~section 2.1.5.)~~

~~3.1.4. Color error analysis~~

~~To gain insight into the possible patterns and extent of~~

~~color discrepancies between the desired colors and their~~

~~reproduction, two sets of tristimulus values were found:~~

~~a) for the original color-stimulus:~~

~~Xi = k Z T0(A) * E(A) * x(A) * ^X, (32a) X~~

~~Yi = k z T0(A) * E(A) * y(A) * AA, (32b) A~~

~~Zi = k Z T(A) * E(A) * z(X) * AX, (32c) A~~

~~b) for the reproduced color-stimulus: 67~~

~~X2 = k Z * * Tr(X) E(A) x(A) * A A, (33a)~~

~~Y2 = k Z * * Tr(A) E(A) y(X) * AA, (33b)~~

~~Z2 = k Z * * Tr(A) E(A) z(A) * A A, (33c)~~

~~k = constant such that R=G=B=1 for Tr=T0=l.~~

~~The X, Y, and Z coordinates were transformed to the CIE~~

~~L*a*b* uniform color space where various comparisons~~

~~between the original and the reproduced color were carried~~

~~out, see Appendix 1.~~

~~In order to determine color variability of the reproduction~~

~~process a numerical value for the amount of color~~

~~difference, delta Ea*t>*, between the desired color and~~

~~its reproduction was calculated. The delta E a t b * values~~

~~were also broken down into their components of metric hue,~~

~~lightness, and metric chroma to determine which attribute~~

~~had the greatest contribution to the color difference. The~~

~~formulas for determining color differences are given in the~~

~~Appendix 1 . 68~~

~~To find out which set of spectral sensitivities reproduced~~

~~the scene with the least average error, for a given set of~~

~~colors, averages and respective standard deviations of the~~

~~following parameters were calculated:~~

~~a) average AEa*t>* color error,~~

~~b) average chroma ratio, .~~

~~The graphs following were then constructed showing the~~

~~data :~~

~~1. histogram of frequency vs. AE ,~~

~~2. a*b* shifts in the a* b* plane,~~

~~3. reproduction lightness vs. original lightness,~~

~~4. reproduction lightness vs. chroma ratio.~~

~~Regarding flat grays it is only possible to plot graphs~~

~~showing histogram of AE color error, and reproduction~~

~~lightness versus original lightness, because chroma ratio~~

~~is undefined for such colors.~~

~~3.1.5. Description of experiment I~~

~~The experiment involved a simulated imaging of real surface colors, using a subtractive color reproduction system computer model whose spectral sensitivities are calculated 69~~

~~on the basis of the primaries determined from Umberger's theory.~~

~~In the experiment a scene is represented in terms of a set of spectral reflectances of real surface colors. For~~

example, it was assumed that an average color scene containing average subject matter can be represented by combining all colors given as spectral reflectances in table IB, with the exception of the 14 flat gray colors, into one file referred to in the text as the Colorset.

~~Each color in such a scene can be treated as representing an element of an array of square patches of equal surface~~

~~area .~~

~~Due to their frequent occurrence in real life, the following primary reference colors were used to determine the primaries of the reproduction system:~~

~~1. Caucasian skin,~~

~~2. northern sky,~~

~~3. grass green,~~

~~4. 18% non selective gray,~~

~~5. average tristimulus values of a given color set. 70~~

The last color was suggested on the basis of primary stability study done earlier (see section 2.2.3). The chromaticities of points to which the patterns of primaries have translated are assumed as representing the average primaries corresponding to the average color of the scene

~~area .~~

~~In table 2 are listed L*a*b* coordinates of Umberger's primaries for the mentioned primary reference colors. The~~

~~L*a*b* primary reference colors have been plotted in~~

~~chromaticity space, see figure 19. The corresponding~~

~~primaries are shown in figure 20.~~

~~3.1.6. Description of experiment II~~

~~if the method of finding It was of interest to determine~~

~~defined as the average the best primary reference color,~~

~~can be applied to any tristimulus value of a set of colors,~~

~~of the Colorset containing given set of colors. A subset~~

~~photographic set papers was chosen for only the colors of~~

~~table IB. The following primary the experiment, see~~

~~reproduction of selected for color reference colors were~~

~~this subset: 71~~

~~PRIMARY REFERENCE COLOR METRIC COLOR a* b* L* CHROMA~~

~~CAUCASIAN SKIN 15. 1 13.8 61 .0 2 0.5~~

~~a) RED 60.0 65.7 56.9 89-0 GREEN- -37.9 53.6 67.2 65.6~~

~~BLUE -68.5 29.4 27 .4 74 . 5~~

~~NORTHERN SKY -3.9 -21.7 73.9 22.0~~

~~b) RED 35.9 42.3 60.0 55.5~~

~~GREEN -67.2 43.2 84.9 79.9~~

~~BLUE 68.9 -113.1 43.2 132.4~~

~~GRASS GREEN -14.3 24.9 42.9 28.7~~

~~c) RED 24.6 50.2 35.6 55 . 9~~

~~GREEN -46.4 53.8 50.9 71.0~~

~~BLUE -6.9 -32.7 17. 3 33.4~~

~~18% GRAY 0.0 0.0 47.0 0.0~~

~~d) RED 37. 1 43.6 42.2 57 . 2~~

~~GREEN -43.7 39.6 56 .4 59.0~~

~~BLUE 29.8 -66.2 24.6 72.6~~

~~AVERAGE TRIST. VAL .~~

~~FOR THE COLORSET 0.9 6.6 61.9~~

~~e) RED 43.2 55.6 53.2 70.4~~

~~GREEN 51 .0 5 2.2 69.9 73.0~~

~~BLUE 31 .3 -73.2 30.2 79.6~~

~~AVERAGE TRIST. VAL.~~

~~FOR PHOTO. SET PAPERS 0. 1 13. 1 67 .6 13. 1~~

~~f) RED 48.3 64.4 59.6 80.5 GREEN 53.4 60. 7 76.8 80.8~~

~~BLUE 29.4 -74.3 32.4 79.9~~

~~TABLE 2~~

~~reference color a* b* L* coordinates of the primary illuminant followed by Umberger's primaries for film A, C 72~~

~~fc>~~

~~e c f~~

~~r- i r- i -I r-i &! l I i I I ' ' ' ' -i l l l | i l l r-j l f I | T I l | r I I~~

FIG. 19 colors: the primary reference A CIELAB a*, b* plot of grass northern sky, c) green, a) Caucasian skin, b) tristimulus value of all colors d 18% gray, e) average and average of film A (the Colorset), f) reproduced by dyes of subset of colors consisting tristimulus value of the

~~photographic set papers. 73~~

~~Sfl-~~

fe>*

~~f f o ? eo o d a c D~~

~~b o &~~

~~i r r- i i r i i i i i i i i i i i i i i i I -i i i i i i i i i l| i' i' l' l' I| i l i r~~

~~0 " 5 f cPe~~

~~-I I I I I r-r i i i i I i i i i I i i i i | i i i i | iKi m =@ 4 m~~

~~FIG. 20~~

CIELAB a*, b* values of Umberger's primaries of the following colors: a) Caucasian skin, b) northern sky, tristimulus value c) grass green, d) 18% gray, e) average of all colors reproduced by dyes of film A (the Colorset), colors of the subset of and f) average tristimulus value of photographic set papers. 74

~~1. average tristimulus value of the Colorset,~~

~~2. average tristimulus value of the photographic set~~

~~papers ,~~

~~3. average chromaticity of the photographic set~~

~~papers .~~

~~The primary reference color of average chromaticity was~~

~~included in the test to explore an alternate way of~~

~~optimizing the spectral sensitivities. 75~~

~~3.2. RESULTS~~

~~3.2.1. RESULT OF EXPERIMENT I~~

~~3.2.1.1. The most appropriate primary reference color for primary determination~~

~~3.2.1.1.1. Reproduction of a scene containing a variety of colors~~

~~Table 3 shows results of the color reproduction of the~~

~~Colorset. Based upon table 3 the smallest average color~~

~~reproduction errors, , were obtained using~~

~~Umberger's primaries found for the following two primary~~

~~reference colors:~~

~~1. 18% gray (under illuminant C),~~

~~of the entire Colorset. 2. average tristimulus value~~

~~show using the average The results in table 3 that,~~

~~colors as the primary tristimulus value of a set of~~

~~average color about the smallest reference color brings~~

~~produces the deviation of color error, and error, standard~~

~~results also unreproducible colors. The smallest number of~~

~~the color reproduction experiments, show that, in all of~~

~~the average color reproduction the standard deviation of~~

~~see table 3. the mean color error, error was larger than 76~~

~~Ll 1 O 1~~

~~cr in i 1 o o O o o~~

~~_l LU d 1 CHOI 1 OJ OJ OJ OJ OJ h- Z _J 1 O 3 O 1 hZQI~~

~~cr in LU 1 x m - _l 1 z - cr CD 1 q; LU LU m Ll cr LU CD X O u in 1 a id cr i- " =3 O x 3 1 in 3 i-D Z Z 3~~

_1 /\ zoo : h- *-. t t t f _l o i i CO N LO HH t LU <+ U 1 1 OJ OJ PT ^r OJ Ul 1 1 Q 0 \ 1 Dtuin "7" - in l i 1 o o o o O U ~T 1- U 1 Z - 3 LU LU v | O Ll Ll 10 UT HH 11 I- 1- .\ IX | CD _l o C 0 1 U Z Z C Z HH _l EOUI i in cn ro cn 3 LU cr LU o O - \ 1 i * OJ *-* -~ o QQIhh u cr i- l i o u g in rcui cr i- lu > 111 U II v a cr c a. in x lu o z in h- CT Ll 1 z ^ cr lu o ii_ LU 1 1 N ro CO in N cr ut o x - o 1 LO ID CO CO OD. Jhh UJ 4- 1 J o o u r- in Q 0 _l 1 1 LO CO N in O _J U LU 3 cr in lu i uo cr a o Q 1 O CO j V | LU Ll CT o u o lu in in a T u -^ 1 U LU LU LU LU 1 2 o ut z h- hh cr Q 1 O LO N r- LO LU ^ i- lu cr cr .-H h- ^ j 1 10 N t UD Ll _i cr c c cr c J 1 . . . . Ll x 3 LU Z Z O tt hh hh LU 1 i lo in cn *? <* a UT Ll _j r. Q 1 a lu lu cr cr o a'

~~_l X LU LU r> i- CD CD m LU X X 1 ^ in cr cr LU i- I 11 cr LU LU j 1 ^ > in o -> ~> CO~~

i in k 2 _i x x c in LU cr o 1- LU 1 i z LU h- u O 1 1 x z cr > .'\ > z cr i 1 t cr CD x LU LU LU .'N CCIilOI i in LU cr CD I 0 XI- u ? lu cr LU L i 1 x o cr CO _> o Q U cr lu v' \.. a. cr i 1 u T CD X Ll 77

~~The reason for having standard deviation larger than the mean can be learned by examining the distributions of the a* b* components of the color differences shown in figures~~

~~and 25. 22, 23, 24, The figures indicate that the level of color error is different for each reproduced color.~~

~~Saturated colors from the yellow, cyan, and magenta hue regions are reproduced with greater error than the remaining colors of the set. There is an "inherent~~

~~difficulty" of reproducing a particular color. For a~~

~~detailed description of the characteristics of color~~

~~reproduction errors refer to section 3.2.2. The standard deviation, for each color reproduction experiment, is greatly affected by the variability in the "inherent~~

~~difficulty" of reproducing a particular color.~~

~~Consequently, a large value of standard deviation results.~~

~~Also, the standard deviation for each color reproduction experiment depends on the choice of the reproduced colors.~~

All this, however, is of no immediate concern. In deciding upon the significance of the differences between the color reproduction experiments, we are primarily interested in the standard deviation resulting from the use of a

~~particular set of spectral sensitivities, not from the~~

~~sample set of reproduced colors. 78~~

~~To the standard keep deviation limited to random error a~~

~~method for the elimination, from experimental data, of~~

~~between color variability of the color error was employed.~~

~~For a color reproduced using two different sets of spectral~~

~~sensitivities the difference between the paired values of~~

~~the modulus of the color reproduction error was used as the~~

~~test statistic. Since the total number of reproduced~~

~~colors is different for each set of spectral sensitivities~~

~~some of the observations had to be discarded. Normal~~

~~distribution of the difference of color reproduction error~~

~~was assumed for the reproduced set of colors.~~

~~Statistical tests of significance were performed on the~~

~~results of color reproduction experiments to decide which~~

~~set of spectral sensitivities produced the smallest color~~

~~reproduction errors. A paired comparison t-test of the~~

~~data was performed [22], [23]. The level of significance~~

~~was assumed to be 0.05. This is a one tailed test, because~~

~~we were interested in specifying a particular direction of~~

~~the possible difference.~~

~~The null hypothesis is that there is no difference in the~~

~~results of color reproduction experiments obtained through~~

~~the use of different spectral sensitivities. All~~

~~comparisons were made relative to the results of color 79~~

~~reproduction obtained with spectral sensitivities related to Umberger's primaries corresponding to the average~~

~~tristimulus value of the Colorset. (The smallest average~~

~~color reproduction error was obtained with this set of spectral sensitivities.) The alternative hypothesis is~~

~~that the spectral sensitivities corresponding to the average tristimulus value of the Colorset produce the~~

~~smallest average color error.~~

~~The results of the tests are shown in table 4. The null~~

~~hypothesis has to be rejected in all four comparisons. The~~

~~spectral sensitivities corresponding to the primary~~

~~reference color of average tristimulus value of the~~

~~Colorset are most effective in reducing the color~~

~~reproduction errors.~~

~~Results of the paired comparison t-test show that the value~~

~~of the test statistic is smallest for the comparison between the primary reference color of average tristimulus~~

~~value of all the colors of the Colorset and the 18% primary~~

~~reference gray color. This result suggest that the average~~

~~color of a scene containing an infinite number of different~~

~~colors can be gray. 80~~

Ll 1- o ut UT 1- LU i O t ID in - r- \~ i ro en co ro 1 111 cr cr 3 U 1 . . . . UT O LU 3 X 1 1 T L0 OJ - cr 3 CD z in i- 1 o o cr lu LU 3 Ll LU H cr h- O co in cr U h- Ll Z > O in O 3 10 3 LU LU o X h- h- Ll Z U z h- LU O O Q O i -< ro oj co H in z cr i 1 UT O IJ) CO Ll in h- U X h- 1 ID 01 01 01 O 3 X Z U 3 Q X | . . . . HH O 3 ~ Z HH i m co in oj LU X LL hh Q |T| X 3 1 3 \- OHO H LU 1 3 u cr x UT Q X LU z z a 3 Z Z n 3 LU cr O O u_ CT O in q H Ll 3 X LU U CD CT UT LU 3 LU 3 Z OCT LU HH HH U 3 z cr 3 _| o "7* Z hh ll OIOCCH . LU 1 HH cr u u cr 1- 1 Ll cr cr i -Ll Q_ LU 3 LU O 1 in lo o LU X LU 1- Ll CT UT 1 > o cr z i cr h- T" ll cr cr i cr in i i- O " c HH |jj HH | H O LU cr cr Jin z O X 1 LU o o u. o z 11 cr o. i i hi ro m lu ii cr T JJOUU V* LU O 1 1 CO O CO 0J CD CD o o in 3 CD 3 LU 1 i ro ro ft X LU LU u li in z

. . . . 3 X O X 1 i cr u o Ll LU _j 3 cr li h i i oj in - o LU Z 3 Ll c HH LU 1 3 X Ll CO o h- u cr 3 Z Ll 1 X U O X m rj t- - X HH O 1 HH H H LU 3 z u h- Ll Ll CT UT HH lu LU LU O LU lu i- i- cr cr in r~t f-1 . | | i-H i t i-H i-H Z CO h hh hh lu m cr CT CD Z 3 UT Ll o O 3 h- hh z Ll 1- 3 3 UT Z h- LU z O cr i i t ro ro lo O LU ij-| q LU u lu in i i t ro ^r in U Ll LU 3 m cr

* h- CO Ll CT 1 | | +~i _| _| O 0. Z 3 LU LU u Z O HH | IjJ HH Z LU X X Ll I 3 X 1 U 3 Z x in CT H Ll H Z 0. 1 Z LU - UT H hh LU 3 Ll i juina Ll ^H ~H hH j J .-H rt i t . 4 cr LU Z Q X LU o LU 3 hh lu cr a. o Ll cr i- in lu 3 in 1 lu lu cr O U Jh cr cr o z X LU LU CO o 1 LU 1 Ll X a a x x id 3 1 LU > in i- z O 1 1 Z cr lu cr - u Ll 1 1 1 X - X in LU X UT O 1 1 > ^ LU z m 1- 3 cr 3 3 o in i i x z m HH Tf O X z Z H- 1 1 UT LU 1 cr t Ll h- z Q X O Z 1 1 LU Z a. m o cr m o lu 1/1 LU 1 i z cr x > X LU Q U i cr cd - x LU -. UT 3 hh z 3 i- X q cr ~ i iu in cr X cr x q lu x cr i i x in x cd r- 3 CD x cr o z CCQ.UI IhlOU II 3 z z cr a- 3 h- z a i i x 3 >? 1 UT HH HH LU CL X O X 1 i o cr x co LU UT cr X LU h- Ll a u lu i 1 Z CD U - LU 3 cr 3 a cr 81

~~3.2.1.1.2. Reproduction of a scene containing colors~~

~~from a limited hue region~~

~~the results Using of color reproduction of the Colorset a~~

~~statistical test was conducted to also determine if for~~

~~colors a from limited hue region a significant reduction of~~

~~color reproduction error is obtained by choosing spectral~~

~~sensitivities corresponding to Umberger's primaries~~

~~calculated for a primary reference color with a certain~~

~~amount of metric chroma. Ten sets of Munsell colors~~

~~corresponding to ten different hue regions were selected~~

~~from the Colorset to represent ten nongray integrating~~

~~scenes. For every color within each hue region a paired~~

~~comparison t-test was conducted between color reproduction~~

~~errors obtained with spectral sensitivities corresponding~~

~~to 18% transmittance primary reference gray color and color~~

~~reproduction errors obtained with spectral sensitivities~~

~~corresponding the primary reference color of northern sky.~~

~~The null hypothesis is that there is no difference in the~~

~~results of color reproduction experiments obtained through~~

~~the use of different spectral sensitivities. The~~

~~alternative hypothesis is that in a given hue region one of~~

~~the two sets of spectral sensitivities will result in a~~

~~smaller average color reproduction error- 82~~

The results of the tests are shown in table 5. The null hypothesis has to be accepted only for colors reproduced from the 5PB hue region. The null hypothesis has to be rejected for the remaining nine comparisons. Colors from hue regions 5B, 5BG, and 5G were reproduced with significantly smaller color reproduction errors using spectral sensitivities corresponding to the primary reference color of northern sky. In the remaining hue

~~regions spectral sensitivities corresponding to 18%~~

~~transmittance gray primary reference color produced~~

~~significantly smaller color reproduction errors than~~

~~spectral sensitivities corresponding to the primary~~

~~reference color of northern sky.~~

~~3.2.1.2. Character of color reproduction errors~~

~~Similarities exist between graphs describing color~~

~~reproduction changes corresponding to the following four~~

~~primary reference colors:~~

~~a) Caucasian skin,~~

~~b) northern sky,~~

~~c) 18% gray,~~

~~of the entire Colorset. d) average tristimulus value 83~~

cr o 3 o cr LU u o X Ll CD CT r- o z lu cr h- x LU lu a in x i- z h- u cr I- X LU I- Ll O in x o 3 3 cr U z o HH O z i in u H 3 r- LU LU 11 1 LU cr LU H" O z I- 3 3 ncn^ait-TLONCOtcn 1 O h- z UT O X CO 3 1 1 CO 01 CO 01 01 CO iN Ol CO 1 JhH. z X X 1 Ll O Lu > ** r- HH .-' 3 || ^H T-l ~H -^H ~H _fl^H 1 Ll O LU m x z II 1 O HH U cr 3 II 1 I- Z J CD 3 II 1 UT n HH ^ X 3 cr Q II 1 LU m in cr cr lu > IOhQ II %_ lu z LU H U h- i 3 u cr IICONCONNOitOJNCO 1 X U hh y Ll u z * i o ut a II HH 1 UT 3_ . UT Ll LU X X u UJ II 1 3 Q HH ~ a h x cr II Z O 3 3 Q UT h- z Ll II 1 1- "7* cr cr (j; 3 o II 1 H- LU LO a i- cr lu I- z HH HH h- II 1 UT X LU " |- X z m Ll cr ii oj t ro t ro ot ut t o - 1 UT Z 1- cr UT U H LU uj m 3 1 LU LU cr LU Z LU cr X co cr x n 1 \- in o 3 cr lu o_ in LU cr HH z H n 1 1 z CQ o m in ~ Ll I- * 3 X O ii 1 H 3 X 3 Ll h- LU /T CL ii 1 X O 3 LU LU 3 u i a cr i U X X 3 CO X n LU H cr i- co u 3 U Ll I- X o CD n hh lu V O U UJ 3 z_ n x a X lu cr cr I- LU HH H n H UT cr H CL X X cr ~y- in ll~NC00T,T-'rn--'C0 CD in ut CD X cr LU 1 1 id ro ^r ai or o oj oj cn cn LU CD LU UT z X H n Z Z LU r- Ll LU Z h- m 3 m 1 iiiDTiD-ro^oin^ro O h- u o - o m cr i- h- n i i i i i i i Q z cr 3 3 O Ll 3 n -cr z X in X z 3 o 3 ii UT X LU H UJ I E X Q O m n O CD H H 3 LU hh cr LU U in LU u lu in 1 o. in cr u cr cr 1 1 ro ut t co co co m ~ id ut o cr > z z a lu 3 LU n ~> i i co id cn - co lo cn r- o in m X O X 3 U 3 3 LU II UT ^r m 3 UT H O z - I- O X Q 1 1 in co oj - o o -co z z X I - cr lu U 1- n LU O O cr o cr a cr > i- 2- . n U HH HH LU CD LU LU LU X 3 LU UT ii Z H h- cr z o z cr Ll m 3 Z n X " u hh _ cr lu LU LU t l 1 1 OJ f OJ t N 01 N LO N (0 U Q 3 ro x in lu h- cr cr z in cr H-rOOiDNOOlDOJ ZQ ~H CL 3 co in o cr z lu Ll O O z > 3 > LU 3 0. X 1 1 ro cn cn - oi - o - ro i h- O cr 11 LU UT 3 UT o cr x Z X LU ii i i I ill z a. i cr o X LU Z ii CD 3 LU I- O Ll Z z cr Ll ii hh c cr 3 O O Z HH o O n in i- Ll O hh lu cr n z cr O U UT H 3 ll m n Ll LU O Z Ll 1- n O Z 3 UT 3 O 3 CD O HH I- h- LU n O 3 Q -S UT cr u 3 cr u 3 LU h- O X H O LU n LU LU 3 in u cr z 3 Z II CC > CD CO CL 3 a LU inzzi cr lu LU O X n>>cDCDCQCocracrcr LU X X LU 3 3 LU O X H J Z II UT UT UT LO UT LO UT LTI LO UT 3 LU h- cr z u. cr Ll I- U 84

~~Thus examples obtained for the primary reference color of~~

~~average tristimulus value of the Colorset shall serve as the basis for describing the character of color reproduction errors. Film A was used in the calculations of color reproduction.~~

~~The histograms of color reproduction error delta E are not~~

~~symmetrical and have a long tail to the right, see~~

~~figure 21. This indicates that there are some colors which~~

~~are reproduced with quite high color errors. The wide~~

~~spread of the results of color error is also responsible~~

~~for standard deviations of the average color errors being~~

~~greater than the average color errors, see table 3. The mode of the histograms are in the interval of color error,~~

~~delta E, between 0 an 5 .~~

~~reference listed Using any one of the four primary colors,~~

~~primaries and their above, to generate Umberger's~~

~~reproduction corresponding spectral sensitivities for the~~

~~similar of a large number of colors, result in looking~~

~~distribution of the a* and b* components; as shown in~~

~~figures 22, 23, 24, and 25. The squares designate the~~

~~reproduced original color and the ends of the lines the~~

~~color . 85~~

~~It appears that the three lines joining the origin with the~~

~~coordinates of the primaries, shown in the figures as~~

~~crosses, divide the entire a* b* plane into three distinct~~

~~regions of hue shifts (see figures 22, 23, 24, 25). The~~

~~hue shifts of the reproduced color tend to point in the~~

~~direction of yellow, magenta, and cyan dyes of the film,~~

~~see figure 22. In other words, the hue shifts~~

~~approximately follow in the direction of the a* b* values~~

~~of the dyes of the film. For comparison, in table 6 are~~

~~given the a* b* coordinates of primaries of the color of~~

~~each dye at unit concentrations.~~

~~Colors which plot in the neighborhood of the lines joining~~

~~the origin of the a* b* coordinates with one of the~~

~~coordinates of Umberger's primaries usually exhibit the~~

~~smallest difference in the a*, b* components of the color difference. Conversely, colors approaching the colorants have the largest color difference.~~

~~Generally, the higher the metric chroma of the original color the larger the increase in metric chroma of the~~

~~reproduced color. On the average there are more colors for~~

which the metric chroma ratio is greater than one, as illustrated in figure 26, and table 3. It is to be noted that an increase in metric chroma is contrary to practical METRIC COLOR NAME a* b* L* CHROMA

~~COLOR OF EACH DYE AT UNIT CONCENTRATION~~

~~YELLOW, cone. : 0,0,1 -8. 1 76.8 94.2 77.2~~

~~MAGENTA, cone. : 0,1,0 59.6 -41.8 61 .7 72.8 CYAN, cone. 1,0,0 30.8 -26.2 80.0 40.4~~

~~TABLE 6~~

~~CIE L* a* b* coordinates of the dyes of film A at unit~~

~~concentration and illuminant C 87~~

~~A A AAA i.ii~~

~~2Z& $Z LDELm~~

~~FIG. 21~~

Histogram of color reproduction error delta E for the set of colors reproduced by dyes of film A (the Colorset). Spectral sensitivities of the color reproduction model correspond to Umberger's primaries found for the primary

~~reference color of the average tristimulus value of the colors of the Colorset. Illuminant C. 88~~

~~i i ' ! ' '~~

~~=8 =@ fie.~~

~~FIG. 22~~

Color reproduction shifts obtained with spectral sensitivities corresponding to Umberger's primaries found for primary reference color of average tristimulus value for all the colors reproduced by dyes of film A (the Colorset). Color reproduction of all colors of the Colorset reproduced by dyes of film A. Illuminant C. [ R, G, B designate Umberger's primaries for the primary reference color. C, M, and Y are the unit concentrations of film A dyes (from table 6).] 89

~~A"'~~

~~R G 111 1 "\ O /P \ ^ 4~~

~~r*' ^ - ftP T o Q J ^a ? ft/"Ho p~~

~~l I i | i r ' I ' t\ I '' i i I i i~~

~~? "Q^\Q* 3^ a b QC^~~

~~J -A M~~

~~\ 0 0 B~~

~~es. f-r-r-r f f i f i i i f i i i i i i i i | | | | | 1 I I I 11 I I I I I I I I II 4~~

~~FIG. 23~~

Color reproduction shifts obtained with spectral sensitivities corresponding to Umberger's primaries found for primary reference color of 18% gray. Color reproduction of all the colors of the Colorset reproduced by dyes of film A. Illuminant C. [ R, G, B designate Umberger's primaries of the primary reference color. C, M, and Y are the unit concentrations of film A dyes (from table 6).] 90

~~to' ^ -~~

~~@ i I I I | i i i i | r r~~

~~rfttfr\ j A M P \~~

~~B e> 11 i i | i i i i | i i r i | i i i i | i i i~~

~~FIG 24~~

Color reproduction shifts obtained with spectral sensitivities corresponding to Umberger's primaries found for primary reference color of Caucasian skin. Color reproduction of all the colors of the Colorset reproduced with dyes of film A. Illuminant C. [ R, G, B designate Umberger's primaries of the primary reference color. C, M, and Y are the unit concentrations of film A dyes (from

~~table 6) . ] 91~~

~~Figure 25~~

Color reproduction shifts obtained with spectral sensitivities corresponding to Umberger's primaries found for primary reference color of northern sky. Color reproduction of all the colors of the Colorset reproduced with dyes of film A. Illuminant C. [ R, G, B designate Umberger's primaries of the primary reference color. C, M, and Y are the unit concentrations of film A dyes (from table 6) . ] 92

~~3- SB~~

~~<9>~~

~~CpP D D~~

~~0 0~~

Figure 26 set of Reproduction Lightness vs . Chroma Ratio for the Colorset). The colors reproduced by dyes of film A (the Umberger's primaries primary reference color, for which tristimulus value of the were determined, is the average of film A. set of colors reproduced with dyes Illuminant C. 93

~~) 4>(B O SS~~

~~FIG. 27~~

Reproduction Lightness vs. Original Lightness for all colors reproduced with dyes of film A (the Colorset). The primary reference color, for which Umberger's primaries were determined, is the average tristimulus value of all colors reproduced with dyes of film A. illuminant C. 94

~~color reproduction which usually produces a decrease.~~

~~figure Also, 27 shows that the average reproduction lightness is generally lower than original lightness. Thus the reproduced colors appear darker and more saturated than the originals.~~

~~3.2.1.3. Investigation into the cause of the large~~

~~increase in metric chroma~~

~~The cause of the large increase in metric chroma which~~

~~occurs for some of the reproduced colors was investigated.~~

~~Three sets of colors were chosen from the colors of the~~

~~Colorset. Each set corresponds to one of the three distinct regions of hue shift which point in the direction of yellow, magenta, and cyan dyes of the film.~~

~~Concentration values required to metamerically match a~~

~~color were compared with concentration values computed by~~

~~the color reproduction system computer model. Table 7~~

~~reproduced shows results of this comparison for colors with~~

~~spectral sensitivities corresponding to Umberger's~~

~~reference color of primaries related to the primary~~

~~northern sky. 95~~

~~Concentration values provided by the computer model are,~~

~~higher generally, than concentrations required for metameric color reproduction. The greatest discrepancy between metameric concentration values and concentration~~

~~values provided by the color reproduction system computer model occurs for the yellow dye for colors located between~~

~~Umberger's green and red primaries and for the magenta dye~~

~~for colors located between Umberger's red and blue~~

~~primaries .~~

~~Usually, the largest discrepancy between computed and metameric concentration value corresponds to the dye which~~

~~is present in largest amount in a metameric match of a particular color. Colors located between Umberger's green~~

~~and red primaries require for their reproduction the~~

~~largest amount of yellow dye, and colors located between~~

~~Umberger's red and blue primaries require the largest~~

~~amount of magenta dye.~~

Moreover, the dye for which the greatest discrepancy between metameric and computed concentrations occurs controls an Umberger's primary whose location on the a*b* plane is diametrically different from the location of the

~~reproduced color. A yellow dye controls Umberger's blue~~

~~the green primary. primary and a magenta dye controls 96~~

~~The excessive amount of one particular dye can result in an~~

~~increase in metric chroma and in a hue shift of the~~

~~reproduced colors in the direction of the hue of one of the~~

~~dyes of the film. See figure 25 where colors laying~~

~~between the red and green primaries are shifted in the~~

~~direction of the hue of the yellow dye, and colors laying~~

~~between the red and blue primaries are shifted in the~~

~~direction of the hue of the magenta dye. Similarly, the~~

~~higher concentration values predicted by the computer model~~

~~can also cause the average reproduction lightness to become~~

~~lower than original lightness, as is documented by~~

~~figure 27.~~

~~On the other hand, for colors located between Umberger's~~

~~green and blue primaries the discrepancy between metameric~~

~~concentration values and concentration values provided by~~

~~the computer model is by one order of magnitude smaller~~

~~than the discrepancy observed during reproduction of the other two sets of colors containing colors of similar metric chroma. See table 7. For colors located between~~

~~Umberger's green and blue primaries the dye for which the greatest discrepancy between computed and metameric dye concentrations will occur is less obvious to pinpoint.~~

~~Also, the a*b* component of color reproduction error is small. See figure 25. After all, according to Umberger's 97~~

~~FILM A, ILLUMINANT C.~~

~~CONCENTRATION VALUES: COLOR COLOR ERROR NAME METAMERIC REPRODUCED DIFFERENCE DEL. Ea*b~~

~~G - B RESULTS OBTAINED FOR COLORS LOCATED BETWEEN GREEN AND BLUE UMBERGER'S PRIMARIES~~

~~5BG 5/4 C -*- 1.092 1 . 159 0.067 1.92 M 0.542 0.544 0.002 Y 0.68 0.687 0.007~~

~~5PB 5/4 C 0.812 0.821 0.009 1.23 M 0.709 -*- 0.688 0.021 Y 0.501 0.492 0.009~~

~~G - R RESULTS OBTAINED FOR COLORS LOCATED BETWEEN GREEN AND RED UMBERGER'S PRIMARIES~~

~~5GY 5/4 C 0.858 0.816 0.042 13.91 M 0.591 0.628 0.037~~

~~Y 1. 161 -*- 1.527 0.366~~

~~5Y 5/4 C 0.628 0.612 0.016 17.27 M 0.692 0.752 0.06~~

~~Y 1.218 -*- 1. 737 0.519~~

~~5YR 5/4 C 0.484 0.514 0.03 5.3 M 0.816 0.918 0. 102~~

~~-*- Y 1 .043 1. 198 0. 155~~

~~5GY 5/4 C 0.858 0.816 0.042 13.91 M 0.591 0.628 0.037~~

~~-*- Y 1 . 161 1.527 0.366~~

~~GRASS C 1 .042 0.992 0.05 19. 19 GREEN M 0.727 0.776 0.049~~

~~Y 1.404 -*- 2.073 0.669~~

~~FOLIAGE C 1.095 1. 118 0.023 19.91 M 0.704 0.764 0.06~~

~~-*- 0.855 Y 1 .328 2. 183~~

~~TABLE 7 (con, 98~~

~~CONCENTRATION VALUES: COLOR COLOR ERROR NAME METAMERIC REPRODUCED DIFFERENCE DEL. Ea*b~~

~~R - B RESULTS OBTAINED FOR COLORS LOCATED BETWEEN RED AND BLUE UMBERGER'S PRIMARIES~~

~~5P 5/4 C -*- 0.589 0.617 0.028 2 .04 M 0.818 0.84 0.022 Y 0.536 0.531 0.005~~

~~5PR 5/4 C 0.475 0.521 0.046 4,.88~~

~~M 0.867 -*- 0.955 0.088 Y 0.695 0.704 0.009~~

~~5R 5/4 C 0.432 0.483 0.051 5 ,.85~~

~~M 0.871 -*- 0.997 0. 126 Y 0.837 0.879 0.042~~

~~CAUCAS . C 0.28 0.324 0,.044 4.8~~

~~-*- SKIN M 0.654 0.75 0,.096~~

~~Y 0. 703 0.761 0,.058~~

~~PURPLE C 0.843 0.94 0.097 11.04 M 1.53-*- 2 0.47 Y 0.687 0.762 0.075~~

~~"-*-" DESIGNATES THE GREATEST DIFFERENCE BETWEEN CONCENTRATION VALUES FOR A PARTICULAR COLOR.~~

~~TABLE~~

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 REPRODUCTION SYSTEM CORRESPOND TO UMBERGER'S PRIMARIES COMPUTED FOR THE PRIMARY REFERENCE COLOR OF NORTHERN SKY. 99

~~the color theory, reproduction system computer model is expected to be optimized, to some extent, for the~~

~~reproduction of colors from the blue and cyan hue region~~

~~through the choice of spectral sensitivities which correspond to Umberger's primaries related to the primary~~

~~reference color of northern sky.~~

~~3.2.1.4. Character of the spectral sensitivities of~~

~~the color reproduction system~~

~~Table 8 and figures 28-32 summarize the results of the~~

~~color-matching functions for the primary reference colors~~

~~listed in table 2. The color-matching functions produced~~

~~by the colors of 18% gray, figure 31, and average~~

~~tristimulus value of the set of colors matchable with dyes~~

~~of film A, figure 32, give similar looking plots of~~

~~color-matching functions.~~

~~it was In the primary stability study (section 2.2.2)~~

~~and blue observed that when several of the red, green,~~

~~rescaled so that their maxima color-matching functions were~~

~~and blue are equal, the superimposed red, green,~~

~~as if were some scaled color-matching functions looked they~~

~~version of one another. 100~~

~~MAXIMA OF CMF COLOR NAME RED GREEN BLUE~~

~~CAUCASIAN SKIN 1.9 2.00 3.50 5.6~~

~~NORTHERN SKY 2.50 2.50 2.50 5.8~~

~~GRASS GREEN 1.70 4.20 2.20 9.5~~

~~18% GRAY 2. 10 2.20 2.80 4.7~~

~~AVER. TRIST. VAL. 2.00 2.20 2.80 4.2 FOR THE COLORSET~~

~~TABLE 8~~

~~The maxima of the spectral sensitivities corresponding to Umberger's primaries and the average color error~~

~~of color reproduction. Colors from The Colorset, film A, illuminant C 101~~

~~CO w 3~~

~~CO I D \~~

~~M H CO T i i~~

~~r- 1 i i i yialEi Miyifiwara lm~~

~~FIG. 28 color of Color-matching functions for primary reference Caucasian skin. Film A, illuminant C. 102~~

~~Offlffl TO^iyii M~~

~~FIG. 29 Color-matching functions for primary reference color of northern sky. Film A, illuminant C. 103~~

~~mmiM (m~~

~~FIG. 30 Color-matching functions for primary reference color of grass green. Film A, illuminant C. 104~~

~~AfiO~~

~~FIG. 31~~

~~reference color of 18% Color-matching functions for primary gray. Film A, illuminant C. 105~~

~~FIG. 32 Color-matching functions for primary reference color of average tristimulus value for all colors matchable by the dyes of film A (the colorset), illuminant C. 106~~

~~The "gain" or scaling factor of the spectral sensitivities~~

~~is just a logarithm exposure shift and can only affect~~

~~color balance. By automatically resetting the gains of the~~

~~individual color channels in the computational subsystem~~

~~color balance can be retained. Such an automatic~~

~~compensation is designed into the computer model (see~~

~~equation where 27) the coefficient k is chosen such that~~

~~the spectral responses fulfil the requirement that R=G=B=1~~

~~when the spectral reflectance factor of the object-color~~

~~stimulus, T0, equals one (T0=l).~~

~~It is the shape of the color-matching functions and not~~

~~"gain" some or scaling factor which provide the correct~~

~~spectral responses necessary to obtain the smallest average~~

~~color error, . The importance of the actual shape~~

~~of the spectral sensitivity curve in bringing down the~~

~~value needs further investigation.~~

~~3.2.1.5. Grass green primary reference color as an exception~~

~~The case of the primary reference color of grass green is~~

~~an exception because it produces plots which differ from~~

~~graphs obtained with all the other primary reference~~

~~colors. This color has the highest metric chroma out of~~

~~see table 2. all the primary reference colors, 107~~

The grass green primary reference color produces a histogram of delta E color error which is asymmetrical and less smooth than the rest of the histograms. Compare figure 33 with figure 21. The mode lies just to the right of the other histograms; at a delta E equal to about 5.5.

Colors similar in hue to grass green, i.e. yellow greens, as well as, colors which are of exactly the opposite hue, i.e. magentas or purples, increase in metric chroma after reproduction, as illustrated in figure 34. Colors which are neither magenta nor yellow green i.e. such as yellow

~~reds or cyans decrease in metric chroma. There are also some colors which primarily undergo a hue shift.~~

~~The plots showing the results of reproduction lightness vs. original lightness obtained for the grass green primary reference color, figure 35, reveal that there are many~~

~~colors which are reproduced lighter than the original~~

~~to reproduce colors color- By comparison, this tendency~~

~~almost nonexistent in lighter than they originally are is~~

~~reproduction lightness vs. the plots showing results of~~

~~the original lightness obtained with, for example, primary~~

~~tristimulus value of the colors reference color of average~~

~~of the Colorset [figure 27]. 108~~

~~ELirA lg~~

~~FIG. 33~~

Histogram of color reproduction error delta E for the set Colorset). of colors reproduced with dyes of film A (the Spectral sensitivities of the color reproduction model the correspond to Umberger's primaries found for primary C. reference color of grass green. Illuminant 109

~~FIG. 34~~

obtained with spectral Color reproduction shifts Umberger's primaries found sensitivities corresponding to color of grass green. Color for primary reference reproduced with dyes of film A reproduction of all colors The three lines join the (the Colorset). Illuminant C. [ primaries. B coordinates of the R, G, origin with the of the primary reference designate Umberger's primaries concentrations dyes of the unit of color. C, M, and Y are film A (from table 6) . ] 110

~~MOIMIL y@Kra~~

FIG. 35 Reproduction Lightness vs. Original Lightness for all the Colorset). The colors reproduced with dyes of film A (the for which Umberger's primaries primary reference color, Film A. Illuminant C. were determined, is grass green. Ill

A comparison of the plot of reproduction lightness vs. chroma ratio for the grass green primary reference color, figure with a 36, corresponding plot for the primary reference color of average tristimulus value, see figure

reveals that for 26, the grass green primary reference color only a small number of the reproduced colors have retained their original chroma. The spread in the values of the saturation ratio is large for the grass green primary reference color and the values do not want to cluster around the value of one, as illustrated in the data

~~in table 3 .~~

~~The possible cause of color errors is an imbalance in the inputs from the image sensors which does not allow~~

~~formation of the proper amounts of dyes required for~~

~~correct reproduction.~~

~~Concluding observation~~

~~Based on the color reproduction study, an observation can be made that using the average tristimulus value of a set~~

~~color to compute Umberger's of colors, as the reference~~

~~color difference for primaries, gives the smaller average~~

~~an to the set. This suggests that there is opportunity 112~~

~~D 8Q grl o d D O~~

~~%D "ooo~~

~~a i % # off~~

~~m ^ DO CD P ?~~

~~s cP~~

~~: H^i~~

FIG. 36 the set of Reproduction Lightness vs. Chroma Ratio for film A (the Colorset). The colors reproduced with dyes of for which Umberger's primaries primary reference color, green. Film illuminant C. were determined, is grass A, 113

optimize for specific sets of colors which are found in the scene. For example, when color ID photos are produced, and the flesh tone will be the prevailing color in the scene, the highest color fidelity of the reproduction can probably be obtained when the spectral sensitivities of the imaging system correspond to the primary reference color of

~~Caucasian skin. To test this theory a follow up experiment was conducted in which a subset of the currently used~~

~~Colorset was reproduced. Among the different primary~~

~~reference colors that were tested was the average~~

~~tristimulus value of this subset of colors, see~~

~~section 3.1.6. 114~~

~~3.2.2. RESULTS OF EXPERIMENT II~~

In table 9 are given results of color reproduction of a subset of the Colorset containing only the colors of photographic set papers. Three different sets of spectral sensitivities were tested for the reproduction of the colors of set papers. The results indicate that the primary reference color defined as average chromaticity of the colors of set papers was most effective in reducing the average color reproduction error. The largest average

color reproduction error was obtained with spectral sensitivities corresponding to the primary reference color of average tristimulus value of the Colorset. In all three color reproduction experiments, the standard deviation of the color reproduction error was larger than the average color error. Consequently, in deciding upon the

~~significance of the differences between the color reproduction experiments, the reason had to be learned for having standard deviation larger than the mean.~~

~~The results of color reproduction are illustrated in~~

~~the figure 37 and figure 38. The squares designate~~

~~designate the position of original color; the ends of lines~~

~~the results of color the reproduced color. A comparison of~~

~~a*b* color space, reproduction errors, illustrated in 115~~

~~between the primary reference color of average tristimulus~~

~~value of colors of photographic set papers and the primary~~

~~reference color of average tristimulus value of the~~

~~Colorset reveals that the latter primary reference color~~

~~produced greater errors for some of the more saturated~~

~~colors. The errors usually involve an increase in~~

~~saturation. This trend is also reflected in table 9 where~~

~~the average chroma ratio is smaller for the~~

~~primary reference color of the average tristimulus value of~~

~~the colors of photographic set papers. Figures 37, and 38~~

~~indicate that saturated colors from the yellow, and cyan~~

~~hue region will be reproduced with greater error than the~~

~~remaining colors of the set. Consequently, the large value~~

~~of standard deviation can be attributed to between color~~

~~variability of the color error which is caused by some~~

~~difficulty" "inherent of reproducing a particular color.~~

~~This observation agrees with an earlier observation made in~~

~~experiment I .~~

~~To keep the standard deviation limited to random error a~~

~~method for the elimination of between color variability was~~

~~employed. The random variable is the difference between~~

~~color reproduction the paired values of the modulus of the~~

~~two different error for a given color reproduced using~~

~~distribution of the spectral sensitivities. Normal 116~~

1 Ll 11 1 | 1 1 O II 1 I 1 1 11 1 j i i cr in ii 1 | 1 i -i lu cr ii 1 | j i LU II 1 j 1 a LU i z cr ii 1 1 1 C Ll a 1 Z II 1 1 1 3 O c 1 Z II 1 | 1 0. i n 1 1 1 CD Z 1 A II UT 1 CO 1 h- UT | Z O 13 0 II OJ i nj 1 OJ 1 LU 1 '4- . LU U 1 1 1 1 1 UT 1- UT 1 Q 0 \ II o 1 o 1 O 1 Z C i in i ii 1 1 1 U O 1 Ll II 1 1 1 _ 1 v || 1 1 1 O Ll I 1 II 1 1 1 14 h1 CL 1 A II 1 1 1 1- 1- II Oil 1 1 1 i_l 21 cr 1 EOUII 1 1 1 Z LU - CD 1 O \ II OT 1 - 1 . 1 Q Q ( o 1 H - - Ol CM 1 1 I O HH H 1 X o in o Q II H u - v _i II CJ Ll o II Z o lu in u A || 01 *t QJ Q CJ LU LU II CO ^r - O O in z h- Q II . a ^ i- uj a z II T t t a i- JttC

~~_l 1 II in i m o a M | II a > a i u X Ll 1 II . u | 1- LU 1 u~~

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~~z u o ii cr 1 a i a i _l \ h- Ll U 1 1 LU a 1 u a i lu a i LU L CT LU II D O 1 3 O 1 Z O 1 Q U a CT II (E Ll 1~~

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~~r- r i^ r -1 i l | l l l 1 | r I ' ' o -i i i i i i^ i | ii i p i i i i i i r \~~

~~b\ g \ or~~

~~A M \~~

~~0 \ B~~

~~&. i ' i ' ' i i i i i i i i i i i i i i i | i i i i | i i i i | ' ' | I I I m =18 =@ =4 2@ m~~

FIG. 37 for the colors of photographic Color reproduction shifts reproduced with spectral olors were set papers. The c to Umberger's primaries found sensitivities corresponding tristimulus ference color of average for the primary re with dyes of film A colors reproduced of all the value designate lluminant C. [ R, G, B (the Colorset) . I to the primary reference Umberger's primaries corresponding concentrations of film A are the unit color. C, M, and dyes (from table 6).] 118

~~fc> -~~

~~<&_~~

~~ts> + (+i \ l p ^1 / /~~

~~\ / *a \ \ a Z3 / \ If~~

~~' ' ' ' ' r-r ' ' ' r- I i / i a tl i i i p-i T~~

~~o P \~~

~~A A \ \ D M A~~

~~( B~~

~~FIG. 38~~

Color reproduction shifts for the colors of photographic set papers. The colors were reproduced with spectral sensitivities corresponding to Umberger's primaries found for the primary reference color of average tristimulus value of photographic set paper colors. Illuminant C, dyes of film A. [ R, G, B designate Umberger's primaries corresponding to the primary reference color- C, M, and Y are the unit concentrations of film A dyes (from table 6).] 119

~~difference of color reproduction error was assumed for the~~

~~reproduced set of colors. Paired comparison t-tests were~~

~~performed on the color reproduction data to decide which~~

~~set of spectral sensitivities produced the best results.~~

~~The level of significance was assumed to be 0.05. This is~~

~~a one tailed because we test, are interested in specifying~~

~~a particular direction of the possible difference.~~

~~The null hypothesis is that there is no difference in the~~

~~results of color reproduction experiments. In the first~~

~~comparison, the alternative hypothesis is that spectral~~

~~sensitivities corresponding to the average tristimulus~~

~~value of colors of photographic set papers produce smaller~~

~~average color error than spectral sensitivities~~

~~corresponding to the average tristimulus value of the~~

~~Colorset. In the remaining two comparisons, the~~

~~alternative hypothesis is that spectral sensitivities~~

~~corresponding to the average chromaticity of colors of~~

~~photographic set papers produce smaller average color error~~

~~than the remaining two sets of spectral sensitivities.~~

~~The results of the tests are shown in table 10. The null~~

~~hypothesis was accepted in one comparison. No difference~~

~~was found between results of color reproduction obtained~~

~~with spectral sensitivities corresponding to the average 120~~

1 UJ ii 1 X ii 1 1- u 1 i a 1 1 n n ni ITT r- II CO CO h ii o F oo a h- - ii o in HH O 1 Ul n a . H H _| Z> 1 LU ii LU a > \~ LU U O i a n y- a o _l m z a u 1 ii LU X Ll LU z o (J 1 ii X a in 3 X Ll _J Z UT , ( hH J hH ii r- a Q h- O z 1 1- h- u LU Z Ll CD U LU z 1 n Ll lu a X U O Z LU in X n D in x LU LU CJ 1 Q O _ 11 U3 OJ a -a Z X X Z J HH ^ i a ii cn LO f* m u in m O U h- LU X ]r 1- 1 HH X n T ID cn LU h O LU h a a Z 1 Q X n HH I LU a 1- X Ll LU 1- ' *-^ 1- _l 1 z 11 OJ OJ o a ut o CJ Z O Ll CJ l-< _l i x :> n X Y. Z 1 Ll LU 1-1 1- 2> 1 UJ n a u II O o a m hh q. 1 UT Q n *-* ld HH G O O LU Q UT h- 1 n - o X UJ UJ a _i m | r t r t r 1 n >-H i- a U UJ a o i- lu i- a 1 n in o X z a UJ U hh x Z LU 1 n x a X Ll a z> i- lu a 1 UJ li l7j h- a cd (J a c 1 Ll n in LU o h- ll a h m uj 1- a 1 Z n UT Ll Ll O o in HH HH ll 1 1 a LU u j a o o _J LU UT Ll h- H i a a n X O X Z UT n hh 2: LU HH 1- LU 1 LU o n a _i m a ID lu m U LU J O i- in 1 U. a UT n o a hh uj LU hh m in i u. a a ll u u O Ll man Ll Z X O u | HH LU HH n LU J O CD O hh j hh 3 HH 1 Q X n a LU O Ll LU 1 Ci H x a H X i a a II N 01 * in X CJ UT O Q HH i- h- o: c i- h- a 1 LU O II N CO OJ a H UT UT _> CD

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X II CD JJO a lu _j a x a u i- i- a H -H H-l II LU X X Ll O OT Z a a -^. -> II a z ~* ~ Ll t O Z CJ LU Z Ll II LU ^_ X UJ UJ X Q O in II m 1- UT UT 1- m a a i- o a II UT JJU .- o a a UJ X II HH UT Z Z HH CO uj in m LU o co a II T~ Z Z H U3 a z lu z a hh HH H- HH O HH lu _i z II 21 C i- o Z Ll II QOhhE HH x tr a ^7" U Z O II >i in in o o. a x m o II O H H- HH d Q X z > J "?" II u u a a x LU Z h- LIT O UT II z 1- h- U X x a u i- II J Q cd a z Q UT II COLJUU OJ Z n Z h- II H a CD CD CD CO Ll ui M lu X z z II 1 z a x x x LO O UT - HZ O UJ II 1 lu lu a a a z a u *-H UT LU Z CD - m z II 1 z a lu uj uj 1-

~~chromaticity of colors of photographic set papers and the spectral sensitivities corresponding to the primary~~

~~reference color of average tristimulus value of colors of~~

~~photographic set papers. The null hypothesis was rejected~~

~~in the remaining two comparisons. Out of the three sets of~~

~~spectral sensitivities that were tested, sensitivities~~

~~corresponding to the primary reference color of average~~

~~tristimulus value of the Colorset were least effective in~~

~~reducing the color reproduction errors. 122~~

~~4. DISCUSSION~~

~~The results of the primary stability study, conducted in~~

~~this indicate that thesis, the effect of various primary~~

~~reference colors, T(A), on chromaticity coordinates of~~

~~Umberger's primaries is substantial. See figure 8. For a~~

~~s cene containing a variety of colors, the chromaticity~~

~~distributions of Umberger's primaries are centered~~

~~approximately around the primaries of an 18% primary~~

~~reference gray color- Evans[19] and Umberger[l] indicated~~

~~that the average transmission function of a reproduced scene~~

~~containing a variety of colors would integrate out to a~~

~~gray. Therefore, the primary stability study implies that~~

~~the patterns of the red, green, and blue Umberger's~~

~~primaries look approximately like translations of the basic~~

~~arrangement of the original colors to the chromaticities of~~

~~the primaries of the average color of the scene.~~

~~Diagrams obtained in this thesis, representing the~~

~~normalized color-matching functions found for a variety of~~

~~Umberger's primaries indicate that for a wide choice of~~

~~primaries the positive portions of the curves can vary only~~

~~16. On the other very slightly. See figures 14, 15, hand,~~

~~primaries affects the choice of chromaticities of the very~~

~~limits of the negative portions strongly the magnitudes and 123~~

of the color-matching functions. MacAdam[24] has made a similar observation. In addition, this thesis has revealed that Lmberger's primaries corresponding to certain saturated primary reference colors can exclude the illuminant from their gamut. See figure 17. Whenever this happens inverted color-matching functions result. See figure 14. The frequency with which this condition occurs has been linked

~~to the type of colorants used. Further work is needed to~~

~~establish dye characteristics which are responsible for this~~

~~phenomenon .~~

~~In the second part of the thesis a scene, referred to as the~~

~~Colorset, containing 210 colors was reproduced. The~~

~~spectral sensitivities of the color reproduction system~~

computer model corresponded to Umberger's primaries related to five different primary reference colors. The smallest average color reproduction error Delta E=4.15, was obtained with sensitivities corresponding to the primary reference

~~color of average tristimulus value for the Colorset. See table 3. The second smallest average color error was~~

~~obtained with an 18% transmittance gray primary reference~~

~~color. Results of a paired comparison T-test between color~~

~~reproduction errors obtained with the different spectral~~

~~sensitivities show that at significance level of 0.05,~~

~~significantly smaller color reproduction errors are obtained 124~~

with spectral sensitivities corresponding to Umberger's primaries found for the primary reference color of average tristimulus value of the Colorset than with the remaining four spectral sensitivities. See table 4.

~~Had a two tailed T-test been conducted at the same~~

~~significance level of 0.05, no significant difference would~~

~~have been found between results obtained with spectral sensitivities corresponding to Umberger's primaries~~

~~established for average tristimulus value for the Colorset and the 18% transmittance gray primary reference color. For this particular paired comparison the table value of 1.96~~

~~exceeds the result of the T-test of 1.81. See table 4.~~

The outcome of the T-tests can be explained by realizing that the metric chroma of the color of average tristimulus value of the Colorset is 6.7, whereas, the metric chroma of the remaining three primary reference colors is greater than

~~20. See table 1. Because of its relatively small metric~~

~~tristimulus value of the chroma, the color of average~~

~~Colorset represents some hue near gray. Therefore, it~~

~~spectral provides results similar to those obtained with~~

~~sensitivities corresponding to the 18% transmittance gray primary reference color. 125~~

~~results of the color Overall, reproduction study indicate~~

~~that for a class of scenes containing an infinite number of~~

~~colors whose average area transmittance color is~~

~~approximately Umberger's gray primaries corresponding to a~~

~~gray color can be used as a general purpose primary set for~~

~~the optimization of the spectral sensitivities of a~~

~~subtractive color reproduction system in order to reduce the~~

~~amount of color reproduction error. The primary stability~~

~~study, conducted in Part One of this thesis, supports the~~

~~observation that the average color of a scene containing a~~

~~variety of colors, such as the Colorset, is approximately~~

~~gray. Thus Umberger's theory successfully predicts the~~

~~optimum average primaries for a gray integrating scene. The~~

~~results indicate that further optimization of spectral~~

~~sensitivities for a particular scene can also be carried out~~

~~with, for example, the method proposed in this thesis of finding the optimum primary reference color defined as the~~

~~average tristimulus value of a set of colors.~~

In the second color reproduction experiment the reliability of the method of finding the optimum primary reference color, for Umberger's primary calculation, defined as the average tristimulus value of a set of colors was tested. A

~~subset of the Colorset known as the Set Papers was~~

~~reproduced. A paired comparison one tailed T-test was 126~~

~~conducted between color reproduction errors obtained with~~

~~the different spectral sensitivities. At significance level~~

~~of 0.05, significantly smaller color reproduction errors~~

~~were obtained with spectral sensitivities corresponding to~~

~~Umberger's primaries established for average tristimulus~~

~~value for the subset than with spectral sensitivities~~

~~corresponding to Umberger's primaries established for~~

~~average tristimulus value for the Colorset. See table 9~~

~~and 10. The method based on finding average chromaticity of~~

~~the subset was not found to provide significantly better~~

~~results. Hence the color defined as the average tristimulus~~

~~value of a set of colors was most effective in reducing~~

~~color reproduction error for that set.~~

~~In testing Umberger's theory an investigation to optimize~~

~~primaries for a nongray integrating scene was also made.~~

~~Munsell colors from ten different hue regions were selected~~

~~to represent ten nongray integrating scenes. For every color within each hue region a paired comparison T-test was~~

~~conducted between color reproduction errors obtained with spectral sensitivities corresponding to 18% transmittance gray primary reference color and to the primary reference~~

~~color of northern sky. See table 5. Colors from hue regions 5B, 5BG, and 5G were reproduced with significantly smaller color reproduction errors using spectral 127~~

~~sensitivities corresponding to the primary reference color~~

~~of northern sky. In the remaining hue regions spectral~~

~~sensitivities corresponding to 18% transmittance gray~~

~~primary reference color produced significantly smaller color~~

~~reproduction errors than spectral sensitivities~~

~~corresponding to the primary reference color of northern~~

~~sky. Thus the approximate choice of the color of northern~~

~~sky as the primary reference color for the reproduction of~~

~~colors in the blue hue region has provided encouraging~~

~~results. The average color of the scene consisting of, for~~

~~example, the 9 reproduced 5B Munsell colors (2/4, 3/4, 4/4,~~

~~5/4, 6/4, 7/4, 7/8, 8/4, 9/2) does not correspond exactly to~~

~~the color of northern sky. Chromaticity of the color of~~

~~northern sky is: x=.26, y=.27 (Y=46.6), whereas, the~~

~~chromaticity of, for example, the average tristimulus value~~

~~of the scene containing the 5B Munsell colors is: x=.27,~~

~~y=.30 (Y=32.1). A more accurate method of estimating the~~

~~primary reference color of a nongray integrating scene may,~~

~~in the future, be even more successful in decreasing color~~

~~reproduction errors.~~

~~Unlike the color of northern sky, the primary reference~~

~~color of grass green was not successful at optimizing the~~

~~spectral sensitivities of the color reproduction system for~~

~~the reproduction of colors from the green hue region. See 128~~

~~table 3 and figure 34. Out of all the primary reference~~

~~color colors, the of grass green has the largest metric~~

~~chroma, (see table 2) and thus is most likely inappropriate~~

~~for use with Umberger's theory in specifying primaries for~~

~~color reproduction.~~

~~Results of the color reproduction study indicate that~~

~~theoretically correct spectral sensitivities proportional to~~

~~Umberger's primaries introduce residual average color~~

~~reproduction errors. For example, the errors amount to~~

~~Delta E = 4.67 for the 18 % transmittance gray primary~~

~~reference color. See table 3 for values of the remaining~~

~~errors. On the other hand, an additive process which~~

~~satisfies completely the sensitivity requirements for a~~

~~given set of primaries would reproduce perfectly all colors~~

~~having chromaticities within the color gamut of the~~

~~primaries. Consequently, additional errors result due to~~

~~the failure to simulate the phenomena of additive mixtures by use of subtractive mixtures. The character of such~~

~~errors is analyzed in following paragraphs.~~

~~Results presented in this thesis show that including~~

~~negative parts of spectral sensitivities causes an increase~~

~~in metric chroma and a general decrease in reproduction~~

~~lightness of the reproduced color. See figures 26, and 27 129~~

~~respectively; also see table 3. An increase in metric~~

~~chroma is contrary to practical color reproduction which is~~

~~usually incapable of negative responses and therefore~~

~~produces a decrease in saturation from the original colors.~~

~~This decrease in reproduction lightness and increase in~~

~~metric chroma is the source of the residual average color~~

~~reproduction error. The metric chroma increase divides the~~

~~a* b* plane into 3 regions of color reproduction shift. For~~

~~example, see figure 25. The hue shifts tend to go in the~~

~~direction of the Yellow, Magenta, and Cyan hue of the dyes~~

~~of the film.~~

~~The metric chroma increase occur for saturated colors from~~

~~spectral regions complementary to the spectrum of each of~~

~~the three Umberger's primaries. For example, yellow colors~~

~~which lie between the green and red Umberger's primaries are~~

~~primary. A saturated color complementary to Umberger's blue~~

~~which is complementary to a particular primary, by~~

~~primary. To definition, contains the least amount of this~~

~~changes in dye reproduce complementary colors large~~

~~suppress the particular concentration are necessary to~~

~~gradient is greatest when primary. Thus the concentration~~

~~to Umberger's primaries. reproducing colors complementary~~

~~precludes the possibility of However, primary instability~~

~~large changes in dye finding primaries representative of 130~~

concentrations. Umberger's theory identifies primaries only for very small concentration changes around some given three starting concentrations. Consequently, large color reproduction errors result, in the form of metric chroma increases, because Umberger's primaries are not well optimized for reproduction of highly saturated complementary colors requiring large concentration changes.

~~The cause of the large increase in metric chroma is~~

illustrated when concentration values required to metamerically match a complementary color are compared with concentration values computed by the color reproduction system computer model, see table 7. Generally, the computer

~~model predicts higher than required concentration values.~~

~~The largest discrepancy in computed concentration value~~

~~corresponds to the dye which is present in largest amount in~~

~~a metameric match of a saturated color complementary to a~~

~~given Umberger's primary. For example, the concentrations~~

~~metameric match of a of cyan, magenta, and yellow dyes of a~~

~~and .69 certain purple color are .84, 1.53, respectively;~~

~~values of the respective whereas, the computed concentration~~

~~greater the and .76. the dyes are .94, 2.0, Summarizing,~~

~~Umberger's mismatch between two particular primaries,~~

~~unstable reproduction primary and a corresponding primary~~

~~concentrations necessary to controlled by metameric dye 131~~

~~reproduce the original color, the higher the discrepancy between the desired and obtained dye concentrations.~~

~~The discrepancy in computed dye concentration can be traced~~

~~also to the spectral sensitivities of the color reproduction~~

~~system. The choice of chromaticities of reproduction~~

~~primaries affects very strongly the magnitudes and limits of~~

~~negative portions of the spectral sensitivities [ 24 ] . See~~

~~figures 14, 15, and 16. The spectral regions of colors~~

~~in complementary to the primaries, for which the discrepancy~~

~~computed dye concentration is the greatest, correlate with~~

~~the negative portions of spectral sensitivities. In~~

~~spectral consequence, most accurate optimization of~~

~~carried out sensitivities can be obtained when it is for~~

~~with the test colors which are in greatest disharmony~~

~~i.e. dark negative parts of spectral sensitivities;~~

~~regions to saturated colors from within hue complementary~~

~~implies that since Umberger's primaries. This, in turn,~~

~~primaries has most effect in proper choice of Umberger's~~

~~reproduction error of some of the most reducing the color~~

~~colors in the reproduced scene saturated colors, different~~

~~in the optimization of the may require unequal weighting~~

~~the general method of finding primary reference color using~~

~~see value. Results of the T-test, the average tristimulus~~

~~colors from within a limited table 5, demonstrate that for 132~~

~~hue region the negative parts of spectral sensitivities can~~

~~be optimized to reduce color reproduction error. In the~~

~~case of a gray integrating scene where a variety of colors~~

~~are present the color reproduction errors for the same hue~~

~~region are greater because the optimum set of spectral~~

~~sensitivities is obtained as a result of a compromise.~~

~~Summarizing, this study shows that not all spectral~~

~~sensitivities serve a particular subtractive color~~

~~reproduction system equally well. When presuming~~

~~color-matching functions for sensitivity distributions,~~

~~accurate primary identification can reduce the color~~

~~reproduction error. This study shows that the primaries~~

~~that enable to reduce the color reproduction error the most~~

~~are closely related to the average color of the reproduced~~

~~scene. The results obtained in this thesis suggest that~~

~~Umberger's theory provides an accurate basis for selecting~~

~~the desirable set of color-matching functions for~~

~~sensitivity distributions for a particular subtractive color reproduction process once the average color of the~~

reproduced scene is estimated. The success of Umberger's theory in reducing discrepancies in colorimetric color reproduction can be attributed to the fact that Umberger's primaries are directly related to the average color of light controlled by the actual dyes in the film. 133

~~5. CONCLUDING REMARKS~~

~~In this thesis, a method, proposed by Umberger, for the~~

~~identification of additive stimuli representative of the~~

~~color of light controlled by each real dye in the film has been examined. Stability of Umberger's primaries has been~~

~~studied. A theoretical color reproduction study was~~

~~conducted to test Umberger's theory.~~

~~Much more work is required to completely characterize a~~

~~subtractive color reproduction system, however, at present~~

~~state of this work a number of conclusions may be drawn.~~

~~Conclusions for the primary stability study~~

~~1. The pattern of primary distribution is a translation of~~

~~the original colors on a chromaticity diagram.~~

~~2. For a scene containing a variety of colors Umberger's~~

~~primaries are centered approximately around the~~

~~primaries of gray colors.~~

~~3. The positive portions of spectral sensitivities for a~~

~~wide variety of primary reference colors are very~~

~~factor. The choice similar. They differ by a scaling 134~~

~~of the primary reference color affects strongly the~~

~~magnitudes and limits of the negative portions of the~~

~~spectral sensitivities.~~

~~4. Inverted color-matching functions result when the~~

~~illuminant lies outside the gamut of Umberger's~~

~~primaries .~~

~~Conclusions for color reproduction study~~

~~least 1. Average tristimulus value of a set of colors gives~~

~~- suggests that average color error for the set this~~

~~specific colors there is an opportunity to optimize for~~

~~- color ID photos.~~

~~sensitivities 2. Including negative parts of spectral~~

~~reproduced metric chroma of the result in an increase in~~

~~color .~~

~~the go in the direction of The hue shifts tend to~~

~~dyes of the film, and cyan hue of the yellow, magenta,~~

~~shifts color reproduction Thus it appears that the~~

~~3 regions of color divide the a* b* plane into~~

~~reproduction shift. 135~~

~~4. Each of the three color reproduction shifts in the~~

~~direction of one of the hue of the dyes of the film is~~

~~caused primarily by the obtainment of higher than~~

~~metamerically required concentration value of one of the~~

~~corresponding dyes.~~

~~5. The dye concentration errors resulting in the color~~

~~reproduction shifts are greatest for saturated colors~~

~~from each of the three spectral regions complementary to~~

~~the spectrum of each of the three Umberger's reproduction~~

~~primaries. Thus, for such a color, the color~~

~~reproduction shifts can be attributed to a discrepancy~~

~~between one of the reproduction primaries and a~~

~~corresponding unstable primary controlled by metameric~~

~~dye concentration required to reproduce the original~~

~~color. The greatest discrepancy between the reproduction~~

~~and the unstable primaries corresponds to the pair of~~

~~primaries from the spectral region complementary to the~~

~~original color.~~

~~the largest color 6. The spectrum of the colors for which~~

~~correlates with the negative reproduction errors result~~

~~sensitivities corresponding to portions of spectral~~

~~Umberger's reproduction primaries. 136~~

~~7. Optimization of ape^LXdj.spectral i?pnsiHvi + i sensitivities, corresponding to~~

~~some primary reference to color, the reproduction of~~

~~specific colors found in a scene involves the proper~~

~~choice of the negative portions of spectral~~

~~sensitivities .~~

~~8. Dmax substitution for negative R, G, B responses of the~~

~~image sensors additionally enhances the metric chroma of~~

~~the reproduction. [see Appendix 5]~~

~~9. All positive sensitivities of the image sensors produce a~~

~~general desaturation of the reproduced colors.~~

~~Conclusions 8 and 9 pertain to appendix 5 and appendix 6.~~

~~Future studies~~

~~There are a number of possibilities for further work on~~

~~topics studied in this thesis. A hypothetical subtractive~~

~~color reproduction process based on Umberger's theory can be~~

~~used to evaluate the optimum combination of the three dyes by tone reproduction theory. In developing color photographic theory the interimage effects should be~~

~~investigated. To facilitate such analysis, the subtractive 137~~

~~color reproduction model could be modified to represent a~~

controlled-dye multiply process where the amount of each of the dyes created in the film is functionally related to all three of the exposures. The theoretical model could be made even more representative of a commercial color photographic process if the relationship between the equivalent neutral densities and the exposure densities was nonlinear. The influence of this nonlinear relationship on color reproduction could then be studied.

~~Further work is also needed to identify the limitations of~~

Umberger's theory. As was demonstrated for the primary reference color of grass green color, primary reference colors with large metric chroma may not be appropriate for the application of Umberger's theory.

~~Finally, an experimental test of the application of the~~

~~movement of the chromaticities of Umberger's primaries to~~

~~of the neutral formed the study the spectral selectivity by~~

~~Umberger's could dyes in the film may be worthwhile. theory~~

~~required in help reduce the amount of empiricism adjusting~~

~~at various color balance of the neutral scale density~~

~~of Umberger's levels. The merits of the application theory~~

~~neutral with regard to changes to study the stability of the~~

~~explored. of illuminant could also be 138~~

~~6. REFERENCES~~

~~1. J.Q. Umberger, Color Reproduction Theory for Subtractive Films. Phot. Sci. . Eng , 7:34(1963).~~

~~2. B.K.P. Horn, Exact Reproduction of Colored Images. Comput. Graphics Image Process., 26:136(1984).~~

~~3. D.B. Judd and G. Wyszecki, "Color in Business Science and 3rd. ed . Industry", , John Wiley and Sons, New York, 1975, p. 234.~~

~~4. A.C. Hardy and F.L. Wurzburg Jr., The Theory of Three-Color reproduction. J. Opt. Soc . Amer., 27:228( 1937) .~~

~~5. R.G.W. Hunt, "Objectives in Color Reproduction," Inter-Society Color Council Proceedings, January-February, 1971, p. 13.~~

~~6. R.W.G. Hunt, "The Reproduction of Color", 3rd. ed., Fountain Press, England, 1975, p. 10.~~

~~7. T.H. James ed., "The Theory of the Photographic Process", 4th ed., Macmillan, New York, 1977, p. 565.~~

~~8. T.J. Woodlief Jr. ed., SPSE Handbook of Photographic~~

~~Science and Engineering , John Wiley and Sons, New York, 1973, p. 297.~~

~~9. D. MacAdam, Subtractive Color Mixture and Color Reproduction, J. Opt. Soc. Amer., 28:466(1938).~~

~~10. A.C. Hardy and F.L. Wurzburg Jr., The Theory of Three-Color reproduction, J. Opt. Soc. Amer.,~~

~~27:228( 1937) .~~

~~11. Ibid, p. 239.~~

~~12. T.J. Woodlief Jr. ed., p. 435.~~

~~13. P- Moon, Reflectance Factors of Some Materials Used in School Rooms, J. Opt. Soc. Amer-, 32: 243 (1942).~~

~~14. P. Moon, Colors of Ceramic Tiles, J. Opt. Soc. Amer-, 31:482 (1941).~~

~~15. P. Moon, Colors of Furniture, J. Opt. Soc. Amer., 32:293 (1942). 139~~

~~16. E. J. Breneman, A Color Chart for Use in Evltinff Quality of Color Phnf Reproduction, <^j 7nr*' 1: 74-78(1957). '~~

~~17. C.S. McCamy, H. Marcus, J.G. Davidson, A Color-Rendition J. Appl. Chart, Phot. Eng.,' 2:95(1976) .~~

~~18. of Courtesy Hemmendinger Laboratories .~~

~~19. Ralph M. Evans, "Accuracy in Color and Television," Photography Color Inter-Society Color Council Proceedings, January-February, 1971, p. 42.~~

~~20. Ralph M. Evans, U.S. Pat. 2,571,697, Oct. 16, 1951.~~

~~21. D. B. Judd and G. Wyszecki, p. 108.~~

~~22. Irvin Miller, John E. Freund, "Probability and Statistics for Engineers", 2nd ed., Prentice-Hall, Inc., New Jersey, 1977, p. 220.~~

~~23. A.D. Rickmers, H.N. Todd, "Statistics: An Introduction", McGraw Hill, New York, 1967, p. 70.~~

~~24. D.L MacAdam, "Colour Science and Colour Photography", The J. Phot. Sci., 14:246(1966).~~

~~25. C.J. Bartleson and F. Grum ed., p. 129.~~

~~26. N. Ohta, Fast Computing of Color Matching by Means of Matrix Representation. Parti: Transmission-Type~~

~~Colorant, Applied Optics, 10. , 9: 2183(1971).~~

~~27. N. Ohta, Metameric Color Matching in Subtractive Color Photography, Phot. Sci. Eng., 16:136-143(1972).~~

~~28. Annual Book of ASTM Standards, E 308-85, April 1985.~~

~~29. Irvin Miller, John E. Freund, p. 169.~~

~~30. D. MacAdam, Photographic Aspects of the Theory of Three-Color reproduction, J. Opt. Soc. Amer.,~~

~~28:412(1938) . 140~~

~~7. APPENDICES~~

~~APPENDIX 1.~~

~~FORMULAS FOR THE L*a*b* COLOR SPACE~~

~~1. CIE L*a*b* [25]~~

~~L* = 116 ! /a _ (Y/Yo) 16 , (l.D~~

~~a* r. 50 [(X/Xo)1'3 - (Y/Yu)i/3] , (1.2)~~

~~b* = 200 [(Y/Yo)1'3 - (Z/Zo)1 3] , (1.3)~~

~~where :~~

~~X, Y, Z - Tristimulus values of the samples,~~

~~Xu, Y0, Z0 - Tristimulus values of the reference white~~

~~( light source ) .~~

~~2. CIE L*a*b* color difference:~~

~~- a*2)2 - 2 - L*2)2 + b* A Ea*b* = [(L*i + (a*i (b*i 2 ) ] ,~~

~~(1.4)~~

~~where :~~

~~a* b* - values the L* i , i , i for original,~~

~~- the reproduction. L*2, a* 2, b* 2 values for~~

~~3. Metric Chroma:~~

~~C*ab = [(a*i) 2 + (b*i) 21 1/2, d-5)~~

~~AC*ab=Ciab-C*2ab, (1-6) 141~~

~~where :~~

~~C*iab - chroma value of the original,~~

~~C*2ab - chroma value of the reproduction,~~

~~4 . Chroma ratio :~~

~~Sratio - C*2ab / C'lab (1.7)~~

~~5. Metric Hue difference:~~

~~(AC*ab)2l1/2 ~ [(AE*ab)2 " (AL*)2 (1.8 AH*ab = 142~~

~~APPENDIX 2.~~

~~THE NEWTON-RAPHSON METHOD~~

~~Metameric color matching can be reduced to solving for concentrations the following simultaneous integral equations for T(X) [26,27]; given the tristimulus values~~

~~and the illuminant:~~

~~X = kktI* / E(A) * T(>J * x(X) * d\ (2.1a) X~~

* Y = k * /e(>) * T(X) * y(>) dX (2.1b) X

* * (2.1c) Z = k * / E(X) * T(X) z(X) dX

where: *

~~(2. id) k= l/( f Mh) * T(A) * y(A) * dX X~~

~~" the color-matching functions, x(X), y(X) z(X) are~~

~~distribution of the E(X) - is the spectral power~~

~~illuminant ,~~

~~transmittance of the dyes. T(X) - is the spectral~~

~~of the written as functions The tristimulus values can be~~

~~magenta, cyan): amounts of the three dyes (yellow,~~

~~Z(ci, C c3). X(ci, c2, c3), Y(Cl, ca, c3), 143~~

~~If those equations are approximated by the Taylor~~

~~expansions for functions of three variables, in which the~~

~~terms higher than second order are neglected, an improved~~

~~approximation to the true solution for dye concentration~~

~~can be obtained. Thus in matrix form it can be written:~~

~~dX dX dX~~

~~etc l dC2 dc 3 AX Ai dY Ay av AY AC 2 (2.2a) dc i dc 2 dc 3 AZ AC 3 dZ dZ dZ~~

~~dc l etc 2 etc 3 or~~

~~Ax Aci~~

~~AY j * AC 2 (2.2b)~~

~~AZ AC 3~~

~~The values of the dye concentrations can be computed to~~

~~obtain any desired degree of accuracy of the color match by~~

~~iterations of the following approximate formula:~~

~~Aci Ax~~

~~A2 J- 1 * AY (2.3)~~

~~AC 3 AZ~~

~~Theoretically, the value of the first Jacobian, J, can be~~

~~concentration obtained by using any three randomly picked~~

~~values . 144~~

~~Steps involved in computation of dye concentrations with the Newton-Raphson Method:~~

~~1. Compute the X, Y, Z tristimulus values of the original~~

~~color ,~~

~~2. Assume some value for the initial concentrations. The~~

~~choice of this constant should assure quick convergence~~

~~of the iterations. For example, the starting~~

~~concentrations can be made equal to minus logarithm to~~

~~the base ten of Y tristimulus value of the original~~

~~color .~~

~~3. Compute film transmittance for these concentrations~~

~~according to Beer's law formula.~~

~~4. Compute the X2, Y2, Z2 tristimulus values of film~~

~~transmittance for the initial set of concentrations.~~

~~5. Find differences of delta X, Y, Z tristimulus values~~

~~and color error delta E,~~

~~the jacobian 6. Calculate the partial differentials for J,~~

~~error is smaller than 7. Check if the CIELAB delta E color~~

~~this is fulfilled the tolerance of the color match, if~~

~~stop the calculations, otherwise,~~

~~8. find the inverse of the Jackobian,~~

~~i=l,2,3 concentration increments, Ac i 9. calculate the~~

~~using equation (2.3),~~

~~ci= ci-i + Ci> 10. find new dye concentration A~~

~~11. return to step 3. 145~~

~~APPENDIX 3.~~

~~COMPUTER PROGRAMMING FOR PRIMARY STABILITY STUDY~~

~~Introduction~~

~~The program MAIN. FOR was written to find Umberger's~~

~~primaries and their corresponding spectral sensitivities~~

~~for a set of input colors and two dye sets, A and B. This~~

~~section describes the program; the inputs, how it functions~~

~~and its outputs. Figure 3.1 is a block diagram of this~~

~~program.~~

~~Program inputs~~

~~This description refers to the blocks of program denoted 1, and 2 on the flow chart diagram, of figure 3.1. These are~~

~~inputs to the program.~~

~~1. Spectral densities, i(X) (i= ! 2 3) of cyan,~~

~~magenta, and yellow dyes defined as equivalent neutral~~

~~densities (E.N.D.'s).~~

~~the light source. 2. Spectral energy distribution of 146~~

~~MAIN. FOR~~

~~INPUT : AE_ x(X), y(X), z(X); xw(X), yw(X), zw(X); epX)~~

~~SPECIFY PRIMARY REFERENCE COLOR IN TERMS OF:~~

~~Ci concentrations T(\) spectral Y, x, y Luminance of dye in film curve and chromaticity~~

~~FIND: X, Y, Z and x, y, z coordinates of color~~

~~FIND: matching concentrations using NEWTON-RAPHSON METHOD~~

~~FIND: Tristimulus J(XiYiZi) and Chromaticity A(xiyiZi) Matrix for Primaries Pi~~

~~primaries FIND: L* a*, b* coordinates of Pi~~

~~A'_for COMPUTE: the Transformation_Matrix and the calculation of r(X), g(X), b(X)~~

~~color-matching functions~~

~~8 COMPUTE: the r(\), g(X), bj X ) and~~

~~r(\) , gw(X) , b(X)~~

~~color-matching functions~~

~~xi, yp OUTPUT: the calculated values of_Pi{Yi( into files ,Iw(X ,bw ( \ ) r(X),g(X),b(X), and rw (X ) )~~

~~END (i= 1, 2, 3)~~

~~for the 'program MAIN. FOR Flow chart diagram of primaries. finding Umberger's 147~~

~~Actually, weighting functions, x"w(X), Yw(X),~~

~~were used z"(X), calculated from CIE 1931 standard~~

~~values of the color matching functions x(X), y(X), z(X)~~

~~for CIE 1931 standard observer and the spectral power~~

~~distribution for the illuminant C [28].~~

~~3. CIE standard values of the color matching functions~~

~~x(X), y(A), z(X).~~

~~4. Color difference, AE , tolerance (specified in CIE~~

~~L*a*b* color space) used in the Newton-Raphson method~~

~~to compute numerically the concentrations of the dyes~~

~~in the film to match the chromaticity of a specified~~

~~real surface color-~~

~~5. The primary reference color, or the color whose~~

~~primaries are to be calculated, can be given in three~~

~~different ways:~~

~~three dyes a) as relative amounts of a set of~~

~~(concentrations of cyan, magenta, and yellow),~~

~~of a particular color, b) as spectral reflectance, T(X),~~

~~and Y tristimulus value. c) as chromaticity (x, y) 148~~

~~Computation of Umberger's primaries~~

~~This description refers to program blocks 3 , 4 , and 5 on the flow chart diagram, see figure 3.1.~~

The MAIN. FOR program calculates chromaticity coordinates and spectral sensitivities of Umberger's primaries [1] from the transmittance function T(X) of a dye image. The cyan, magenta, and yellow dye concentrations define the transmittance function T(X). Unless the input color (the primary reference color) for which Umberger's primaries are to be determined is specified in terms of concentrations the program must initially determine the three matching dye concentrations required to reproduce this color. The

~~problem is equivalent to metameric color matching. Color matching, in this case is the determination of the concentrations of the cyan, magenta, and yellow dyes that~~

~~values as the input yield the same X, Y, and Z tristimulus~~

~~and Z color- Therefore, it is necessary to find the X, Y,~~

~~color tristimulus values of the original color. When the~~

~~transmission is specified in terms of a reflection or~~

~~used to find the function, T(X), the following formulas are tristimulus values: 149~~

~~X = k* 2 T(X)*xw(X) * AX, (3.la)~~

~~Y = k* 2 T(X)*y(/) * A X, (3>lb)~~

~~Z z k* 2 * T(X)*z(X) AX, (3.1C)~~

~~where :~~

~~k= * l/[ 2 . yw(X) AX] (3. Id)~~

~~Xw(X), y(X), zw(X) - are weighting functions,~~

~~calculated from CIE 1931 standard values of the color~~

~~matching functions x(X), y(A), z(X) for CIE 1931 standard~~

~~observer and the spectral power distribution for the~~

~~illuminant C. Therefore:~~

~~x(X) = x(X)*E(X),~~

~~yw(X) = y(A)*E(/),~~

~~z(X) = z(X)*E(X).~~

~~Weighting functions were substituted for the product of~~

~~spectral power distribution of the illuminant and spectral~~

~~sensitivity to ensure better accuracy of all computations~~

~~involving tristimulus values.~~

~~When the input color is specified in terms of luminance and chromaticity, Y, x, y, the X, Y, and Z tristimulus values are calculated as follows: 150~~

~~Y/y=X+Y+Z, (3i2b)~~

~~X = x*Y/y (3.2a)~~

~~Z = z*Y/y> (3.2c) where :~~

~~z=l-x-y. (3. 2d)~~

~~The necessary dye concentrations of cyan, magenta, and~~

~~yellow to produce a certain color, assuming Beer's law, can~~

~~be easily calculated to any desired accuracy by means of~~

~~the iterative Newton-Raphson Technique, [26,27]~~

~~(see Appendix 2).~~

~~To obtain quicker convergence the iterations were usually~~

~~started with the concentrations being made all equal to~~

~~logarithm to the base ten of Y tristimulus value of the~~

~~original color.~~

~~The colorimetric matches of some colors required negative~~

~~amounts of dye, which is impossible to achieve. Therefore,~~

~~unmatchable within the all such colors were declared as~~

~~dropped from further gamut of a particular film and were~~

~~analysis .~~

~~determined the transmittance Once the concentrations were~~

~~to the match, was synthesized curve, T(X), corresponding 151~~

~~according to Beer's law formula. See equation (9). Fo r a~~

~~color, C, reproduced the by film, the tristimulus values~~

~~of the R, G, and B Umberger's primaries or Pi (i=l,2,3), as expressed in the individually X, Y, Z primary coordinate~~

~~system, are obtained from the following set of equations:~~

~~= Pi(Xi,Yi,Zi) dC/dci , 1=1,2,3 (3.3) where :~~

~~= cIC/dci -2.3 J T(X) i(A) dC ; (3.4) X~~

~~Xi = k*(-2.3) 2 T(X)*ePX)*xw(A) *AX, (3.5a) A~~

~~Yi = k*(-2.3) 2 T(X)*ei(X)*yw(/) * X, (3.5b) A~~

~~Zi = k*(-2.3) 2 T(X)*ei(A)*Zw(A) * A- (3.5c) A and k= l/[ 2 E(X)*y(A) * AA], (3.5d) ePA) - extinction coefficient.~~

~~As in the previous computation of tristimulus values, equations (3.1), weighting functions were substituted for the product of spectral power distribution of the~~

~~illuminant and spectral sensitivity.~~

~~primaries were determined Chromaticity coordinates of the from the following equations: 152~~

~~x=X/(X+Y+Z), = y Y/(X+Y+Z), Z=Z/(X+Y+Z) (3.6)~~

~~Also, to allow presentation of the results in a more~~

~~uniform color space the tristimulus values of a given~~

~~primary reference color and of its primaries were~~

~~transformed to the CIE L*a*b* color space according to the~~

~~formulas in Appendix 1 .~~

~~Computation of the color-matching functions~~

~~This section describes computations performed by program~~

~~blocks denoted by numbers 7, and 8 in the flow chart~~

~~diagram, see figure 3.1.~~

~~The tristimulus values of the r"(X), 1f(A)> anl b(A)~~

~~color-matching functions can be calculated by substituting~~

~~for x, y, and z the tristimulus values of the x(A), y(A), and z(X) color-matching functions in the following~~

~~relationship:~~

~~R x A' G = -i * y (3.7) B z~~

~~The transformation matrix, A', is based on the xi, yi,~~

~~i= and Zi chromaticities of the R, G, B primaries for 1,~~

~~2, 3 respectively. 153~~

~~xl x2 x3 cr 0 0 yi y2 y3 0 eg 0 (3.8) zl z2 z3 0 0 cb~~

~~The three proportionality coefficients cr, eg, and cb~~

~~serve to normalize the matrix so that tristimulus values of~~

~~CIE illuminant C (Xc=98.074, Yc=100, Zc=118.23) are~~

~~obtained for unit amounts of R, G, and B primaries~~

~~(R=G=B=1). Therefore, the three proportionality~~

~~coefficients are calculated as follows:~~

~~cr Xc eg A-i * Yc (3.9) Cb Zc~~

~~where A denotes the chromaticity matrix:~~

~~x i xa X3 yi ya ys (3.10) z i z a z 3~~

~~The transformation matrix is obtained by rescaling the~~

~~chromaticity matrix:~~

~~cr 0 0 A' = A * 0 c< 0 (3.11) 0 0 cb~~

~~The transformation matrix was used for the following~~

~~purposes~~

~~functions 1. To find the 7(A), g(A) bO> color-matching~~

~~of Umberger's primaries. 154~~

~~2. Additionally, the values of the ~(X), gw(X), and~~

~~b(A) weighting functions were calculated by~~

~~substituting in equation (3.7) for x, y, and z the~~

~~values of the x(A), 7w(A), and z(X) weighting~~

~~functions calculated from CIE 1931 standard values of~~

~~the color matching functions x(X), y(A) "z(A) fr CiE~~

~~1931 standard observer and the spectral power~~

~~distribution for the illuminant C. These weights were~~

~~used in the second part of the thesis in the color~~

~~reproduction computer model as the actual spectral~~

~~responses of the color reproduction system.~~

~~Program outputs~~

~~program block denoted This description refers to the by~~

~~see figure 3.1. These number 9 in the flow chart diagram,~~

~~are outputs of the program.~~

~~coordinates x and y of 1. Luminance Y and chromaticity~~

~~CIE 1976 a*, and b* Umberger's primaries. Also, L*,~~

~~were supplied. coordinates of primaries~~

~~functions of 2. The 7(A), KA), b(A) color-matching~~

~~Umberger's primaries.~~

~~functions. weighting 3. The rw(A), Iw(A), and b(A) 155~~

~~APPENDIX 4.~~

~~THE COLOR REPRODUCTION PROGRAM~~

~~Introduction~~

~~This section describes the color reproduction program~~

~~REP. the how FOR; inputs, it functions, and its outputs.~~

~~Figure 4.1 is a block diagram of this program.~~

~~The program can theoretically reproduce a number of colors~~

~~represented by their spectral reflectances and the resultant color differences from the original color can be examined in~~

~~CIE L*a*b* color space.~~

~~inputs to the color reproduction program~~

~~This section refers to program blocks 1, and 2 in figure 4.1.~~

~~- functions 1. Xw(A), 7w(A), Zw(X) weighting~~

~~calculated from CIE 1931 standard values of the color~~

~~for CIE 1931 standard matching functions x(A), ?(A), z(A)~~

~~for observer and the spectral power distribution the~~

~~illuminant C [28] . REP. FOR~~

~~INPUT_: l(X), 62(X), 3(X) ; xw(XP yw(X^ zw(X2 ; So ; rw(X), gw(A), bw(X)~~

~~INPUT: T0(X) of original coloj~~

~~COMPUTE :~~

~~R, G, B Spectral Responses of the Film~~

~~COMPUTE: concentrations ci, c2, cj of dyes in the film~~

~~COMPUTE: Tr(X) of the Film according to Beer's law~~

~~COMPUTE: Xi, Yi, Zi and Li*, ai*, bi* of the original color and X2, Y2, Z2 and La*, aj*, b2* of the color reproduced by the film~~

~~COMPUTE: DEL. E color error, metric chroma, hue angle etc,~~

~~OUTPUT RESULTS as files for plotting, documentation etc,~~

~~END~~

~~FIG. 4.1~~

~~Flow chart diagram of the FOR, color reproduction program REP. 157~~

~~2. - rw(X), gw(A), and bw(A) three red, green, and~~

~~blue weighting functions corresponding to Umberger's~~

~~primaries for a chosen primary reference color calculated~~

~~from CIE 1931 standard values of the color matching~~

~~functions x(A), y(A), z"(A ) for CIE 1931 standard observer~~

~~and the spectral power distribution for the illuminant~~

~~C. For a description of this calculation refer to~~

~~Appendix 3. These weights were used in the color~~

~~reproduction computer model as the actual spectral~~

~~responses of the color reproduction system under~~

~~illuminant C.~~

~~yellow 3. Spectral densities, i (A ) , of cyan, magenta, and~~

~~dyes scaled in terms of equivalent neutral~~

~~densities (E.N.D. 's) .~~

~~4. The spectral reflectance, T0(A), f the original color-~~

~~Steps involved in color reproduction~~

~~This section describes program blocks 3, 4, and 5 in~~

~~figure 4.1. 158~~

~~The R, G, B responses of the image sensors to a given~~

~~object-color stimulus are described by the formulas:~~

~~R = k 2 T0(X) * ?w(X) *AX, (4.1a) A~~

~~G = k 2 T0(X) * gw(X) */\X, (4.1b) A~~

~~B = k 2 T0(X) * bw(A) *A\, (4.1c)~~

~~where :~~

~~T0(X) - the spectral reflectance factor of the object-color~~

~~stimulus ,~~

~~k is chosen such that R=G=B for S0 = 1,~~

~~k= * l/[ 2 yw(X) A \] , A~~

~~- rw(A) i yw(X), z"w(X) are weighting functions.~~

~~Weighting functions were substituted for the product of~~

~~spectral power distribution of the illuminant and spectral sensitivity to ensure better accuracy of all computations~~

~~involving tristimulus values.~~

The R, G, B spectral responses are used to determine the dye concentrations ci, ca, ca of the reproduced color in the transparency. The amount of dye in each of the three dye layers of the film required for the reproduction of some

~~given color was determined using the following relationships: 159~~

~~1. If B > 1.0 then c = = R, G, i 0 , i 1,2,3, (4.2)~~

~~2. If 10->"ax < R, G, B <_ 1.0 then~~

~~d = -log R,~~

~~c2 = -log G, (4.3)~~

~~c3 = -log B,~~

~~10-Dma* 3. If R, G, B <_ then the color is declared as unreproducible and it is rejected from further computations.~~

~~This is equivalent to a color photographic process with the~~

sensitometric characteristics shown in figure 18 in part two of the thesis. Note that Ci can not be computed using the logarithm function for negative exposures. A method for resolving this problem is explained in Appendix 5.

~~The last relation not only checks for negative exposures but it also prevents the density from becoming infinite for positive exposure values approaching zero. Maximum density~~

~~was assumed to be equal to 3.5. of the dye, Dmax ,~~

~~The spectral transmittance, Tr(A), of the three~~

~~superimposed dye layers of the reproduced color was~~

~~synthesized according to the formula for Beer's law.~~

~~+ Tr(A) = exp{-2.3[ci*i(A) + c2*e2(A) c3*e3(A)]} (4.4)~~

~~are the same as The extinction coefficients, epA), the~~

~~section spectral densities for a particular film. See 2.1.5. 160~~

~~color error analysis~~

~~This section refers to program blocks 6, 7, and 8 in figure 4.1.~~

~~To gain insight into the possible patterns and extent of~~

~~color discrepancies between the desired colors and their reproduction, two sets of tristimulus values were found:~~

~~a) for the original color-stimulus:~~

~~Xi : k2 T0(A) * x(A) * A X, (4.5a)~~

~~Y: = k 2 To(X) * yw(A) * AA, (4.5b) A~~

~~Zi = k 2 T0(X) * z(X) * AX, (4.5c) X~~

~~b) for the reproduced color-stimulus~~

~~X2 = k 2 Tr(X) * x(X) * AX (4.6a) X~~

* Y2 = k 2 Tr(X) * Yw(X) AA, (4.6b) A

~~Za = k 2 Tr(X) * zw(X) * A X, (4.6c; A~~

~~S0=Tr=l k = constant such that R=G=B=1 for 161~~

In order to determine color variability of the reproduction process a numerical value for the amount of color difference, delta Ea*b, between the desired color and its reproduction was calculated. The delta Ea*b* values were also broken down into their components of metric hue, lightness, and metric chroma to determine which attribute had the greatest

~~contribution to the color difference.~~

~~The various comparisons between the original and the~~

~~reproduced color were carried out in L*a*b* color space[25] and required finding the following:~~

~~1. L*a*b* coordinates of the original and reproduced color,~~

*'3 - L* = 116 (Y/Yo) 16 , (4.7)

~~[(X/Xo)1'3 - a* = 50 (Y/Y0)1/3] , (4.8)~~

~~[(Y/Yo)1^3 - b* = 200 (Z/Zo)1'3] , (4.9)~~

~~where :~~

~~- the X, Y, Z Tristimulus values of samples,~~

~~source. - the light X0, Y0, Z0 Tristimulus values of~~

~~AEa*b* = 2. AEa*b* color error,~~

~~2 - 2 - a* + b* a , - L*a)2 a (b*i ) ] (4.10) =[(L*i + (a*i )~~

~~where :~~

~~- values for the original, L*i, a*i, b*i~~

~~reproduction. - values for the L*2, a* 2, b*2 162~~

~~3. metric chroma,~~

~~C*ab = a*i)2 + (b*i)2]W2 [( . (4.11)~~

~~4. chroma ratio,~~

~~: Sratio C*2ab / C*iab . (4.12)~~

~~5. metric hue error,~~

~~2 - AH*ab = [( AE*ab) ( AL*) 2 - ( &C*ab) 2] 1/2. (4.13)~~

~~For a set given of stimuli, the following parameters were~~

~~calculated:~~

~~a) average AE a * b * color error and its standard deviation,~~

~~b) average chroma ratio and its standard deviation,~~

~~c) histogram frequency function of AEab color error.~~

~~Program outputs~~

~~This section refers to program block 8 in figure 4.1.~~

~~The following data was output to enable graphical~~

~~presentation of the results:~~

~~1. frequency vs. delta E color error , for plotting of~~

~~the histograms, (bin size =.5 AE)~~

~~2. pairs of a*i, b* i values for the original and~~

~~reproduced color, 163~~

~~3. reproduction L* lightness, 2 , vs. original~~

~~L* lightness , i ,~~

~~4. Reproduction lightness, L*2, vs. chroma~~

~~ratio , S r a t i o~~

~~For a given set of stimuli, a documentation file was created containing a listing of the following:~~

~~a) name of the primary reference color together with~~

~~its luminance, Y, and x, y chromaticity~~

~~coordinates ,~~

~~b) A^E color error of every reproduced color in the~~

~~set of colors,~~

~~c) the average color error and its standard deviation,~~

~~d) average chroma ratio and its standard deviation. 164~~

~~APPENDIX 5.~~

~~Dmax SUBSTITUTION FOR RELATIVE CONCENTRATIONS~~

~~WHEN NEGATIVE SPECTRAL RESPONSES ARE OBTAINED~~

~~Introduction~~

~~A color reproduction study was conducted, in part two of the~~

~~thesis, to test Umberger's theoryfl]. The study explored the effect of different primary reference colors, T(A), on the accuracy of color reproduction when the spectral~~

~~sensitivities of the subtractive color reproduction system~~

~~computer model are derived from Umberger's primaries computed~~

~~for the primary reference color T(A).~~

~~A subtractive color reproduction system computer model~~

[APPENDIX 4] was built for the simulated imaging of real surface colors. The model, which is representative of a color reversal film, can reproduce a given color by providing a corresponding spectral transmittance curve of the

~~superimposed three dye layers of the film. The computer~~

~~model is based on additive color reproduction theory.~~

~~According to additive color reproduction theory, see~~

~~between the section 1.1, there is a linear relationship~~

~~reproduction system and the spectral primaries of the color 165~~

~~produce both positive and negative spectral responses.~~

~~However, negative spectral responses are not possible to realize with real photographic systems.~~

~~In previous computations, relating to the color reproduction study, highly saturated colors which produced negative~~

exposures were declared as unreproducible . In an attempt to reproduce such colors, whenever a negative exposure was obtained, an arbitrary value of Dmax = 3.5 was chosen for corresponding concentration. This procedure is in agreement

~~with the assumption that in a color reversal film low levels of exposure produce high density values. The objective of this experiment was to examine the implications of such a~~

~~substitution for negative spectral exposures.~~

~~Experimental procedure~~

~~was conducted in which the A color reproduction experiment~~

~~second part of the original computer program used in the~~

~~constant Dmax value for thesis was modified to allocate a~~

~~exposure is obtained. concentration whenever a negative This 166~~

~~modification refers to program block 4 in figure 4.1; see~~

~~Appendix 4 and section 3.1.3 of the color reproduction~~

~~study. This is the computational transform which relates the~~

~~spectral exposures of the three film sensitivity layers to~~

~~the amounts of dye concentrations required to synthesize the~~

~~spectral transmittance of the film.~~

~~The amount of dye in each of the three dye layers of the film~~

~~required for the reproduction of a given color was determined~~

~~using the following relationships:~~

~~1. if R, G, B > 1.0 then Ci = 0, i = 1,2,3, (5.1)~~

~~2. if 10-Dn>a* < R, G, B <_ 1.0 then~~

~~ci = -log R,~~

~~c2 = -log G, (5.2)~~

~~c3 = -log B,~~

~~10-">ax 3. if R, G, B <_ then ci = Dmax, (5.3) where: R, G, B are the red, green, and blue exposures of the~~

~~film. This is equivalent to a color photographic process with the sensitometric characteristics shown in figure 5.1.~~

The last relationship not only sets the concentration equal to a constant Dmax value for negative exposures but it also prevents the density from becoming infinite for positive exposure values approaching zero. Maximum density of the dye was assumed to be equal to 3.5. Equivalent Neutral Density

~~-2 -1 relative Log E~~

~~FIG. 5.1~~

~~Equivalent sensitometric characteristic used in model 168~~

~~For a description of the remainder of the program refer to~~

~~section 3.1.3. and Appendix 4.~~

~~Except for substituting a constant Dmax value for~~

~~concentration corresponding to negative exposure the~~

~~conditions of the experiment are exactly the same as those~~

~~listed in the second part of the thesis, section 3.1.5.~~

~~A scene is represented in terms of a set of spectral~~

~~reflectances of real surface colors. By combining all colors given as spectral reflectances in table IB, with the exception of the 14 flat gray colors, into one file referred~~

to in the text as the Colorset an average scene containing average subject matter was created. Each color in such a scene can be treated as representing an element of an array of square patches of equal surface area. Throughout the experiment CIE illuminant C was used. This was selected, instead of the modern equivalent D65, because a significant

~~colorimetric data base of real surface colors gathered from the literature used this illuminant.~~

~~The primaries and the corresponding spectral sensitivities of~~

~~the color reproduction system were determined for the primary~~

~~of reference color of the average tristimulus value the~~

~~Colorset. This color was suggested on the basis of primary~~

~~section 2.2.3). For a stability study done earlier (see 169~~

~~description of the calculation of the spectral responses of~~

~~the color reproduction system computer model refer to the~~

~~primary stability study in section 2.1.3.~~

~~The color reproduction system computer model was then used to~~

~~reproduced the scene, represented by the Colorset. For a~~

~~particular color, of the Colorset, the R, G, and B spectral~~

~~exposures of the image sensors were computed. See equations~~

~~(28a), (28b), and (28c). For each spectral exposure a~~

~~corresponding concentration value of the dye in the film was~~

~~assigned in accordance with equations (5.1), (5.2), and~~

~~(5.3). The spectral transmittance Tr(X) of the three~~

~~superimposed dye layers of the reproduced color was~~

~~synthesized according to the formula for Beer's law, equation~~

~~(9). Color error analysis of the results of color~~

~~reproduction were conducted for each pair of original and~~

~~reproduced color; they are described in section 3.1.4 and~~

~~Appendix 4. Moreover, the results of Dmax substitution were compared with previously obtained results when colors yielding negative spectral exposures were rejected. See~~

~~section 3.2.1.2. To find out which experimental conditions~~

~~reproduced the scene (the Colorset) with the least average error the following parameters were calculated:~~

~~error and its a) average AEa*b* color~~

~~respective standard deviation, 170~~

~~average chroma b) ratio, and its~~

~~respective standard deviation.~~

~~The graphs were following then made showing the results of color reproduction:~~

~~1. histogram of frequency vs. AE,~~

~~2. metric chroma shifts in the a* b* plane,~~

~~3. reproduction lightness vs. original lightness,~~

~~4. reproduction lightness vs. chroma ratio.~~

~~Results & discussion~~

~~Substitution of a constant, Dmax, value for concentration when negative exposures are acquired adds, primarily, a longer tail to the color difference histogram, compare~~

~~figure 5.2 with figure 21. It is now possible to obtain color reproduction of all colors matchable by dyes of a given film. A longer tail implies that the previously~~

~~unreproducible colors have been reproduced with a high color~~

~~error- Color reproduction using Dmax substitution for~~

~~concentrations when negative spectral responses of the image~~

~~average sensors are obtained increased the value of the color~~

~~corresponds reproduction error from 4.15 which to the~~

~~negative exposures were reference case when colors producing~~

~~both cases the standard rejected to 11.64. See table 5.1. In~~

~~average color error. deviation remained larger than the 171~~

~~A comparison of color shifts in a*b* plane with the case when no colors producing negative exposures were allowed, reveals~~

~~all that of the newly added colors are reproduced with the~~

~~highest increase in metric chroma. Compare figure 5.3 with~~

~~figure 22. The metric chroma increases follow the same three principal hue directions of yellow, cyan, and magenta as in~~

~~the case when no negative exposures were permitted, refer to~~

~~section 3.2.1.2. The color reproduction errors seem to be more pronounced for colors producing negative exposures. The~~

~~colors producing negative exposures have a chroma ratio~~

~~larger than one, compare figure 5.4 with figure 26.~~

~~Substitution of a constant value of 3.5 for concentration,~~

~~when negative exposures are acquired, produces the largest~~

~~average chroma ratio. See table 5.1. Also, a majority of~~

~~colors producing negative exposures have much lower~~

~~reproduction lightness than colors producing all positive~~

~~figure 27. exposures, compare figure 5.5 with~~

~~= 3.5 is Judging from figure 5.3, the value of Dmax evidently~~

~~increases become large. too high and the saturation very~~

~~optimized to produce more The value of Dmax can be~~

~~do all colors become satisfactory results. Not only~~

~~Dmax is used, but the value reproducible when the optimized~~

~~decreased. See reproduction error is of the average color~~

~~that were conducted, the table 5.1. Out of all the trials 172~~

~~value of the average chroma ratio for this optimized case is the closest to one.~~

~~Results of this experiment indicate that majority of colors, producing negative exposures, do not lie at the outer most boundaries of the color gamut of the dyes because the optimum~~

~~concentration value of about 1.8 which was substituted for~~

~~negative exposures to reduce the average color reproduction~~

~~error is less than the assumed maximum density value of 3.5~~

~~that a single dye can provide. The relationship between the~~

~~optimum concentration value substituted for negative~~

~~exposures and the average metric chroma of a set of colors~~

~~producing negative exposures needs to be investigated.~~

~~Conclusions~~

~~concentration when Substitution of a constant Dmax value for~~

~~exposures are acquired for some of the colors negative~~

~~reproduction and makes possible enhances metric chroma of the~~

~~matchable dyes of a given color reproduction of all colors by~~

~~5.1 indicate that for a film. Results presented in table~~

~~optimum value for Dmax can be particular set of colors an~~

~~< AE> , can be found for which the average color error,~~

~~minimized. 173~~

~~Ll II O II II Ct m HO o Ct -I Id Ct II - I O x co o n oj OJ I- OJ I U_ E _J II O O O II I- 2 U II 2 II O~~

~~I- Ld u o t- CQ II H , - L ~ in z II I- o u in n Ld 'I Dan m in z a a a n co z - DO e lu o j II OJ - to ct o ii if) m a. e a. cj n m j~~

~~X _| Old n Ld uj - z or n ct 2 n Q _l ii X h- n 10 Ct Ld n 21- r> -in in ro T I u q- u it oj "Uqq: OJ I in Ld Id Q o \ II O I OCL 2 in L II o J O I in -* u II o 2 O II Ld Id N I Ld y.~~

~~HH -H Ct _J II to X ro | 0 X O II X I- n E II I U E U n a Y - X I J \ ii uj tr H HI I Id L a. II 3 O a e i Q U II II X li. a o o I 174~~

~~t?t< H8_~~

~~njuj no~~

~~^. Kb~~

~~MS-~~

~~"PA/' t /A AA AAP^v AAA /\/ \A~~

~~=i? gyr^~~

~~FIG. 5.2 set error delta E for the color jduction 175~~

~~FIG. 5.3~~

Color reproduction shifts obtained with spectral sensitivities correspondi ng to Umberger's primaries found for primary reference color of average tristimulus value of all the colors reproduced with dyes of film A (the Colorset). Color reproduction of all colors of the Colorset reproduced with dyes of film A. Illuminant C. For negative spectral responses the concentration is substituted with Dmax=3. 5. [ R, G, B designate Umberger's primaries of the primary reference color. C, M, and Y are the unit concentrations of film A dyes (from table 6).] 176

~~(3)~~

~~@= DQD eg~~

FIG. 5.4 Reproduction Lightness vs. Chroma Ratio for the set of film A (the Colorset). The colors reproduced by dyes of which Umberger's primaries primary reference color, for tristimulus value of the were determined, is the average of film A. For negative set of colors reproduced with dyes was substituted for spectral responses Dmax=3.5 concentration. Illuminant C. 177

FIG, 5.5 Lightness for all Reproduction Lightness vs Original The of film A the Colorset ). colors reproduced by dyes ( for which Umberger's primaries primary reference color, of the average tristimulus value were determined, is the dyes of film A For negative set of colors reproduced by Dmax=3.5 was substituted for spectral responses

~~concentration. Illuminant C. 178~~

~~APPENDIX 6.~~

~~COLOR REPRODUCTION WITH ALL POSITIVE~~

~~SPECTRAL SENSITIVITIES~~

~~Introduction~~

In part two of the a thesis color reproduction study was conducted to test Umberger's theory[l]. The study explored the effect of different primary reference colors, T(X), on the accuracy of color reproduction when the spectral

~~sensitivities of the subtractive color reproduction system~~

~~computer model are derived from Umberger's primaries computed for the primary reference color T(X)<~~

~~A subtractive color reproduction system computer model~~

~~[APPENDIX 4] was built for the simulated imaging of real surface colors. The model, which is representative of a color reversal film, can reproduce a given color by~~

~~transmittance curve of providing a corresponding spectral~~

~~the film. The computer the superimposed three dye layers of~~

~~reproduction theory. model is based on additive color~~

~~reproduction theory, see According to additive color~~

~~the linear relationship between section 1.1, there is a~~

~~spectral reproduction system and the primaries of the color 179~~

responses needed for a colorimetric match. This implies that for all practically available sets of primaries negative spectral responses need to be provided in some parts of the spectrum. Such theoretical spectral sensitivities which can produce both positive and negative spectral responses were used in the color reproduction study conducted in part two of the thesis. However, negative spectral responses are not possible to realize with real photographic systems. (Nevertheless, in a few systems, excluding photography, they can be realized by using additional detectors). It was of interest to determine how

~~color reproduction will be affected if the negative parts of the spectral sensitivity curves are eliminated in the~~

~~subtractive color reproduction system computer model.~~

~~Experimental procedure~~

~~A color reproduction experiment was conducted in which the~~

~~image sensors of the color reproduction system have only the~~

~~positive portions of the theoretical spectral sensitivities~~

~~original computed on the basis of Umberger's primaries. The~~

~~of the thesis was computer program used in the second part~~

~~spectral sensitivities. modified to eliminate the negative~~

~~color reproduction Figure 6.1. is a block diagram of the~~

~~blocks 3 and 4 in program named REP. FOR. Program 180~~

~~figure 6.1. represent the modification. After the negative~~

~~parts of the color reproduction system's spectral~~

~~sensitivities are cut off the remaining positive portions of~~

~~the sensitivity curves are rescaled so that their responses~~

~~to a spectrally flat 100% reflecting white stimulus viewed~~

~~under illumnant C are equal to one. The rescaling is~~

~~in order to necessary retain the gray balance of the~~

~~system. The three scaling factors by which the curves are~~

~~multiplied are the inverses of the sums of the remaining~~

~~positive parts of the color-matching functions. For a~~

~~description of the remainder of the steps involved in color~~

~~reproduction and of the computer model refer to section~~

~~3.1.2. and Appendix 4 respectively -~~

~~Except for utilizing only the positive portions of spectral~~

~~sensitivities the conditions of the experiment are exactly~~

~~the same as those listed in the second part of the thesis,~~

~~section 3.1.5. A scene is represented in terms of a set of~~

~~spectral reflectances of real surface colors. By combining~~

~~all colors given as spectral reflectances in table IB, with~~

~~the exception of the 14 flat gray colors, into one file~~

~~color referred to in the text as the Colorset an average~~

~~was created. Each scene containing average subject matter~~

~~as representing an color in such a scene can be treated~~

~~patches of equal surface element of an array of square~~

~~illuminant C was used. area. Throughout the experiment CIE 181~~

~~REP. FOR~~

~~INPUT :_ elt e2, e3 ; **(*)_ y(X_), zw(A_) ; s0 ; r(\), gw(X), b(X)~~

~~INPUT: T0(X) of original color~~

~~CUT OFF NEGATIVE PARTS of Color-Matching Functions~~

~~Rescale the Color-Matching Functions~~

~~COMPUTE : R, G, B Spectral Responses of the Film~~

~~COMPUTE: concentrations ci, C2, C3 of dyes in the film~~

~~COMPUTE: Tr(X) of the Film according to Beer's law~~

~~COMPUTE: Xi, Yi, Zi and Li*, ai*, bi* of the original color and X2, Y2, Z2 and L2*, a2*, b2* of the color reproduced by the film~~

~~COMPUTE: DEL. E color error, metric chroma, hue angle etc~~

~~OUTPUT RESULTS as files for plotting, documentation etc.~~

~~END~~

~~FIG. 6.1~~

~~Flow chart diagram of the color reproduction program modified to cut off negative spectral sensitivities. 182~~

~~This was selected, instead of the modern equivalent D65, because a significant colorimetric data base of real surface colors gathered from the literature used this illuminant.~~

~~Due to their importance in real life, the following primary reference colors were used to determine the primaries of the~~

~~color reproduction system:~~

~~1. Caucasian skin,~~

~~2 . northern sky ,~~

~~3 . grass green ,~~

~~4. 18% non selective gray,~~

~~5. average tristimulus values of a given color set.~~

~~(The last color was suggested on the basis of primary stability study done earlier (see section 2.2.3)).~~

~~For each primary reference color the spectral responses of the color reproduction system computer model were~~

~~calculated. For a description of this calculation refer to the primary stability study in section 2.1.3. The negative~~

~~portions of the spectral sensitivities were eliminated and~~

~~the curves were rescaled.~~

~~was reproduced The scene, represented by the Colorset, with~~

~~color each set of spectral responses of the reproduction~~

~~particular system computer model. For a color, the R, G,~~

~~image sensors were and B spectral exposures of the 183~~

~~computed. See equations 28a, 28b, and 28c in section 3.1.3. For each spectral exposure a corresponding~~

~~concentration value of the dye in the film was assigned in accordance with relationships (29), and (30). The spectral~~

transmittance Tr e p . (X) of the three superimposed dye layers of the reproduced color was synthesized according to the formula for Beer's law, equation (9). Color error analysis of the results of color reproduction were conducted

~~for each pair of original and reproduced color; they are described in section 3.1.4. Moreover, to find out which set~~

~~of spectral sensitivities reproduced the scene with the~~

~~least average error, for a given set of colors, the~~

~~following parameters were calculated:~~

~~a) average AEa*b* color error and its standard deviation,~~

~~b) average chroma ratio and its standard deviation,~~

~~The following graphs were then made showing the results of~~

~~color reproduction:~~

~~1. histogram of frequency vs. A E,~~

~~the a* b* 2. metric chroma shifts in plane,~~

~~original 3. reproduction lightness vs. lightness,~~

~~4. Reproduction lightness vs. chroma ratio. 184~~

~~Results~~

~~For all five primary reference colors graphical presentation of the results of color reproduction produced similar~~

plots. looking The outcome of color reproduction with all positive spectral sensitivities shall be illustrated with results obtained for primary reference color of average tristimulus value of the Colorset.

The color error histogram mode has increased to between 8 and 10 delta E color error relative to the reference case, where the spectral sensitivities were allowed to have both positive and negative responses. See figure 6.2. Table 6.1

~~indicates that by omitting the negative portions of the theoretically required spectral sensitivities the average color reproduction error can increase about 1.8 times. The~~

~~standard deviation is now smaller than the average color error. On the average however, it remains greater than the~~

~~standard deviation obtained for the reference histogram when~~

~~both positive and negative responses were allowed. See table 6.1.~~

~~An overall decrease in chroma ratio below the value of one~~

~~confirmation of this trend is observed, see figure 6.5. A~~

~~is also found in table 6.1 where for each primary reference~~

~~for all the colors that color, the average chroma ratio, 185~~

Ll O cn OJ ro ro OJ LO UD LO LO i in o ct m o o o o o o O o o o V 2 i t i-H -H ( Id Ct | 1 i-4 -rM 1 -M t-H I J UJ X CO o OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ _J X E _l o o O O O X K X ' ' 1 1 1 < OO _ _H u 2 O OJ OJ CM OJ OJ HH 2 r- Id J ld u ~ - Ct 2 1- U. Ll I O Ld X O O Id in Ld H Ct Id Ct J Ct X Ld Ld 1- ct a cq o H m Ll U1 LU Ld _j CL Ld Ld UJ CD Ct CJ O cn o OJ o CO o m o OJ O X O SX UJ E 2 O U LO UD UD 1- i- LO LO _l m O O Q HH o > - 2 3 U a 3 in x m ~ 1- Ld Ld 2 UJ H Ct J I HH 11 HH X CQ 1- ct a- in 3 N ^ CO * N T _ T LO T 0. 0. x z Id <+ OJ OJ OJ OJ ro oj T OJ OJ OJ U 2 2 Id Q 0 Ld O O ut - in in o d 6 o d o d d d d 3 O Ct O CL - O Ll o a _i 1- Ct H- (E x a O ct in cl 1- CD UJ Id X - X UJ Ct O 3 Ct U 2 O LO - - OJ cn cn CO OJ OT HH 2 2 O Id UJ CJ O - - || OJ UD - in - ij] O UD O J o co a Ct H Ld U 2 ct m h- X X -H o - o - o HH Q -1 O X UJ X HH Ld Z U Ct H Ct Ld UT CO Ld X Id O 2 3 2 H 3 Ld -1 l-H 1-1 O Ct 2 HZ Ld N CO - u in - OhJh ct q: 3 CL X Z Ld in x o a u o in Ld * * * * * 2 Jh UJ ct O ID CO L0 t 01 N ID Tl N cn cn LO CO LO o in o - Ct Ll LU O - HH - ID CO N LO O T T O UD UD LO N N lu u in 3 _l I- -. z Ct 1- X O UJ U'J CM O in oj oi OT CD t 01 cn t OJ Oi CJ 1- 2 LU O Z X O

~~i ?-, i-H t ~ Q 2 Id in _J Id O 3 X O Q UT Ld - - Ll 3 _J U Ct I 1- X O H CO - O Ct Ll CL in ID CO CO LO CO CO CO CO CD CD 2 UT Ld h- O O Z Ll~~

_l Id LU _J U LU J Ld LU _J UJ Ld J Id Id zzu Ll Id O ~7" ~ X 2 2 X 2 ^- X 2 z X 2 X Z Z X Ld Ld in m Ld UJ Ld UJ Id (J 10 X CL i- m m O O O ago O O O O O O O O O 1- 1- UJ J Ct Id ct ?** - O i2 2 z_ 2 2 2 2 2 2 Z X _J CO o o CO o ICQh UT J X J 1 Ct u Id O 2 O 1- Ct UJ u Ct U -- U 2 , o u o ct h- H- 1 _l 111 _l ct i- K "*_ m o a x o UT k 2 -H uj u in 3 o in UJ Ct UT 1- Id z UJ Ct Ct -._ U CL X 2 cl o o UD > Z O Ct CO X Id Ll J Ct CO O CO Ct Ld _J UT Id X Ct O X X UT CO X LU CJ Ll Id UJ E LU U Ll H 10 Ct o 2 _l s? _l "f CO HH |J_ o Ct X UJ UJ Ct LU c o ct CO 3 X X O X * 1- 1- a Ct U CD 4 X 3 U 2 * 186

~~T-n- I ' ' ' ' I SO SI so ss 40 DSMTA S~~

~~FIG. 6.2~~

Histogram of color reproduction error delta E for the set of all colors reproduced with dyes of film A (the Colorset). Spectral sensitivities of the color reproduction model correspond to Umberger's primaries found for the primary reference color of average tristimulus value of all the colors of the Colorset. Spectral sensitivities are without their negative parts. Illuminant C. 187

were reproduced is listed. Figure 6.3 shows the color vectors pointing radially towards the origin of the a*b* coordinate plane. The C* shifts are the highest for the most saturated colors, and they decrease for colors laying closer to the origin.

~~There are now a lot more colors than previously, which have higher reproduction lightness than their original lightness, see figure 6.4. The points cluster tightly on both sides of~~

~~the diagonal line running at 45 degrees on the graph and~~

~~representing the ideal case of reproducing the lightness.~~

~~It was of interest to test whether the two color~~

~~reproduction processes, with and without negative spectral~~

~~variability. The test can be sensitivities, have similar~~

~~color conducted by pooling variances of the average~~

~~reference differences corresponding to the different primary~~

~~color reproduction colors listed in table 6.1 for the two~~

~~with this analysis the processes. In order to proceed~~

~~each of the two populations has requirement for normality of~~

~~the Central Limit Theorem[29] to be fulfilled. According to~~

~~the means approaches that of distribution of the average of~~

~~for sample size approaching the normal distribution~~

~~case is about 150 and infinity. The sample size in our~~

~~such an assumption. should be sufficient to justify 188~~

~~FIG. 6.3~~

~~KOMM, y@MTOll~~

FIG. 6.4 Lightness for all Reproduction Lightness vs. Original of film A (the Colorset). The colors reproduced with dyes value for color is average tristimulus primary reference sensitivities are set. The spectral all colors of the parts Film A. Illuminant C. without the negative 190

~~rf)iM|iiiiMii|iiiiiiii|in I I 1 I i i i 1 1 1 1 uMrHlHfrTT,in|ni"i'i|miiq'M||"l'"l|"| ' I|M1|11I|111|~~

FIG. 6.5 Reproduction Lightness vs. Chroma Ratio for the set of colors reproduced with dyes of film A (the Colorset). The primary reference color is the average tristimulus value of the set of colors reproduced with dyes of film A. The spectral sensitivities have no negative parts. Film A, Illuminant C. 191

~~The null hypothesis is that there is no significant difference in the variability of the two color reproduction methods of the Colorset; the alternate hypothesis is that~~

~~using both positive and negative spectral sensitivities~~

~~produces greater variability in resultant average color~~

~~error. The hypothesis are:~~

~~= H 0 : a 1 a 2 ; H 1 : 0 i < 0 2~~

~~The level of significance is assumed to be 0.01. The number~~

~~of degrees of freedom in both cases is the same and equals~~

~~4. The ratio = table F is found to be: F4 4 .01 16.0. A~~

~~variance of 4.36 is obtained when both positive and negative~~

~~spectral sensitivities are allowed and a variance of 0.13 is~~

~~obtained when all positive spectral sensitivities are used.~~

~~The calculated F ration is 4.36/0-13 = 33.54. The~~

~~calculated F ratio exceeds the value of the table F ratio~~

~~and we have to reject the null hypothesis.~~

~~The variance in the color reproduction process with respect~~

~~to the choice of the primary reference color when only all~~

~~utilized positive spectral sensitivities are is~~

~~when both positive and negative significantly smaller than~~

~~used. for all positive spectral sensitivities are Also,~~

~~values of standard deviations of spectral sensitivities the~~

~~the same. See table 6.1. the average chroma ratio are~~

~~illustration of the results of the Additionally, graphical~~

~~reproduction with all positive spectral outcome of color 192~~

~~sensitivities using different primary reference colors produced similar looking plots. Based upon the above~~

~~findings it can be concluded that once the negative parts of~~

~~the color-matching functions are cut off, the choice of the~~

~~primary reference color plays a smaller role in affecting~~

~~the results of color reproduction.~~

~~Discussion~~

~~The study revealed that the simple neglect of negative~~

~~regions of spectral sensitivities caused a decrease in~~

~~of color average chroma ratio and resulted in similar levels~~

~~set of the reproduction errors; i.e. a change from one~~

~~other is of slight positive sensitivity regions to any~~

~~reproduction. significance to the process of color~~

~~of the merits of the MacAdam [30], in his theoretical survey~~

~~sensitivities in an additive simple neglect of negative~~

~~chroma of also a decrease of metric color process, obtained~~

~~experiments show chromaticities. Results of my reproduction~~

~~identification is not absolutely that accurate primary~~

~~color the additive or the subtractive necessary in either~~

~~which negative values of reproduction processes in~~

~~neglected. such a sensitivities are In theoretical spectral~~

~~analyzed in terms of system can be case, a subtractive~~

~~additive theory. 193~~

The decrease in metric chroma and an increase in the value of reproduction lightness can be related to smaller than required dye concentrations. The absence of negative portions of spectral sensitivities translates into exposure values that are higher than those that would be obtained with spectral sensitivities having both positive and negative regions. In the color model, exposure density is proportional to dye concentration. Therefore, higher exposure values are transformed into lower than theoretically required concentration values and a decrease

in metric chroma results. Also, only slight changes in color reproduction errors are obtained since, as MacAdam[24] pointed out, the differences between the positive regions of spectral sensitivities are of slight significance and they

~~will produce similar exposure values.~~

~~Conclusions~~

~~All positive sensitivities of the image sensors produce a general desaturation of the reproduced colors as evidenced~~

~~ratio. See table 6.1 and figure by a decrease in chroma~~

~~for the Colorset is 6.2. The average color error, < AE>,~~

~~negative parts of higher than when both positive and~~

~~used. The choice of the spectral sensitivities are primary~~

~~a major role in affecting the reference color stops playing 194~~

~~results of color reproduction if only the positive parts of~~

~~spectral sensitivities are used. See table 6.1 195~~

~~APPENDIX 7.~~

~~GRAY SCALE REPRODUCTION WITH UMBERGER'S PRIMARIES~~

~~Introduction~~

~~In part two of the thesis a color reproduction study was~~

~~conducted to test the usefulness of various Umberger's~~

~~primaries for color reproduction of a given scene. A~~

~~subtractive color reproduction system computer model was~~

~~built for the simulated imaging of real surface colors.~~

~~The model is representative of a color reversal film. The~~

~~model can reproduce a given color by providing a~~

~~corresponding spectral transmittance curve of the~~

~~superimposed three dye layers of the film. Additive color~~

~~reproduction theory served as the basis for construction of~~

~~the model. Accordingly, the model has theoretical spectral~~

~~sensitivities corresponding to the color-matching functions~~

~~of average Umberger's primaries obtained for a given primary reference color.~~

Fourteen flat gray colors, chosen to represent the gay scale, using various spectral sensitivities, calculated on the basis of Umberger's theory, were imaged in the computer model. In the computer experiment the negative parts of

~~or spectral sensitivities could be included ignored in the 196~~

calculations. The objective was to examine how color reproduction of gray colors is affected by the choice of spectral sensitivities of the color reproduction system corresponding Umberger's primaries. Umberger's theory was

~~tested for the reproduction of spectrally flat gray colors,~~

~~Experimental procedure~~

~~For a detailed description of the steps involved in color~~

~~reproduction and of the computer model itself refer to~~

~~section 3.1.2. and Appendix 4.~~

~~A modified version of the color reproduction computer model~~

~~was also used in the experiment. It was of interest to~~

~~find out how color reproduction of spectrally flat gray~~

~~colors will be affected if the negative parts of the~~

~~eliminated in the spectral sensitivity curves are~~

~~computer model. subtractive color reproduction system~~

~~exposures Usually, it is not possible to realize negative~~

~~a detailed description with real photographic systems. For~~

~~color reproduction computer of the modified version of the~~

~~model refer to Appendix 6. 197~~

The conditions of the experiment are similar to those listed in the second part of the thesis, section 3.1.5. In the experiment, the gray scale represents the scene that is to be reproduced. A set of fourteen spectrally flat gray colors was generated ranging from 0-5 to 95 percent reflectance. Throughout the experiment CIE illuminant C was used. This was selected, instead of the modern

~~equivalent D65, because a significant colorimetric data base of real surface colors gathered from the literature~~

~~used this illuminant. By choosing illuminant C a measure~~

~~of consistency could be retained with the different color~~

~~reproduction experiments which were done previously.~~

~~Due to their importance in real life, the following primary~~

~~reference colors were used to determine the primaries of~~

~~the color reproduction system:~~

~~1. Caucasian skin,~~

~~2. northern sky,~~

~~3. grass green,~~

~~4. 18% non selective gray,~~

~~of a given color set. 5. average tristimulus values~~

~~the basis of primary (The last color was suggested on~~

~~(see section 2.2.3)). stability study done earlier 198~~

~~For each primary reference color the spectral responses of~~

~~the color reproduction system computer model were~~

~~calculated. For a description of this calculation refer to the primary stability study in section 2.1.3.~~

~~The scene, represented by the gray scale, was reproduced with each set of spectral responses of the color reproduction system computer model. In the first trial~~

~~both the positive and negative parts of the spectral~~

~~sensitivities were allowed. In the second trial the~~

~~negative parts of spectral sensitivities were eliminated~~

~~and the sensitivities were rescaled in order to retain the gray balance of the system. See Appendix 6 for details.~~

~~For a particular color, the R, G, and B spectral exposures of the image sensors were computed. See equations 28a,~~

~~28b, and 28c. For each spectral exposure a corresponding~~

~~concentration value of the dye in the film was assigned in accordance with relationships (29), and (30). The spectral transmittance Tr(X) of the three superimposed dye layers~~

~~of the reproduced color was synthesized according to the formula for Beer's law, equation (9). Color error analysis~~

~~of the results of color reproduction were conducted for~~

~~each pair of original and reproduced color; they are described in section 3.1.4. Moreover, to find out which~~

~~set of spectral sensitivities reproduced the scene with the least average error, for a given set of colors, the following parameters were calculated: 199~~

~~a) average /\Ea*bi color error and its~~

~~standard deviation,~~

~~The following graphs were then made showing the results of color reproduction:~~

~~1. histogram of frequency vs. AEa*t>*,~~

~~2. reproduction lightness vs. original lightness,~~

Regarding flat grays it is only possible to plot graphs showing histogram of /\E color error, and reproduction lightness versus original lightness, because chroma ratio is undefined for such colors.

~~Re suits-discussi on~~

~~The results of color reproduction of the 14 flat gray~~

~~colors are independent of the choice of the primary reference color, see table 7.1. Using only the positive~~

~~parts of the color-matching functions does not affect the~~

~~results .~~

~~The histogram of color reproduction error delta E for the~~

~~that the errors are small set of 14 flat gray colors shows~~

~~see and are confined to values ranging from 0 to 2 , figure 7.1. The errors tend to decrease for lighter~~

~~reproduction lightness colors, see table 7.2. The 200~~

~~corresponds rather well with original lightness, see~~

~~figure 7.2. The errors should be small because the concentrations are scaled in terms of END ( Equivalent~~

~~' Neutral Density). Since END s are normalized to provide a unit neutral visual density under normal viewing illuminant a change in lightness of the neutral would involve~~

~~rescaling of the END's by a constant factor. Precision~~

~~errors accumulated in the process of computation are the~~

~~probable cause of color errors being greater than zero.~~

~~All of the reproduced colors fall outside the interval of~~

~~delta E color error of 0.003 which has been arbitrarily~~

~~chosen to designate the boundary between grays and~~

~~nongrays. Thus according to this convention all of the~~

~~reproduced colors are no longer gray, see table 7.2.~~

~~conclusions~~

~~A fairly accurate color reproduction of the gray scale is~~

~~possible even when the color reproduction system's spectral~~

~~sensitivities are not linear transforms of the~~

~~eye. color-matching functions of the 201~~

~~Ll U~~

~~cl m T'TI'T'TIT'tltT in CJ Ld Ct a CO O o E _l j O O o X Z iJ o~~

~~V Ld X o _l a _l CO o~~

~~o m i- in x ct~~

~~a o _l o m Ld o O O I O O I O O I o o Ll _i CO ct o x 2 CL CL U CL O Ld o CD Z Ct Ll UJ H Ll~~

~~X Z. A- O UJ HH Ct 1- UJ Ll Ld TTI^^I^tlfT CJ Ll O i-tiTtiTi-i-T^r O Id id '+ Q CL IOC' m Q 0 _l O O I O O I o o O ct UT UJ CL > o CL Ct~~

~~_l UJ X o CL 2 CJ~~

~~X UT LO I UD UD I UT UD I LO LO _l~~

~~_J O UT Ld O O I O O I O O I O O in u o Q O z o o Ll -i X >-^ o a t- X u m :> CD I O I CD I CO z i-~~

~~Ll Ld I Ld I Ld I Id o _i u Ll o z J 2 in i-i o i o i i o CD uj in g T" Ll U ct o ? X U h- X LU 5; U 1 Z CL Ld o Ct J~~

Ld _f I > I I o Ll UT I X I ii I Id I UT I Id I CL Z I I Id I X I Z I Ct I > N - | ct |(J II UT I Id I I Ct x ix i in i co Ld u i h i m i _J O I CL IX I K CD CL X I O I Ct I CO X I- o. U 12 I CD I - U 202

~~DELTA E COLOR % REFLECTANCE ERROR~~

0.5% DELTA E = 1.00 2.0% DELTA E = 1.25 2.5% DELTA E = 1.21 5% DELTA E = 1.04 10% DELTA E = 0.83 20% DELTA E "Z 0.61 30% DELTA E - 0.47 40% DELTA E - 0.37 50% DELTA E 0.29 60% DELTA E = 0.22 70% DELTA E = 0. 16 80% DELTA E = 0.11 90% DELTA E - 0.05 95% DELTA E 0.03

~~AVERAGE DELTA E = 0.55 ELTA E STANDARD DEVIATION z 0.44~~

~~TABLE 7 . 2~~

~~Color error Delta Ea*b* for 14 flat gray colors. Primary reference color: Caucasian skin, Y= 29.24 x=0.377 y= 0.336. Film A, and illuminant C 203~~

~~EiWA i~~

~~FIG. 7.1~~

~~error del. E for the set of Histogram of color reproduction color is Caucasian film flat grays. Primary reference skin, A, illuminant C. 204~~

~~@0@0[MIL u@Kra[~~

~~FIG. 7.2 Reproduction Lightness vs. Original Lightness for the set of flat grays. The primary reference color is Caucasian skin. Film A. Illuminant C. 205~~

~~APPENDIX 8~~

~~FORTRAN CODE LISTING 206~~

* MAIN PROGRAM MAIN. FOR PAUL R. 8ARTEL

THIS PROGRAM CALCULATES THE COLOR-MATCHING FUNCTIONS (SENSITIVITIES) OF THE PRIMARIES * DUE TO THE TRANSMITTANCE FUNCTION OF THE DYE IMAGE. *

~~REQD. SUBROUTINES: NR, EXTCOOEF, SCALEX, WEIGHTILL, TRIST1, CROMAT, SUBYXY, LAB, AINV,~~

******************************************************** INTEGER I.J, J COUNTER ? NU, J OF SAMPLES FOR CALCULATION OF TRISTIMULUS VALUES f N, J * OF DATA POINTS IN ROW OR COLUMN ? COU, i COUNTER ? ITER 1 * OF ITERATIONS IN NEWTON RAPSON

REAL SOURCE (80,80), ILLUMINANT + XDYDZD (3), XD YD ZD TRISTIMULUS VALUES OF ILLUMINANT SAMPLE (31,380), SPECTRAL REFLECTANCE OF ORYGINAL COLOR CMFXYZ (3,80), COLOR-MATCHING FUNCTIONS X Y Z ? ILLXYZ (3,80), COLOR-MATCHING FUNCTIONS XYZ * ILLUMINANT CMFRGB (3,80), COLOR-MATCHING FUNCTIONS RGB ILLRGB (3,80), COLOR-MATCHING FUNCTIONS RGB * ILLUMINANT

EXTC80 .3), EXTINCTION COEFFICIENTS * XYZ(3, 380), XYZ TRISTIMULUS VALUES OF COLORS XYZPC3 ), 1 XYZ TRISTIMULUS VALUE FOR NR.FOR RGBC3, 30), RGB TRISTIMULUS VALUES OF A COLUR C(3), INITIAL CONCENTRATIONS - INPUT TC80D, SPECTRAL TRANSMITTANCE OF COLOR FILM ZI, Y BAR VALUE OF ILLUMINANT

? CROMC3 ,3), CHROMATICITY MATRIX OF R G B PRIMAR. CROMSC 3,3), CHROMATICITY MATRIX SCALED TO ILLUMIN INVCRO MC3.3), INVERSE OF CHROMATICITY MATHIX CRGB(3 ), SCALING FACTORS FOR CHROMATICITY MATR CONSTC 3), 1/ (X ? Y ? Z) FOR CHROMATICITIES JACC3, 3), JACKOBIAN - PARTIAL DERIVATIVES ZH7S) X CHROMATICITIES OF LAMBDA Z2(75) Y CHROMATICITIES OF LAMBDA JF(3), JGC3), (-1)*JAC TO FILN A* B JH(3), LABSC3 CRC3.3 80), CHROMATICITY COORDINATE RIM, XD+YD+ZD RIMX, ChROMATICITIES OF THE SOURCE RIMY

CHARACTER ? DATFIL30, SPECTRAL CURVES OF COLORS ANSWER*!, Y/N ANSWER COLOR + LABEL(380)*30, NAME OF SAMPLE OF FILM + LABEL1*30, CHOICE SCALED OR UNSCALED f LABEL230, UNMATCHABLE ? LBEL30 NAME OF COLOR 207

************************************************************************** C INPUT OF NECESSARY DATA:

~~N=31 CON-2. 30258509~~

~~_. _r , . , , ______~~

~~C XYZ COLOR-MATCHING FUNCTIONS:~~

~~0PEN(1,FILE='XYZ.DAT< ' ,STATUS=OLD )~~

~~DO 1 1=1, N M READU,*) CMFXYZC1,I),CMFXYZ(2,I),CMFXYZ(3,I) *{ 1 CONTINUE~~

~~CLOSE(l,STATUS='KEEP*)~~

* WRITEC6,*) ( ( CMFXYZCI.J), J=1,N ), 1=1,3)

~~C ^EXTINCTION COEFFICIENTS:~~

~~CALL EXTCOOEF (EXT.LABEL1) *.__._._.____...... _..__..__._-...._ C SCALING OF THE EXTINCTION COOEFFICIENTS~~

~~CALL SCALEX (EXT.LABEL2)~~

*______._- C WEIGHTS FOR ILLUMINANT * CMFXYZ :

~~CALL WEIGHTILL (ILLXYZ)~~

~~OPEN(12,FILE='XYZ-CROM,DAT' * ,STATUS='OLD ) * DO 122 1=1,75 * READU2,*)Zl(I),Z2(I) ! SPECTRUM LOCUS CROHATICITIES *122 CONTINUE * CLOSE(12,STATUS-'KEEP')~~

~~**************************************************************************~~

~~C PRELIMINARY CALCULATION OF THE TRISTIMULUS VALUES OF THE ILLUMINANT:~~

~~DO 4 1=1,3 JiJSl'illl = JISJ1 3*N DO 5 J=1,N ill!~~

~~XDYDZD(I) = ILLXYZ(I,J) ? XDYDZD(I)~~

~~5 CONTINUE 4 CONTINUE~~

~~WRITE(6,1015) ******** t 1015 FORMATUX, /,/,/, '***** XDYDZD(I) ,/,/, * 5X,'XD YD ZD ',/./)~~

~~WRITE(6,*) (XDYDZD(I),I=1,3)~~

~~C CALCULATE SOURCE CROMAT1CITY COORDINATES: RIM = XDYDZD(1)+XDYDZD(2)+XDYDZD(3) 208~~

RIX = XDYDZD(1)/RIM RIY = XDYDZD(2)/RIM ***********************************************************************

~~C SAMPLE REFLECTANCE - TRANSMITTANCE C OPEN OUTPUT FILES FOK : CROMATICITY.DAT - RESULTS OF CALCULATIONS ? SOURCE C LAB, DAT - SAME AS ABOVE BUT IN L*B*A* SPACE~~

* CREATE A FILE FOR NONMATCHABLE COLORS FOR THE NR.FOR SUBROUTINE

OPEN( 7, FILES' OPEN( 8, FILEs' OPENC 9, FILES' OPEN( IO.FILEl OPEN( 14, FILEs OPEN( 15, FILEs OPEN( 16, FILEs OPEN( 17, FILEs OPEN( 18, FILE= OPEN( 19, FILEs OPEN( 20, FILES OPEN( 21, FILES OPEN( 22, FILE= OPEN( 23, FILEs

* HEADINGS

~~WRITE(7,*)' COLORS THAT COULD NOT BE MATCHED' WRITE(21,*) ' COLORS THAT GIVE NEGATIVE COLOR-MATCHING FUNCTIONS* WRITE(7,*)' '~~

WRITE(21,*)' ' ***********************************************************************

********* MAIN MENU ********* (977)

977 WRITEC6,1016) 1016 F0RHAT(/,/,/, IX, 'SPECIFY THE COLOR OF THE DYE IMAGE IN TERMS OF: ',/,/, IX, '1. CONCENTRATIONS CI, C2, C3',/,/, IX, '2. SPECTRAL CURVE T (WAVELENGTH)',/,/, IX, '3, COLOR Y, X, Y', /,/,/, IX,' PICK ONE',/,/,/)

~~REA0C5,*) COU NU=1~~

~~IF(COU.EQ,l)THEN~~

~~INITIALIZE:~~

~~DU Isl,3 DO K=l,3 JAC(I,K)=0. END DO END DO 209~~

~~-RITE(6,2010) 2010 F0RMAT(/,1X,'GIVE SAMPLE ',/,/) READ(5,*)JK *RITE(6,2020) 2020 F0RMAT(/,1X, 'GIVE SAMPLE NAME',/,/) READ(S,'(A) ) LAbEL(JK)~~

WRITE(6,*)' ' WRITE(6,*) 'SPECIFY THE FIRST CONCENTRATION;' READ(5,*), Cd) WRITE(6,*) 'SPECIFY THE SECOND CONCENTRATION:' READ(5,*) C(2) WRITE(6,) 'SPECIFY THE THIRD CONCENTRATION:' READ(5,) CC3)

*------_--- __.__._

~~DO 6 J=1,N~~

~~T(J)s EXP( -CON*( EXT(J,1)*C(1) + EXT(J.2)*C(2) ? EXT(J,3)*C(3) ) IW = 390 10 * J WRITE(14,*)IW,T(J)~~

~~6 CONTINUE~~

~~DO 7 1=1,3 DO 8 Ksl,3 DO 9 J=1,N~~

~~JAC(I,K) = JAC(I.K) ? ILLXYZ(I.J) * T(J) * EXTCJ.K)~~

~~9 CONTINUE 8 CONTINUE 7 CONTINUE~~

~~WRITE(6,*)'THE JACKOBIAN ' DO 10 1=1,3 DO 11 J=l,3 JAC(I.J) s -CON * JAC(I.J) WRITE(6,*)JAC(I,J) 11 CONTINUE 10 CONTINUE~~

CALL TRIST1 (T, ILLXYZ,XYZ, 1 ,N , 1 ) CALL CROMAT (XYZ,CR,1) DO J=1,NU WRITE(20,*)CR(1,J),CR(2,J) END DO *...._.-...__....-_.-_-..-___._...._.--_.--_.-_-.-.___.--. * SPECTRUM OF THE MODULATED EXTINCTION COEFFICIENT DO 118 K=l,3 DO 119 J=1,N

~~IW =390 ? 10 * J TRN s T(J) * EXT(J,K) WRIT(14,*)IW,TRN~~

~~119 CONTINUE 118 CONTINUE~~

~~GOTO HI 1 NEXT, COMPUTE CHROMATICITIES 210~~

~~ELSEIF(COU.EQ.2)THEN~~

~~1009 WRITE(6,*)' WRITE(6,*) 'SPECIFY FILE NAME OF THE SPECTRAL CURVES READ(5, '(A) ') DATFIL WRITE(7,*)' ', DATFIL, LABEL1 WRITE(21,*)' ', DATFIL, LABEL1~~

~~OPEN(4,FILEsDATFIL,STATUS='OLD',ERR=379) UJ N*NU~~

~~DO J=1,000 READ(4,'(A)',ENO=222) LABEL(J) DO Isl,N READ(4,) SAMPLE (I,J) END DO~~

~~IF( SAMPLE(l,J).GT.1.0.OR.SAMPLE(15,J),GT.1.0 )THEN~~

~~DO 72 1=1, N SAMPLE(I,J) = SAHPLE(I,J)/100. 72 CONTINUE~~

~~ENDIF~~

~~END DO 222 NUsJ-1 WRITE(6,*)'NU=' ,NU~~

~~CALL TRIST1 (SAMPLE , ILLXYZ, XYZ , NU , N , 1 )~~

~~CALL CROMAT(XYZ,CR,NU) FIND CHROMATICITIES 00 Jsl.NU WRITE(20,*)CR(1,J),CR(2,J) END DO~~

~~WRITE(6,*)' '~~

~~WRITE(6,) 'TRISTIMULUS VALUES FOR THE SAMPLE ARE:' WRITE(6,*)' ' DO Jsl,NU WRITE(6,'(A)') LABEL(J) WRITE(6,) XYZ(2,J),CR(1,J),CR(2,J) WRITE(6,*) XYZ(1,J),XYZ(2,J),XYZ(3,J) END DO~~

CL0SE(4,STATUS='KEEP') GOTO 110 J NEXT, FIND CONCENTRATIONS, NR.FUR ENDIF *************************************************************************

~~C INPUT OF Y X Y OF REAL OBJECTS AND CONVERSION TO XYZ~~

~~CALL SUBYXY (XYZ, NU, LABEL, DATFIL) WRITEC7,*)' ', DATFIL, LABEL1 WRITE(21,145) 145 F0RMAT(///,15X,** ***** ***',//) WRITE(21,*)' '. DATFIL, LABEL1~~

~~CALL CROMAT(XYZ,CR,NU) 211~~

DO J=1,NU WRITE(20,*)CR(1,J),CR(2,J) END DO WRITE(6.*)'NU' ,NU ********************** *****************************,*****,************** C NEWTON-RAPSON COMPUTATION OF MATCHING CONCENTRATIONS: Cd), C(2), C(3)

~~110 DO 888 JK=1,NU~~

* WRITE(6,*)' ' * WRITE(6,*)'FOR THE NEWTON-RAPSON SUBROUTINE' WRITE(6,*)' ' * WRITE(6,*)GIVE VALUE FOR COLOR ERROR' * WRITE(6,*) ' * READ(6,*)EPS EPS=,001

*- DO 14 1=1,3 XYZP(I)-XYZ(I,JK) * WRITE(6,*)'XYZP',I. XYZP(I) 14 CONTINUE LBEL=LABEL(JK) *.-_-__--..------.-.-_- CALL NR (LBEL,XYZP,JAC,N,XDYDZD,EXT,ILLXYZ,EPS,C,ITER,NO) IF (NO.EQ.l)THEN INOMATCH = INOMATCH + 1 GOTO 888 ENDIF

*..__.-___.___._..-..--.__ _-__-_._- _--.-. - - C OUTPUT OF CONCENTRATIONS + AVERAGES (MATCH.DAT) WRITE(18,*)' '

~~' WRITEU8,*) 'SAMPLE : ,JK , LABEL (JK) WRITE(18,*)' WRITE (18,*) XYZP(1),XYZP(2),XYZP(3) WRITEC18,*)' '~~

~~' WRITEU8,*) 'TOTAL NUMBER OF ITERATIONS: .ITER WRITEC18,*)' '~~

~~' = WRITEdB,*) 'CONCENTRATIONS , (C(I) .1 1 , 3) AVC1=AVC1*C(1) AVC2=AVC2+C(2) AVC3sAVC3*C(3) WRITEdB,*)' ' * WRITE(18,) 'JACKOBIAN :' * WRITE(18,*)((JAC(I,J),J=1,3),I=1,3) * WRITE(18,*)' '~~

~~**************************************************************************~~

~~C FINDING THE X,Y,Z TO R,G,B TRANSFORMATION, R=G=B=1 FOR ILLUMINANT~~

~~C COMPUTE THE CHROMATICITIES~~

~~111 DO 15 K=l,3 CONST(K) = l./(JAC(l,K)+JAC(2,K)--JAC(3,K)) JF(K)=(-1.)*JAC(K,1) * WRITE(6,*)JF(K) JG(K)=(-1)*JAC(K,2) * WRITE(6,*)JG(K) JH(K)=(-1)* JAC(K,3) * WRITE(6,*)JH(K) 212~~

~~15 CONTINUE *--__...-._.._.-.~~

~~WRITE(6,*)' '~~

* WRITE(6,*) 'THE CHROnATICITY MATRIX * WRITE(6,*)' '

~~DO 16 1=1,3 DO 17 K=l,3 CROM(I,K)=JAC(I,K)*CONST(K) * WRITE(6,*) CROM(I.K) 17 CONTINUE 16 CONTINUE~~

* ZUP=1. IF( ZUP.EQ.1.)THEN CROM(l,l)=,619 1 TUBE BL 7 CROM(l,2)=.234 CROMC1, 3)3,148 CROM(2,l)=.341 CROM(2,2)=.659 CROM(2,3)=.067 CROM(3,l)s,04 CROM(3,2)=.107 CROM(3,3)=,785 ENDIF CROM(l,l)=,67 CROM(l,2)=.21 CROM(l,3)s.l4 CROM(2,l)s,33 CROM(2,2)s.71 CROM(2,3)s,08 CROM(3,1)=,0 CROM(3,2)=,08 CROM(3,3)=.78

~~C OUTPUT OF PRIMARY CHROMATICITIES TO PRIMXY.DAT~~

~~DO 166 1=1.3 WRITEC9,*) CROM(l,I),CROM(2,I) 166 CONTINUE~~

*...__.._..______...._.-___. .- -.--- C OUTPUT OF A* B* TO L*A*B* FILE

~~CALL LAB(JF,XDYDZD,LABS) * WRITE(6,) 'LABS(2) = ',LABS(2) WRITEdO,*) LAbS(2),LABS(3) CALL LAB(JG.XDYDZD.LABS) WRITEdO,*) LABS(2),LABS(3) CALL LAB(JH.XDYDZD.LABS) WRITEdO,*) LABS(2),LABS(3)~~

~~CALL AINV (CROM.INVCROM)~~

~~DO 1=1,3 CRGB(I)=0, ENO DO 213~~

~~C COMPUTE THE SCALING FACTORS FOR THE CHROMATICITY MATRIX DO 18 1=1,3 DO 19 K=l,3~~

~~CRGB(I)=INVCROM(I,K)*XDYDZD(K)/100 ? CRGB(I)~~

~~19 CONTINUE 18 CONTINUE~~

.-_-_-___. C *** SCALE THE CHROMATICITY MATRIX ***

~~DO 20 1=1,3 DO 21 Ksl,3~~

~~CROHS(I,K)=CROM(I,K)*CRGB(K)~~

~~21 CONTINUE 20 CONTINUE~~

* ....-.... - ._.-._ ___... C COMPUTE THE XYZ TO RGB TRANSFORMATION MATRIX

~~CALL AINV(CROMS,INVCROM)~~

* WRITE(6,*)'THE TRANSFORMATION INVERSE CROH MATRIX :' * WRITE(6,) ( ( INVCROM(I,J),Jsl,3), 1=1,3) * WRITE(6,*)' '

*__..___._____..-.-_-..-.-.-...--_____-__.____.-..-_-_....__. C OUTPUT OF TRANSFORMATION CONSTANTS WRITE(19,*) LABEL(JK) WRITE(19,*)XYZ(2,JK).CR(1,JK),CR(2,JK) WRITE(19,*)INVCROM(l,l),INVCROM(l,2),INVCROM(l.3) WRITE(19,*)INVCROM(2,l),INVCROM(2.2),INVCROM(2.3) WRITEd9,*)INVCROM(3,l),INVCROM(3,2),INVCROM(3,3)

*.____-.____._....-.--.--.-. -...._-._--_..--_-.__...___-

~~C INITIALIZE :~~

~~DO 212 K=1,N DO 214 J=l,3 = CMFRGB(J.K) ,0 214 CONTINUE 212 CONTINUE _..._____.______._.-.._-.----.-...._-__.-_---..--_-...... C CALCULATE THE RGB COLOR-MATCHING FUNCTIONS C FOR PLOTS~~

~~DO 22 K=1,N DO 23 J=l,3 DO 24 1=1,3~~

~~CMFRGB(J.K) = CMFRGB(J.K) ? INVCRO( J, I) *CMFXYZ(I,K)~~

~~24 CONTINUE 23 CONTINUE 22 CONTINUE~~

~~C- 214~~

~~C OUTPUT TO 3 SEPARATE FILES; USED FOH PLOTTING GRAPHS C AND ONE BIG FILE USED FOR COLORIMETRIC QUALITY FACTOR CALCULATION C WAVELENGTH V.S. COLOR-MATCHING FUNCTION~~

* 99 FORMAT(X.I3,X,F10.6,X,F10.6,X,F10.6) 99 FORMAT(X,I3,X,F12.7)

DO 30 1 = 1, N IWs 390 ? 10*1 WRITE(15,99)IW,CMFRGB(1,I) WRITE(16,99)IW,CMFRGB(2,I) WRITE(17,99)IW,CMFRGB(3,I) WRITE(23,*)CMFRGB(1,I),CMFRGB(2,I),CMFRGB(3,I) 30 CONTINUE CLOSE(23,STATUS='KEEP') J ASSURES STORING OF CMF FOR ONLY ONE COLOR

*- ....._____.__.__ * OUTPUT OF COLORS WITH STRANGE COLOR MATCHING FUNCTIONS

~~357 F0RMAT(7X,I3,X,2(1X,A))~~

- 771 F0RMAT(/,15X, ,/) IF(CMFRGB(1,22),LT.0.)THEN WRITE(21,771) WRITEC21,357)JK,LABEL(JK), RED COLOR-MATCHING FUNCTION' WRITE(21,*)' =' Y =',XYZ(2,JK),'X ,CR(1 , JK) , Y s-U,CR(2,JK) WRITE(21,*) ' CONCENTRATIONS: , (C(I) ,1=1 ,3) ELSEIF(CMFRGB(2,14).LT.0)THEN WRITE(21,771) WRITE(21,357)JK,LABEL(JK),' GREEN COLOR-MATCHING FUNCTION'

WRITE(21,*) -' ' Y si,XYZ(2,JK),'X ,CR(1 , JK) , Y =',CR(2,JK) WRITE(21,*)' CONCENTRATIONS: , (C( I) , 1=1 , 3) ELSEIF(CMFRGB(3,5).LT,0)THEN WRITE(21,77l) FUNCTION' WRITE(21357)JK,LABEL(JK) , BLUE COLOR-MATCHING WRITE(21,*)' s' ' Y s',XYZ(2,JK),'X ,CR(1 , JK) , Y s',CR(2,JK) WRITE(21,*)' CONCENTRATIONS: , (C(I) ,Isi ,3) ENDIF *__._._. -- C CALCULATE THE RGB COLOR-MATCHING FUNCTIONS * ILLUMINANT C THIS WILL BE USED TO DO THE ACTUAL COLOR REPRODUCTION

~~DO 250 K=1,N DO 260 J=l,3 ILLRGB(J,K)=0. 260 CONTINUE 250 CONTINUE *-~~

~~DO 25 K=1,N DO 26 J=l,3 DO 27 1=1,3~~

~~ILLRGB(J,K) = ILLRGB(J.K) + IHVCROMU, I) *ILLXYZ(I, K)~~

~~27 CONTINUE 26 CONTINUE 25 CONTINUE~~

*______---.

~~C OUTPUT OF (RGBCMF * ILL) FOR COLOR REPRODUCTION PURPOSES 215~~

FILE=' ILLRGB-W.DAT' ' ' OPEN (11, ,STATUS=NEW ) WRITEdl," (A) ' ) LABEL(JK) WRITE (11,*) XYZ(2,JK),CR(1,JK),CR(2,JK) DO 29 1=1, N WRITE(11,*)ILLRGB(1,I),ILLRGB(2,I),IL,,RGB(3,I) 29 CONTINUE CLOSE(ll,STATUS='KEEP' )

C- C OUTPUT TO DOCUMENTATION FILE *

~~WRITE(8,908) 908 FORMAT('l') i ALWAYS PRINTS AT TOP OF NEXT PAGE~~

~~WRITE(8,*) WRITE(8,*) '.DATFIL WRITEC8,*)'~~

~~WRITE(8,*)' '.LABEL1,' '.LABEL2~~

~~WRITE(8,)' WRITE(8,) SAMPLE : ',JK,' '".LABEL(JK) WRITEC8,*)'~~

~~WRITE(8,)' CROMATICITIES:~~

~~WRITE(8,*)'~~

~~=' WRITE(8,*)' '.'Y =',XYZ(2,dK).'X =',CR(1,JK),'Y ,CR(2,JK)~~

~~WRITE(8,*)'~~

~~WRITE(8,*)' TOTAL NUMBER OF ITERATIONS: ',ITER~~

~~WRITE(8,*)' ' WRITE(8,*)' CONCENTRATIONS , (C(I) ,1=1 , 3)~~

~~WRITE(8,*)'~~

~~WRITE(8,*)' Y.' WRITE(8,*)' PRIMARY CHROMATICITY COORDINATES, IN Y, X,~~

~~WRITEC8,*)'~~

~~WRITE(8,*)' '~~

WRITE(8,*)' ','RED Y s >, JAC(2,1)*(-1),'X = ',CROM(l,l), Y = ',CROM(2,D = WRITE(8,*)' ', 'GREEN Y = ', JAC(2,2)*(-1),'X ',CR0M(1,2), Y = ,CROM(2,2) WRITE(8,*)1 i < = JAC(2,3)*(-1),'X = , BLUE Y ',CROM(l,3), IY s ,CROM(2,3) WRITE(8,*)' VALUES' WRITE(8,*)' REFERENCE WHITE TRISTIMULUS

~~WRITE(8,*)' ' s ,XdYDZD(2) 'Z = ',XDYDZD(3) WRITE(8,*)' ','X s ',XDYDZD(t),'Y ,~~

~~WRITE(8,*)' C(J)' WRITEC8,*)' '.'TRANSFORMATION CONSTANTS,~~

~~WRITE(8,*)' s ',CRGB(2),'CB = WRITE(8,*)' ,'CR s ',CRG6(1),'CG ',CRGB(3)~~

~~WRITEC8,*)'~~

~~MATRIX' WRITEC8,*)' TRANSFORMATION~~

~~______------' WRITE(8,*)'~~

~~WRITEC8,*)' = WRITE(8,)' '.'All = ',INVCROM(l,l),'Al2 ',INVCROM(l,2),~~

~~'A13 = ',INVCROMd,3) C = WRITE(8,*)' ,'A21 ',INVCROM(2,l),'A22 ',INVCP0M(2,2).~~

~~r A23 = .INVCROM(2,3) = = ,INVCR0M(3,2) , WRITEC8,*)' ','A31 ,INVCROM(3, 1 ) , A32~~

~~C 'A33 = ,INVCROM(3,3) WRITE(8,*)' ' 216~~

~~WRITE(8, WRITE(8,* SPECTRAL SENSITIVITIES' WRITE(8, WRITE(8,* WRITE(8,* WAVELENGTH, NM B' WRITE(8,* WRITE(8,~~

~~44 F0RMAT(12X,I3,14X,F12.7,2X,F12.7,2X,F12,7)~~

~~DO 33 1=1, N IW= 390 ? 10*1 WRITE(8,44)IW,CMFRGB(1,I),CMFRGB(2,I),CMFRGB(3,I) 33 CONTINUE~~

~~CALCULATION OF AVERAGES~~

~~CAPX=CAPX+XYZ(1,JK) CAPY=CAPY*XYZ(2,JK) CAPZ=CAPZ*XYZ(3,JK)~~

~~AVCRXsAVCRX+CRd , JK) AVCRY=AVCRY*CRC2,JK)~~

~~AVPRCAPY=AVPRCAPY+JAC(2,1)*(-1.)~~

~~AVPRX=AVPRX*CROM (1 , 1 ) AVPRY=AVPRY*CROM(2,l)~~

~~AVPGCAPYsAVPGCAPY+JAC(2,2)*(-l.)~~

~~AVPGX=AVPGX+CROM d , 2 )~~

~~AVPGYsAVPGY+CROM (2 , 2 )~~

~~AVPBCAPYsAVPBCAPY+JAC(2,3)*(-l.) AVPBX=AVPBX*CROM(l,3) AVPBY=AVPBY+CROM(2,3)~~

~~WRITE(6,)'JK=',JK~~

~~888 CONTINUE NUXs NUX+NU-INOMATCH INOMATCHsO~~

~~WRITE(6,*)'DO YOU WANT TO DO MORE CALCULATIONS ? (Y/N)' READ(5,'(A)')ANSWER IF(ANSWER.EQ.'Y'. OR. ANSWER, EQ.'Y') GOTO 977~~

~~C OUTPUT SOURCE CROMATICITIES WRITE(6,) RIX.RIY i SCREEN WRITE(9,) RIX.RIY ! PRIMXY.DAT WRITE(20,) RIX.RIY ! COLORXY.DAT~~

*-__._.._.. - C OUTPUT OF THE ZERO LINE

~~DO 37 1=1, N DO 38 J=l,3 CMFRGB(J,I)=0,0 38 CONTINUE IW= 390 ? 10*1 WRITEdc,99)IW,CMFRGB(l,I) 217~~

~~WRITE(16,99)IW,CMFRGB(2,I) WRITE(17,99)IW,CMFRGB(3,I) 37 CONTINUE~~

~~AVC1=AVC1/NUX AVC2=AVC2/NUX AVC3=AVC3/NUX~~

~~WRITE(22,908) WRITE(22,*)'~~

~~WRITE(22,*)' AVERAGES'~~

~~WRITE(22,*)' WRITEC22,*)' '.'NAME OF LAST FILE , DATFIL WRITE(22,*)' WRITE(22,*)' '.LABELl,' '.LABEL2 WRITE(22,*)'~~

~~WRITE(22,*)' WRITE(22,*)' AVERAGE TRISTIMULUS VALUES; WRITE(22,*)' ------_ i~~

~~WRITE(22,*)'~~

~~WRITE(22,*)' ,'X si,CAPX/NUX,'Y st,CAPY/NUX,'Z s',CAPZ/NUX WRITE(22,*)' WRITE(22,*)' AVERAGE CHROMATICITIES FOR THOSE TRISTIMULUS VALUES: WRITE(22,*)'~~

~~WRITE(22,*)'~~

~~SUMA s l./(CAPX CAPY CAPZ) WRITE(22,*)' '.'Y =',CAPY/NUX,'X =',CAPx*SUMA,'Y =',CAPY*SUMA WRITE(22,*)'~~

~~WRITE(22,*)' WRITE(22,*)' AVERAGE CROMATICITIES:~~

~~WRITE(22,*)' -a------i~~

~~WRITE(22,*)'~~

~~WRITE(22,*)' '.'Y si,CAPY/NUX,'X =',AVCRX/NUX,'Y =',AVCRY/NUX~~

~~WRITE(22,*)'~~

~~WRITEC22,*)' AVERAGE'~~

~~WRITE(22,*)' ' CONCENTRATIONS , AVC1 , AVC2 , AVC3 WRITE(22,*)'~~

~~WRITE(22,*)' WRITE(22,*)' PRIMARY CHROMATICITY COORDINATES, IN Y, X, Y,' WRITE(22,*)' ------.------a------i~~

WRITE(22,*)' ' WRITE(22,*)' ,'RED Y s ', AVPRCAPY/NUX,'X s '.AVPRX/NUX, Y s ",AVPRY/NUX s = ' WRITE(22,*)' ', 'GREEN Y i, AVPGCAPY/NUX.'X .AVPGX/NUX, C Y = '.AVPGY/NUX WRITEC22,*)' ','BLUE Y = ', AVPBCAPY/NUX.'X = '.AVPBX/NUX, < C 'Y s ,AVPBY/NUX WRITEC22,*)' '

~~************************** ************************ ************************~~

' CLOSE (7 ,STATUS= KEEP ) NOMATCH.DAT CLOSE(8,STATUS='KEEP') DOC. DAT CLOSE(9,STATUS='KEEP) PRIMXY.DAT CLOSE(10,STATUS='KEEP') LAB. DAT CLOSE(14,STATUSs'KEEP') MODEXT.DAT CLOSEdS.STATUSs'KEEP') CMFR.DAT CLOSE(16,STATUSs'KEEP') CMFG.DAT CLOSE(17,STATUSs'KEEP') CMFB.DAT ' CLOSE(18 KEEP ) AVERAGES MATCH.DAT 218

~~CL0SE(19,STATU5='KEEP' ) TRANSFORMATION CONSTANTS TRANSF.DAT CLOSE(20,STATUS='KEEP' ) COLORXY.DAT CLOSE (21, ST ATUSs' KEEP') COLORS.DAT CLOSE(22,STATUS='KEEP')CLOSE(22,ST AVERAGES.DAT~~

*****************************************************<********************* WRITE(6,*)'

~~WRITE(6,*)'~~

~~WRITE(6,*)' THE CALCULATIONS ARE STORED IN THE FOLLOWING DATA FILES :' WRITE(6,*)' i WRITE(6,*)' DOC. DAT-DOCUMENTATION FILE'~~

WRITE(6,*)' _------____ i WRITEC6,*)' FILES FOR PLOTING GRAPHS :< WRITE(6,*) WRITE(6,*) CMFR.DAT WAVELENGTH AND COLOR-MATCHING FUNCTION' WRITE(6,*) CMFG.DAT -*- -- -- i WRITE(6,*) CMFB.DAT -- -- __ i WRITE(6,*)' CMFRGB.DAT -"- -- ALL 3' WRITEC6,*)' COLORXY.DAT CHROMATICITIES OF ORIGINAL COLORS' WRITE(6,*)' ODDCOLORS.DAT > COLORS THAT GIVE THE OPPOSITE CMF' WRITE(6,*)< MODEXT.DAT MODIFIED EXTINCTION COEFFICIENTS ' WRITE(6,*)' LAB. DAT L* A* B* COORD. FOR PRIMARIES' WRITE(6,*)' PRIHXY.DAT CHROMATICITIES OF PRIMARIES' ILLRGB-W.DAT SPECTRAL SENSITIVITIES FOR REPRODUCTION' MATCH.DAT LABELS, CONCENTRATIONS, NO. OF ITERATIONS'* NOMATCH.DAT LIST OF COLORS FOR WHICH THERE IS NO MATCH' WRITE(6,*) TRANSF.DAT TRANSFORMATION MATRIX FROM XYZ TO RGB' WRITE(6,) AVERAGES.DAT AVERAGE CHROMATICITIES, CONCENT. ETC.* GOTO 303

ERROR! 379 CLOSE(UNIT= 4,STATUS= ' DELETE' ) WRITE (6,1901) 1901 F0RMAT(/, IX, 'ERROR SPECIFYING FILE NAME',/. IX, 'WOULD YOU LIKE TO TRY ANOTHER NAME (Y OR N) ?',$) READ(5,'(A)') ANSWER IF(( ANSWER. EQ.'Y'. OR. ANSWER. EQ.'Y'). AND, COU.EQ. 2 )THEN GOTO 1009 ENDIF

303 STOP END ***********************************************************************

~~SUBROUTINE CROMAT(XYZ.CR.NU)~~

~~REAL XYZ(3,380),CR(3,380)~~

~~DO Ksl.NU CONST=l./(XYZ(l,K)+XYZ(2,K)+XYZ(3,K)) DO 1=1,3 CR(I,K)=XYZ(I.K)*CONST END DO END DO RETURN END 219~~

**********,******,*********,****,***,,*,*,,,

~~REPRODUCTION PROGRAM REP.fOk PAUL R. BARTEL~~

THIS PROGRAM CALCULATES THE SPECTRAL TRANSMITTANCE OF THE REPRODUCED COLOR USING A GIVEN SET OF COLOR-MATCHING FUNCTIONS (SENSITIVITIES) OF THE PRIMARIES DUE TO THE TRANSMITTANCE FUNCTION OF THE DYE IMAGE.

INPUT: SPECTRAL REFLECTANCE OF COLORS *************************************** ****************

~~INTEGER I,J, I COUNTER ? NU, J * OF SAMPLES FOR CALCULATION OF TRISTIMULUS VALUES ? N i # OF DATA POINTS IN ROW OR COLUMN~~

~~REAL ? SOURCE(80,80), 1 ILLUMINANT ? XDYDZD(3), ! XD YD ZD TRISTIMULUS VALUES OF ILLUMINANT ? SAMPLE(31,380), J SPECTRAL REFLECTANCE OF ORYGINAL COLOR~~

? CMFXYZ(3,80), COLOR-MATCHING FUNCTIONS X Y + ILLXYZ(3,80). COLOR-MATCHING FUNCTIONS XYZ ILLUMINANT ? CMFRGB(3,80), COLOR-MATCHING FUNCTIONS R G + ILLRGB(3,80), COLOR-MATCHING FUNCTIONS RGB ILLUMINANT

* EXT(80,3), EXTINCTION COEFFICIENTS

+ XYZ1(3,20), ! XYZ ORIGINAL TRISTIMULUS VALUES OF A COLOR + XYZ2(3,20), ! XYZ TRISTIMULUS VALUES UF REPRODUCTION ? RGB(3,20), 1 RGB TRISTIMULUS VALUES OF THE ORIGINAL COLOR + C(3), 1 CALCULATED CONCENTKATIONS ? T(80), I SPECTRAL TRANSMITTANCE OF COLOR FILM

? -I. 1 Y BAR VALUE OF ILLUMINANT ? ZK75), 1 X CHROMATICITIES OF LAMBDA ? Z2(7S), ! Y CHROMATICITIES Of LAMBDA + HISTOdOO), 1 HISTOGRAM ARRAY ? LABSK3), ! ORIGINAL L* A* B* COORDINATES ? LABS2(3) ! REPRODUCED L* A* B* COORDINATES

CHARACTER DATFIL*30, ? ANSWER*i, ? LABEL(380)*30, ? LABEL1*30, ! CHOICE OF FILM ? LABEL2*30, ! SCALED OR NOT ? LABELDE*32, ! LABEL FOR GRAYNESS THEST ? RFCOL*30 S NAME OF REFERENCE COLOR ************************************************************************** C INPUT OF NECESSARY DATA:

* -_

~~N = 31 COV=2. 302585 220~~

~~WRITE(6,54) 54 FORMAT(//,7X, 'FOR UNREPRODUCIBLE COLRS SPECIFY: (1 OR 2)', * //,7X,'l, SKIP REPRODUCTION OF THIS COLOR', * //,7X,'2. MAKE CONCENTRATION = 0 OR DMAX',//)~~

~~READ(5,*)A WRITEU,*)' IF(A.EQ.2)THEU WRITE(6,*)' ', 'INPUT VALUE FOR DMAX' READ(S,*)DMAX WRITE(6,*)' ' ENDIF~~

" - WRITE(6,55) 55 FORMAT(//,7X,'l. CONTRAST=l, LOG EXPOSUREsO', * //,7X,'2. SPECIFY YOUR OWN ?',//) READ(5,*) AB IF(AB.EQ.2)THEN WRITE(6,) 'SPECIFY CONTRAST ?' READ(5,*)GAM WR1TE(6,) 'SPECIFY LOG EXPOSURE ?' READ(5,*)ALF ELSE GAM=1. ALF=0. ENDIF

~~C XYZ COLOR-MATCHING FUNCTIONS:~~

~~FILEs ' STATUSs ' ' OPEN ( 1 , XYZ, DAT , OLD )~~

~~DO 1 1 = 1, N READd,*) CMFXYZ(1,I),CMFXYZ(2.I),CMFXYZ(3,I) CONTINUE~~

~~' CLOSE( 1, STATUSs' KEEP )~~

~~C RGB COLOR-MATCHING FUNCTIONS:~~

~~FILEs ' STATUSs OLD OPEN ( 1 , CMFRGB . DAT , )~~

~~DO 1=1, N READd,*) CMFRGB (1,1), CMFRGB (2, 1), CMFRGB (3, 1) END DO~~

~~STATUSs ' KEEP CLOSE ( 1 , )~~

* WRITE(6,*) ( ( CMFXYZ(I.J). J=1,N ), Isl,3)

~~c""intpu"of^rgbcm~*~illT"fur COLOR REPRODUCTION PURPOSES~~

~~' ' ILLRGB- STATUSs OLD ) OPEN (1 1 ,FILEs * . U AT ,~~

~~READ(ll,'(A)')REFCOL~~

~~READ(U,*)YC,XS,YS DO 29 Isl,N~~

~~READ(11,*)ILLRGB(1,1),ILLRGB(2,I),ILLRGB(3,I)~~

~~29 CONTINUE ' ' CLOSE (11, STATUSs KEEP )~~

~~" * 221~~

~~C CUTTING OFF THE NEGATIVE PARTS OF THE CMF~~

~~CALL NONEGCMF(ILLRGB,CMFHGB, CMFXYZ, CQR.CQG, COB)~~

~~OPEN(U,FILE='ZUPl.DAT' ' ,STATUS='NEW ) OPEN FILEs ' ' ' (111 , ZUP2 . DAT , STATUSs hEw ) WRITEdll,*) 'RGB NO NEGATIVE PARTS' WRITEdl,*) 'ILLRGB NO NEGATIVE PARTS'~~

~~DO 1=1, N WRITE(111,*)CMFRGB(1,I),CMFRGB(2,I),CMFRGB(3,I) WRITE (11,*) ILLRGB (1,1), ILLRGB (2, 1), ILLRGB (3, 1) END DO CLOSE(lll,STATUSs'KEEP') CLOSE (11, STATUSs ' KEEP ' )~~

~~C EXTINCTION COEFFICIENTS:~~

~~CALL EXTCOOEF (EXT.LABELl) *_. -.- _. * SCALING OF THE EXTINCTION COEFFICIENTS CALL SCALEX (EXT.LABEL2)~~

~~~ ~~ C WEIGHTS FOR ILLUMINANT * CMFXYZ :~~

~~CALL WEIGHTILL (ILLXYZ)~~

~~**************************************************************************~~

~~C PRELIMINARY CALCULATION OF THE TRISTIMULUS VALUES OF THE ILLUMINANT:~~

~~DO 4 1=1,3 l!!!!*!!!! = !!!!! 3*N DO 5 J = 1,N id!~~

~~XDYDZD(I) = ILLXYZ(I.J) + XDYDZD(I)~~

~~5 CONTINUE 4 CONTINUE~~

********i WRITE(6, *)'***** XDYDZD(I)

~~WRITE(6,*)' '~~

~~WRITE(6,*)'XD YD ZD WRITE(6,*)' '~~

~~WRITE(6,) (XDYDZD(I),I=1,3) C C CALCULATE SOURCE CROMATICITY COORDINATES: C RIM = XDYDZ0d)fXDYDZD(2)+XDYDZD(3) RIX = XDYDZD(1)/RIM RIY = XDYDZD(2)/RIM~~

~~***********************************************************************~~

~~C SAMPLE REFLECTANCE - TRANSMITTANCE C OPEN OUTPUT FILES FOR : ? - RESULTS OF CALCULATIONS SOURCE CROMATICITY " DAT L*B*A* * IN SPACE C LAB. DAT SAME AS ABOVE BUT~~

~~FILE=' STATUS='NEW') OPEN(8, LAB. DAT', 222~~

0PEN(9,riLE='CR0MATICITY.DAT' ,STATUSs'NEW') OPEN FILE= 'HUECOORD.DAT' STATUSs 'NEW' (10, , ) FILEs ' ' OPEN d 1 , SR ATIOL . DAT , STATUSs NEW ) OPEN ( 12, FILE=' LOVSLR.DAT' ,STATUS='NEW ) OPEN(13,FILE='HISTO.DAT' STATUSs' ' , NEW ) OPEN(14,FILE='STAT.DAT' STATUSs' ' , NEW ) OPEN(16,FILEs'CALC,UAT' STATUSs' ' , NEW )

~~WRITE(9,*) RIX.RIY OUTPUT SOURCE CROMATICITIES~~

~~IF(A,EO,2)THEN WRITE (14,*)' ', 'VALUE GIVEN FOR DMAX = '.DMAX ENDIF~~

~~IF(AB.EQ.2)THEN WRITE (14,*)" ' WRITE (14,*)' ', 'CONTRAST : ',GAM WRITE (14,*)' ' (14,*)' ' WRITE '.'LOG EXPOSURE: ,ALF WRITE (14,*)' ' ENDIF~~

C OUTPUT TO STAT. DAT A MESSAGE: CHOPPING OFF OF THE NEG. LOBES IF ( ILLRGB (1,13).GE.0.0) THEN WRITE (14,*)' WRITE (14,*)' ','THE COLOR MATCHING FUNCTIONS * HAVE NO NEGATIVE PARTS' WRITE (14,*)' ' FACTORS:' WRITE (14,*)' '.'COLORIMETRIC QUALITY (14,*)' ' WRITE '.'RED ,CQR WRITE (14,*)' ', 'GREEN '.CQG WRITE (14,*) ','BLUE '.CQB WRITE (14,*)' ENDIF

~~***********************************************************************~~

~~C INPUT SPECTRAL CURVES OF THE COLOR:~~

~~1001 WRITE(6,1010) 1010 FORMAT(/, /,/,/,/, IX, 'SPECIFY THE FILE NAME OF * THE SPECTRAL 11 CURVE',/,/, * 10X,' TO EXIT WRITE 1',/,/) READ(5,'(A)') DATFIL~~

~~*********************V**************************************************~~

~~IF(DATFILd:l).Q.'l') GOTO 880 ! EXIT PROGRAM~~

~~**************************************************************************~~

WRITE (14,*)' *,LABEL1 (14,*)' ' WRITE .,,--. (14,*)' ' FILE: WRITE , 'INPUT ', DATFIL ' WRITE (14,*)' (14,*)' COLOR: '.ReFCOL WRITE '. 'REFERENCE (14,*)' ' WRITE ',XS,' Y= (14,*)' .'Y= X= ',YS WRITE ',YC WRITE (14,473) 473 FORMAT(///)

~~STATUSs' OLD', ERR=379) N*NU OPEN (4, FILE=DATFIL, 223~~

~~NUsi ,,. ***************************************************,***********,***** DO 777 JK=1,5000 READ(4,'(A)',NDs880) LABEL(JK) WRITEdb,*) ' WRITE(16,*) ' i WRITE(16,*) ' ' WRITE(16,*) LABEL (JK)~~

~~Ksl DO 1=1, N READ(4,) SAMPLE (I,K) * WRITE(16,*) SAMPLE (I,K) END DO~~

~~IF( 5AMPLEd,K).GT.1.0.0R.SAMPLE(15,K),GT.1.0 )THEN~~

~~DO 72 1=1, N SAMPLE(I.K) = SAMPLE(I,K)/100. 72 CONTINUE~~

~~ENDIF * END DO~~

*. .. C COMPUTE SPECTRAL RESPONSES TO THE ORIGINAL STIMULUS:

CALL TRIST1 (SAMPLE, ILLRGB, RGB, NU.N.l) ! FILM (RGB) CALL TRIST1(SAMPLE,ILLXYZ,XYZ1,NU,N,1) ! EYE (XYZ) CALL LAB(XYZ1,XDYDZD,LABS1) ! L*A*B*

~~WRITE(16,*) 1 WRITE(16,*) 'THE RESPONSES:' WRITE(16,*)'RED = '. RGBd.l) WRITE(16,) 'GREEN = ', RGB(2,1) WRITE(16,*)'BLUE s , RGB(3,1)~~

*_._._.____ C COMPUTE MATCHING CONCENTRATIONS OF FILM:

~~IF(A.EQ.1)THEN DO 1=1,3~~

IF(RGB(I,l),LE.0.OR, RGB(I, 1) .GT, 100. )THEN WRITE(16,*)' WRITE (16,*) I*****************************' WRITE(16,*)LABEL(JK),RGB(I,1) WRITE(14,*)' ',LABEL(JK) WRITE(16,*)'THIS COLOR IS NONREPRODUCABLE IUNMATCH s IUNMATCH +1 WRITE (16,*) *****************************' WRITE(16,*)' '

~~GOTO 777 ENDIF END DO - *.__...._... - -~~

~~DO 1=1,3 Cd) = - GA* * LOG10( RGB(I,1)/100. ) ALF END DO 224~~

~~ELSE DO 1=1,3 IF(RGB(I,1).LE.10**(-DMAX) )THEN Cd) = DMAX ELSEIF(RGB(I,1).GT.100)THEN C(I)=0. ELSE C(I) = - GAM * LOG10( RGB(I,1)/100, ) + ALF ENDIF END DO~~

~~ENDIF~~

~~WRITE(16, i t WRITE(16,* 'THE concentrations:' * WRITE(16, WRITE(16, RED ',C(D WRITE(16,* WRITE(16,* ' GREEN *,C(2) * WRITE(16, WRITE(16,* BLUE ',C(3) WRITE(16,* i i *-~~

~~C COMPUTE SPECTRAL TRANSMITTANCE OF THE FILM:~~

~~DO 6 J=1,N~~

~~T(J)= EXP( -COV*( EXT(J,1)*C(1) ? EXT(J,2)*C(2) + EXT(J,3)*C(3) ) )~~

~~6 CONTINUE *_ C COMPUTE SPECTRAL RESPONSES OF THE EYE TO THE REPRODUCTION:~~

~~CALL TRIST1(T,ILLXYZ,XYZ2,NU,N,1) CALL LAB(XYZ2,XDYDZD,LABS2)~~

~~**************************************************************************~~

~~C CREATE OUTPUT FOR GRAPHS:~~

~~*__...------C A* B* PLANE: C L* A* B*~~

COORDINATES' WRITE(16,*)' L* A* B*

~~'ORIGINAL' WRITE(16,) WRITE(16,*)' ', LABS1(1),LABS1(2),LABS1(3) WRITE(16,*) 'REPRODUCED WRITE(16,*)' ' LABS2(1),LABS2(2),LABS2(3)~~

~~A* B* CONNECT THOSE POINTS c WRITE(8,*) LABS1(2),LABS1(3) WRITE(B,*) LABS2(2),LABS2(3) ------* HISTOGRAM C DELTA E, COLOR DIFFERENCE FOR~~

~~(LABS1(1)-LABS2(1))**2 ? (LABS1 (2)-LABS2(2) ) **2 ? DE = SQRT( * (LABS1(3)-LABS2(3))**2 )~~

~~0,0001 )THEN IF( SQRT(LABS1(2)**2+LABS1(3)**2) .LT. 225~~

~~GRAYFLAGsl DE s SQRT((LABS1(1)- LABS2(1))**2 ? LABS2(2)**2 ? LABS2(3)**2 ) IF(DE.GT.,003)THEN i LABELDE s REPRODUCED COLOR Is NOT A GRAY' ENDIF ENDIF~~

~~WRITE(16,*)' '~~

~~WRITE(16,*)'DE =',DE WRITE(16,*)' '~~

~~= INDEX INT((DE ? .5)/. 5) HISTO(INDEX) = HISTO(INDEX) ? 1~~

~~IF(GRAYFLAG,EQ.1)THEN WRITE(14,*)' , LABELDE LABELDEs' ' ENDIF~~

~~WRITE(14,*)' ,LABEL(JK),*DE =',DE~~

~~AVDE = AVDE ? DE SAVDE = SAVDE ? DE**2~~

- * . .. C HUE CIRCLE: IFCGRAYFLAC.NE.DTHEN IF( LABS1(2).GT.0.0 )THEN ANGO = ATAN(LABS1(3)/LABS1(2)) ELSEIF( LABS1(2),EQ,0.0.AND.LABS1(3),GT,0.0)THEN ANGO = 3.14159265/2. ELSEIF( LABSl(2).EQ.0.0.AND.LABSl(3),LT.O.O)THEN ANGO = 3.14159265/2. ? 3.14159265 ELSEIF( LABS1(2).EQ.0.0,AND.LABS1(3),EQ.0.0)THEN ANGO s 0.0 ELSE ANGO s 3,14159265 ? ATAN(LABS1 (3)/LABSl (2) ) ENDIF ** ** ** IF( LABS2(2).GE,0.0 )THEN ANGR ATAN(LABS2(3)/LABS2(2)) ELSE ANGR > 3.14159265 ? ATAN(LABS2(3)/LABS2(2) ) ENDIF

~~WRITE(16,*)' ANGO', ANGO,' ANGR', ANGR 'ANGO' ' ' WRITE(16,) ,ANG0*57. 2957795, ANGR ,ANGR*57 .2957795~~

~~Rl=40. R2=60.~~

~~XTO = Rl * COS(ANGO) ! A* YTO = Rl * SIN(ANGO) ! B* WRITEdO, *)XTO,YTO 1 ORIGINAL HUE COORDINATE~~

~~XTO s R2 * COS(ANGR) ! A* YTO = R2 * SIN(ANGR) ! B* WRITEdO, *)XTO, YTO I REPRODUCED HUE COORDINATE~~

~~--- *-__ _-. SATURATION RATIO: C REP. L* V.S. 226~~

~~IF(LABS1(2).EQ.O.O,AND.LABS1(3).EO.O.O)THEN~~

~~SRATIO s 10000 ELSE SRATIO s (5QRT(LABS2(2)**2+LABS2(3)**2))/ * (SQRT(LABS1(2)**2+LAB51(3)**2)) ENDIF~~

~~AVSRATIO s AVSRATIO + SRATIO SDSRATIO = SDSRATIO ? SRATIO**2~~

~~WRITEdl,*) SRATIO, LABS2(1) ENDIF GRAYFLAG=0~~

~~" """ C L REP, V.S, ORIG. L* :~~

~~WRITE(12,) LABS1(1),LABS2(1)~~

*-- . C OUTPUT TO THE SCREEN

~~WRITE(16,*)'~~

~~WRITE(16,) 'TRISTIMULUS VALUES FOR THE SAMPLE ARE:' WRITE(16,*)' WRITE(16,*)((XYZKI,J),Isi,3),Jsl,NU)~~

~~WRITE(16,*)'~~

WRITE(16,*) 'TRISTIMULUS VALUES FOR THE REPRODUCTION ARE: WRITE(16,*)' ' WRITE(16,*)((XYZ2(I,J),I=1,3),J=1,NU) a******************,*****,***,****************************,,*,, C OUTPUT TO THE SCREEN

* DO 28 1=1, N * IWs 390 ? 10*1 * WRITE(6,99)IW,CMFRGB(1,I),CMFRGB(2,I),CMFRGB(3,I) * 28 CONTINUE

***********************************************,************,*, 777 CONTINUE ************************************************************************** GOTO 1001 ***************************************************,**** ******* ********* 880 NU=JK-1 CLOSE(4,STATUS='KEEP')

~~DO INDEX=1,100 WRITE (13,*) INDEX*. 5, HISTO(INDEX) END DO * NT=NU-IUNMATCH~~

~~AVDE=AVDE/NT AVSRATIO=AVSRATIO/NT~~

~~WRITE(14,*)' '~~

~~',' WRITE(14,*)' AVERAGE DELTA E '.AVDE WRITE(14,*)' 227~~

~~IF(NU.GT.1)THEN WRITE(14,*)' ', 'DELTA E STANDARD DEVIATION s ', SQRT( (SAVDE- NT*(AVDE**2) )/ (NT-1) )~~

~~SDEVSRs - SQRT( (SDSRATIO NT*(AVSRATIO**2) ) / (NT-t ) ) ENDIF WRITEC14, WRITE(14, WRITE(14, ' WRITE(14, '.'AVERAGE SATURATION RATIO: .AVSRATIO WRITE(14,*) ' IF(NU.GT.1)THEN~~

~~= 1 WRITE(14, ','SATUR. RATIO SDEV. ,SDEVSR ENDIF WRITE(14, WRITEC14, WRITE(14, WRITE(14, ',' * OF UNREPRODUCIBLE COLORS: ', IUNMATCH WRITE(14, WRITE(14, ',' TOTAL OF COLORS: ",NU WRITE(14,~~

~~CLOSE ( 8, STATUS: 'KEEP') CLOSE ( 9, STATUS: 'KEEP') CLOSE( 10, STATUS: KEEP') CLOSE ( 11, STATUS: KEEP') CLOSE ( 12, STATUS: 'KEEP') CLOSE ( 13, STATUS: 'KEEP') CLOSE ( 14, STATUS: 'KEEP')~~

~~WRITE(6,*)'~~

~~WRITE(6,*)THE CALCULATIONS ARE STORED IN THE FOLLOWING DATA FILES : ' WRITE(6,*)' i WRITE(6,*)''DOC, DAT-DOCUMENTATION FILE' WRITE(6,*)'~~

WRITE(6,*)' WRITE(6,*)''FILES FOR PLOTING GRAPHS I' WRITE(6,*) WRITE(6,*)''LAB. DAT L*A*B* SPACE' WRITE(6,*)'CHROMATICITY.DAT CHROMATICITY DIAGRAM' WRITE(6,*)''HUECOORD.DAT FOR HUE CIRCLE' WRITE(6,*)'LOVSLR.DAT L* ORIG. V.S. L* REP.' WRITE(6,*)''HISTO.DAT DEL. E HISTOGRAM' WRITE(6,*)''STAT. DAT STATISTICS DELT E' WRITE(6,*)'SRATIOL.DAT REP. LIGHTN. V.S. SATUR. RATIO' WRITE(6,*)'CALC.DAT CALCULATIONS OF L* A* B* ETC.'

~~WRITE(6,*)'~~

GOTO 303 379 CL05E(UNIT= 4,STATUS='DELETE*) WRITE (6,1901) 1901 FORMAT(/, IX, 'ERROR SPECIFYING FILE NAME',/ IX, 'WOULD YOU LIKE TO TRY ANOTHER NAME (Y OR N) ?',S) READ(5,'(A)') ANSWER IF( ANSWER. EQ.'Y'. OR, ANSWER. EQ.'Y')THEN GOTO 1001 ENDIF

~~303 STOP 228~~

~~C CHOPPING OFF OF THE NEGATIVE LUBES OK (KGbCMKlLL)~~

~~SUBROUTINE !40NEGChF( ILLRGB, CMKRGB.CMt XYZ, CQh , COG, COB )~~

REAL + ILLRGBC3,U0), ! COLOR-MATCHING FUNCTIONS RGB * iLbUhlNAMT ? CMFRGB(3,B0), ! CULUK-MATCHING FUNCTIONS R, G, B CMFXYZC3.60), I CuLuR-HATCHING tUt.CTIUNS X, Y, Z ? CQC3,B0), 1 ORTHUGONAi. COLOR IMlxTURt CUHVtS ? M(3,3) ! ORTHOGONAL COLOR MIXTURE MATRIX

~~N = 31 COV=2. 302585 M(l,l)=-.4066 M(2,l)=.4066 M(3,l)=-.1791 MCI, 2)=. 5521 M(2,2)a-,0433 M(3,2)s,1018 MC1,3)=0. MC2,3)*0. MC3,3)=,281~~

~~WRITE( 6 175) 175 FORMATC/.1X, 'DO YOU WANT TO CHOP OF* IHE NEGATIVE LOBES ?' * OF RGBCMF*ILL ,/,/)~~

~~READ(S,'(A)') ANSWER~~

~~EQ.'Y1 ' * )ThEN IF(ANSWER. .OR. ANSHER ,E0, Y~~

~~R = .0~~

~~G s ,0~~

~~8 = .0 DO 30 1 = 1, N~~

~~IF(ILLRGBU,I).LT.O.O)THEN ILLRGBd, I) = 0.0 CMFRGB(1,I)=0,0 ENDIF~~

~~IFCILLRG8(2,I),LT.0.0)THEN~~

~~ILLRGB(2,I)=0.0 CMFRGB(2,I)=0.0 ENDIF~~

~~IF(ILLRGB(3,I).LT,0.0)THEN~~

~~ILLRGB(3,I)=0,0 CHFPGBC3,I)=0.0 ENDIF~~

~~R a R ? ILLRGBd, II G * G ? ILLRGB(2,I) B = B ? ILLRGb(3,I)~~

~~RED = RED ? CMFRGBC1.I) GHEEN s GREEN ? CMFRGB(2,1) BLUE = BLUE + CNFRG3(3.I)~~

~~30 CONTINUE 229~~

~~C INVERSE MATRIX CALCULATION AINV.FOK~~

~~SUBROUTINE AINV(XI.C)~~

~~REAL C(3,3),XI(3,3),X(3,3),RP,A~~

~~INTEGER I, J~~

~~C SUBSTITUTION OF INTERNAL MATRIX FOR INPUT MATRIX C IN CASE IF INPUT MATRIX IS TO REMAIN UNCHANGED~~

~~OO 1 1=1,3 DO 2 J=l,3~~

~~X(I,J)=XI(I,J)~~

~~2 CONTINUE 1 CONTINUE~~

~~C CALCULATION OF THE DETERMINANT A OF MATRIX X~~

~~SI = X(2,2)*X(3,3)-X(3,2)*X(2,3) S2 X(2,1)*X(3,3)-X(3,1)*X(2,3) S3 X(2,1)*X(3,2)-X(3,1)*X(2,2)~~

~~A = ( X(l,t)*Sl - X(1,2)*S2 i>X(l,3)*S3 )~~

* WRITE(6,*)'As ',A

~~C CALCULATION OF THE ADJOINT MATRIX C INTERCHANGE THE ROWS WITH COLUMNS~~

~~DO 3 1=1,2 DO 4 J=I+1,3~~

~~RP=X(I,J) X(I,J)=X(J,I) X(J,I)=RP~~

~~4 CONTINUE 3 CONTINUE~~

~~C CALCULATION OF THE COFACTORS~~

~~C(l,l)sX(2,2)*X(3,3)-X(3,2)*X(2,3) C(l,2)s(-l)*(X(2,l)*X(3,3)-X(3.1)*X(2,3)) C(l,3)sX(2,l)*X(3,2)-X(3,l)*X(2,2)~~

~~C(2,1)=(-1)*(X(1,2)*X(3,3)-X(3,2)*X(1,3)) C(2,2)=X(1,1)*X(3,3)-X(3,1)*X(1,3) C(2,3)=(-1)*(X(1,1)*X(3,2)-X(3,1)*X(1,2))~~

~~C(3,1)=X(1,2)*X(2,3)-X(2,2)*X(1,3)~~

~~CC3,2)s(-l)*(X(l,l)*X(2,3)-X(2,l)*X(l,3))~~

~~C(3,3)sX(l,l)*X(2,2)-X(2,l)*X(l,2)~~

~~C DIVIDE THE ADJOINT MATRIX BY THE DETERMINANT~~

~~Asl./A DO 10 1=1, 3~~

~~DO 20 J=l, 3~~

~~C(I,J) = C(I,J)*A~~

~~20 CONTINUE 10 CONTINUE~~

~~RETURN END 230~~

~~***************************************~~

~~L*A*B* SUBROUTINE~~

LAB. FOR ***************************************

~~SUBROUTINE LAB(XYZ,XDYDZD,LABS)~~

~~REAL XYZ(3),LABS(3),R(3),F(3),E,A,ALF,B,XDYDZD(3)~~

~~E=. 008856~~

~~DO 1 1=1,3 R(I)=XYZ(I)/XDYDZD(I) 1 CONTINUE~~

~~IF(R(2).GT,E)THEN A=116. ALF=l./3. B-16. ELSE AS903.3 ALF=1. B=0.0 ENDIF~~

~~LABS(i)=A*(R(2))**ALF + B~~

~~DO 3 1=1,3~~

~~IF(R(I).GT.E)THEN~~

~~A=l. ALF=l./3. B=0~~

~~ELSE~~

~~A=7.787 ALF=1.0 B=16/116~~

~~ENDIF~~

~~F(I)=A*(R(I))**ALF ? B~~

~~3 CONTINUE~~

~~LABS(2)=500.0*(F(1)-F(2))~~

~~LABS(3)s200.0*(F(2)-F(3))~~

~~RETURN END 231~~

~~***********************************************~~

~~OL*A*B* SUBROUTINE I DLAB.FOR~~

~~PAUL R. BARTEL COMPUTES PARTIAL DIFFERENTIALS~~

~~OF L* A* B* WITH RESPECT TO~~

~~CONCENTRATIONS.~~

~~***********************************************~~

~~SUBROUTINE DLAB(XYZ,XDYDZD, JACDLABS)~~

~~REAL~~

~~1 INPUT: ? XYZ(3), ! X Y Z TRISTIMULUS VALUES ? JAC(3,3), ! JACKOBIAN ? XOYDZD(3), ! ILLUMINANT TRISTIMULUS VALUES~~

~~OUTPUT : ? DLABS(3,3), PARTIAL DERIVATIVES~~

~~INTERNAL VARIABLES~~

~~i ? R(30, RATIOS : X/XD, ETC. < + DF(3,3), PARTIAL DERIVATIVES OF FUNCTIONS ? E, I BOUNDRY VALUE i ? A, COEFFICIENT ? ALF, I COEFFICIENT i ? B, COEFFICIENT ? S INTERMEDIATE VALUE~~

~~=.008856~~

* WRITE(6,*) i i ARE' * WRITE(6,*) 'THE RATIOS

~~DO 1 1=1,3 R(I3=XYZ(I)/XDYDZD(I) WRITE(6,*) R(I) CONTINUE WRITE(6,*)' '~~

~~IF(R(2).GT.E)THEN A=U6. ALF=l,/3, B=-16. ELSE A=903.3 ALF=1 B=0.0 232~~

~~ENDIF~~

~~S=A*(R(2))**ALF DO 2 J=l,3 DLABS(l,J)r-S * ALF * (l./XYZ(2)) * JAC(2,J) 2 CONTINUE~~

~~DO 3 1=1,3~~

~~IF(R(I).GT,E)THEN~~

~~A=l ALF=l./3, B=0~~

~~ELSE~~

~~A=7.787 ALF=1.0 B=16/116~~

~~ENDIF~~

~~S=A*(R(2))**ALF DO 4 J=l,3 DF(I,J) = S * ALF * d,/XYZ(D) * JAC(I,J) 4 CONTINUE~~

~~3 CONTINUE~~

~~DO 5 J=l,3 DLABS(2,J) = 500,0*(DF(i,J)-DF(2,J)) DLABS(3,J) = 200,0*(DF(2,J)-DF(3,J)) 5 CONTINUE~~

~~RETURN END 233~~

~~************************************************* C TRISTIMULUS CALCULATION TRIST1.FOR * C WRITTEN BY PAUL R. BARTEL * ********** ****i- **********************************~~

~~SUBROUTINE TRIST1 (SAMPLE, ILLCMF, XYZ, NU,N ,OU )~~

~~INTEGER N, ? NU, ! TOTAL * OF SAMPLES ? OU ! WRITE OUTPUT Y=0, NOsl~~

REAL ? LAMBDA(80), ! WAVELENGTH ? ILLCMF(3,80), ! XYZ COLOR-MATCHING FUNCTIONS * ILLUM + XYZ(3,180), ! XYZ TRISTIMULUS VALUES + SAMPLE(31,380), i SPECTRAL REFLECTANCE OF THE SAMPLE ? KA, ! SCALING COEFFICIENT ? CR(3,380), ! CHROMATICITY COORDINATE ? CONST, 1 CONSTANT + SOURCE(80) 1 ILLUMINANT

~~****************************************************~~

~~C CALCULATION OF TRISTIMULUS VALUES * KA=0.0 * WRITE(6,*)'*TRIST2* ',( (ILLCMFd, J) , Jsl ,N) ,1=1 , 3)~~

* DO 5 J=1,N 1 SCALING CONSTANT * KA=KA*ILLCMF(2,J) * 5 CONTINUE * KAslOO./KA

~~C RESETING OF THE VALUES X,Y,Z~~

~~DO 1 1=1,3 DO 2 K=1,NU XYZ(I,K)sO,0 2 CONTINUE 1 CONTINUE~~

DO 10 lsl,3 li!!Jl!*!!!=!!!!J 3*NU DO 15 K=1,NU Id DO 16 Jsl,N Hi XYZ(I,K)s XYZ(I,K) ILLCMFd, J)*SAMPLE(J,K) 16 CONTINUE * XYZ(I,K)sKA*XYZ(I,K) 15 CONTINUE 10 CONTINUE **************************************************

~~C CALCULATION OF CHROMATICITY COORDINATES DO 11 K=1,NU~~

~~CONST=l/(XYZd,K)+XYZ(2,K)*XYZ(3,K))~~

~~DO 12 1=1,3 CR(I,K)=XYZ(I,K)*CONST~~

~~12 CONTINUE~~

************************************************** 234

~~C OUTPUT IF(OU,EQ.0)THEN~~

~~WRITE(6,*)' '~~

~~TRIST1' WRITE(6,*) 'BEGIN WRITE(b,)'~~

~~WRITE(6,*)' '~~

~~VALUES:' WRITE(6,) 'TRISTIMULUS WRITE(6,*)'~~

~~WRITE(6,*)'X= ',XYZ(1,K) WRITE(6,*)'Y= ',XYZ(2,K) WRITE(6,*)'Zs ,XYZ(3,K)~~

~~WRITE(6,*)'~~

~~WRITE(6,) 'CHROMATICITY COORDINATES' WRITE(6,*)' '~~

~~WRITE(6,*)'Xs ,CR(1,K) WRITE(6,*)'Y= ,CR(2,K) WRITE(6,*)Zs ,CR(3,K) ENDIF 11 CONTINUE~~

~~IF(OU.EQ,0)THEN~~

~~WRITE(6,*)' ' ' WRITE(6,*)'END TRIST1~~

~~WRITE(6,*)'~~

~~ENDIF RETURN END 235~~

******************************************************* WEIGHTILL.FOR

~~PROGRAM TO INPUT WEIGHTS OF ILLUMINANTS~~

~~PAJL R. BARTEL~~

~~*******************************************************~~

~~SUBROUTINE WEIGHTILL (ILLXYZ)~~

~~******** *********~~

~~INTEGER I,J, 1 COUNTER ? N, ! OF DATA POINTS IN ROW OR COLUMN + ANS~~

~~REAL ? ILLXYZ(3,80) COLOR-MATCHING FUNCTIONS XYZ * ILLUMINANT~~

~~************************************************************************** C INPUT OF NECESSARY DATA: *~~

~~Ns3l~~

~~: WEIGHTS FOR ILLUMINANT * CMFXYZ :~~

~~WRITE (6 11. 11 F0RMAT(1X,//, 'WHICH ILLUMINANT TO USE ?? ',//,lX, '1. A',//, IX, 2. C',//,1X, '3. D65',//,1X, 4, F2',//,20X, 'PICK ONE.',//)~~

~~READ(5,*) ANS~~

IF(ANS.EQ.1)THEN OPEN (3, FILEs 'ILLA-W, DAT', STATUSs 'OLD') ELSEIF(ANS,EQ.2)THEN OPEN (3, FILEs 'ILLC-W, DAT ', STATUSs 'OLD') ELSEIF(ANS,EQ,3)THEN OPEN(3,FILEs'ILLD65-W,DAT',STATUSs'OLD') ELSE ' ILLF2- ' ' .DAT STATUSs DATA OPEN ( 3 , FILE= W , OLD ) ! FOR PETER'S ENDIF

~~DO 3 Isl,N READd, *) ILLXYZ(1,I),ILLXYZ(2,I),ILLXYZ(3,I) CONTINUE~~

~~CLOSE(3,STATUS='KEEP') !!!! WRITE(6,) (SOURCE(l,I),Isl,N)~~

~~RETURN END 236~~

************ v***************************************^*,,

~~SUBROUTINE YXY.FOR~~

~~INPUT OF Y X Y FOR : MAIH.FOR~~

~~PAUL R. BARTEL~~

~~****************************************** ***********, SUBROUTINE SUBYXY (XYZ, NU, LABEL, DATFIL) **************************************************************************~~

INTEGER I,J, 1 COUNTER ? NU, ! OF SAMPLES FOR CALCULATION OF TRISTIMULUS VALUES ? N, ! OF DATA POINTS IN ROW OR COLUMN ? COU, J COUNTER ? DIGITS, ! USED IN FORMAT STATEMENT + SPACES ! USED IN FORMAT STATEMENT

~~REAL + XYZ(3,380) ! XYZ TRISTIMULUS VALUES OF COLORS~~

~~CHARACTER DATFIL*30, ANSWER*1,LABEL(180)*30~~

************************************************************************** C INPUT OF Y X Y OF REAL OBJECTS AND CONVERSION TO XYZ

~~WRITE(6,70) 70 FORMAT(//, IX, 'CHOSE INPUT:',//, * IX, '1. FILE NAME WITH (Y, X, Y, LABEL) ?',//, * IX,' OR',//, * IX, '2. INPUT Y, X, Y, BY HAND',//)~~

~~READ (5,*)ANS IF ( ANS.EQ.DTHEN WRITE(6,71) 71 F0RMAT(/,1X, 'GIVE: FILE NAME WITH (Y, X, Y, LABEL)',//) READd, '(A)') DATFIL OPEN (l.FILEsDATFIL, STATUSs 'OLD')~~

~~ARE:' WRITE(6,*)'THE XYZ VALUES OF THE SAMPLE SET~~

~~WRITE(6,*)'~~

*._.._._____...--..-..- . ---

~~DIGITSsS SPACESs2~~

~~GO TO 144~~

~~22 DIGITS=4 SPACESsl REWIND 1~~

~~144 DO 12 Isl,400~~

~~READ(1, 72, ERR=22,END=222) XYZ(2,I), XYZd.D, XYZU.I), LABEL(I) 72 FORMAT(F,,X,Fb.4,X,F5.4,X,A30)~~

* WRITE(6,*) LABEL(I) * WRITE(6,) XYZ(2,I),XYZ(1,I),XYZ(3,1) 237

~~XTEM = XYZ(2,I)*XYZd,I)/XYZ(3,I) XYZ(3,I) = XYZ(2,I)*( 1. - XYZd.I) - XYZ(3, I) )/XYZ(3, I) XYZ(1,I) s XTEM~~

* WRITE(6,*) XYZ(l.I), XYZ(2,I), XYZ(3,I) 12 CONTINUE *-

~~222 NU= I - 1 WRITE(6,*)'NU=',NU~~

~~STATUSs ' ' CLOSE ( 1 , KEEP )~~

~~ELSE~~

~~1 = 1 WRITE(6,73) 73 F0RMAI(//,1X,'GIVE : Y, X, Y, ?',//)~~

~~READ(5,) XYZ(2,I), XYZd.I), XYZ(3,Z) WRITE(6,*)'GIVE I LABEL ?' WRITE(6,*)'_ READ(5,'(A)') LABELd) DATFIL=LABELd)~~

~~XTEM = XYZ(2,I)*XYZ(1,I)/XYZ(3,I) XYZ(3,I) = XYZ(2,I)*( 1. - XYZd.l) - XYZ(3,I) )/XYZ(3, I) XYZ(1,I) s XTEM~~

* WRITE(6,) I, XYZd.I), XYZ(2,I), XYZ(3,I) NU=1 ENDIF

~~**************************************************************************~~

~~RETURN END 238~~

~~*******************************************************~~

~~NEWTON-RAPSON SUBROUTINE~~

~~NR.FOR~~

~~THIS SUBROUTINE COMPUTES THE MATCHING DYE~~

~~CONCENTRATIONS FOR A GIVEN SET OF XYZ VALUES~~

REQD. SUBROUTINES: LAB, TRIST1, DLAB, AINV, ********************************************************

~~XYZ SUBROUTINE NR (LABEL , , JAC , N , XDYDZU , EXT , ILLCMF , EPS , C , ITER , NO )~~

~~INTEGER~~

* I,J,N,NU,K, 1 COUNTERS * ITER, ! * OF ITERATIONS ? NO ! NO MATCH INDICATOR

~~REAL ! INPUT :~~

? XYZ(3), ! XYZ, OF THE COLOR TO BE MATCHED + EXT(80,3), 1 EXTINCTION COEFFICIENTS + ILLCMFd, 80), ! COLOR-MATCHING FUNCTIONS * ILLUMINANT -> XDYDZDd), ! TRISTIMULUS VALUE OF ILLUMINANT ? EPS, 1 TOLERANCE OF THE COLOR MATCH

~~! OUTPUT :~~

~~? JAC(3,4). ! JACKOBIAN ? C(3), DYE CONCENTRAIONS C ? ITER, ! OF ITERATIONS (INTEGER) c ? NO ! NO MATCH INDICATOR (INTEGER)~~

~~1 INTERNAL VARIABLES :~~

MIXURE ? T(80), ! TRANSMITTANCE OF DYE ? DELTA (3), 1 COLOR DIFFERENCES ? DLABS(3,3), PARTIAL DIFFERENTIALS MATRIX MATRIX ? INVDLABS(3,3), 1 INVERSE OF PARTIAL DIFF. ? XYZ2(3), ! RGB VALUES OF THE DYE MIXTURE ? INVJAC(3,3), ! INVERSE OF JACKOBIAN CONCENTRATION ? DC(3), ! INCREMENT OF DYE L*A*B* COLOR ? LABK3), ! OF ORYGINAL L*A*B* MATjCHED COLOR * LAB2(3) ! OF

~~CHARACTER DATFIL*8, ANS*1, LABEL*30~~

~~**************************************************************************~~

~~CON=2. 30258509 NO=0 * WRITE(6,*)' 1' * WRITE(6,*)'NEWTON RUNNING * WRITE(6,*)' '~~

~~ITER=0 239~~

DO 1 1=1,3 Cd)=0. * C(I)=1/ (2*LOG10(XYZ(2))) 1 CONTINUE * WRITE(6,*) 'STARTING CONCENTRATION: ",C(1) * WRITE(6,*)' ' ______C FIND L*A*B* CHROMATICITY CO0RDINATEs"of"oRYGINAL_COLOR c CALL LAB(XYZ,XDYDZD,LAB1) * WRITE(6,*) 'ORYGINAL L* A* B*' * WRITE(6,*) (LAB1(I),I=1,3) * WRITE(6,*)'

~~C CALCULATE FILM TRANSMITTANCE~~

~~100 B1=0 B2=0 B3 = 0 * WRITE(6,*)'BACK IN THE LOOP'~~

~~DO 2 Jsl,N~~

~~T(J) s EXP( -CON*( EXT(J,1)*C(1) ? EXT( J,2)*C(2) ? + EXT(J,3)*C(3) ) )~~

~~B1=B1*T(J)*ILLCMF(1,J) B2=B2*T(J)*ILLCMF(2,J) B3=B3+T(J)*ILLCMF(3,J)~~

~~2 CONTINUE~~

* WRITE(6,*)' * WRITE(6,*) 'Bl=',Bl * WRITE(6,*)'B2=',B2 'B3=' * WRITE(6,*) ,B3 * WRITE(6,*)' '

*******""~CALCULATE TRISTIMULUS VALUES OF ThE NEW~DYE MIXTURE

NUsl CALL TR1ST1(T,ILLCMF,XYZ2,NU,N,1) ! IsNO OUTPUT * WRITE(6,) 'THE NEW TRISTIMULUS VALUES ARE : ' * WRlTE(6,*)(XYZ2(I),lsl,3) * WRITE(6,*)' ' *______-_ C FIND L*A*B* CHROMATICITY COORDINATES OF THE NEW DYE MIXTURE

~~CALL LAB(XYZ2,XDYDZD,LAB2)~~

* WRITE(6,*) 'NEW L* A* B*' * WRITE(6,*) (LAB2(I),I=1,3) * WRITE(6,*)' '

~~_____. *______C DISCREPANCY BETWEEN THE TWO TRISTIMULUS VALUES DIFFERENCES:' * WRITE(6,) 'COLOR 240~~

~~DEsO.O DO 3 1=1,3~~

~~DELTA(I) = LABld) - LAB2CD DE = DE ? ( DELTA(I) ) **2 * WRITE(6.*) DELTA(I) 3 CONTINUE * WRITE(6,*)' '~~

~~OE=SQRT(DE) WRITE(6,*)'DE= ,DE * WRITE(6,*)' '~~

~~C CALCULATE THe"jACKOBIAN~~

~~DO 4 1=1,3 DO 5 Ksl,3 JAC(I,K)0.0 5 CONTINUE 4 CONTINUE~~

~~DO 6 1=1,3 DO 7 Ksl,3 00 8 J=1,N~~

~~JAC(I,K) = JAC(I.K) + ILLCMFd, J) * T(J) * EXT(J,K)~~

~~8 CONTINUE 7 CONTINUE 6 CONTINUE~~

~~DO 9 1=1,3 DO 10 K=l,3 JAC(I,K)= -CON * JAC(I,K)~~

~~.10 CONTINUE 9 CONTINUE * WRITE(6,*) 'JACKOBIAN: ' * WRITE(6,*)((JAC(I,J),J=1,3),I=1,3) * WRITE(6,*)' '~~

~~c""check~if"the match~satisfies"the~~

~~if( (de.lt.eps) )then GOTO 200 ELSE~~

C ~~FIND~THE NEW PARTIAL DIFFERENTIALS OF L* A* B*

~~CALL DLAB(XYZ2,XDYDZD,JAC,DLABS)~~

~~LABS' * WRITE(6,) 'DELTA * WRITE(6,*) ((DLABS(I,J),Jsl,3),I=l,3) * WRITE(6,*)' '~~

~~C CALCULATE THE INVERSE OF THE JACKOBIAN~~

~~CALL AINV(DLABS.INVDLABS) 241~~

*______C INITIALIZE VARIABLE

~~DO 11 1=1,3 DC(I)sO. 11 CONTINUE~~

*______-.______. C CALCULATE THE NEW CONCENTRATION INCREMENTS

~~DO 12 1=1,3 DO 13 Jsl,3 DC(I)=DC(I) + INVDLABS(I,J)*DELTA(J) 13 CONTINUE 12 CONTINUE~~

~~C COMPUTATE THE NEW DYE CONCENTRATIONS~~

~~DO 14 1=1,3 C(I)=C(I)+DC(I) 14 CONTINUE~~

* WRITE(6,*)' ' * WRITE(6,) 'THE CONCENTRATIONS ARE :' * WRITE(6,*)' ' * WRITE(6,*)'Clsi,C(l),C(2),C(3) * WRITE(6,*)' '

~~ITER=ITER+1 'ITERs * WRITE(6,) , ITER ' * WRITE(6,*)'~~

~~GOTO 100 ENDIF~~

* _ THE DYES C CHECK IF THE COLOR IS WITHIN THE COLOR GAMUT OF

~~200 IF((C(1).LT,0.0).OR,(C(2).LT.O.O).OR.(C(3).LT,0.0))IHEN NOsl~~

~~WRITE(6,*) ' '~~

~~DYES' COLOR GAMUT OF THE WRITE(6!*)?THIS COLOR LIES OUTSIDE OF THE~~

~~WRITE(6,*)' ' !' WRITE(6,*)' AND CAN NOT BE MATCHED~~

~~WRITE(6,*)' '~~

~~WRITE(6,*)'Cls,C(l) WRITE(6,*)'C2=',C(2) WRITE(6,*)'C3=',C(3) WRITE C 6 * ) ' ' VALUES IN A FILE" WRITE(6,*)'DO YOU WANT TO STORE THE XYZ ANS= 'Y' * READ(5,'(A)') ANS~~

~~WRITE(6,*)' '~~

~~' EQ.'Y" Y )THEN (ANS. .OR. ANS.EQ. IF ' ' ,STATUS=' FILE= > NOMATCH.DAT OLD ) * OPEN (7 , WRITE(7,554)LABEL --,,,.,, s '.(XYZ(I),Isl,3) WRITE(7,) ' ','XYZ ENDIF~~

~~WRITE(6,*)' '~~

~~554 FORMAT(/,10X,A) ENDIF * CLOSE(7,STATUS='KEEP') RETURN END 242~~

~~C CHOPPING OFF 0* THE NEGATIVE LOBES OK (KGbCMt'MLL)~~

~~SUBROUTINE HONEGCMFC ILLRGB, CMFRGb , Cut XYZ.COk ,CUG , CUb)~~

~~REAL~~

~~+ ILLRGB(3,BO) , ! COLOR-MATCHING FUNCTIONS RGB * ILLUMINANT~~

~~+ CMFRGB(3,80) , ! COLOR-MATCHING FUNCTIONS R, G, B t CMFXYZ(3,8U), I CuLuR-MATCHING tUhCTIUNS X, Y, Z + CQ(3,U0), J ORTHOGONAL COLOR MIXTURE CUkVtS + M(3,3) ! ORTHOGONAL COLOR MIXTURE MATRIX~~

~~N=31 COV=2. 302585 MCI, 1)=-. 4066 M(2,l)=.4066 M(3,n=-.n9i M(l, 2)=. 5521 M(2, 2)3-, 0433 M(3,2)a,1018 Hd,3) = 0. M12,3)=0. MC3,3)=,2B1~~

* WR I TE (6 _ 7 J 175 F0RMAT(/,1X, "DO YOU KANT TO CHOP OF* THE NEGATIVE LOBES * OF RGBCMF*ILL ?',/,/)

~~READC5, '(A) ' ) ANSWER~~

~~EQ.'Y' ' ' )ThEN IFCANSWER. .OR, ANSWER. EO. Y~~

~~R = ,0~~

~~G s .0~~

~~B = ,0 DO 30 1=1, N~~

~~IF (ILLRGBd, I ).LT.O,0)THEN ILLRGBd, I)=0,0 CMFRGB(l,I)-0,0 ENDIF~~

~~IF(ILLRGBC2,I),LT,0.0)THEN ILLRGB(2,I)=0.0 CMFRGB(2,I)=0.0 ENDIF~~

~~IF(ILLRGB(3,I).LT.O.0)THEN ILLRGB13,I)=0.0 CMFRGB(3,I)=0.0 ENDIF~~

~~R s R ? ILLRGBd, I) G = G ? ILLRGB(2,I) B = B ? ILLRGB(3,I)~~

~~RED = RED ? CMFRGBd.I) GREEN = GREEN + CMFRGb(2,I) BLUE = BLUE ? CMFRGB(3,I)~~

~~30 CONTINUE 243~~

~~R 3 100,/R G s 100, /G B > 100, /B~~

~~RED = 100, /RED GREEN = 100. /GREEN BLUE a 100,/bLUE~~

~~DO 1=1, N ILLRGBd, I) 3 R ILLRGBd, I) ILLRGBd, I) = G * ILLRGBd, I) ILLRGBd, 1) = B * ILLRGBd, I)~~

~~CMFRGBd,I) = RED * CMFRGb(l,I) CMFRGBd.I) * GREEN * CMFRGBd.I) CMFRGBd.I) = BLUE * CMFRGB(3,I) END DO~~

~~ENDIF~~

~~C CALCULATE ORTHOGONAL COLOR-MIXTURE CURVES~~

~~DO 201 1=1, 3 DO 202 K=l,3 DO 203 J=1,N CQ(I,J)BCQd,J)+Md,K)CMFXYZ(K,J) 203 CONTINUE 202 CONTINUE 201 CONTINUE~~

~~ZUP = 1 IFCZUP.EQ.DTHEN WRITEC6,*)' CI C2 C3' DO J=1,N WRITE (6,*) CQd, J), CO( 2, J), CO (3, J) END DO ENDIF~~

~~COLORIMETRIC QUALITY FACTOR~~

~~DO 1=1, N~~

~~SURl=SURltCMFRGBd,l)CQ(l,I~~

~~SUR2=SUR2+CMFRGBd,I)CQ(2,I SUR3=SUR3+CMFRGBC1,I)CQ(3,1~~

~~SUGl=SUGl*CMFRGB(2,I)*CQd,I SUG2=SUG2 + CMFRGBC2,I)*COd,I SUG3=SUG3+CMFRGbd,I)*COC3,I~~

~~SUBl=SUBl+CMFRGB(3,I)*CQd,I~~

~~SUB2=SUb2+CMFrGBC3,I)*CQ(2,I~~

~~SUB3=SUB3+CMFRGB(3,I)CQ(J,I~~

~~SUR 3 SUR + CMFHGB(1,I)**2 SUG = SUG + CMFRGB(2,I)*2 SUB = SUB + CMFRGB(3,I)**2~~

~~END DO 244~~

~~SUR1=SUR1*2 SUR2aSUR2**2 SUR3aSUR3**2~~

~~SUGl3SUGl**2 SUG2=SUG2**2 SUG3aSUG3**2~~

~~SUB1=SUB1*2 SUB23SUB2*2 SUB3aSUB3**2~~

~~CQR=(SUR1+SUR2+SUR3)/SUR COGs(SUGl*SUG2+SUG3)/SUG CQBs(SUBl+SUB2+SUB3)/SUB~~

~~WRITE(6,*)' '.'COLORIMETRIC QUALITY FACTOR RED'.CQF WRITE(6,*)' '.'COLORIMETRIC QUALITY FACTOR GREEN', CQG WRITE16,*)' '.'COLORIMETRIC QUALITY FACTOR BLUE', COB~~

~~RETURN END 245~~

~~***************************** **************************~~

~~EXTCOUEF.IrOK PROGRAM TO INPUT EXTINCTION COEFFICIENTS PAUL R. BARTEL~~

~~**************************** ************************ ^**~~

~~SUBROUTINE EXTCOOEF (tXT.LABELl ) INTEGER I, ! COUNTER ? N 1 i OF DATA POINTS IN ROW Ok COLUMN~~

~~REAL + EXT(80,3) ! EXTINCTION COtFFICItNIS~~

~~CHARACTER LABEL1*30 ************************************************************************** C INPUT OF NECESSARY DATA: *______Ns3l *______C EXTINCTION COEFFICIENTS:~~

~~' WKITE(6,*) CCHOOSE EXTINCTION COEFFICIENTS : WRITE(6,*) i VHRITEC6,*) 1. EKTACHROME 200' WRITE(6,) i WRITE(6,*) 2. EKTACHROME AERECON S0-lb5' WKITEC6,*) i~~

~~READ(5,*)ANS~~

~~IF(ANS.EQ.1)THEN LABEL1=' EKTACHROME 200' 'EKTCMY.DAT' ' ' OPEN (2, FILEs ,STATUS=OLD ) ! KODAK ELSE LABELls'AERECON SO-1551 FILE=' PETERS.DAT' ATUS= ' OLD ' DATA OPEN (2, ,ST ) ! PcTER'S ENDIF~~

~~DO 2 1 = 1, N READ(2,*) EXTCI.l), EXTCI.2), EXKI.3) CONTINUE CL0SE(2,STATUS='KEEP' )~~

~~RETURN END 246~~

**********?**********************************, ^,,.m4

~~SCALEX.FOR~~

~~EXTINCTION COEFFICIENT SCALING PROGRAM PAUL R. BARTEL~~

ThIS PROGRAM CALCULATES THE SCALED EXTINCTION COEFFICIENTS OF THE DYES. *******************************************************

~~SUBROUTINE SCALEX (EXT.LABEL2)~~

******** ********* INTEGER I, J, ! COUNTER f N ! # OF DATA POINTS IN ROW OR COUkN

~~REAL + EXT(80,3), ! EXTINCTION COEFFICIENTS + R1MAX, + R2MAX, R3MAX~~

~~CHARACTER ANSWER*1 ,LABEL2*30~~

************************************************************************** C INPUT OF NECESSARY DATA: *______N = 31

~~WRITE(6,*) WRITE(6,) WRITE(6,) SCALING OF THE EXTINCTION COEFFICIENTS WRITE(6,*) WRITE(6,*) SO THAT: HAX( EXT ) WRITE(6,) WRITE(6,) YES / NO WRITE(6,*) READ(5, '(A) ' ) ANSWER~~

~~IF (ANSWER. EQ.'Y')THEN LrABEL2=' SCALED EXTINCTION COEFFICIENTS' WRITE(6,*) 'SCALING' R1MAX = -999999999^9999999.0 R2MAX = -99999999999999999.0 R3MAX = -99999999999999999,0~~

DO 1=1, N ! FIND THE MAX HERE 1 ! R1MAX MAX(R1MAX,EXT(I,D) R2MAX MAX(R2MAX,EXT(I,2)) R3MAX MAX(R3MAX,EXT(I,3)) END DO AX' WRITE (6,*) 'RIM .R1MAX WRITE (6,*) 'R2MAX',R2MAX 'R3MAX' WRITE(6,) .R3MAX

~~R1MAX = 1,/(2.3*R1MAX) R2MAX = l./(2.3*R2MAX) 247~~

~~R3MAX = l./(2.3*H3MAX)~~

~~DO 71 1=1,31 EXT(I.l) = EXT(I,1)*R1MAX EXT(I,2) = EXT(I,2)*R2MAX EXT(I,3) = EXT(I,3)*R3MAX 71 CONTINUE ENDIF *-..------.-----.------.----.~~

* WRITE(6,*) (( EXT(I.J), 1=1, N ), J=l,3)

*______-______- -.

~~RETURN END~~