COLOR REPRODUCTION OF FACIAL

PATTERN AND ENDOSCOPIC IMAGE BASED

ON COLOR APPEARANCE MODELS

December 1996

Francisco Hideki Imai

Graduate School of Science and Technology

Chiba University, JAPAN

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Dedicated to my parentsDedicated to my parents

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COLOR REPRODUCTION OF FACIAL

PATTERN AND ENDOSCOPIC IMAGE BASED

ON COLOR APPEARANCE MODELS

A dissertation submitted to the Graduate School ofScience and Technology of Chiba University in partial

fulfillment of the requirements for the degree of

Doctor of Philosophy

by

Francisco Hideki Imai

December 1996

iv

Declaration

This is to certify that this work has been done by me and ithas not been submitted elsewhere for the award of anydegree or diploma.

Countersigned Signature of the student

___________________________________ _______________________________

Yoichi Miyake, Professor Francisco Hideki Imai

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The undersigned have examined the dissertation entitled

COLOR REPRODUCTION OF FACIAL PATTERN AND ENDOSCOPIC IMAGE

BASED ON COLOR APPEARANCE MODELS

presented by _______Francisco Hideki Imai____________, a candidate for the degree of

Doctor of Philosophy, and hereby certify that it is worthy of acceptance.

______________________________ ______________________________

Date Advisor Yoichi Miyake, Professor

EXAMINING COMMITTEE

____________________________

Yoshizumi Yasuda, Professor

____________________________

Toshio Honda, Professor

____________________________

Hirohisa Yaguchi, Professor

____________________________

Atsushi Imiya, Associate Professor

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Abstract

In recent years, many imaging systems have been developed, and it became increasingly

important to exchange image data through the computer network. Therefore, it is required to

reproduce color independently on each imaging device. In the studies of device independent

color reproduction, colorimetric color reproduction has been done, namely color with same

chromaticity or tristimulus values is reproduced. However, even if the tristimulus values are

the same, color appearance is not always same under different viewing conditions. Therefore

we must introduce color appearance prediction for color reproduction of image.

In this dissertation, a new color reproduction method based on color appearance

prediction is introduced for color reproduction of facial pattern and endoscopic image.

First, spectral reflectance of skin color was analyzed by principal component analysis,

and it was shown that the spectral reflectance of skin can be estimated by three principal

components. On the basis of these experimental results, spectral reflectances of facial

pattern taken by HDTV camera was estimated, and computer simulation of colorimetric color

reproduction has been done using those obtained spectral reflectances.

Color appearance models of von Kries, Fairchild, LAB were also introduced to this

color reproduction algorithm. The image calculated by those models were compared with

the color hardcopies under various illuminants (“A”, “Day Light”, “Horizon”, and “Cool

White”) using memory matching technique. It was found that the Fairchild model is most

significant to estimate the color appearance of skin color chart under different illuminants.

However, the model was not significant to apply to estimation of color appearance in facial

pattern. Therefore, modified Fairchild model was introduced to estimate the color

appearance of facial pattern. It was shown in psychophysical experiments that the model can

estimate well the color appearance of facial pattern compared to other models.

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These experiments have been done in the dark environment. However, the practical

image on a CRT is usually watched under the environmental illuminant. We must apply

color appearance models to reproduce image on a CRT under various illuminants, specially

for remote diagnosis of endoscopic images. It is necessary to do a gamut-mapping for

image which cannot be reproduced in gamut of CRT. However, up to this time, there is not

any way to quantify how gamut-mapping affects the perceived color appearance. A

psychophysical metric based on Mahalanobis distance was introduced to evaluate the

influence of gamut-mapping in the color appearance instead of conventional color difference.

The distance is calculated by covariance matrix of metric lightness, chroma and hue angle

obtained by psychophysical experiments.

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ACKNOWLEDGMENTS

At first, I would like to thank Prof. Yoichi Miyake for his supervision, giving

the opportunity to work at his image processing laboratory. I also would like

to thank Dr. Hideaki Haneishi and Dr. Norimichi Tsumura for their fruitful

comments and advices. Special note of thanks goes to Prof. Hirohisa Yaguchi

for his collaboration.

I would like to express my gratitude to Dr. Nobutoshi Ojima of Kao

Corporation, for his cooperation and useful advice.

Thanks are also due to Kenji Koyama, Toshiki Saito and Takafumi

Horiuchi for many helps in the psychophysical experiments, and many thanks

to Reiko Fukumasu for her kindness and patience in being a model for the

pictures. I am also indebted to Mr. Yasuaki Yokoyama for many helps in

using the computers and devices at the laboratory, and to Mr. Kenji Hara for

his kind collaboration. Special thanks to everyone who participated in the

psychophysical experiments as observer.

I am deeply grateful to my parents, brother, sister for their love and

affection.

Finally, I would like to acknowledge the financial support given by Chiba

Prefecture Government from 1993 April to 1995 March and by Brazilian

Government, CNPq, Ministry for Science and Technology, for the scholarship

from 1996 September to the end of the course. I am also grateful to many

other people, whose names cannot be mentioned one by one, that in some

way have contributed for the accomplishment of this research.

Francisco Hideki Imai

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CONTENTS

Chapter Page

1 INTRODUCTION 1

1.1 Color reproduction on CRT and hardcopy 3

1.1.1 Colorimetric color reproduction 3

1.1.2 Color appearance models 4

1.1.3 Limitation of the traditional color reproduction methods 5

1.2 Purpose and approach of this research 6

1.3 Organization of this dissertation 7

2 PREDICTION OF SPECTRAL REFLECTANCE OF A FACIAL

PATTERN IMAGE TAKEN BY HDTV CAMERA 8

2.1 Introduction 8

2.2 Principal component analysis of the spectral reflectances of human skin and

their linear approximation 8

2.3 Estimation of the skin spectral reflectance 15

2.4 Characterization of HDTV camera 18

2.5 Conclusion 22

3 COLORIMETRIC COLOR REPRODUCTION OF FACIAL

PATTERN IMAGE ON CRT 23

3.1 Introduction 23

3.2 Tristimulus values of facial pattern image 24

3.3 Calibration of CRT 24

3.4 Experiments and their results 27

3.5 Conclusion 34

4 COLORIMETRIC COLOR REPRODUCTION OF FACIAL PATTERN

IMAGE ON HARDCOPY 36

4.1 Introduction 36

4.2 Color reproduction method for hardcopy under various illuminants 36

4.3 Multiple regression analysis using skin spectral reflectances 37

4.4 Experimental results 40

4.5 Conclusion 42

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5 COLOR REPRODUCTION OF FACIAL PATTERN IMAGE BASED ON

COLOR APPEARANCE MODELS 43

5.1 Introduction 43

5.1.1 Chromatic adaptation models 43

5.1.2 Viewing techniques for cross-media comparison 49

5.2 Color appearance matching method 50

5.3 Psychophysical experiments 52

5.4 Experimental results 60

5.5 Conclusion 63

6 MODIFIED FAIRCHILD CHROMATIC ADAPTATION MODEL FOR

FACIAL PATTERN IMAGES 64

6.1 Introduction 64

6.2 Modified Fairchild chromatic adaptation model 64

6.3 Psychophysical experiments to tune color balance 65

6.4 Comparison of the modified Fairchild model with other color appearance

models. 67

6.5 Conclusion 76

7 COLOR REPRODUCTION OF ENDOSCOPIC IMAGES UNDER

ENVIRONMENTAL ILLUMINATION 77

7.1 Introduction 77

7.2 Color reproduction method for endoscopic images under environmental

illumination 78

7.3 Gamut-mapping of endoscopic image 83

7.3.1 Gamut-mapping in 1976 CIELUV L*C*h color space 83

7.3.2 Perceptual Mahalanobis distance 84

7.3.3 Psychophysical experiments 86

7.4 Analysis of gamut-mapping for endoscopic images 88

7.5 Conclusion 92

8 CONCLUSION 93

REFERENCES 95

LIST OF PRESENTATIONS AND PUBLICATIONS RELEVANT TO THE

PRESENT THESIS 107

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LIST OF TABLES

Table 1. Averaged spectral reflectance of the sampled human skin. 10

Table 2. The first, second and third principal components of the spectral reflectance of

human skin. 13

Table 3. Experimental setting of the CRTs. 27

Table 4. Coefficients obtained by quadratic curve fitting for CRTs (Nanao FlexScan

56T and AppleColor MO401) in a dark environment. 29

Table 5. Coefficients obtained by linear curve fitting for CRTs (Nanao FlexScan 56T

and AppleColor MO401) in a dark environment. 32

Table 6. The tristimulus values of six skin color patches under illuminant “A”. 53

Table 7. XL, YL, ZL tristimulus values of reflected light on CRT under various

illuminants. 82

Table 8. Variances and covariances of metric lightness, chroma and hue angle of

endoscopic image. 86

Table 9. Result of psychophysical experiments performed by Hara with the

collaboration of physicians. 88

Table 10. Variation of coefficients φ, ε, β, γ andα in the Eq. (7-10). 89

xii

LIST OF FIGURES

Figure 1. History of the color research. 1

Figure 2. Distribution of skin colors used in principal component analysis. 9

Figure 3. Averaged spectral reflectance of human skin. 9

Figure 4. Cumulative contribution ratio of principal components of the skin spectral

reflectance. 11

Figure 5. The first, second and third principal components of the spectral reflectance

of the skin. 12

Figure 6. Comparison between measured and predicted relative spectral reflectance of

human skin. 15

Figure 7. Diagram of the portrait image acquisition and the prediction of the spectral

reflectance of each pixel in the image. 19

Figure 8. Diagram of the proposed colorimetric color reproduction method to predict

the tristimulus values of facial pattern image under various illuminants on a CRT in a

dark environment. 23

Figure 9(a). The relationship between input levels of CRT (Nanao FlexScan 56T) and

luminance of phosphor. 28

Figure 9(b). The relationship between input levels of CRT display (AppleColor

MO401) and luminance of phosphor. 29

Figure 10(a). X-Y and Z-Y relationship for each RGB channel of the CRT (Nanao

FlexScan 56T). 30

Figure 10(b). X-Y and Z-Y relationship for each RGB channel of the CRT

(AppleColor MO401). 31

Figure 11. Relative spectral radiant power and chromaticities of four illuminants used

in the experiment. 33

Figure 12. A facial pattern image reproduced colorimetrically on CRT under four

illuminants; (a) “Horizon,” (b)“A,” (c)“Cool White,” (d)“Day Light,” illuminants.34

Figure 13. Diagram of the color reproduction method for hardcopy of skin color image

under various illuminants. 37

Figure 14. Diagram of the multiple regression analysis. 38

Figure 15. Averaged color differences ∆Eab between skin color patches displayed on CRT

and the corresponding hardcopies under four illuminants. 40

Figure 16. Printed facial pattern image under four different illuminants, (a) “Horizon”,

(b) “A”, (c) “Cool White”, (d) “Day Light” illuminants. 41

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Figure 17. Comparison between averaged spectral reflectance of human skin and

printed skin color. 42

Figure 18. Diagram of color reproduction of facial pattern images on CRT based on

color appearance models. 51

Figure 19. Predicted color appearance of skin color patches under various illuminants;

(a) illuminant “A”, (b) “Horizon”, (c) “Cool White”, (d) “Day Light”. 54

Figure 20. Color appearance predictions of a facial pattern image under illuminant “A”;

(a) XYZ, (b) CIELAB, (c) von Kries, (d) Fairchild. 55

Figure 21. Color appearance predictions of a facial pattern image under “Horizon”;

(a) XYZ, (b) CIELAB, (c) von Kries, (d) Fairchild. 56

Figure 22. Color appearance predictions of a facial pattern image under “Cool White”;

(a) XYZ, (b) CIELAB, (c) von Kries, (d) Fairchild. 57

Figure 23. Color appearance predictions of a facial pattern image under “Day Light”;

(a) XYZ, (b) CIELAB, (c) von Kries, (d) Fairchild. 58

Figure 24. Arrangement of psychophysical experiment to compare skin color images

on a CRT with a hardcopy in a standard illumination booth using memory matching. 59

Figure 25. Percentage of selection of each color appearance model for skin color

patch reproduction. 61

Figure 26. Percentage of selection of each color appearance model for facial pattern

image reproduction. 62Figure 27(a). A number of selection when KM , KS are changed from 2.9 to 3.2 and

KL = 2.9. 65Figure 27(b). A number of selection when KM , KS are changed from 2.9 to 3.2 and

KL = 3.0. 66Figure 27(c). A number of selection when KM , KS are changed from 2.9 to 3.2 and

KL = 3.1. 66Figure 27(d). A number of selection when KM , KS are changed from 2.9 to 3.2 and

KL = 3.2. 67Figure 28. A facial pattern image reproduced on a CRT for illuminant “A”;

(a) XYZ, (b) Modified Fairchild (Custom model), (c) von Kries, (d) Fairchild. 68

Figure 29(a). Averaged interval scale of model performance for illuminant “A”. 69

Figure 29(b). Averaged interval scale of model performance for “Day Light”. 70

Figure 29(c). Averaged interval scale of model performance for “Cool White”. 70

Figure 30. A skin color patch reproduced on CRT for illuminant “A”; (a) RLAB 96,

(b) Modified Fairchild (Custom model), (c) von Kries, (d) LLAB models. 71

Figure 31. A facial pattern image reproduced on CRT for illuminant “A”; (a) RLAB 96,

(b) Modified Fairchild (Custom), (c) von Kries, (d) LLAB models. 72

xiv

Figure 32. Percentage of skin color patch that was selected on CRT as the best one

in 3 kind of illuminants. 73

Figure 33. Percentage of selection for reproduced facial pattern image chosen as the

best one on CRT display in 3 kind of illuminants. 74

Figure 34(a). Averaged interval scale of model performance for illuminant “A”. 75

Figure 34(b). Averaged interval scale of model performance for “Day Light”. 75

Figure 34(c). Averaged interval scale of model performance for “Cool White”. 76

Figure 35. Diagram of color reproduction method to reproduce the appearance of

endoscopic images on CRT under various illuminants. 78

Figure 36(a). Spectral reflectance of CRT without radiation from CRT under

illuminant “A”. 80

Figure 36(b). Spectral reflectance of CRT without radiation from CRT under

“Cool White”. 81

Figure 36(c). Spectral reflectance of CRT without radiation from CRT under “Day

Light”. 81

Figure 37. Relationship between L*u*v* and L*C*h color spaces. 84

Figure 38. Stomach endoscopic image. 89

Figure 39. Reproduced image on CRT under illuminant “A”. 90Figure 40. Reproduced stomach endoscopic image under illuminant “A”, for φ=0.95,

ε=3, β=1.0, γ=1 andα=0 of Eq. (7-10). 91

Chapter 1

1

CHAPTER 1

INTRODUCTION

Studies of color have been introduced in human life and culture since the beginning of

recorded history. Figure 1 shows a diagram of the history of color research.

Å@ Philosophicalspeculation on color

Greek and Chinese speculation on the nature of color

500 - 300 B.C.

Pre-scientific color studies

17th century

Physical approach to relate color with corresponding stimuli

Color Science

New challenge

Matching tristimulus values and appearance of original scene with the reproduced images and gamut-mapping

Cross-media color Å@reproduction

Matching tristimulus values and appearance of color images between devices

Color imaging

Physical Measurement

Color representation

15th century

Search for color organization and representation

C I E colorimetry

1931

Physical relationship between stimulus and color perception

Color appearance1976-1996

Pshychophysical relationship between stimulus and color sensation

Figure 1. History of the color research.

In the pre-scientific color studies, Chinese and Greek philosophers only

speculated on the nature of color. During the 15th century, color organization and

representation were searched.

The color science began with the establishment of a correspondence between

color and its physical stimuli in the 17th century. In the 19th century, the advance of

Chapter 1

2

sciences such as physics and chemistry1 contributed for the development of color

science. The color science also developed with the advances in the study of physiology

and psychophysics.2 CIE (Commission Internationale de l’Eclairage) specified the

colorimetry in 1931 giving a physical relationship between measured stimulus and color

response based on a standard observer. However, the CIE colorimetry cannot predict

the appearance of color well, because it is based on adapted eyes in pre-defined

laboratory conditions, unlike the environment where most colors are seen. The

specification3 and prediction4 of color appearance have been studied in the last 20 years.

The study of color appearance considers the influence of environmental factors in the

sensation of color.

The increasing speed of computing equipment and devices, scanner, digital

camera, printer and CRT display (CRT), allowed the development of techniques5 for

color imaging. The color science is applied to color imaging to produce cross-media

reproductions. It also gives new tools to the color scientists with which they can

improve the studies of human color vision.

A new challenge in color imaging systems is to match the color appearance of

original scene with reproduced images. In the area of multimedia where we can access

color images through the world wide network of computers, the WYSIWYG (what you

see is what you get) fidelity in the reproduction of color has become very important.

The traditional cross-media reproduction systems6,7 does not consider the original scene.

The reproduction of the colors in the original scene can be achieved considering original

spectral reflectances.8 The reproduction of the skin color appearance is also important to

the cosmetic industry.

The color appearance reproduction of the original scene is also very important in

the area of telemedicine such as diagnosis of electronic endoscopic image. The

endoscopic image is not always viewed in a dark environment, and viewing condition is

Chapter 1

3

dependent on the environment of the hospital. In remote diagnosis, however, the

endoscopic images are usually sent to physicians in various illuminated environments.

Therefore, we need to consider the outer illuminant condition in the color reproduction

system. Unfortunately, the processed endoscopic images cannot always be represented

inside the color gamut of CRT particularly due to the saturation in the red channel. In

such cases, gamut mapping is required. A new challenge in the endoscopic image

reproduction system is to evaluate the influence of gamut-mapping in the color

appearance of the reproduced image.

1.1 Color reproduction on CRT and hardcopy

The accurate reproduction on CRT and hardcopy has been studied by many

researchers.9-11 In the following subsections some types of color reproduction are

described.

1.1.1 Colorimetric color reproduction

The study of color science developed in the last century with the advance of physics and

physiology.12-21 These studies constituted the base of the colorimetry.22 The

colorimetry is obtained by measurement of chromatic properties of the objects by

instruments such as spectrophotometer and colorimeter.23

In colorimetric color reproduction, chromaticities and relative luminances of

reproduced color are equal to those of the original.24 It is possible to achieve device

independent color reproduction, in matching the chromaticities and relative luminances

of the original with the reproduced images.

1.1.2 Color appearance models

Colorimetric color reproduction works well to reproduce the appearance of colors if the

reproduction is viewed under the identical viewing condition of the original image.

Chapter 1

4

However, the use of colorimetric color reproduction is not enough to predict the

appearance of colors under various environmental conditions. There are many

environmental factors which give the influence upon the appearance of colors such as

the illuminant,25-27 effect of background and surround,28-32 and the size of the colored

area33 . One of the most significant factors affecting color appearance is the change of

visual color sensitivities corresponding to changes of the illumination. This

phenomenon is known as chromatic adaptation.34-37

There are two types of chromatic adaptation mechanisms: sensory and

cognitive.38 Sensory mechanisms are based on the sensitivity control in the

photoreceptors and neurons in the first stages of the visual system and considers

changes in the white point, luminance of illuminant and other aspects of the viewing

conditions. Many models have been proposed to measure the appearance of color.39-46

The first model of sensory chromatic adaptation was proposed by Johaness von

Kries.47,48 Subsequent models of chromatic adaptation proposed by C. J. Bartleson,49

K. Richter,50 R. W. G. Hunt,51-54 Y. Nayatani and coworkers,55-64 M. D. Fairchild,65,66

M. R. Luo and coworkers67-69. Color spaces such as CIELUV70 , CIELAB,70

RLAB,38,71,72 LLAB73,74 are also used to predict color appearance. There is also neural

models such as the ATD model proposed by S. L. Guth.75-77 Another color appearance

model is the Retinex theory proposed by E. Land that considers a spatial distribution of

all pixels in the field of view.78-80 On the other hand, cognitive mechanisms are

influenced by observers’ knowledge of image content. The quantification of the

cognitive mechanisms is very complex because its psychological nature. Then, no

model has been proposed for cognitive mechanisms.

Various color appearance models have been applied to color reproduction of

complex images81 and evaluated by RIT group.38,82-84 These experiments show that a

Chapter 1

5

perfect color appearance model is not available and each model has advantages and

disadvantages.

1.1.3 Limitation of the conventional color reproduction methods

The conventional color reproduction methods have three considerable limitations.

First, these methods cannot reproduce correctly the color appearance of the original

scene under various illuminants on CRT and hardcopy using only three input channels

due to the occurrence of metameric pairs24 of original and reproduced image. These

metameric pairs are stimuli that are visually identical but spectrally different. A method

to estimate the spectral composition of the color stimulus from the input signals is

required to predict the metamerism in the reproduction on CRT and hardcopy under

various illuminants.

Second, many reproduction methods using color appearance models have been

proposed. However, none of them has been applied specifically to skin color that is one

of the most important colors for the evaluation of reproduction quality. A comparative

experiment between color patches and complex images is also not available for

reproduction systems using color appearance models.

Third, some of these systems include gamut-mapping to reproduce images inside the

color gamut of CRT displays. However, these methods do not consider yet how gamut-

mapping actually modifies the color appearance of the reproduced image. It is desirable

to minimize the effect of gamut-mapping in the color appearance reproduction. Then, a

perceptual metric based on psychophysical experiments is required to quantify the effect

of gamut-mapping on the color appearance of reproduced images.

Chapter 1

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1.2 Purpose and approach of this research

The purpose of this dissertation is to match the color appearance of an original scene

under various illuminants with its reproductions on CRT and hardcopy. In this

dissertation, facial pattern and endoscopic image are considered as original scene.

Particularly, this study examines the performance of chromatic adaptation models for

facial pattern image. This study also investigates the evaluation of gamut mapping

influence on the color appearance of endoscopic image reproduced on a CRT under

environmental illumination. The gamut-mapping is required in endoscopic images

because these images generally have saturation of the red channel on CRT due to their

reddish nature.

As a first approach to this color appearance matching, the spectral reflectance of

original scene is estimated using the principal component analysis. Then, the estimated

spectral reflectance is used to predict the tristimulus values of the original scene under

various illuminants. The predicted tristimulus values are reproduced on hardcopy by a

printer calibration using a database of spectral reflectance. Chromatic adaptation models

are introduced to reproduce the color appearance of hardcopy on CRT.

Next, reproduction on CRT of skin color patches and facial pattern images using

various color appearance models are compared by psychophysical experiments. The

performance of color appearance models is compared for various illuminants and

differences between reproduction of skin color patches and facial pattern image are

examined to find an effective model for facial pattern reproduction.

A perceptual distance using covariance matrix for CIELUV metric lightness,

chroma and hue angle is defined based on Mahalanobis distance. This distance is

applied to evaluate various gamut-mapping techniques required to reproduce endoscopic

image on CRT under environmental illumination.

Chapter 1

7

1.3 Organization of this dissertation

In Chapter 2, a technique for two-dimensional prediction of the spectral reflectance of

facial pattern from the RGB three channel image taken by HDTV camera is proposed

based on principal component analysis. Chapter 3 shows a method to reproduce

colorimetrically facial pattern images under various illuminants on CRT in a dark

environment, and Chapter 4 describes a method to reproduce colorimetrically facial

pattern images as hardcopy. Chapter 5 presents a color reproduction based on color

appearance models and psychophysical experiments are performed to evaluate various

color appearance models. In Chapter 6, a modified Fairchild chromatic adaptation

model for facial pattern images is introduced. In Chapter 7, a color appearance

reproduction of endoscopic images on a CRT under various illuminants is described and

a perceptual color distance based on Mahalanobis distance is introduced to evaluate

gamut-mapping. In Chapter 8, the conclusion and the summary of the proposed color

reproduction methods are presented.

Chapter 2

8

CHAPTER 2

PREDICTION OF SPECTRAL REFLECTANCE OF A FACIAL

PATTERN IMAGE TAKEN BY HDTV CAMERA

2.1 Introduction

Spectral reflectance of the object should be measured to predict the color of object under

various illuminants. The spectral reflectance can be represented in a multidimensional

space. Generally, we can obtain only three-channel data from input devices. The

estimation from three-dimensional space to multi-dimensional space can be achieved

using principal components of spectral reflectance.85-89 In this chapter, a method to

predict the spectral reflectance of a portrait image taken by a HDTV camera is described.

2.2 Principal component analysis of the spectral reflectances of human skin and

their linear approximation

Ojima and his coworkers measured one hundred eight spectral reflectances of skin in

human face for 54 Mongolians (Japanese women) who are between 20 and 50 years

old.90 The Munsell values of the skins had a range as follows; H=2YR-8YR, V=5-7,

C=2-5, and the distribution of these skin colors in CIE 1976 L*a*b* color space is

shown in Fig. 2.

Chapter 2

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The spectral reflectances were measured at intervals of 5 nm between 400 nm

and 700 nm. Therefore, the spectral reflectance is described as vectors o in 61-

dimensional vector space. Figure 3 shows the averaged spectral reflectance of human

skin, and these values are given in Table 1.

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Figure 3. Averaged spectral reflectance of human skin.

Chapter 2

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Table 1. Averaged spectral reflectance of the sampled human skin.

Wavelength (nm) Relative spectral reflectance (%)

400 15.98 405 16.20 410 16.41 415 16.62 420 16.83 425 17.35 430 17.86 435 18.93 440 19.99 445 21.16 450 22.33 455 23.22 460 24.11 465 24.77 470 25.41 475 25.94 480 26.46 485 27.07 490 27.68 495 28.43 500 29.18 505 29.88 510 30.57 515 30.87 520 31.16 525 31.11 530 31.05 535 31.03 540 31.00 545 31.26 550 31.51

Wavelength (nm) Relative spectral reflectance (%)

555 31.88 560 32.24 565 32.46 570 32.67 575 33.36 580 34.05 585 36.23 590 38.41 595 40.80 600 43.19 605 44.79 610 46.38 615 47.32 620 48.26 625 48.82 630 49.38 635 49.87 640 50.35 645 50.78 650 51.21 655 51.53 660 51.84 665 52.18 670 52.51 675 52.86 680 53.20 685 53.54 690 53.88 695 54.12 700 54.35

The covariance matrix of the spectral reflectance was calculated for the principal

component analysis. The eigenvectors of the covariance matrix are named as principle

component vectors. Then, the spectral reflectance of human skin can be expressed as a

linear combination of the principle component vectors as follows:

o = o + α iuii =1

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∑ , (2-1)

Chapter 2

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where o is the averaged spectral reflectance, ui (i=1...61) are the eigenvectors and αi

(i=1...61) are the eigenvalues corresponding to the eigenvectors ui (i=1...61)

respectively. The eigenvectors are combined in order of magnitude of the eigenvalues.

The cumulative contribution rates of the principle component vectors are shown

in Fig. 4.

Order of principal component

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reflectance.

From this figure, we can see that the cumulative contribution rate from first to third

components is about 99.5%. Then, the spectral reflectance of human skin can be

represented approximately 99.5% by using linear combination of three principal

components u1, u

2, u

3. The three principal components are shown in Fig. 5.

Chapter 2

12

-2

-1

0

1

2

3

4

400 450 500 550 600 650 700

First

Third

Second

Wavelength (nm)

Rel

ativ

e sp

ectr

al r

efle

ctan

ce

Figure 5. The first, second and third principal components of the spectral reflectance of

skin.

The values of the principal components are given in Table 2. Therefore the Eq. (2-1)

can be represented approximately as follows:

o ≅ o + α ii=1

3∑ ui = o + u1 u2 u3( )

α1

α2

α 3

. (2-2)

Chapter 2

13

Table 2. The first, second and third principal components of the spectral reflectance of

human skin.

WavelengthÅ@ 1st PrincipalÅ@2nd PrincipalÅ@ 3rd Principal (nm) Component Component Component

Å@Å@400 Å@2.258 Å@0.326 Å@-0.514Å@Å@405 Å@2.232 Å@0.306 Å@-0.506Å@Å@410 Å@2.207 Å@0.284 Å@-0.497Å@Å@415 Å@2.177 Å@0.267 Å@-0.491Å@Å@420 Å@2.149 Å@0.250 Å@-0.486Å@Å@425 Å@2.184 Å@0.242 Å@-0.488Å@Å@430 Å@2.218 Å@0.234 Å@-0.488Å@Å@435 Å@2.326 Å@0.198 Å@-0.488Å@Å@440 Å@2.435 Å@0.161 Å@-0.510Å@Å@445 Å@2.527 Å@0.102 Å@-0.533Å@Å@450 Å@2.619 Å@0.041 Å@-0.557Å@Å@455 Å@2.665 Å@0.000 Å@-0.572Å@Å@460 Å@2.711 -0.040 Å@-0.588Å@Å@465 Å@2.735 -0.064 Å@-0.589Å@Å@470 Å@2.758 -0.086 Å@-0.592Å@Å@475 Å@2.767 -0.112 Å@-0.590Å@Å@480 Å@2.776 -0.138 Å@-0.589Å@Å@485 Å@2.800 -0.158 Å@-0.572Å@Å@490 Å@2.824 -0.177 Å@-0.554Å@Å@495 Å@2.878 -0.192 Å@-0.508Å@Å@500 Å@2.933 -0.208 Å@-0.461Å@Å@505 Å@2.983 -0.251 Å@-0.390Å@Å@510 Å@3.033 -0.294 Å@-0.321Å@Å@515 Å@3.044 -0.410 Å@-0.225Å@Å@520 Å@3.056 -0.526 Å@-0.130Å@Å@525 Å@3.045 -0.682 Å@-0.018Å@Å@530 Å@3.035 -0.837 Å@ 0.094Å@Å@535 Å@3.019 -0.942 Å@ 0.172Å@Å@540 Å@3.003 -1.047 Å@ 0.250Å@Å@545 Å@2.971 -1.087 Å@ 0.266Å@Å@550 Å@2.940 -1.129 Å@ 0.283Å@Å@555 Å@2.915 -1.173 0.307Å@Å@560 Å@2.891 -1.213 Å@ 0.330Å@Å@565 Å@2.897 -1.335 0.424Å@Å@570 Å@2.902 -1.453 Å@ 0.517Å@Å@575 Å@2.927 -1.477 Å@ 0.564Å@Å@580 Å@2.950 -1.500 0.611Å@Å@585 Å@3.028 -1.202 Å@ 0.526Å@Å@590 Å@3.107 -0.903 Å@ 0.441Å@Å@595 Å@3.154 -0.455 Å@ 0.319Å@Å@600 Å@3.202 -0.006 0.199

Chapter 2

14

WavelengthÅ@1st Principal 2nd Principal 3rd Principal (nm) Component Component Component

Å@Å@605 Å@3.195 Å@0.285 Å@ 0.158Å@Å@610 Å@3.188 Å@0.576 Å@ 0.117Å@Å@615 Å@3.152 Å@0.711 Å@ 0.130Å@Å@620 Å@3.117 Å@0.846 Å@ 0.142Å@Å@625 Å@3.062 Å@0.899 Å@ 0.165Å@Å@630 Å@3.006 Å@0.952 Å@ 0.186Å@Å@635 Å@2.944 Å@0.978 Å@ 0.209Å@Å@640 Å@2.882 Å@1.004 Å@ 0.231Å@Å@645 Å@2.816 Å@1.019 Å@ 0.257Å@Å@650 Å@2.751 Å@1.034 Å@ 0.284Å@Å@655 Å@2.694 Å@1.040 Å@ 0.307Å@Å@660 Å@2.639 1.046 Å@ 0.331Å@Å@665 Å@2.585 1.057 Å@ 0.359Å@Å@670 Å@2.530 1.069 Å@ 0.386Å@Å@675 Å@2.469 1.083 Å@ 0.416Å@Å@680 Å@2.407 1.098 Å@ 0.445Å@Å@685 Å@2.354 1.106 Å@ 0.471Å@Å@690 Å@2.302Å@ 1.114 Å@ 0.497Å@Å@695 Å@2.253 1.119 Å@ 0.524Å@Å@700 Å@2.202 1.124 Å@ 0.550

Figure 6 shows a comparison between measured and predicted relative spectral

reflectance of human skin by principal component analysis. From this figure it is

possible to conclude that the linear approximation of the spectral reflectance using three

principal components works well.

Then, the spectral reflectance of each pixel of image can be predicted from the

tristimulus values of each pixel and the spectral radiance of the illuminant, as is

performed in electronic endoscopic images91 .

Chapter 2

15

0

10

20

30

40

50

60

400 500 600 700

Wavelength (nm)

( ) Measured spectral reflectance of human skin

( ) Predicted spectral reflectance of human skin by three principal components

Spe

ctra

l ref

lect

ance

(%

)

Figure 6. Comparison between measured and predicted spectral reflectance of human

skin.

2.3 Estimation of the skin spectral reflectance

Considering the result of above principal component analysis, we can estimate the

spectral reflectance of skin using the tristimulus values. The tristimulus values can be

easily measured by a colorimeter. The spectral reflectance of skin is estimated as

follows. As well known, the tristimulus values X, Y, Z can be calculated by Eq. (2-3).

X = K E(λ)x (λ)O(λ )λ = 400

700

∑ , (2-3a)

Y = K E(λ )y (λ)O(λ)λ = 400

700

∑ , (2-3b)

Z = K E(λ )z (λ)O(λ )λ = 400

700

∑ , (2-3c)

Chapter 2

16

where λ is the wavelength, O(λ) is the spectral reflectance, E(λ) is the spectral radiance

of the illuminant, x (λ) , y (λ) , z (λ ) are color matching functions and K is a coefficient

given by Eq. (2-4).

K =1

E(λ) y (λ)dλλ= 400

700

∫(2-4)

By vector notations, Eq. (2-3) can be expressed as follows:

X= Ket X o, (2-5a)

Y = Ke tY o, (2-5b)

Z= Ke tZ o, (2-5c)

where .[ ]t represents the transpose of .[ ], the vectors e, o are vector notations of E(λ)

and O(λ) respectively, and the matrixes X , Y , Z are represented as follows:

x λ( ) → X =

x 1 λ1( ) O

x 2 λ2( )O

O x n λ n( )

, (2-6a)

y λ( ) → Y =

y 1 λ1( ) O

y 2 λ2( )O

O y n λ n( )

, (2-6b)

z λ( ) → Z =

z 1 λ1( ) O

z 2 λ2( )O

O z n λn( )

. (2-6c)

Chapter 2

17

From Eq. (2-2), the Eq. (2-5) can be written as,

X ≅ Ket X o + u1 u2 u3( )α 1

α2

α 3

, (2-7a)

Y ≅ KetY o + u1 u2 u3( )α 1

α2

α 3

, (2-7b)

Z ≅ Ket Z o + u1 u2 u3( )α 1

α2

α 3

. (2-7c)

The Eq. (2-7) can be rewritten as follows:

X ≅ Ke t X o + Ke t X u1 X u2 X u3( )α1

α2

α3

, (2-8a)

Y ≅ KetY o + Ket Y u1 Y u2 Y u3( )α1

α2

α3

, (2-8b)

Z ≅ Ke tZ o + Ke t Z u1 Z u2 Z u3( )α1

α2

α3

. (2-8c)

We can consider the first term of Eq. (2-8) as a contribution of the averaged spectral

reflectance to the tristimulus values, and the second term as a contribution of three

eigenvectors. Then, we can rewrite the Eq. (2-8) as follows:

XYZ

≅

X

Y

Z

+

X1 X2 X3

Y1 Y2 Y3

Z1 Z2 Z3

α1

α2

α3

, (2-9)

Chapter 2

18

where X , Y , Z are the averaged tristimulus values and Xi ,Yi , Zi (i=1,2,3) are the

tristimulus values corresponding to the three eigenvectors of skin spectral reflectance.

Then, the eigenvalues α1 , α2 , and α3 are given by

α1

α2

α3

=

X1 X2 X3

Y1 Y2 Y3

Z1 Z2 Z3

−1X

Y

Z

−

X

Y

Z

. (2-10)

The spectral reflectance of human skin can be estimated by above eigenvalues and three

principal components by Eq. (2-2).

2.4 Characterization of HDTV camera

Figure 7 shows the schematic diagram of the image acquisition and the estimation of the

spectral reflectance in each pixel of the image based on the characterization of the

HDTV camera. In the previous sections, it was shown how spectral reflectances of

human face can be estimated from the device independent tristimulus values X, Y, Z

using Eqs. (2-2) and (2-10). In this section, X, Y, Z in each pixel of original scene is

calculated from the R, G, B three color channels of the HDTV camera.

The output color channel values Ro, Go, Bo of an ideal HDTV camera can be

given by the Eq. (2-11),

Ro = E(λ )r (λ)O(λ )λ = 400

700

∑ , (2-11a)

Go = E(λ)g (λ)O(λ)λ =400

700

∑ , (2-11b)

Bo = E(λ )b (λ)O(λ)λ =400

700

∑ , (2-11c)

where r (λ ), g (λ) , b (λ) are the spectral sensitivities of the camera, E(λ) is the spectral

radiance of the illuminant and O(λ) is the spectral reflectance of the object.

Chapter 2

19

( R, G, B )

( X, Y, Z )

O(λ)=O(λ)+α1u1(λ)+α2u2(λ)+α3u3(λ)

First, second and third principal componentsof the spectral reflectance of human skin

M1

HDTVcamera

Figure 7. Diagram of the portrait image acquisition and the prediction of the spectral

reflectance of each pixel of the image.

However, the actual output color channel values R’, G’, B’ of a HDTV camera is given

by Eq. (2-12);

′ R =K r . fr (Ro) , (2-12a)

′ G = Kg . fg(Go) , (2-12b)

′ B = Kb . fb (Bo ), (2-12c)

Chapter 2

20

where f r , fg , fbare non-linear functions, and Kr , Kg , Kb are white balance constants.

The non-linearity between R, G, B level and luminance was linearized using the

following quadratic equations;92

′ R = −5.50 + 4.26 × 10−1 Ro + 2.04 × 10−3 Ro2 , (2-13a)

′ G = −6.06 ×10−1 + 2.90 × 10−1Go + 2.66 ×10−3 Go2 , (2-13b)

′ B = −7.37 ×10−1 + 2.31 ×10−1 Bo + 3.11× 10−3Bo2 . (2-13c)

Generally the r (λ ), g (λ) , b (λ) are different from visual color matching

functions. Then, it is necessary to find a color transformation function that gives the

device independent tristimulus values X, Y, Z from the HDTV camera output channels

R’, G’, B’. Ojima and his coworkers showed that a color transformation matrix M1

shown in Eq. (2-14) gives sufficient accuracy for the HDTV camera calibration,92

X

Y

Z

= M1

′ R

′ G

′ B

1

(2-14)

This matrix M1 can be determined by the following technique. The tristimulus values of

a series of color patches are measured by a colorimeter and are digitized by HDTV

camera. The values of R’, G’, B’ channels in Eq. (2-13) are calculated from the output

values R, G, B of the HDTV camera. The matrix M1 can be determined by the multiple

regression analysis of measured X, Y, Z tristimulus values and calculated R’, G’, B’

color channel values of digitized color patches.

The tristimulus values X, Y, Z of thirty-nine selected patches of Japanese skin

color were measured by a spectrophotometer (Minolta CM1000). The Munsell values

of the patches have a range as follows; H=0YR-10YR, V=5-8, C=2-5.

Chapter 2

21

The skin color patches were digitized under Metal halide lamp (RDS, with color

temperature of 5,700 K) illumination at 2o field of view by a HDTV camera (Nikon

HQ1500C). The calculated color transform matrix M1 is shown in Eq. (2-15).

M1 =2.09 × 10−1 5.37 × 10−2 5.09 × 10−2 −2.41

1.17 × 10−1 2.07 ×10− 1 −4.80 × 10−3 −2.05

7.69 ×10−4 7.67 ×10− 3 3.65 ×10− 1 −0.827

(2-15)

The accuracy of this color transformation is verified by ∆E*ab color

difference93,94 between the tristimulus values Xm, Ym, Zm, and Xe, Ye, Ze. Xm, Ym, Zm are

measured using a spectrophotometer (Minolta CM1000) and Xe, Ye, Ze, are estimated

using the matrix M1 in Eq. (2-15). The color difference is calculated as shown in Eq.

(2-16)

∆E*ab = Lm* − Le

*( )2+ am

* − ae*( )2

+ bm* − be

*( )2, (2-16)

where ( Lm* , am

* , bm* ) and ( Le

* , ae* , be

* ) are the CIELAB 1976 metric lightness and the

coordinates calculated from Xm, Ym, Zm and Xe, Ye, Ze, respectively.

The averaged color difference ∆E*ab was 1.0 and the maximum color difference

∆E*abmax was 2.3. This result shows that the color transformation by matrix M1 in Eq.

(2-14) has sufficient accuracy to calculate the X, Y, Z necessary to estimate the spectral

reflectance.

Chapter 2

22

2.5 Conclusion

In this chapter, a method to predict the spectral reflectance of a portrait image digitized

by a HDTV camera is described. Spectral reflectance of Japanese women’s skin was

estimated with 99.5% accuracy using the first, second and third principal components of

the spectral reflectance of skin. The obtained color difference less than 2.30 indicates

that the camera calibration was performed with sufficient accuracy to calculate the

tristimulus values.

Chapter 3

23

CHAPTER 3

COLORIMETRIC COLOR REPRODUCTION OF FACIAL PATTERN

IMAGE ON CRT

3.1 Introduction

Figure 8 shows a schematic diagram of colorimetric color reproduction for facial pattern

image on CRT in a dark environment. A facial pattern image is taken by a HDTV

camera under illuminant with spectral radiance E1(λ).

HDTV

( R, G, B )

( X, Y, Z )

CRT display

(Rc, G

c, B

c )

X',Y' Z',( )

(

(

E1(λ) E2(λ)

M2

M1

O(λ)

O(λ)

(

(

camera

Figure 8. Diagram of the proposed colorimetric color reproduction method to predict

the tristimulus values of facial pattern image under various illuminants on a CRT in a

dark environment.

Chapter 3

24

The tristimulus values X, Y, Z of the portrait image is calculated from three

channels R, G, B values of the HDTV camera using transformation matrix M1 as shown

in the previous chapter. In the proposed method, the two-dimensional spectral

reflectance of the object in the scene is calculated using the tristimulus values of the

digitized image based on the principal component analysis of the spectral reflectance of

human skin. Then, the tristimulus values of the image under a new illuminant with

spectral radiance E2(λ) can be predicted from the estimated spectral reflectance. The Rc,

Gc, Bc input values of CRT is calculated by color transform matrix M2 obtained by the

colorimetric calibration of the CRT.

3.2 Tristimulus values of facial pattern image

The tristimulus values X', Y', Z' of skin color under a selected illuminant can be easily

calculated from the estimated spectral reflectance O(λ) and the spectral radiance E2(λ)

of the illuminant.95 The tristimulus values X’, Y’, Z’ are calculated as follows:

X' = K O(λ )E2 (λ)λ = 400

700

∫ x (λ)dλ (3-1a)

Y' = K O(λ)E2(λ)λ = 400

700

∫ y (λ)dλ (3-1b)

Z' = K O(λ)E2(λ)λ = 400

700

∫ z (λ )dλ (3-1c)

3.3 Calibration of CRT

Many methods to calibrate a computer controlled color monitor have been proposed.96-

101 In general cases, it is possible to define a two-stage model for CRT to transform Rc,

Gc, Bc input values to the tristimulus values X’, Y’, Z’.102,103 The first stage is a nonlinear

transformation from Rc, Gc, Bc values to phosphor luminances produced by digital-to-

Chapter 3

25

analog converter. The second stage is a linear transformation where the monitor

phosphor luminances are transformed to the X’, Y’, Z’ values. The calculation of the

transformation M2 in the schematic diagram of Fig. 8 was performed as follows.

A steady CRT with fixed luminance, contrast, white point, and gamma is used.

Color patches are displayed on the CRT in a dark environment to avoid interference with

external light sources. The luminance L and the tristimulus values X, Y, Z were

measured at the displayed color patches in each channel. The luminance colorimeter is

adjusted at the position of the observer eyes because the angle of incidence of the beams

can influence the measurements.104

The relationship between the input level and luminance is plotted and the Eq. (3-

2) can be derived from curve fitting for quadratic curves.

LR = a0 Rc2 + a1Rc + a2 (3-2a)

LG = b0G c2 + b1Gc + b2 (3-2b)

LB = c0 Bc2 + c1Bc + c2 (3-2c)

These equations show the relationship between the luminance and input levels, where

LR , LG , LB are the luminance of red, green, and blue phosphors respectively, and ai , bi ,

ci (i = 0 to 2) are coefficients.

The tristimulus values X, Y, Z on CRT can be decomposed as follows:

X

Y

Z

=

XR + XG + XB

YR + YG + YB

ZR + ZG + ZB

, (3-3)

where Xi , Yi , Zi (i = R, G, B) are the tristimulus values corresponding to the emission of

red, green, blue phosphor, respectively. A theoretical relationship between X-Y, Z-Y for

each phosphor is given by

XR = xR

yR

YR , (3-4a)

Chapter 3

26

XG = xG

yG

YG , (3-4b)

XB = xB

yB

YB , (3-4c)

ZR = zR

yR

YR , (3-4d)

ZG = zG

yG

YG , (3-4e)

ZB = zB

yB

YB . (3-4f)

However the linear curve fitting introduces an offset error in the Eq. (3-4). This error is

considered in the following linear equations:

XR = aRYR + bR (3-5a)

XG = aGYG + bG (3-5b)

XB = aBYB + bB (3-5c)

ZR = cRZR + dR (3-5d)

ZG = cGZG + dG (3-5e)

ZB = cBZB + dB (3-5f)

where ai , bi , ci , di (i = R, G, B) are coefficients.

From Eqs. (3-3) and (3-5), the following equation is obtained;

X

Y

Z

=

aRYR + aGYG + aBYB + bR + bG + bB

YR + YG + YB

cRYR + cGYG + cBYB + dR + dG + dB

. (3-6)

The Eq. (3-6) can be rewrited as follows;

X

Y

Z

= A

YR

YG

YB

+

bR + bG + bB

0.0

dR + dG + dB

, (3-7)

Chapter 3

27

where

A=

aR aG aB

1.0 1.0 1.0

cR cG cB

. (3-8)

The luminance can be calculated from the Eq. (3-9) as follows;

LR

LG

LB

=

YR

YG

YB

= A-1

X − bR − bG − bB

Y

Z − dR − dG − dB

. (3-9)

Then, using the Eqs. (3-3) and (3-8), the transformation from the tristimulus values X, Y,

Z to the input levels Rc, Gc, Bc can be achieved.

3.4 Experiments and their results

Two CRTs (Nanao Flex Scan56T Monitor and AppleColor High-Resolution RGB

Monitor Model MO401) with fixed luminance, contrast, white point, and gamma were

calibrated. These CRTs will also be used in the experiments of Chapter 7. The setting

of the CRTs is shown in Table 3.

Table 3. Experimental setting of the CRTs.

CRT Luminance (cd/m2) Contrast White point gamma

Nanao Flex Scan56T 93.3 Maximum D65 1.80

Apple MO401 71.5 Maximum D65 1.80

Twenty-six color patches were displayed on each CRT in a dark environment.

The luminance L and the tristimulus values X, Y, Z of the displayed color patches in

each channel were measured by a luminance colorimeter (TOPCOM BM-7).

Figures 9(a) and 9(b) show the relationship between input levels of CRT and

luminance of phosphor for Nanao Flex Scan56T CRT and AppleColor MO401 CRT

Chapter 3

28

respectively. From Figs. 9(a) and 9(b) it is possible to determine the coefficients shown

in Table 4 of the quadratic equation (3-2).

Fig. 4 Monitor output luminance.

BBBBBBBBBBBBBBBBBBBBBBBBBBB

JJJJ

JJ

J

JJJJJJJJJJJJJJJJJJJJ

HHHHHHH

HHHHHHHHHHHHHHHHHHHH0

10

20

30

40

50

60

70

0 50 100 150 200 250 300

B

G

R

Input Level (8 bits)

Lum

inan

ce o

f pho

spho

r (c

d/m

2 )Figure 9(a). The relationship between input levels of CRT (Nanao Flex Scan56T) and

luminance of phosphor.

Figures 10(a) and 10(b) show the X-Y and Z-Y relationship for each RGB

channel of Nanao Flex Scan56T CRT and AppleColor MO401 CRT respectively.

Chapter 3

29

BBBBBBBBBBBBBBBBBBBBBBBBBBB

JJJJJJJJJJJJJJJJJ

JJJJJJJJJJ

HHHHHHHHHHHHHHHHHHHHHHHHHHH0

10

20

30

40

50

60

0 50 100 150 200 250 300

Input levels (0-255)

G

R

BLum

inan

ce o

f pho

spho

r (c

d/m

)2

Figure 9(b). The relationship between input levels of CRT (AppleColor MO401) and

luminance of phosphor.

Table 4. Coefficients obtained by quadratic curve fitting for CRTs (Nanao FlexScan

56T and AppleColor MO401) in a dark environment.

Monitor Nanao Flex Scan56T Apple MO401

a0 1.216 × 10−4 1.536 × 10−4

a1 6.212 × 10−2 1.482 × 10−3

a2 − 5.592 × 10−1 −1.745 ×10−1

b0 3.270 × 10−4 4.339 × 10−4

b1 1.863 × 10−1 9.552 × 10−2

b2 −1.714 ×100 −7.855 ×10−1

c0 6.138 × 10−5 5.225 × 10−5

c1 6.782 × 10−3 8.492 × 10−3

c2 − 1.122 × 10−1 −9.007 × 10−2

Chapter 3

30

BBBBB

BB

BBBBBBBBBBBB

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25

YR

XR

BBBB

BBB

BBBBBBBBBBBB

0 5 10 15 20 25

YR

ZR

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0

a) R channel ( X-Y) b) R channel ( Z-Y)BBBBBB

BBBBBBBBBBBBBBB

0

5

10

15

20

25

30

35

0 10 20 30 40 50 60 70

YG

XG

BBBBBB

BBBB

BBBBBBBBBBB

0

2

4

6

8

10

12

14

0 10 20 30 40 50 60 70Y

YG

ZG

c) G channel ( X-Y) d) G channel ( Z-Y)

BBBBBBBBBBBBBBBBBBBBBBB

B0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7

YB

XB

BBBBBBBBBBBBBBBBBBBBBBBB0

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6 7

YB

ZB

e) B channel ( X-Y) f) B channel ( Z-Y)

Figure 10(a). X-Y and Z-Y relationship for each RGB channel of the CRT (Nanao Flex

Scan56T).

Chapter 3

31

YRa) R channel ( X-Y)

XR

YRb) R channel ( Z-Y)

ZR

YGc) G channel ( X-Y)

XG

YGd) G channel ( Z-Y)

ZG

YBe) B channel ( X-Y)

XB

YBf) B channel ( Z-Y)

ZB

BBBBBB

BBBBBBBBBBBBBBBBBBBBB0

2

4

6

8

10

12

14

0 1 2 3 4 5 6

BBBBBB

BBBBBBBBBBBB

BBBBBBBBB0

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6

BBBBBBBBBBBBBBBBBBBBBBBBBBB0

5

10

15

20

25

0 10 20 30 40 50 60

BBBBBBBBBBBBBBBBBBBBBBBBBBB0

2

4

6

8

10

12

0 10 20 30 40 50 60

BB

BB

BBBBB

BB

BBBBBBBBB

BBBBBBB0

5

10

15

20

25

0 2 4 6 8 10 12 14

BB

BBBB

BBB

BB

BBBBBBBB

BBBBBBBB0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14

Figure 10(b). X-Y and Z-Y relationship for each RGB channel of the CRT

(AppleColor MO401).

Chapter 3

32

From Figs. 10(a) and 10(b) it is possible to determine the coefficients shown in

Table 5 for linear Eq. (3-7).

Table 5. Coefficients obtained by linear curve fitting for CRTs (Nanao FlexScan 56T

and AppleColor MO401) in a dark environment.

Monitor Nanao Flex Scan56T AppleColor MO401

aR 1.773 × 100 1.791× 100

aG 4.882 × 10−1 4.867 × 10−1

aB 2.429 × 100 2.420 × 100

bR 1.372 × 10−1 4.909 × 10−2

bG 3.714 × 10−2 1.020 × 10−2

bB −2.258 ×10−2 2.220 × 10−3

cR 7.242 × 10−2 7.719 ×10 -2

cG 1.934 × 10−1 1.967 × 10 -1

cB 1.314 × 101 1.293×101

dR 6.663 × 10−3 2.238 × 10 −4

dG −5.807 × 10−2 −4.334 × 10−2

dB −1.391 × 10−1 3.079 × 10−2

Five facial pattern images with 1920 by 1035 pixels were taken by a HDTV

camera under the same conditions used for camera calibration. The model is a Japanese

young woman. The tristimulus values X’, Y’, Z’ were calculated using the estimated

Chapter 3

33

spectral reflectance under four illuminants; “Day Light”, “A”, “Cool White”, and

“Horizon”. Those spectral radiances and chromaticities are shown in Fig. 11. The

calculated tristimulus values were converted to Rc, Gc, Bc values and they are displayed

on CRT.

"Horizon"

"Day Light"

"Cool White"

Wavelength (nm)

"A"x=0.46 y=0.42

x=0.50 y=0.42

x=0.32 y=0.34

x=0.39 y=0.41

Rel

ativ

e ra

dian

t pow

er

Figure 11. Relative spectral radiant power and chromaticities of four illuminants used in

the experiment.

Figure 12 shows the hardcopy of the predicted facial pattern printed directly

from the input levels Rc, Gc, Bc without any preprocessing or color correction. Actually,

these images should be observed on CRT. We can see that the portrait images under

"A" and "Horizon" illuminants seem reddish, because longer wavelength components

are predominant in these illuminants as shown in Fig. 11.

Chapter 3

34

(a)“Horizon” (b)“A”

(c)“Cool White” (d)“Day Light”

Figure 12. A facial pattern image reproduced colorimetrically on CRT under four

illuminants; (a) “Horizon,” (b) “A,” (c) “Cool White,” (d) “Day Light” illuminants.

Chapter 3

35

3.5 Conclusion

In this chapter, a colorimetric color reproduction method for portrait image on CRT in a

dark environment was proposed. In this method, the tristimulus values of each pixel of

the image were calculated using the estimated spectral reflectance, the spectral radiance

of the illuminant and the color matching functions. The calculated tristimulus values

were transformed to R, G, B values of CRT. A portrait image under various illuminants

was reproduced on CRT. The portrait images under “Horizon” and illuminant “A”

seem very reddish because the predominance of the long-wavelength components in

such illuminants. However, the portrait images under “Horizon” and illuminant “A”

do not seem actually so reddish when viewed under such illuminants because the

chromatic adaptation is not considered yet in this reproduction method.

Chapter 4

36

CHAPTER 4

COLORIMETRIC COLOR REPRODUCTION OF FACIAL

PATTERN IMAGE ON HARDCOPY

4.1 Introduction

Color correction is necessary to match the tristimulus values of hardcopies with those in

the original scene. The colorimetric calibration of printers for color correction is

difficult because this calibration depends on the observing environment and specially on

the illuminants. Various color transform corrections have been proposed for

colorimetric calibration.6,105,106 In this chapter, the printer calibration is achieved by

making color transformation function during the printing process, using the data base of

input values to printer and spectral reflectances, measured before the printing.

4.2 Color reproduction method for hardcopy under various illuminants

Figure 13 shows the schematic diagram of the colorimetric color reproduction of facial

pattern image on hardcopy under various illuminants. In this reproduction method, the

tristimulus values X'', Y'', Z'' of a printed skin color image under an illuminant with

spectral radiance E3(λ) were matched to the tristimulus values X', Y', Z' calculated using

principal components of the spectral reflectance of the skin. To achieve the matching,

the matrix M3 was used to transform the CRT input levels Rc , Gc , Bc to printer input

levels Rp , Gp , Bp . The matrix M3 is a function of the spectral radiance E3(λ) of the

illuminant for viewing of hardcopy and this matrix is calculated by multiple regression

analysis using a data base of input values to the printer and measured spectral

Chapter 4

37

reflectances. It is noted that we do not need to measure the tristimulus values of the

color patches under each illuminant for calibration.

HDTV

( R, G, B )

( X, Y, Z )

CRT display

Hardcopy

Printer

(Rc, Gc, Bc ) (Rp, Gp, Bp )

(X", Y", Z" )X', Y' Z',( ) =

(

(

E1(λ ) E2(λ ) E3(λ )

M3(E3(λ ))

((

(

M2

M1

O(λ)

O(λ)

(

(

Figure 13. Diagram of the color reproduction method for hardcopy of skin color image

under various illuminants.

4.3 Multiple regression analysis using skin spectral reflectances

Figure 14 shows a schematic diagram of the multiple regression analysis using the

database. One hundred eight skin color patches were printed using a laser thermal

development and transfer printer (Fujix Pictrography 3000) with printer input level Rpn ,

Gpn , Bp

n . The spectral reflectance On λ( ) of each patch was measured by a

spectrophotometer (Datacolor Spectraflash 500).

In the on-line calibration, the tristimulus values X n" ,Yn ", Zn " were calculated

under a selected illuminant E3(λ) using the data base. The tristimulus values X n" , Yn ",

Chapter 4

38

Zn " for each patch were transformed to Rcn , Gc

n , Bcn CRT input levels using the

transformation matrix M2. The coefficients (ai,j ) (i=1...3, j=1...11) of matrix M3 in the

Eq. (4-1) were determined by multiple regression analysis107.

M2

(n=1 to 108)

E3 (λ)Input: Spectral radiance

M3(E3 (λ))

X Y Zn )( , ,n n" " "

Gnn

R )( , , Bn

p p p

B cnn

cR )( , ,Gn

c

nO λ( )X Y Z'n )( , ,

n n' '

Multiple regression analysis

Database

Measured once

Output:

Printedoff-l ine

Off- l ineOn-l ine

CRT displayHardcopy

Figure 14. Diagram of the multiple regression analysis.

The accuracy of this colorimetric color reproduction was evaluated by averaged

color differences of fifty-five skin color patches used in the multiple regression analysis.

The color difference was calculated between CRT and hardcopy, with and without color

transformation.

Chapter 4

39

RP

GP

BP

=

a1,1 a1,2 ... a1,11

a2,1 a2,2 ... a2,11

a3,1 a3,2 ... a3,11

RC

GC

BC

RC2

GC2

BC2

RCGC

GCBC

RCBC

RCGC BC

1

(4-1)

As shown in Fig. 15, the averaged color difference ∆E*ab was 19.9 without the color

transformation, and 4.5 with the color transformation. Thereafter, fifty-five skin color

patches, not used in multiple regression analysis, were printed with color transformation

by M3. The averaged color difference ∆E*ab was 4.9. We can conclude that the

proposed color transformation is effective to match the skin color between displayed

image and hardcopy. The matrix M3 was calculated using a workstation (SPARC

station II; Sun micro system Inc.) in an average time of 25 seconds.

Chapter 4

40

B

BBBBBBBBBBBBBB

BBB

B

BBBB

B

B

B

BBBBBBBBBBBB

BBB

BBBB

BBBBBBBBB

JJJJJJJJJ

JJJJJJJJJ

JJJJJJJJJ

JJJJJJJJJJJJJJJJJJ

JJJJJJJJJ

10 20 30 40 500

5

10

15

20

25

Before Calibration

After Calibration

Sample number of skin color patch

Col

or D

iffer

ence

L*a

*b*

Figure 15. Averaged color differences ∆Eab between skin color patches displayed on

CRT and the corresponding hardcopies under four illuminants.

4.4 Experimental results

The portraits used in Chapter 3 was reproduced under four kinds of illuminants;

“Horizon”, “A”, “Cool White”, and “Day Light” in a standard illumination booth

(Macbeth Spectralight II). The spectral radiance of each illuminant is shown in Fig. 11.

The portrait images printed using transformation matrix M3 is shown in Fig. 16.

Chapter 4

41

(a)“Horizon” (b)“A”

(c)“Cool white” (d)“Day Light”

Figure 16. Printed facial pattern image under four different illuminants, (a) “Horizon”,

(b) “A”, (c) “Cool White”, (d) “Day Light” illuminants.

It is noted that the printed images under "A" and "Horizon" illuminants are not

reddish as the corresponding portrait images on CRT as shown in Fig. 12 because each

image will not be observed under the illuminant used in the calibration. Here, it is also

noted that colors of printed portrait images under different illuminants in Fig. 16 are

slightly different. If the spectral reflectance of print is as same as the spectral reflectance

of human face, there is no difference in the printed images due to the illuminants.

Averaged spectral reflectance of printed skin is shown in Fig. 17. It is clear that the

spectral reflectance of human skin and printed skin color are different.

Chapter 4

42

0

10

20

30

40

50

60

400 450 500 550 600 650 700

Averaged spectral reflectanceof skin

Averaged spectral reflectanceof printed skin color

Wavelength (nm)

Spe

ctra

l re

flect

ance

(%

)

Figure 17. Comparison between averaged spectral reflectance of human skin and

printed skin color.

4.5 Conclusion

In this chapter, skin color images are reproduced colorimetrically on hardcopy under

various illuminants. The averaged color difference of 4.9 between the measured and

predicted tristimulus values shows sufficient accuracy of the proposed colorimetric color

reproduction.

It is noticed that the color reproduction of portrait on CRT is different from the

hardcopy under various illuminants because the chromatic adaptation is not considered

yet in the reproduction on CRT.

The color reproduction described in this paper is not applicable to the lips, hair,

eyes and so on, because only the spectral reflectance of human skin was considered

here.

Chapter 5

43

CHAPTER 5

COLOR REPRODUCTION OF FACIAL PATTERN IMAGE BASED ON

COLOR APPEARANCE MODELS

5.1 Introduction

Experimental methods to predict the tristimulus values of skin color under various

illuminants on CRT and hardcopy were described in Chapters 3 and 4. In this chapter a

method of color reproduction based on color appearance models is described. This

reproduction can be made matching the appearance of CRT with the reproduction on

hardcopy under various illuminants.

Some color appearance models are introduced in the colorimetric color

reproduction on CRT. However, there is not a standard color appearance model to

match the skin color appearance. Then, a comparison between color appearance models

is required to select a suitable model for skin color appearance reproduction. In this

chapter an outline of some color appearance models and viewing techniques for

psychophysical experiments are also presented.

5.1.1 Chromatic adaptation models

A) von Kries model

The von Kries coefficient law is based on the complete adaptation of human color visual

system to the white point of the illuminant. The cone fundamental tristimulus values L,

M, S are simply multiplicated by constant values, respectively. The constant values are

taken to be the inverses of the respective cone responses for the maximum signal of the

Chapter 5

44

illuminant. Then, the responses at new adapting field, La , Ma , and Sa can be written as

follows:

La = kLL , kL =LNa

LNo

, (5-1a)

Ma = kMM , kM =MNa

MNo

, (5-1b)

Sa = kSS , kS =SNa

SNo

, (5-1c)

where, L, M, and S are the excitations of cones on retina at original adapting field, k L ,

k M , and kS are multiplicative factors, LNa , MNa , and SNa are cone excitations for the

white point of new adapting illuminant, and LNo , MNo , and SNo are the cone excitations

for the white point of original illuminant.

B) CIELAB (LAB) color space

In 1976, CIE recommended CIELAB color space for color-difference metric which also

incorporates a modified form of the von Kries model, X/ XN , Y/YN , and Z/ ZN as shown

in Eq. (5-2),

L* = 116Y

YN

13

−16 , (5-2a)

a* = 500X

XN

13

−Y

YN

13

, (5-2b)

b* = 200Y

YN

13

−Z

ZN

13

, (5-2c)

where XN , YN , and ZN are the tristimulus values of the illumination white point.

Chapter 5

45

The tristimulus values Xa , Ya , Za at the new adapting field can be calculated as

follows:

Xa =a*

500+

L* +16

116

3

′ X N , (5-3a)

Ya =L* + 16

116

3

′ Y N , (5-3b)

Za =L* +16

116

−

b*

200

3

′ Z N , (5-3c)

where ′ X N , ′ Y N , and ′ Z N are the tristimulus values of the white point of the adapting

illuminant. CIELAB was not standardized to be a color appearance model. However it

provides a good approximation for color appearance in near-daylight conditions.

C) Fairchild color appearance model

The Fairchild color appearance model uses incomplete chromatic adaptation of cones to

the white point. This model is based on von Kries coefficient law, with an introduction

of a functional expression proposed by Hunt46 for incomplete levels of adaptation as

shown in Eq. (5-4).

′ L = ρLL/L

N, (5-4a)

′ M = ρM M/MN , (5-4b)

′ S = ρS S/SN , (5-4c)

where L’, M’, and S’ are the cone excitations considering a certain degree of chromatic

adaptation, ρL

,ρM , and ρS are parameters to represent degree of chromatic adaptation of

cones, respectively. LN

, MN , SN are respectively the L, M, S cone responses to the white

Chapter 5

46

point of the illuminant. Equation (5-4) can be expressed in matrix form as shown in Eq.

(5-5).

L'

M'

S'

= A

L

M

S

, (5-5)

The matrix A is

aL 0 0

0 aM 0

0 0 aS

, (5-6)

where

aL = ρL /LN , (5-7a)

aM = ρM/MN , (5-7b)

aS = ρS/SN . (5-7c)

The degree of chromatic adaptation can be calculated as follows:

ρL =

1 + YNυ + lE( )

1+ YNυ + 1/lE( ) , (5-8a)

ρM =1 + YN

υ + mE( )1+ YN

υ + 1/mE( ) , (5-8b)

ρS =1+ YN

υ + sE( )1+ YN

υ + 1/sE( ) , (5-8c)

where YN is the luminance of the illuminant, υ is an exponent that defines the shape of

the degree of the adaptation function and lE , mE , and sE are the fundamental

chromaticity coordinates of the adapting stimulus. Originally, Fairchild used the

exponent υ equal to 0.22 as suggested for a dark environment. This exponent value

Chapter 5

47

was set equal to 0.29 in the refinement of RLAB model by Fairchild.72 The lE , mE , and

sE values are calculated as follows:

lE =

3LN

LN + MN + SN

, (5-9a)

mE =3MN

LN + MN + SN

, (5-9b)

sE =3SN

LN + MN + SN

, (5-9c)

From the Eqs. (5-4) to (5-9), we can see that the adaptation will be less complete

for increasing values of the saturation of the adapting stimulus. The equations above

also show that the adaptation will be more complete for increasing values of the

luminance of the adapting stimulus.

The final step in the calculation of adaptation cone signals is a transformation

considering interaction among cones given by Eq. (5-10). This transformation allows

the model to predict increases of the perceived colorfulness called Hunt effect. This

transformation also allows the prediction of the increases of contrast with increasing

luminance, called Stevens effect.108

La

Ma

Sa

=1 c c

c 1 c

c c 1

′ L

′ M

′ S

, (5-10)

where c is calculated as follows:

c = 0.2190 − 0.0784log10

(YN

) . (5-11)

The entire model to predict the tristimulus values XA , YA , ZA in a second adapting

condition from the tristimulus values X, Y, Z in a first adapting condition can be

expressed by a single matrix equation as follows,

Chapter 5

48

XA

YA

ZA

= M−1A2−1C2

−1C1A1M

X

Y

Z

, (5-12)

where matrix M is the transformation from tristimulus values to cone fundamental

primaries. Matrix A1 and C1 respectively the matrices of Eqs. (5-6) and (5-10) for

adapting condition 1. Matrix A2 and C2 are respectively the matrices of Eqs. (5-6) and

(5-10) for adapting condition 2.

Fairchild and Berns incorporate this chromatic adaptation model into CIE 1976

(L*, a*, b*) color space in the RLAB color appearance model.38 This color space can

determine the required colors for reproduction across changes in media and viewing

conditions. This model can also be used for calculating metrics of lightness, chroma,

hue and color difference.

D) LLAB color appearance model.

In the model proposed by Luo and coworkers,73,74 the Rr , Gr ,Br cone responses at new

adapting field is calculated from the Rs , Gs , Bs cone at original adapting field using the

following equations;

Rr = D(Ror

Ros

) +1 − D

Rs , (5-13a)

Gr = D(Gor

Gos

) +1 − D

Gs , (5-13b)

Br = D(Bor

Bos

) +1 − D

Bsβ , for Bs ≥ 0 (5-13c)

Br = − D(Bor

Bos

) +1 − D

Bsβ , for Bs < 0 (5-13d)

Chapter 5

49

where β = (Bos

Bor

)0.0834 , Ros , Gos , Bos are the cone responses for the white point under

original adapting field; Ror , Gor Bor are the cone responses for the white point in the

environment in which the image will be reproduced; D value is 1.0 for hardcopies and

0.7 for CRT in dim surround.

5.1.2 Viewing techniques for cross-media comparison

The comparison of color appearance models is based on the recommendations of many

technical committees such as CIE Technical Committee 1-34, “Testing Colour-

Appearance Models in order to establish standard guideline for coordinated research on

evaluation of color appearance models for hardcopy and image on CRT”. 109-111 The

recommended methods use psychophysical experiments to select a suitable color

appearance model for cross-media reproduction. The psychophysical experiments for

the comparison of color appearance models are based on many viewing techniques such

as successive-binocular, simultaneous-binocular, simultaneous-haploscopic, successive-

Ganzfeld haploscopic, and memory matching technique. In the memory matching

technique, the illumination booth with the hardcopy and the CRT are placed at 90

degrees from each other ensuring that observers can not see both images on CRT and

the hardcopy at the same time. In this technique observers are asked to observe the

image in the booth before observing the image on CRT to compare images under

different conditions. In this technique observers are allowed to look at both hardcopy

and CRT only once. The successive-binocular viewing is equal to the memory

technique except that observers are allowed to look at both hardcopy and CRT as much

time as necessary to compare images. In the simultaneous-binocular technique, the

hardcopy in the illumination booth and the image on CRT are place side by side and the

observer is instructed to see the hardcopy and image on CRT with both eyes. In the

Chapter 5

50

simultaneous-haploscopic technique observers are instructed to observe the hardcopy

with one eye and the image on CRT with the other eye. This technique allows that each

eye adapts to a different white point while comparing the images. The successive-

Ganzfeld haploscopic viewing technique112 is similar to the simultaneous-haploscopic

viewing technique except that observers are not allowed to view both the hardcopy and

image on CRT at the same time. In this technique covers with a neutral field switches

over each eye allowing adaptation while the other eye is observing the image.

These viewing techniques have been compared by psychophysical methodology

such as the experiments performed by Braun and Fairchild.113 The binocular

matching114 was more preferred than haploscopic matching. It happens because the

binocular viewing is more natural way of viewing, and it is easier (it is accomplished

without the necessity of any special device) and more comfortable for the observer than

haploscopic viewing. These experiments also show that a successive color viewing was

preferred than a simultaneous color viewing because successive matching yielded the

shorter matching times115 and interocular interactions can be controlled116. Based on the

considerations above, the memory matching that combines easiness, successive color

matching and binocular color matching is preferred than other viewing techniques117 to

compare reproduced images using various color appearance models. Therefore,

memory matching technique will be used in the psychophysical experiments.

5.2 Color appearance matching method

Figure 18 shows a schematic diagram of the skin color reproduction method based on

color appearance model. Using color appearance models, the tristimulus values

Xa, Ya , and Za after the chromatic adaptation can be calculated from the tristimulus

values X’, Y’, Z’ obtained by colorimetric color reproduction. At first, X’, Y’, Z’ are

transformed to cone fundamental tristimulus values L, M, and S. The Hunt-Pointer-

Chapter 5

51

Estévez transformation are used to calculate L, M, S values, as shown in Eqs. (5-14) and

(5-15).38 This transformation is normalized to CIE Illuminant D65.

CRT display

(La, Ma, Sa )

-1

M

(Xa, Ya, Za )

Color Transform Matrix

E(λ )

PrincipalComponents

( L, M, S )

O(λ)

Colorimetric prediction

Calculatedtristimulus values

( Color appearance models

(X', Y', Z' )

(X', Y', Z' )

M

Figure 18. Diagram of color reproduction of facial pattern images on CRT based on

color appearance models.

L

M

S

= M

′ X

′ Y

′ Z

(5-14)

M =0.40 0.71 −0.08

−0.23 1.17 0.05

0.00 0.00 0.92

(5-15)

Chapter 5

52

Thereafter, the calculated L, M, and S values are used to estimate fundamental

tristimulus values La , Ma , and Sa corresponding to the cone responses after the

chromatic adaptation using color appearance models. The predicted values La , Ma , and

Sa were calculated using von Kries, and Fairchild models. Next, Xa, Ya , and Za

considering chromatic adaptation are calculated by the inverse of matrix M . Finally, the

predicted tristimulus values Xa, Ya , and Za are reproduced on CRT using color

transform matrix.

5.3 Psychophysical experiments

Psychophysical experiments were performed to select a suitable color appearance model

for the reproduction of skin color images on CRT in a dark environment. The images

on CRT were compared with a hardcopy illuminated in a standard illumination booth

(Macbeth Spectralight II). The booth contains four illuminants; “Horizon”, “A”,

“Cool White”, and “Day Light”. The spectral radiances of these illuminants are

shown in Fig. 11. We reproduced five facial pattern images of a Japanese woman and

six skin color patches. The chromaticities of skin color patches are extracted from the

facial pattern images and the tristimulus values of the six color patches under “ A ”

illuminant are shown in Table 6.

Chapter 5

53

Table 6. The tristimulus values of the six skin color patches under illuminant “A”.

Patch X Y Z

1 105 90 20

2 72 66 18

3 75 70 19

4 38 37 12

5 47 45 13

6 72 61 14

Four images were generated on CRT for each illuminant; an image generated by

X’, Y’ and Z’ without considering chromatic adaptation, named XYZ image; an image

generated by von Kries color appearance model, von Kries image; an image generated

by Fairchild model, Fairchild image; and an image generated by CIELAB model,

CIELAB image. Figure 19 shows an example of predicted color appearance for the skin

color patches under various illuminants. The reproduction for each color appearance

model is shown in Figs. 20, 21, 22 and 23 respectively, under illuminant “A”,

“Horizon”, “Cool white”, and “Day Light”.

Chapter 5

54

XYZ CIELAB XYZ CIELAB

von Kries Fairchild von Kries Fairchild

(a) illuminant “A” (b) “Horizon”

XYZ CIELAB XYZ CIELAB

von Kries Fairchild von Kries Fairchild

(c) “Cool White” (d) “Day Light”

Figure 19. Predicted color appearance of skin color patches under various

illuminants; (a) illuminant “A”, (b) “Horizon”, (c) “Cool White”, (d) “Day Light”.

Chapter 5

55

(a) XYZ (c) CIELAB

(c) von Kries (d) Fairchild

Figure 20. Color appearance predictions of a facial pattern image under

illuminant “A”; (a) XYZ, (b) CIELAB, (c) von Kries, (d) Fairchild.

Chapter 5

56

(a) XYZ (c) CIELAB

(c) von Kries (d) Fairchild

Figure 21. Color appearance predictions of a facial pattern image under

“Horizon”; (a) XYZ, (b) CIELAB, (c) von Kries, (d) Fairchild.

Chapter 5

57

(a) XYZ (c) CIELAB

(c) von Kries (d) Fairchild

Figure 22. Color appearance predictions of a facial pattern image under “Cool

White”; (a) XYZ, (b) CIELAB, (c) von Kries, (d) Fairchild.

Chapter 5

58

(a) XYZ (c) CIELAB

(c) von Kries (d) Fairchild

Figure 23. Color appearance predictions of a facial pattern image under “Day

Light”; (a) XYZ, (b) CIELAB, (c) von Kries, (d) Fairchild.

Chapter 5

59

Figure 24 shows a viewing technique using memory matching that was used to

select a suitable color appearance model to reproduce skin color images on CRT.

90o

Standard Illumination Booth

Observer

1 m

1 m

CRT Display

w=10 cm for facial pattern imagew=5 cm for skin color patchh=6 cm for facial pattern imageh=5 cm for skin color patch

w

w

h

h

Figure 24. Arrangement of psychophysical experiment to compare skin color images

on a CRT with a hardcopy in a standard illumination booth using memory matching.

Both CRT and hardcopy were arranged at an equal viewing distance of approximately 1

m from the observer. The images, whether it is on the CRT or in the illumination booth,

would be observed with both eyes. The observer can see the CRT and the hardcopy

only once to obtain a comparative judgment.

Chapter 5

60

Ten observers took part in this experiment. They were asked to read the

following instructions before the experiment;

“In this experiment, you must compare a color image in the standard illumination booth

with four reproductions displayed on CRT simultaneously. At first, you will look at the

printed skin color image in the illuminant booth after adapting for a minute. You will be

asked to memorize the skin color of the image. Turn towards the CRT, and look at the

displayed neutral gray field. After adapting to the neutral gray field for a minute,

examine the four reproductions and select the one that looks most like the hardcopy that

you memorized. You must choose the reproduction on CRT based only on color

judgment. You must judge only considering if the reproduction looks like the original

hardcopy and not in the image quality or preference.” The observers were asked to look

the image for about one minute because Fairchild and Reniff84 found that chromatic

adaptation at constant luminance was 90% complete after approximately 60 seconds.

The position of each model on the CRT was randomized for each set of predicted

images.

5.4 Experimental results

Figure 25 shows the percentage of skin color patch that was selected as the best one in 4

kinds of models on CRT. Figure 25(a) shows the percentage of selection under various

illuminants. From Fig. 25(a), we can see that the color appearance of patch by Fairchild

model was chosen as the best one. Figure 25(b) shows the percentage of selection for

each illuminant. It is possible to observe that the incomplete adaptation, Fairchild model,

was effective under “Horizon”, “Cool White” and illuminant “A”. However, under

“Day Light”, Fairchild model was selected as well as the model proposed by von Kries.

Chapter 5

61

(a) Selected model under various illuminants.

0102030405060

708090

100

XYZ von Kries FairchildCIELAB

Per

cent

age

chos

en Illuminant "A"

"Day Light"

"Horizon"

"Cool White"

(b) Selected model under each illuminant.

Figure 25. Percentage of selection of each color appearance model for skin color patch

reproduction.

On the other hand, Fig. 26 shows the percentage of selection of each color

appearance model for reproduced facial pattern image. Figure 26(a) shows the

percentage of selected models under various illuminants. It is clear that Fairchild model

Chapter 5

62

was chosen as well as the color patches. Figure 26(b) shows the percentage of selected

model for each illuminant.

0102030405060

708090

100

CIELAB von Kries FairchildXYZ

Per

cent

age

chos

en

Face1

Face2

Face3

Face4

Face5

(a) Selected model under various illuminants.

XYZ CIELAB Fairchild0

102030405060

708090

100

von Kries

Per

cent

age

chos

en

Illuminant "A"

"Day Light"

"Horizon"

"Cool White"

(b) Selected model under each illuminant.

Figure 26. Percentage of selection of each color appearance model for facial pattern

image reproduction.

Chapter 5

63

It is clear that, there is no significant difference among illuminants for each model for

facial pattern images.

The comparison of the results obtained in Figs. 25 and 26 shows that the

performance of Fairchild model was not so good for facial pattern images as in the case

of skin color patches. The model proposed by Fairchild was applied well to skin color

patches but it was not effective for facial pattern images as skin color patches. Facial

skin color is one of the human memorized colors. We can believe that this difference in

the performance of Fairchild model is due to the memorized colors118.

5.5 Conclusion

A color reproduction method based on color appearance models was used to match the

appearance of skin color on CRT with hardcopy under various illuminants. The

colorimetric color reproduction was compared with images reproduced using color

appearance models proposed by von Kries, Fairchild and CIELAB color space. The

results of psychophysical experiments using memory matching showed that the

incomplete chromatic adaptation model proposed by Fairchild is a better model than

CIELAB or von Kries. It confirms that an incomplete chromatic adaptation model is

effective for complex image.119 However, the model proposed by Fairchild does not be

applied to facial pattern image as well as skin color patches. These results show that

more studies of the influence of memorized facial skin color are necessary.

The effect of surround on CRT120 and the effect of individual variation of color

matching functions121,122, could also be applied to skin color reproduction.

Chapter 6

64

CHAPTER 6

MODIFIED FAIRCHILD CHROMATIC ADAPTATION MODEL

FOR FACIAL PATTERN IMAGES

6.1. Introduction

The incomplete chromatic adaptation model proposed by Fairchild could be applied well

for skin color patches as shown in a previous chapter. However this model could not

apply to facial pattern image as well as for skin color patches. Therefore, I tried to

modify Fairchild model for facial pattern images.

6.2. Modified Fairchild chromatic adaptation model

Coefficients KL, KM, KS, were introduced in Eq. (5-9) as follows,

lE =

KLLN

LN + MN + SN

, (6-1a)

mE =K

MMN

LN + MN + SN

, (6-1b)

sE =K

SSN

LN + MN + SN

. (6-1c)

In the Fairchild model, the coefficients KL , KM, KS are defined as 3.0. These color

coefficients provide adjustment of the degree of color balance for facial pattern images.

Chapter 6

65

6.3. Psychophysical experiments to tune color balance.

Psychophysical experiments using memory matching were performed to select the

optimum coefficients of color balance for facial pattern image. The coefficients KL ,

KM , KS were varied from 2.9 to 3.2 in intervals of 0.1 unit. These 64 combinations of

coefficients were used to reproduce a facial pattern image under three kinds of

illuminants (“A”, “Day Light”, “Cool White”). The observer was asked to select on

CRT the most similar image to the original hardcopy using memory matching as

described in Chapter 5. The results of this experiment were shown in Figs. 27(a), (b),

(c), and (d).

2.9 3.0 3.1 3.2 2.9 3.0 3.1 3.2 2.9 3.0 3.1 3.2 2.9 3.0 3.1 3.2

2.9 2.9 2.9 2.9 3.0 3.0 3.0 3.0 3.1 3.1 3.1 3.1 3.2 3.2 3.2 3.2

2.9 2.9 2.9 2.9 2.9 2.9 2.9 2.9 2.9 2.9 2.9 2.9 2.9 2.9 2.9 2.9

Nu

mb

er o

f se

lect

ion

tim

es

KS

KM

KL

Figure 27(a). A number of selection when KM , KS are changed from 2.9 to 3.2 and

KL = 2.9.

Chapter 6

66

Nu

mb

er o

f se

lect

ion

tim

es

2.9 3.0 3.1 3.2 2.9 3.0 3.1 3.2 2.9 3.0 3.1 3.2 2.9 3.0 3.1 3.2

2.9 2.9 2.9 2.9 3.0 3.0 3.0 3.0 3.1 3.1 3.1 3.1 3.2 3.2 3.2 3.2

3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0

KSKM

KL

Figure 27(b). A number of selection when KM , KS are changed from 2.9 to 3.2 and

KL = 3.0.

Nu

mb

er o

f se

lect

ion

tim

es

2.9 3.0 3.1 3.2 2.9 3.0 3.1 3.2 2.9 3.0 3.1 3.2 2.9 3.0 3.1 3.2

2.9 2.9 2.9 2.9 3.0 3.0 3.0 3.0 3.1 3.1 3.1 3.1 3.2 3.2 3.2 3.2

3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1

KS

KM

KL

Figure 27(c). A number of selection when KM , KS are changed from 2.9 to 3.2 and

KL = 3.1.

Chapter 6

67

Nu

mb

er o

f se

lect

ion

tim

es

2.9 3.0 3.1 3.2 2.9 3.0 3.1 3.2 2.9 3.0 3.1 3.2 2.9 3.0 3.1 3.2

2.9 2.9 2.9 2.9 3.0 3.0 3.0 3.0 3.1 3.1 3.1 3.1 3.2 3.2 3.2 3.2

3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1

KSKMKL

Figure 27(d). A number of selection when KM , KS are changed from 2.9 to 3.2 and

KL = 3.2.

From Figs. 27(a), (b), (c), and (d), it is decided to choose KL =3.1, KM =2.9,

KS =3.1 as optimum coefficients of color balance for facial pattern image.

6.4. Comparison of the modified Fairchild model with other color appearance

models.

A) Experiment A (Modified Fairchild, XYZ, von Kries, Fairchild)

The coefficients of color balance in the modified Fairchild incomplete chromatic

adaptation equations were set as KL =3.1, KM =2.9, KS =3.1 and the performance of this

modified model was compared with colorimetric color reproduction and other color

appearance models (von Kries, Fairchild) by psychophysical experiments. The

reproduced images under illuminant “A” are shown in Fig. 28.

Chapter 6

68

(a) XYZ (b) Custom

(c)von Kries (d) Fairchild

Figure 28. A facial pattern image reproduced on a CRT for illuminant “A”; (a) XYZ,

(b) Modified Fairchild (Custom model), (c) von Kries, (d) Fairchild.

Psychophysical experiments were performed using memory matching. A

hardcopy in a standard illuminant booth was compared with a pair of reproductions on

CRT in a dark environment. Ten observers were asked to select the reproduction on

CRT that provides the best match in color appearance with the hardcopy. The choices of

reproduction on CRT were converted to an interval scale of color reproduction quality

for various models using Thurstone’s law of comparative judgments123. Using

statistical procedures described by Torgeson124 the averaged z-scores for each model

were calculated. These z-scores give interval scale values of each model indicating their

Chapter 6

69

performance in the reproduction of the original hardcopy. A confidence interval of 95%

for the averaged value is calculated in Eq. (6-2).

±1.960.707

N M, (6-2)

where N is the number of observation for a sample, M is the number of tested models.

In our experiment, the confidence interval around each scale value was 0.283, where

N=15 and M=4. The performances of two models are considered as equivalent if the

average of one model falls within the error bar of another model. The results of these

experiments are shown in Figs. 29(a), (b), and (c), where “Custom” indicates the

modified Fairchild model for facial pattern image. The central bar in each plot of Figs.

29(a), (b), and (c) indicate the averaged interval scale value and the bars indicate the error

in 95% confidence interval. In the case of the XYZ image under “Day Light”

illuminant it was not possible to calculate the z-score because XYZ reproduction was not

selected at all.

Figure 29(a). Averaged interval scale of model performance for illuminant “A”.

Chapter 6

70

Figure 29(b). Averaged interval scale of model performance for “Day Light”.

Figure 29(c). Averaged interval scale of model performance for “Cool White”.

The statistical result of these comparisons showed that the modified Fairchild

model (Custom model) had the best averaged z-scores for all kind of illuminants. The

XYZ image showed the worst results because this reproduction does not consider

chromatic adaptation.

Chapter 6

71

B) Experiment B (Modified Fairchild, von Kries, RLAB 96, LLAB)

XYZ and Fairchild reproductions were replaced by the RLAB refinement

published in 1996 (RLAB 96),72 and LLAB model73,74 to refine and update the

psychophysical experiments. These models were tested for both skin color patches and

facial pattern images. Figure 30 shows a reproduced skin color patch under illuminant

“A”. Figure 31 shows the reproduced facial pattern image under illuminant “A”.

(a) RLAB 96 (b) Custom

(c)von Kries (d) LLAB

Figure 30. A skin color patch reproduced on CRT display for illuminant “A”; (a)

RLAB 96, (b) Modified Fairchild (Custom model), (c) von Kries, (d) LLAB models.

Chapter 6

72

(a) RLAB 96 (b) Custom

(c)von Kries (d) LLAB

Figure 31. A facial pattern image reproduced on CRT display for illuminant “A”; (a)

RLAB 96, (b) Modified Fairchild (Custom), (c) von Kries, (d) LLAB models.

Chapter 6

73

Six color patches were examined by two observers and a facial pattern image was

observed by ten observers. Figure 32 shows the percentage of skin color patch that was

selected on CRT as the best one in 3 kind of illuminants. On the other hand, Fig. 33

shows the percentage of selection for the facial pattern image chosen as the best one on

CRT display in 3 kind of illuminants..

von Kries RLAB 96 Custom LLAB0

5

10

15

20

25

30

35

40

45

50Illuminant "A"

"Day Light"

"Cool White"

Per

cen

tag

e ch

ose

n

Figure 32. Percentage of skin color patch that was selected on CRT as the best one in 3

kind of illuminants.

Chapter 6

74

von Kries RLAB 96 Custom LLAB0

5

10

15

20

25

30

35

40

Illuminant "A"

"Day Light"

"Cool White"

Per

cen

tag

e ch

ose

n

Figure 33. Percentage of selection for reproduced facial pattern image chosen as the

best one on CRT display in 3 kind of illuminants.

From Fig. 32, it is clear that the color appearance of patch by RLAB 96 model

was chosen as the best one. In this case the modified Fairchild model did not perform

well as RLAB 96 model because the coefficients of color balance were adjusted for

facial pattern image and not for skin color patches. From Fig. 33 it is possible to see

that LLAB model performed well for illuminant “A” but it could not predict well other

illuminants used in the experiment. On the other hand, von Kries model performed well

for “Day Light“ and “Cool White” but it presented poor results for illuminant “A”.

RLAB 96 model performed relatively well, however the modified Fairchild model

(Custom model) presented the overall best result under all kind of illuminants.

The result was also analyzed statistically. Figures 34(a), (b), and (c) show the

averaged interval scale values for each reproduced facial pattern image under various

illuminants.

Chapter 6

75

Figure 34(a). Averaged interval scale of model performance for illuminant “A”.

Figure 34(b). Averaged interval scale of model performance for “Day Light”.

Chapter 6

76

Figure 34(c). Averaged interval scale of model performance for “Cool White”.

From Figs. 34(a) and (b) it is clear that von Kries and RLAB 96 models are

approximately same in statistical values for facial pattern image reproduction under “A”

and “Day Light” illuminants. From Fig. 34(c) it can be also found that von Kries and

LLAB models are approximately same in statistical values for reproduction under “Cool

white” illuminant. It is also possible to see from Fig. 34(c) that RLAB 96 and Custom

models are approximately same in statistical values for reproduction under “Cool

white” illuminant.

6.5. Conclusion

It was found from the psychophysical experiments that the performance of color

appearance models for facial pattern depends on the illuminant. The modified Fairchild

color appearance model (custom model) performed well for facial pattern images and

showed the best averaged z-scores for all kind of illuminants. We can conclude that the

proposed modified Fairchild model can be performed well to reproduce facial pattern

images.

Chapter 7

77

Chapter 7

COLOR REPRODUCTION OF ENDOSCOPIC IMAGES UNDER

ENVIRONMENTAL ILLUMINATION

7.1 Introduction

In recent years, electronic endoscope has been widely used for diagnosis of various

kinds of diseases. The color of stomach and intestine mucosa gives significant

information for diagnosis of many diseases such as gastritis, cancer and so on.

Sometimes the physician needs to ask another specialist for the diagnosis. The process

of sending and receiving images from one hospital to another has been possible with the

advance of telecommunication systems. However, in these systems the viewing

conditions and devices vary case-by-case. Then, it is necessary to consider the influence

of the environmental conditions on the appearance of reproduced image. The

endoscopic images are generally viewed by physician in dark environment of an

operation room. However, when the images are viewed in another room, such as

meeting room, it is necessary to consider the influence of environmental illuminant on

the appearance of endoscopic images. It is necessary to do gamut-mapping for image

which cannot be reproduced in the gamut of CRT. However, there is not any way to

quantify how gamut-mapping affects the perceived color appearance.

In this chapter, a perceptual color difference is defined to evaluate gamut-

mapping for endoscopic image reproduced on CRT under environmental illumination

instead of the traditional color difference. The perceptual color difference is defined by

Mahalanobis distance which is calculated using the covariance matrix of metric

lightness, chroma and hue angle.

Chapter 7

78

7.2 Color reproduction method for endoscopic images under environmental

illumination

Figure 35 shows a schematic diagram of a color reproduction method to reproduce the

appearance of endoscopic images on CRT under various illuminants.

RGBCRT 1

ChromaticAdaptation

CRT 2

CRTCalibration

Gamut- mapping

O(λ)

E(λ)

Substractionof reflectedlight on CRT

I l luminant CRT1 White point CRT2 White pointÅ@ Illuminant

White point

Adaptationto CRT andilluminant

X'Y'Z'

L'C'h

R'G'B'

XYZ

X"Y"Z" XLYLZL

LCh

Figure 35. Diagram of color reproduction method to reproduce the appearance of

endoscopic images on CRT under various illuminants.

Chapter 7

79

In Fig. 35, the R, G, B original endoscopic image is transformed to X, Y, Z using the

characteristics of the CRT in the dark environment. The color appearance is calculated

from X, Y, Z values and represented in CIELUV L*, C*, and h values. The gamut-

mapping was performed to adjust the L*, C*, h values on CRT 1 to the L*’, C*’, h’

values on CRT 2 under various illuminants. The inverse chromatic adaptation is

performed to get X’, Y’, Z’. The XL YL, ZL tristimulus values of the reflected light on

CRT surface are subtracted from X’, Y’, Z’ to give X”, Y”, Z” tristimulus values of

emitted light on CRT surface. Finally, the X”, Y”, Z” was transformed to the device

dependent R,’ G ’, B’ that are displayed on CRT. XL, YL, ZL can be calculated from the

spectral reflectance of the CRT surface ρ(λ) using the following equations;

XL = K E(λ )ρ(λ)400

700

∫ x (λ)dλ , (7-1a)

YL = K E(λ )ρ(λ)400

700

∫ y (λ)dλ , (7-1b)

ZL = K E(λ )ρ(λ)400

700

∫ z (λ)dλ , (7-1c)

K =100/ E(λ )400

700

∫ y (λ)dλ , (7-1d)

where E(λ) is the spectral radiance of the illuminant.

The measurement of spectral reflectance ρ(λ) of the CRT depends on the

viewing angle, so it was assumed that the endoscopic images are displayed on the center

of the CRT and the observer watched the images in a fixed position in front of the CRT.

The spectral reflectance ρ (λ) of the CRT was obtained dividing the amount of radiant

power reflected on CRT by the amount of radiant power reflected on the white perfect

diffuser. The amounts of radiant power of three illuminants (“A”, “Cool white” and

“Day Light” whose relative spectral radiances are given in Fig. 11) were measured on a

Chapter 7

80

white diffuser with reflectance of approximately 90%. Eventual scattering of light inside

the CRT was ignored. The spectral reflectance was calculated for three kinds of

illuminants to examine the illuminant dependence of the spectral reflectance as shown in

Figs. 36(a), (b) and (c), respectively under “A”, “Cool white” and “Day Light.” As

expected, the spectral reflectance has approximately the same shape for these three kinds

of illuminants.

0

2

4

6

8

12

14

16

18

20

400 450 500 550 600 650 700

Wavelength (nm)

10

Spe

ctra

l ref

lect

ance

(%

)

Figure 36(a). Spectral reflectance of CRT without radiation from CRT under illuminant

“A”.

Chapter 7

81

02

4

6

8

10

12

14

16

18

400 450 500 550 600 650 700

Wavelength (nm)

Spe

ctra

l ref

lect

ance

(%

)

Figure 36(b). Spectral reflectance of CRT without radiation from CRT under “Cool

White”.

0

2

4

6

8

10

12

14

400 450 500 550 600 650 700

Wavelength (nm)

Spe

ctra

l ref

lect

ance

(%

)

Figure 36(c). Spectral reflectance of CRT without radiation from CRT under “Day

Light”.

XL, YL, ZL were calculated using spectral reflectance ρ(λ) for each illuminant and the

values are shown in the Table 7.

Chapter 7

82

Table 7. XL, YL, ZL tristimulus values of reflected light on CRT under various

illuminants.

Illuminant Illuminant “A” “Cool White” “Day Light”

XL 6.24 5.84 1.88

YL 5.52 5.83 2.95

ZL 3.68 4.07 4.24

The incomplete chromatic adaptation model proposed by Fairchild was used to

predict the color appearance as in the case of skin color. The chromatic adaptation on

CRT in a dark environment occurs in relation to the white point of the CRT. In the case

of illuminated CRT, Katoh considered mixed chromatic adaptation.10,11,125 Katoh found

that human visual system is 60% adapted to CRT white point and 40% to the ambient

light. However, as Katoh stated, the degree of adaptation depends on the time of

observation and the distance from the CRT. In medical systems, it is difficult to

reproduce the same experimental conditions used by Katoh. Then, it is assumed that

chromatic adaptation occurs to the white point of CRT added to the tristimulus values of

reflected light on CRT. The color reproduction of the tristimulus values X’, Y’, Z’ of

CRT under illumination could be predicted from the X, Y, Z of the CRT in the dark

environment using a simple linear transformation of multiplying matrices as shown in

Eq. (7-2), which was rewritten from Eq. (5-12).

X'

Y'

Z'

= M−1A2−1C2

−1C1A1M

X

Y

Z

, (7-2)

Chapter 7

83

7.3 Gamut-mapping of endoscopic image

7.3.1 Gamut-mapping in 1976 CIELUV L*C*h color space

The objective of gamut-mapping is to find a way to display the processed colors that are

out of color gamut in CRT. The gamut-mapping should ensure that the appearance of

the reproduction is as close to the original as possible.73 This appearance fidelity of the

reproduced image to the original is very important in remote diagnosis for endoscopic

images, because diagnosis of physicians is mainly based on the appearance of color.

The Luv*, Cuv*, huv metric lightness, chroma, and hue angle respectively were

used for gamut-mapping because these color attributes have a psychophysical meaning.

The relationship between the tristimulus values and the L*, u*, v* are given by Eq. (7-3)

and the relationship between L*, u*, v* and Luv*, Cuv*, huv is shown in Fig. 37.

L* = 116Y

Yn

1

3

−16 forY

Yn

> 0.008856 , (7-3a)

L* = 903.3Y

Yn

forY

Yn

≤ 0.008856 , (7-3b)

Cuv* = (u*)2 + (v* )2 , (7-3c)

huv = tan−1 u*

v*

, (7-3d)

where

u* = 13L* (u' −un' ) , (7-3e)

v* = 13L*(v' −vn ' ) , (7-3f)

u' =4X

X +15Y + 3Z, (7-3g)

un' =4 Xn

Xn + 15Yn + 3Zn

, (7-3h)

v' =9Y

X +15Y + 3Z, (7-3i)

Chapter 7

84

vn' =9Yn

Xn + 15Yn + 3Zn

, (7-3j)

C*

h0 v *

u*

v *

u*

h = 0o

h = 90o

h = 180o

h = 270o

L*Yellow

Green

Blue Red

Figure 37. Relationship between L*u*v* and L*C*h color spaces.

7.3.2 Perceptual Mahalanobis distance

The gamut-mapping algorithms are evaluated using psychophysical techniques,

as performed by Katoh126,127 considering differences in metric lightness (∆L), chroma

(∆C ), and hue angle (∆h). However, the weighted color difference ∆E which was

proposed by Katoh, as shown in Eq. (7-4), does not consider the correlation between the

lightness, chroma and hue angle.

∆E =∆L*

Kl

2

+∆Cab

*

Kc

2

+∆Hab

∗

Kh

2

12

, (7-4)

where ∆L* , ∆Cab* , ∆Hab

* are differences in lightness, chroma, and hue respectively. Kl ,

KC , Kh are mapping coefficients for each attribute of color.

Chapter 7

85

The CIE 1994 total color-difference128 shown in Eq. (7-5) uses correlation

between hue and chroma in the estimation of weighting functions. However, it does not

consider the correlations between lightness and hue, lightness and chroma.

∆E94* =

∆L*

kL SL

2

+∆Cab

*

kCSC

2

+∆Hab

*

kHSH

2

12

(7-5)

where kL , kC , kH are parametric factors, SL , SC , SH are weighting functions. SL =1;

SC =1+0.045Cab* ; SH =1+0.015Cab

* are currently recommended by CIE.

A perceptual color distance based on Mahalanobis distance is defined using

covariance matrix of perceptually equivalent metric lightness, chroma and hue angle of

endoscopic images. The Mahalanobis distance129 makes uniform the influence of the

distribution of each attribute and is defined as follows;

d = ∆L ∆C ∆h[ ]VLL VLC VLh

VCL VCC VCh

VhL VhC Vhh

−1∆L

∆C

∆h

1

2

, (7-6)

where VLL, VCC , Vhh are the variances of metric lightness, chroma, hue angle, respectively.

On the other hand, VLC(VCL ), VLh (VhL ), VCh (VhC ) are the covariances between metric

lightness and chroma, lightness and hue angle, and chroma and hue angle, respectively.

This perceptual distance can be used to evaluate gamut-mapping. The gamut-mapping

that provides the shortest perceptual Mahalanobis distance is considered as the best

reproduction.

Chapter 7

86

7.3.3 Psychophysical experiments

Psychophysical experiments were performed to find a covariance matrix to

define the Mahalanobis distance for endoscopic image. For this purpose, the lightness

of endoscopic image was changed by -4, -2, 0, 2, 4 units, the chroma was changed by -6,

-3, 0, 3, 6 units, and the hue angle was changed by -2, -1, 0, 1, 2 degrees depart from the

original image. Every possible combination of these three color attributes was prepared

as 125 sets of endoscopic images. Each image was displayed randomly. Ten observers

who are students and staff of our laboratory were asked to watch each pair on CRT and

they were asked to select if two images are the same or not. The statistical result of this

experiment is shown in Table 8.

Table 8. Variances and covariances for metric lightness, chroma and hue angle of

endoscopic image.

Attribute Symbol Value

Variance of metric lightness VLL5.818

Variance of metric chroma VCC11.29

Variance of metric hue angle Vhh1.326

Covariance between metric lightness and chroma VLC(VCL ) 2.664

Covariance between metric lightness and hue angle VLh (VhL ) 0.2198

Covariance between metric chroma and hue angle VCh (VhC ) -1.544

From Table 8, the variance of chroma is greater than variance of lightness; and then the

variance of lightness greater than variance of hue angle.

Chapter 7

87

The perceptual Mahalanobis distance can be calculated by Eq. (7-7),

d = ∆L ∆C ∆h[ ]0.2047 −0.0630 −0.1071

−0.0630 0.1247 0.1556

−0.1071 0.1556 0.9530

∆L

∆C

∆h

1

2

. (7-7)

The presence of negative non-diagonal terms in the matrix of Eq. (7-7) is corresponding

to the correlation of lightness and chroma, and lightness and hue angle, and it suggests

to decrease the perceptual color distance when ∆Γ × ∆Θ > 0 , where Γ and Θ are L, C,

h. On the other way, the positive non-diagonal terms are corresponding to the

correlation between metric chroma and hue angle and it indicates to decrease the

perceptual color distance when ∆Γ × ∆Θ < 0 .

Hara and coworkers carried out psychophysical experiment,130,131 with

collaboration of five physicians. They changed the metric lightness, chroma and hue

angle in order to reproduce a preferred endoscopic image on CRT. In this experiment,

they only examined variance of metric lightness, chroma, hue angle and covariance

between metric chroma and hue angle as shown in Table 9. Unfortunately, it is not

possible to calculate the perceptual Mahalanobis distance using the result of Hara’s

experiment.

Chapter 7

88

Table 9. Result of psychophysical experiments performed by Hara with the

collaboration of physicians.

Statistical value of color attribute Symbol Value

Variance of metric lightness VLL23.56

Variance of metric chroma VCC34.08

Variance of metric hue angle Vhh7.44

Covariance between metric chroma and hue angle VCh VhC( ) -8.97

However, they found that the variance of metric chroma was greater than that of

lightness, the variance of lightness was greater than that of hue angle, and covariance

between chroma and hue angle have a negative value like the results of the

pshychophysical experiments shown in Table 8.

7.4 Analysis of gamut-mapping for endoscopic images

Scaling and translation of metric hue angle, chroma and lightness were done for

gamut-mapping as shown in Eq. (7-8);

h' = h + α , (7-8 a)

C'= βC + γ , (7-8 b)

L' =φ L + ε , (7-8 c)

where h, C, L are the hue angle, chroma and lightness respectively before the mapping,

the h’, C’, L’ are the mapped hue angle, chroma and lightness respectively, and α , γ, β,

ε and φ are coefficients of hue angle, chroma translation, chroma scaling, lightness

translation , and chroma scaling, respectively. Only one coefficient was used for hue

angle since both scaling and translation of hue angle produces rotation of mapped points

around lightness axis. The parameters were varied in intervals as described in Table 10.

Chapter 7

89

Table 10. Variation of coefficients φ, ε, β, γ andα in the Eqs. (7-10).

Coefficient Initial value Final value Interval unit

φ 0.95 1.00 0.05

ε -3 3 1

β 1.0 1.0 0

γ -10 10 1

α -1 1 1

A stomach endoscopic image was reproduced from a CRT (Nanao FlexScan

56T) in a dark environment (corresponding to CRT 1 in Fig. 35) to a CRT (AppleColor

High-Resolution RGB Model MO401) under illuminant “A” (CRT 2 in Fig. 35). The

characteristics of CRT were described in Chapter 3. Figure 38 shows the endoscopic

image to be displayed on a CRT in a dark environment.

Chapter 7

90

Figure 38. Stomach endoscopic image.

This image was chosen because it presents dark and bright regions that are generally

difficult to reproduce simultaneously inside the color gamut of the CRT.

Figure 39 shows a reproduction of stomach image shown in Fig. 38 on a CRT

under illuminant “A”. This image was not reproduced inside the color gamut of the

CRT. In this case 2.76% of the pixels was out of gamut in red channel, 0.86% of pixels

were out of gamut in green channel, and however, all pixels were inside the gamut in

blue channel. Lightness, chroma and hue angle mapping was applied to the image in

Fig. 39 and the perceptual Mahalanobis distance produced by each mapping were

calculated when 99% of the pixels are reproduced inside color gamut of the CRT for all

the combinations of coefficients α, β, γ, ε, and φ changed as shown in Table 10.

Figure 39. Reproduced image on CRT under illuminant “A”.

Chapter 7

91

The minimum averaged perceptual Mahalanobis distance was 1.357 for φ=0.95, ε=3,

β=1.0, γ=1 and α=0, coefficients of Eq. (7-8). The Eq. (7-8) can be rewritten as

follows;

h' = h , (7-9 a)

C' = C +1 , (7-9 b)

L' = 0.95L + 3, (7-9 c)

The image was reproduce inside the color gamut of the CRT for 99.17% in red channel,

99.99% in the green channel, and 100.00% in the blue channel. The reproduced

endoscopic image for these coefficients is shown in Fig. 40.

Figure 40. Reproduced stomach endoscopic image under illuminant “A”, for φ=0.95,

ε=3, β=1.0, γ=1 and α=0 of Eq. (7-8).

Chapter 7

92

This result shows that it is better to adjust metric lightness and chroma

simultaneously and maintain the hue angle unchanged to minimize changes in the color

appearance. The hue angle is the appearance attribute that can be distinguished with the

highest precision and the psychophysical experiments showed that human visual system

is very sensitive for changes in hue.

7.5 Conclusion

A method to reproduce endoscopic images on illuminated CRT was proposed. This

color reproduction method uses color appearance models and gamut-mapping. Gamut-

mapping was performed in 1976 CIELUV L*C*h color space by scaling and

translation of the color attributes. A perceptual Mahalanobis distance was defined to

evaluate the proposed gamut-mapping techniques. This perceptual distance is calculated

using covariance matrix of perceptually equivalent metric lightness, chroma and hue

angle and indicates how the color appearance of reproduced endoscopic image is

affected by gamut-mapping. Experiments using this perceptual color distance showed

that a mapping that minimizes changes in color appearance was obtained for φ=0.95,

ε=3, β=1.0, γ=1 and α=0, coefficients of Eq. (7-8). Therefore, it is better to map

lightness and chroma simultaneously and maintain hue angle unchanged.

Chapter 8

93

CHAPTER 8

CONCLUSION

Many aspects and problems involving color reproduction of original scene under

various illuminants have been studied, specially for skin color and endoscopic images.

At first, spectral reflectance of facial pattern images taken by HDTV camera was

estimated using three principal components of skin spectral reflectance. Computer

simulation of colorimetric color reproduction was done using those obtained spectral

reflectance. The predicted images were reproduced colorimetrically on CRT and

hardcopy. Color appearance models were also introduced into colorimetric color

reproduction method to predict the color appearance of skin colors under various

illuminants on CRT. Computer simulations of Fairchild, von Kries and LAB

chromatic adaptation models were compared with the color hardcopies by

psychophysical experiments using memory matching technique. These experiments

showed that the incomplete chromatic adaptation model proposed by Fairchild can be

used for a suitable prediction for color appearance of skin color patches. However,

Fairchild model was not so effective for facial pattern images as skin color patches.

Coefficients of Fairchild model were adjusted to reproduce facial pattern images by

psychophysical experiments. The modified Fairchild model showed the best overall

performance compared to the other color appearance models under various

illuminants.

Chapter 8

94

The proposed color reproduction method based on color appearance models was

also applied to endoscopic image on CRT under environmental illumination. However,

gamut-mapping is required for images that is not reproduced inside the gamut of CRT.

From this experiment, we introduced a new perceptual color distance based on

Mahalanobis distance for gamut-mapping. Mahalanobis distance was calculated using

covariance matrix of metric lightness, chroma and hue angle obtained by

psychophysical experiments. Therefore, I consider that the distance could be used as

part of an extension of CIE 1994 total color-difference ∆E94* as perceptual color

distance. Various gamut-mapping techniques were evaluated using this perceptual

color distance. As a result, it was shown that the lightness and chroma should be

mapped simultaneously preserving the hue angle for effective color reproduction of

endoscopic image.

In this dissertation, the scope of the study was limited to specific application

such as facial pattern and endoscopic image reproduction. However, I believe that the

methods developed in this research can be extended to the reproduction of other types

of complex images, such as fine art image, and landscape pictures.

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Papers

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LIST OF PUBLICATIONS AND PRESENTATIONS

RELEVANT TO THE PRESENT THESIS

PAPERS IN JOURNALS

1) Imai, F. H., Tsumura, N., Haneishi, H., Miyake, Y., “Principal component analysis of

skin color and its application to colorimetric color reproduction on CRT display and

hardcopy,” J. Imaging Sci. Technol. 40, 422-430 (1996).

2) Imai, F. H., Tsumura, N., Haneishi, H., Miyake, Y., “Prediction of color reproduction

for skin color under different illuminants based on the color appearance models,” J.

Imaging Sci. Technol 41, 166-173 (1997).

3) Miyake, Y., Imai, F. H. , “Image reproduction in multimedia age,” Kagaku Kougyo 47,

45-51 (1996), (in Japanese).

4) Imai, F. H., Tsumura, N., Haneishi, H., Miyake, Y., “Improvement of Incomplete

Chromatic Adaptation Model for Facial Pattern Images”, ,” J. Imaging Sci. Technol

42, 264-268 (1998).

Papers

108

PAPERS IN CONFERENCES

1) Imai, F. H., Tsumura, N., Haneishi, H., Miyake, Y., “Color reproduction of human skin

based on a color appearance model,” Proc. of Color Forum Japan ‘95, (1995).

2) Koyama, K., Imai, F. H., Tsumura, N., Haneishi, H., Miyake, Y., “Color reproduction

of human skin based on a color appearance model (II),” Proc. of The 43rd Spring

meeting, 1996: The Japan Society of Applied Physics and Related Society, 938, (1996).

3) Imai, F. H., Tsumura, N., Haneishi, H., Miyake, Y., “Principal component analysis of

skin color and its application to portrait color reproduction,” Proc. of World Techno

Fair in Chiba ‘96, Imaging Science and Technology, Evolution and Promise, 254-261,

(1996).

4) Imai, F. H., Tsumura, N., Haneishi, H., Miyake, Y., “Color reproduction of human skin

under different illuminants using color appearance models,” Proc. of SPSTJ

Symposium on Digital Photography ‘96, 35-38, (1996).

5) Imai, F. H., Tsumura, N., Haneishi, H., Miyake, Y., “Color reproduction of human skin

under various illuminants based on chromatic adaptation models,” Proc. of The Korean

Printing Society, Vol. 14. 2, 14-18, (1996).

6) Imai, F. H., Tsumura, N., Haneishi, H., Miyake, Y., “Spectral reflectance of skin color

and its applications to color appearance modeling,” Proc. of IS&T/SID Fourth Color

Imaging Conference, 121-124, (1996).

7) Horiuchi, T., Imai, F. H., Tsumura, N., Haneishi, H., Miyake, Y., “Color reproduction

of human skin based on color appearance model (III) - Customized Incomplete

Adaptation Model,” Proc. of The 44th Spring meeting, 1997: The Japan Society of

Applied Physics and Related Societies, 876 (1997).

Papers

109

8) Saito, T., Imai, F. H., Tsumura, N., Haneishi, H., Miyake, Y., “Color reproduction of

electronic endoscope image under different illuminant (II),” Proc. of The 44th Spring

meeting, 1997: The Japan Society of Applied Physics and Related Societies, 909

(1997).

9) Imai, F. H., Tsumura, N., Haneishi, H., Miyake, Y., “Modified Fairchild’s color

appearance model for facial pattern images under various illuminants,” Proc. of AIC

Color 97 Kyoto, The 8th congress of the International Colour Association, 578 (1997).

10)Tsumura, N., Imai, F.H., Saito, T., Haneishi, H., Miyake, Y., “Color Gamut Mapping

based on Mahalanobis Distance for Color Reproduction of Electronic Endoscope

Image under Different Illuminant”, Proc. of IS&T/SID Fifth Color Imaging

Conference, 158-162 (1997).