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SPIE PRESS
P.O. Box 10
Bellingham, WA 98227-0010
ISBN: 9780819485649
SPIE Vol. No.: PM206
This full-color book begins with a detailed study of the nature of color
images–including natural, multispectral, and pseudocolor images–and
covers acquisition, quality control, and display of color images, as well
as issues of noise and artifacts in color images and segmentation for the
detection of regions of interest or objects.
The book is primarily written with the (post-)graduate student in mind,
but practicing engineers, researchers, computer scientists, information
technologists, medical physicists, and data-processing specialists
will also benefit from its depth of information. Those working in
diverse areas such as DIP, computer vision, pattern recognition,
telecommunications, seismic and geophysical applications, biomedical
applications, hospital information systems, remote sensing, mapping,
and geomatics may find this book useful in their quest to learn advanced
techniques for the analysis of color or multichannel images.

Library of Congress Cataloging-in-Publication Data
Rangayyan, Rangaraj M.
Color image processing with biomedical applications / Rangaraj M. Rangayyan,
Begona Acha, Carmen Serrano.
p. ; cm. -- (Press monograph 206)
Includes bibliographical references and index.
ISBN 978-0-8194-8564-9
1. Imaging systems in medicine--Data processing. 2. Diagnostic imaging--
Digital techniques. 3. Color photography. 4. Image processing. I. Acha,
Begona. II. Serrano, Carmen, Ph. D. III. Title. IV. Series: SPIE monograph ; 206.
[DNLM: 1. Image Processing, Computer-Assisted--methods. 2. Staining and
Labeling--methods. W 26.55.C7]
R857.O6R36 2011
616.07'54--dc23
2011021979
Published by
SPIE
P.O. Box 10
Bellingham, Washington 98227-0010 USA
Phone: +1 360.676.3290
Fax: +1 360.647.1445
Email: Books@spie.org
Web: http://spie.org
Copyright © 2011 Society of Photo-Optical Instrumentation Engineers (SPIE)
All rights reserved. No part of this publication may be reproduced or distributed
in any form or by any means without written permission of the publisher.
The content of this book reflects the work and thoughts of the author(s).
Every effort has been made to publish reliable and accurate information herein,
but the publisher is not responsible for the validity of the information or for any
outcomes resulting from reliance thereon.
Printed in the United States of America.
First Printing

Dedication
To Mayura, my wife,
for adding color to my life
Raj
To my father
Bego
To my big and colorful family
Carmen
Todo es de color (Lole y Manuel)

Contents
Preface xi
Acknowledgments xvii
Symbols and Abbreviations xxi
1 The Nature and Representation of Color Images 1
1.1 Color Perception by the Human Visual System . . . . . . . . 3
1.1.1 The radiant spectrum . . . . . . . . . . . . . . . . . . 4
1.1.2 Spectral luminous efficiency . . . . . . . . . . . . . . 7
1.1.3 Photometric quantities . . . . . . . . . . . . . . . . . 7
1.1.4 Effects of light sources and illumination . . . . . . . . 10
1.1.5 Color perception and trichromacy . . . . . . . . . . . 12
1.1.6 Color attributes . . . . . . . . . . . . . . . . . . . . . 12
1.1.7 Color-matching functions . . . . . . . . . . . . . . . . 14
1.1.8 Factors affecting color perception . . . . . . . . . . . . 17
1.2 Representation of Color . . . . . . . . . . . . . . . . . . . . . 30
1.2.1 Device-independent color spaces and CIE standards . 31
1.2.2 Device-dependent color spaces . . . . . . . . . . . . . 38
1.2.3 Color order systems and the Munsell color system . . 52
1.2.4 Color-difference formulas . . . . . . . . . . . . . . . . 53
1.3 Illustrations of Color Images and Their Characteristics . . . . 60
1.3.1 RGB components and their characteristics . . . . . . 60
1.3.2 HSI components and their characteristics . . . . . . . 62
1.3.3 Chromatic and achromatic pixels . . . . . . . . . . . . 65
1.3.4 Histograms of HSI components . . . . . . . . . . . . 73
1.3.5 CMY K components and their characteristics . . . . . 76
1.4 Natural Color, Pseudocolor, Stained, Color-Coded, and Mul-
tispectral Images . . . . . . . . . . . . . . . . . . . . . . . . . 81
1.4.1 Pseudocolor images of weather maps . . . . . . . . . . 84
1.4.2 Staining . . . . . . . . . . . . . . . . . . . . . . . . . . 84
1.4.3 Color coding . . . . . . . . . . . . . . . . . . . . . . . 88
1.4.4 Multispectral imaging . . . . . . . . . . . . . . . . . . 91
1.5 Biomedical Application: Images of the Retina . . . . . . . . . 97
1.6 Biomedical Application: Images of Dermatological Lesions . . 99
1.7 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
vii

viii Color Image Processing
2 Acquisition, Creation, and Quality Control of Color Images 103
2.1 Basics of Color Image Acquisition . . . . . . . . . . . . . . . 103
2.1.1 Color image sensors . . . . . . . . . . . . . . . . . . . 103
2.1.2 Dark current correction . . . . . . . . . . . . . . . . . 106
2.1.3 Demosaicking . . . . . . . . . . . . . . . . . . . . . . . 106
2.1.4 White balance . . . . . . . . . . . . . . . . . . . . . . 109
2.1.5 Color transformation to unrendered color spaces . . . 110
2.1.6 Color transformation to rendered color spaces . . . . . 115
2.2 Quality and Information Content of Color Images . . . . . . 117
2.2.1 Measures of fidelity . . . . . . . . . . . . . . . . . . . 118
2.2.2 Factors affecting perceived image quality: contrast,
sharpness, and colorfulness . . . . . . . . . . . . . . . 121
2.3 Calibration and Characterization of Color Images . . . . . . 124
2.3.1 Calibration of a digital still camera . . . . . . . . . . . 125
2.3.2 Characterization of a digital still camera . . . . . . . . 127
2.3.3 International Color Consortium profiles . . . . . . . . 128
2.4 Natural and Artificial Color in Biomedical Imaging . . . . . . 129
2.4.1 Staining in histopathology and cytology . . . . . . . . 131
2.4.2 Use of fluorescent dyes in confocal microscopy . . . . 143
2.4.3 Color in fusion of multimodality images . . . . . . . . 146
2.4.4 Color coding in Doppler ultrasonography . . . . . . . 150
2.4.5 Use of color in white-matter tractography . . . . . . . 155
2.5 Biomedical Application: Endoscopy of the Digestive Tract . . 162
2.6 Biomedical Application: Imaging of Burn Wounds . . . . . . 163
2.6.1 Influence of different illumination conditions . . . . . 166
2.6.2 Colorimetric characterization of the camera . . . . . . 168
2.7 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
3 Removal of Noise and Artifacts 173
3.1 Space-Domain Filters Based on Local Statistics . . . . . . . 174
3.1.1 The mean filter . . . . . . . . . . . . . . . . . . . . . . 175
3.1.2 The median filter . . . . . . . . . . . . . . . . . . . . 177
3.1.3 Filters based on order statistics . . . . . . . . . . . . 181
3.2 Ordering Procedures for Multivariate or Vectorial Data . . . 184
3.2.1 Marginal ordering . . . . . . . . . . . . . . . . . . . . 185
3.2.2 Conditional ordering . . . . . . . . . . . . . . . . . . 185
3.2.3 Reduced ordering . . . . . . . . . . . . . . . . . . . . 187
3.3 The Vector Median and Vector Directional Filters . . . . . . 188
3.3.1 Extensions to the VMF and VDF . . . . . . . . . . . 190
3.3.2 The double-window modified trimmed mean filter . . 190
3.3.3 The generalized VDF–double-window–α-trimmed mean
filter . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
3.4 Adaptive Filters . . . . . . . . . . . . . . . . . . . . . . . . . 191
3.4.1 The adaptive nonparametric filter with a Gaussian
kernel . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

Table of Contents ix
3.4.2 The adaptive hybrid multivariate filter . . . . . . . . . 194
3.5 The Adaptive-Neighborhood Filter . . . . . . . . . . . . . . 196
3.5.1 Design of the ANF for color images . . . . . . . . . . 196
3.5.2 Region-growing techniques . . . . . . . . . . . . . . . 197
3.5.3 Estimation of the noise-free seed pixel . . . . . . . . . 201
3.5.4 Illustrations of application . . . . . . . . . . . . . . . 203
3.6 Biomedical Application: Removal of Noise Due to Dust in
Fundus Images of the Retina . . . . . . . . . . . . . . . . . . 210
3.7 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
4 Enhancement of Color Images 215
4.1 Componentwise Enhancement of Color Images . . . . . . . . 216
4.1.1 Image enhancement in the RGB versus HSI domains 216
4.1.2 Hue-preserving contrast enhancement . . . . . . . . . 217
4.1.3 Enhancement of saturation . . . . . . . . . . . . . . . 219
4.1.4 Selective reduction of saturation . . . . . . . . . . . . 220
4.1.5 Alteration of hue . . . . . . . . . . . . . . . . . . . . . 221
4.2 Correction of Tone and Color Balance . . . . . . . . . . . . . 223
4.3 Filters for Image Sharpening . . . . . . . . . . . . . . . . . . 229
4.3.1 Unsharp masking . . . . . . . . . . . . . . . . . . . . . 229
4.3.2 Subtracting Laplacian . . . . . . . . . . . . . . . . . . 234
4.4 Contrast Enhancement . . . . . . . . . . . . . . . . . . . . . 235
4.5 Color Histogram Equalization and Modification . . . . . . . . 239
4.5.1 Componentwise histogram equalization . . . . . . . . 244
4.5.2 3D histogram equalization . . . . . . . . . . . . . . . . 246
4.5.3 Histogram explosion . . . . . . . . . . . . . . . . . . . 250
4.5.4 Histogram decimation . . . . . . . . . . . . . . . . . . 251
4.5.5 Adaptive-neighborhood histogram equalization . . . . 251
4.5.6 Comparative analysis of methods for color histogram
equalization . . . . . . . . . . . . . . . . . . . . . . . . 257
4.6 Pseudocolor Transforms for Enhanced Display of Medical Im-
ages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
4.7 The Gamut Problem in the Enhancement and Display of Color
Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
4.8 Biomedical Application: Correction of Nonuniform Illumina-
tion in Fundus Images of the Retina . . . . . . . . . . . . . . 269
4.9 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
5 Segmentation of Color Images 275
5.1 Histogram-based Thresholding . . . . . . . . . . . . . . . . . 275
5.1.1 Thresholding of grayscale images . . . . . . . . . . . 276
5.1.2 Thresholding of color images . . . . . . . . . . . . . . 279
5.2 Color Clustering . . . . . . . . . . . . . . . . . . . . . . . . . 283
5.2.1 Color feature spaces and distance measures . . . . . . 285
5.2.2 Algorithms to partition a feature space . . . . . . . . 286

x Color Image Processing
5.3 Detection of Edges . . . . . . . . . . . . . . . . . . . . . . . . 297
5.3.1 Edge detectors extended from grayscale to color . . . 298
5.3.2 Vectorial approaches . . . . . . . . . . . . . . . . . . . 302
5.4 Region Growing in Color Images . . . . . . . . . . . . . . . . 311
5.4.1 Seed selection . . . . . . . . . . . . . . . . . . . . . . . 312
5.4.2 Belonging conditions . . . . . . . . . . . . . . . . . . . 316
5.4.3 Stopping condition . . . . . . . . . . . . . . . . . . . . 317
5.5 Morphological Operators for Segmentation of Color Images . 319
5.5.1 The watershed algorithm for grayscale images . . . . . 322
5.5.2 The watershed algorithm applied to color images . . . 324
5.6 Biomedical Application: Segmentation of Burn Images . . . . 325
5.7 Biomedical Application: Analysis of the Tissue Composition
of Skin Lesions . . . . . . . . . . . . . . . . . . . . . . . . . . 330
5.8 Biomedical Application: Segmentation of Blood Vessels in the
Retina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
5.8.1 Gabor filters . . . . . . . . . . . . . . . . . . . . . . . 337
5.8.2 Detection of retinal blood vessels . . . . . . . . . . . . 339
5.8.3 Dataset of retinal images and preprocessing . . . . . . 339
5.8.4 Single-scale filtering and analysis . . . . . . . . . . . . 341
5.8.5 Multiscale filtering and analysis . . . . . . . . . . . . 341
5.8.6 Use of multiple color components for improved detec-
tion of retinal blood vessels . . . . . . . . . . . . . . 343
5.8.7 Distinguishing between retinal arteries and veins . . . 344
5.9 Biomedical Application: Segmentation of Histopathology Im-
ages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
5.9.1 Color separation in histopathology images . . . . . . . 346
5.9.2 Segmentation of lumen in histopathology images . . . 349
5.9.3 Detection of tubules in histopathology images . . . . . 350
5.10 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
6 Afterword 355
References 357
Index 395
About the Authors 403

Preface
The Importance of Color
Color plays an important role in our visual world: we are attracted more by
tones of color than by shades of gray. The human visual system (HVS) can
sense, analyze, and appreciate more tones of color than shades of gray at a
given time and under a given set of viewing conditions. The colors and skin
tones of our bodies, the colors and texture of the clothes we wear, and the
colors of the natural scenery that surrounds us are all innate aspects of our
lives. Who would not be thrilled to view a meadow filled with a splash of
colorful flowers? Who would not be mesmerized by the extravagant colors of
corals and tropical fishes in a reef? Who would not be excited with a surprise
gift of a bouquet of flowers with a burst of colors?
Color permeates our world and life. We are so accustomed to color that
we use related words, for example, “colorful,” to describe nonvisual entities
such as personalities. Indeed, a world without color would be very dull —
and gray!
The Growing Popularity of Color Imaging
With the increasing popularity of computers and digital cameras as personal
devices for education, research, communication, professional work, as well as
entertainment, the use of images in day-to-day life is growing by leaps and
bounds. Personal computers (PCs) have standard features and accessories for
the acquisition of images via scanners, still cameras, and video cameras, as
well as easy downloading of images from the Internet, the Web, or storage
devices such as compact discs (CDs) and digital versatile (or video) discs
(DVDs). The acquisition, manipulation, and printing of personal or family
photos have now become an easy (and even pleasant!) task for an individual
who is not necessarily at ease with computers. Needless to say, color is a
significant aspect of all of the above.
xi

xii Color Image Processing
From Grayscale to Color Image Processing
Digital image processing (DIP) — the manipulation of images in digital format
by computers — has been an important field of research and development
since the 1960s [1–12]. Much of the initial work in DIP dealt exclusively with
monochromatic or grayscale images. (See the special issues of the Proceedings
of the IEEE, July 1972 and May 1979, for historically significant papers on
DIP.) In fact, the processing of images in just black and white (binary images)
has been an important area with applications in facsimile transmission (fax)
and document analysis.
As the knowledge and understanding of techniques for DIP developed, so
did the recognition of the need to include color. With remote sensing of the
Earth and its environment using satellites [13], the need also grew to consi-
der more general representations of images than the traditional tristimulus or
three-channel characterization of natural color images. Multispectral or hy-
perspectral imaging with tens of channels or several hundred bands of spectral
sensitivity spanning a broad range of the electromagnetic spectrum well be-
yond the range of visible light is now common, with real-life applications
including land-use mapping, analysis of forest cover and deforestation, detec-
tion of lightning strikes and forest fires, analysis of agricultural plantations
and prediction of crop yield, and extreme weather or flood warning.
Nowadays, medical diagnosis depends heavily upon imaging of the human
body. Most medical images, such as those obtained using X rays and ultra-
sound, are scalar-valued, lack inherent color, and are represented as monochro-
matic or grayscale images. However, (pseudo-)color is used for enhanced vi-
sualization in the registration of multimodality images. Limited colors are
used to encode the velocity and direction of blood flow in Doppler imaging.
Staining in pathology and cytology leads to vividly colored images of various
tissues [14–17]. Even in the case of analysis of external signs and symptoms,
such as skin rashes and burns, color imaging can play important roles in en-
hanced visualization using polarized lighting, transmission, and archival. The
application of DIP techniques to images as above calls for the development of
specialized techniques for the representation, characterization, and analysis of
color.
Initial work on color image processing (CIP) was based on the direct (and
simplistic) application of grayscale DIP techniques to the individual chan-
nels of color or multispectral images. Although some useful results could
be obtained in this manner, it was soon realized that it is important to de-
velop specialized techniques for CIP, taking into consideration the correlation
and dependencies that exist between the channels [1–5, 12, 18–20]. (See the
January 2005 special issue of the IEEE Signal Processing Magazine on color
image processing.) Whereas several books are available on the science of color
perception, imaging, and display [12,21–28], very few books on DIP have sig-

Preface xiii
nificant examples, sections, or chapters on CIP [1–5,11,12,20,24], and fewer
still are dedicated to CIP [18,19,29,30]. In this book, we shall mainly consider
techniques that are specifically designed for CIP.
The Plan of the Book
We begin with a detailed study of the nature of color images. In addition to
natural color images, we take into consideration multispectral and pseudocolor
images in specialized areas such as photogrammetric and biomedical imaging.
Chapter 1 provides descriptions of the HVS, color perception, color-matching
functions, and systems for the representation of color images. A pertinent
selection of biomedical applications is provided at the end of each chapter,
including diagnostic imaging of the retina and imaging of skin lesions.
In Chapter 2, we present details regarding the acquisition, creation, and
quality control of color images. Despite the simple appearance and usage of
digital cameras, the chain of systems and techniques involved in the acquisi-
tion of color images is complex; regardless, the science of imaging is now a
well-developed and established subject area [12,24,31]. Several operations are
required to ensure faithful reproduction of the colors in the scene or object
being imaged, or to assure a visually pleasing and acceptable rendition of the
complex tonal characteristics in a portrait; the latter hints at the need to in-
clude personal preferences and subjective aspects, whereas the former implies
rigid technical requirements and the satisfaction of quantitative measures of
image characteristics. In addition to processes involving natural color images,
we describe techniques related to staining in pathology and the use of fluo-
rescent dyes in confocal microscopy for imaging of biomedical specimens. We
present biomedical applications including the acquisition of images of burn
wounds and endoscopy.
In Chapter 3, we study the issue of noise and artifacts in color images as
well as methods to remove them. The need to consider the interrelationships
that exist between the components or channels of color images is emphasized,
leading to the formulation of vector filters.
In spite of the high level of sophistication (and cost) of cameras and image-
acquisition systems, it is common to acquire or encounter images of poor
quality. Image quality is affected by several factors, including the lighting
conditions, the environment, and the nature of the scene or object being im-
aged, in addition to the skills and competence of the individual capturing the
image. The topic of image enhancement is considered in Chapter 4, including
methods for hue-preserving enhancement, contrast enhancement, sharpening,
and histogram-based operations.

xiv Color Image Processing
Segmentation for the detection of regions of interest or objects is a critical
step in the analysis of images. Although a large body of literature exists
on this topic, it is recognized that no single technique can directly serve a
new purpose: every application or problem demands the development of a
specific technique that takes into account the particular characteristics of the
images and objects involved. The problem is rendered more complex by the
multichannel nature of color images. In Chapter 5, we explore several methods
for the detection of edges and objects in color images. Several biomedical
applications are presented, including the segmentation and analysis of skin
lesions and retinal vasculature.
Chapter 6 provides a few closing remarks on the subjects described in the
book and also on advanced topics to be presented in a companion book to
follow.
The Intended Audience and Learning Plans
The methods presented in the book are at a fairly high level of technical and
mathematical sophistication. A good background in one-dimensional signal
and system analysis [32–34] is required in order to follow the procedures and
analyses. Familiarity with the theory of linear systems, signals, and trans-
forms, in both continuous and discrete versions, is assumed. Furthermore,
familiarity with the basics of DIP [1–9] is assumed and required.
We only briefly study a few representative imaging or image-data acquisition
techniques. We study in more detail the problems present with images after
they have been acquired, and concentrate on how to solve the problems. Some
preparatory reading on imaging systems, equipment, and techniques [12,24,31]
would be useful, but is not essential.
The book is primarily directed at engineering students in their (post-)gra-
duate studies. Students of electrical and computer engineering with a good
background in signals and systems [32–34] are expected to be well prepared
for the material in the book. Students in other engineering disciplines or in
computer science, physics, mathematics, or geophysics should also be able to
appreciate the material in this book. A course on digital signal processing
or digital filters [35] would form a useful link, but a capable student without
familiarity of this topic may not face much difficulty. Additional study of a
book on DIP [1–9] can assist in developing a good understanding of general
image-processing methods.
Practicing engineers, researchers, computer scientists, information techno-
logists, medical physicists, and data-processing specialists working in diverse
areas such as DIP, computer vision, pattern recognition, telecommunications,
seismic and geophysical applications, biomedical applications, hospital infor-

Preface xv
mation systems, remote sensing, mapping, and geomatics may find this book
useful in their quest to learn advanced techniques for the analysis of color or
multichannel images.
Practical experience with real-life images is a key element in understand-
ing and appreciating image analysis. We strongly recommend hands-on ex-
periments with intriguing real-life images and technically challenging image-
processing algorithms. This aspect can be difficult and frustrating at times,
but provides professional satisfaction and educational fun!
Rangaraj Mandayam Rangayyan, Calgary, Alberta, Canada
Begoña Acha Piñero, Sevilla, España (Spain)
Marı́a del Carmen Serrano Gotarredona, Sevilla, España (Spain)
July 2011

Acknowledgments
Writing this book on the exciting subject of color image processing has been
difficult, challenging, and stimulating. Simultaneously, it has also yielded
more knowledge and deeper understanding of the related subject matter, and
satisfaction as each part was brought to a certain stage of completion.
Our understanding and appreciation of related material have been helped
by the collaborative research and studies performed with several graduate
students, postdoctoral fellows, research associates, and colleagues. We thank
the following for their contributions to this book:
• Dr. Mihai Ciuc, Universitatea Politehnica Bucureşti, Bucharest, Roma-
nia, for his contributions to earlier research work and publications on
color image processing as well as for providing several examples of fil-
tered or enhanced images and related data.
• Dr. Fábio José Ayres and Shantanu Banik, University of Calgary, for
help with image-processing algorithms and MATLAB R
programming.
• Dr. Hallgrimur Benediktsson, Dr. Serdar Yilmaz, and Sansira Semi-
nowich, University of Calgary, for providing images and information
related to color imaging in histology and pathology.
• Dr. Paulo Mazzoncini de Azevedo Marques and Dr. Marco A.C. Frade,
Universidade de São Paulo, Ribeirão Preto, São Paulo, Brasil, for pro-
viding color images of skin ulcers and for their collaboration on related
projects.
• Dr. Philippe Pibarot, Québec Heart and Lung Institute, Québec City,
Province of Québec, Canada, for providing color Doppler echocardio-
graphic images.
• Hanford Deglint, ITRES Research Limited, Calgary, Alberta, Canada,
for providing CASI images of the campus of the University of Calgary
and related notes.
• Dr. Enrico Grisan and Dr. Alfredo Ruggeri, Università degli Studi di
Padova, Padova, Italy, for providing illustrations of their results of pro-
cessing fundus images of the retina.
• Dr. Maitreyi Raman, University of Calgary, for providing images and
notes on endoscopy.
xvii

xviii Color Image Processing
• Dr. Myriam Oger, GRECAN — François Baclesse Cancer Centre, Caen,
France, for providing histology images and related data.
• Dr. Karl Baum, Rochester Institute of Technology, Rochester, NY, for
providing images, advise, and comments on multimodality image fusion.
• Patrick Weeden, Weather Central LLC, Madison, WI, for providing tem-
perature prediction maps and related notes.
• Aurora Sáez Manzano, Departamento de Teorı́a de la Señal y Comu-
nicaciones, University of Seville, Spain, for her invaluable assistance in
implementing several algorithms described in this book and providing
the resulting images.
• Irene Fondón Garcı́a, José Antonio Pérez Carrasco, Carlos Sánchez Men-
doza, Francisco Núñez Benjumea, and Antonio Foncubierta Rodrı́guez,
Departamento de Teorı́a de la Señal y Comunicaciones, University of
Seville, Spain, for their assistance.
• Dr. Juan Luis Nieves Gómez, Departamento de Óptica, Facultad de
Ciencias, University of Granada, Spain, for providing the measurements
of the sensitivity values for the Retiga 1300 camera by QImaging.
• Dr. Tomás Gómez Cı́a from Servicio de Cirugı́a Plástica y Grandes Que-
mados (Hospitales Universitarios Virgen del Rocı́o, Sevilla) for taking
the burn images.
• Shantanu Banik, Faraz Oloumi (University of Calgary), Hanford Deglint,
Dr. Paulo Mazzoncini de Azevedo Marques, Dr. Denise Guliato (Uni-
versidade Federal de Uberlândia, Uberlândia, Minas Gerais, Brasil),
Dr. José I. Acha (University of Seville), and Dr. Mihai Ciuc for re-
viewing parts of the book.
• Garwin Hancock and Steven Leikeim, Department of Electrical and
Computer Engineering, University of Calgary, for help with color-coded
electrical and communications circuits.
• Enrique de la Cerda Cisneros (Seville, Spain) for taking our pictures.
• The anonymous reviewers for their careful reading and suggestions for
improvement of the book.
The book has benefited significantly from illustrations and text provided
by a number of researchers worldwide, as identified in the references and per-
missions cited. We thank them all for enriching the book with their gifts of
knowledge and kindness. Some of the test images used in the book were ob-
tained from the Center for Image Processing Research, Rensselaer Polytechnic
Institute, Troy, NY, www.ipl.rpi.edu; the Digital Retinal Images for Vessel

Acknowledgments xix
Extraction (DRIVE) database, www.isi.uu.nl/Research/Databases/DRIVE;
and the Structured Analysis of the Retina (STARE) database, www.ces.clem-
son.edu/∼ahoover/stare; we thank them for the resources provided.
Several research projects provided us with the background, material, ex-
amples, and experience that have gone into the writing of this book. We
thank the Natural Sciences and Engineering Research Council of Canada,
the University of Calgary, the Comisión Interministerial para Investigaciones
Cientı́ficas of Ministerio de Ciencia y Tecnologı́a of Spain, and Universidad
de Sevilla for supporting our research projects.
We thank the Killam Trusts for awarding (Raj Rangayyan) a Killam Res-
ident Fellowship and the University of Calgary for awarding the “University
Professor” position to facilitate work on this book.
We thank CRC Press for permission to use material from previous pub-
lications and the LaTeX stylefile for the book, and Shashi Kumar, LaTeX
Help Desk, Glyph International, Noida, India, for assistance with the LaTeX
stylefile.
We thank SPIE Press for inviting us to write this book and for completing
the publication process in a friendly and efficient manner.
Rangaraj Mandayam Rangayyan, Calgary, Alberta, Canada
Begoña Acha Piñero, Sevilla, España (Spain)
Marı́a del Carmen Serrano Gotarredona, Sevilla, España (Spain)
July 2011

Symbols and Abbreviations
Bold-faced letters represent vectors or matrices. Variables or symbols used
within limited contexts are not listed here; they are described within their
context. The mathematical symbols listed may stand for other entities or
variables in different applications; only the common associations used in this
book are listed for ready reference.
arctan inverse tangent, tan−1
arg argument of
au arbitrary units
A area
AC alternating current
ADC analog-to-digital converter
AHMF adaptive hybrid multivariate filter
AMNFG2 adaptive multichannel nonparametric filter with
Gaussian kernel
ANCE adaptive-neighborhood contrast enhancement
ANF adaptive-neighborhood filter
ANHE adaptive-neighborhood histogram equalization
ANN artificial neural network
ANNS adaptive-neighborhood noise subtraction
ATMF alpha-trimmed mean filter
AUC area under the ROC curve
AVIRIS Airborne Visible/Infrared Imaging Spectrometer
Av camera aperture setting
Az area under the ROC curve
b bit
B, b blue component
B byte
BMP bitmap
cd candela
cm centimeter
C cyan component
CAD computer-aided diagnosis
CASI Compact Airborne Spectrographic Imager
CBIR content-based image retrieval
CCD charge-coupled device
xxi

xxii Color Image Processing
CCITT Comité Consultatif International Téléphonique et
Télégraphique
CD compact disc
CDF cumulative (probability) distribution function
CDR chroma dynamic range
CFA color filter array
CFM color filter mosaic
CIE Commission Internationale de l’Eclairage
CIECAM CIE color appearance model
CIE L∗
a∗
b∗
the CIE L∗
a∗
b∗
color space
CIE L∗
u∗
v∗
the CIE L∗
u∗
v∗
color space
CIP color image processing
CMC British Colour-Measurement Committee of the
Society of Dyers and Colourists
CMOS complementary metal-oxide semiconductor
CMY K [cyan, magenta, yellow, black] representation of color
CRT cathode-ray tube
CT computed tomography
CYGM cyan, yellow, green, and magenta
d derivative or differentiation operator
dpi dots per inch
DAB diaminobenzidine
DAC digital-to-analog converter
DC direct current
DDF distance-directional filter
DICOM Digital Imaging and Communications in Medicine
DIP digital image processing
DNA deoxyribonucleic acid
DRIVE Digital Retinal Images for Vessel Extraction
DSC digital still camera
DT-MRI diffusion tensor MRI
DVD digital versatile (or video) disc
DW-MTMF double-window modified trimmed mean filter
exp (x) exponential function, ex
E irradiance
E[ ] statistical expectation operator
Ev illuminance
E(λ) spectral irradiance
EBU European Broadcasting Union
ECG electrocardiogram
EHz exahertz = 1018
Hz
EM electromagnetic
Erf error function (integral of a Gaussian)
f(m, n) a digital scalar or grayscale image,
typically original or undistorted

Symbols and Abbreviations xxiii
f(x, y) a scalar or grayscale image,
typically original or undistorted
f(m, n), fn an image where each pixel is a vector,
a color image
f matrix or vector representation of an entire image
Ff (l) CDF of image f
FN false negative
FNF false-negative fraction
FOV field of view
FP false positive
FPF false-positive fraction
g(m, n) a digital scalar or grayscale image,
typically processed or distorted
g(x, y) a scalar or grayscale image,
typically processed or distorted
g(m, n), gn an image where each pixel is a vector,
a color image
g matrix or vector representation of an entire image
G, g green component
GB gigabyte
GHz gigahertz = 109
Hz
GI gastrointestinal
GVDF generalized vector directional filter
GVDF-DW-αTM GVDF - double window - α-trimmed mean filter
h hour
hl data-dependent smoothing term
h(m, n) impulse response of a discrete-space system
h(x, y) impulse response of a continuous-space system
H entropy
H hue component
H
as a superscript, Hermitian (complex-conjugate)
transposition of a matrix
H&E hematoxylin and eosin
HCI [hue, chroma, intensity] representation of color
HDTV high-definition television
HLS [hue, lightness, saturation] representation of color
HSI [hue, saturation, intensity] representation of color
HSV [hue, saturation, value] representation of color
HVS human visual system
i index of a series
I the identity matrix
I radiant intensity
I intensity component
Iv luminous intensity

xxiv Color Image Processing
ICC International Color Consortium
IEC International Electrotechnical Commission
IEEE Institute of Electrical and Electronics Engineers
IESNA Illuminating Engineering Society of North America
ISO International Organization for Standardization
ITU International Telecommunication Union
j index of a series
j
√
−1
JBIG Joint Bi-level Image (experts) Group
JPEG Joint Photographic Experts Group
k kilo (1, 000)
kHz kilohertz = 103
Hz
km kilometer = 103
m
K black component
K kilo (210
= 1, 024)
K Kelvin (unit of absolute temperature)
K covariance matrix
Km maximum spectral luminous efficacy
K(λ) spectral luminous efficacy
lm lumen
ln natural logarithm (base e)
lx lux, unit of illuminance
L radiance
Lv luminance
L(λ) spectral radiance
LCD liquid crystal display
LDR luminance dynamic range
LIDAR light detection and ranging
LLMMSE local linear minimum mean-squared error
LMMSE linear minimum mean-squared error
LMS long, medium, and short (wavelength)
LMS least mean squares
LSB least significant bit
LSI linear shift-invariant
LUT look-up table
m meter
max maximum
min minimum
mm millimeter = 10−3
m
(m, n) indices in the discrete space (image) domain
mod modulus or modulo
M radiant exitance
M magenta component
Mv luminous exitance

Symbols and Abbreviations xxv
MA moving average
MB megabyte
MHz megahertz = 106
Hz
MLP multilayer perceptron
MMF marginal median filter
MMSE minimum mean-squared error
MOS metal-oxide semiconductor
MP megapixels
MPEG Moving Picture Experts Group
MR magnetic resonance
MRI magnetic resonance imaging
MRS magnetic resonance spectroscopy
MS mean squared
MSE mean-squared error
MV D minimum vector dispersion
MV DED minimum vector dispersion edge detector
MV R minimum vector range
n an index
nit unit of luminance
nm nanometer = 10−9
m
NCD normalized color difference
NE normalized error
NMSE normalized mean-squared error
NTSC National Television System Committee (of the US)
OD optical density
OECF optoelectronic conversion function
pf (l) normalized histogram or PDF of image f
pixel picture cell or element
pm picometer = 10−12
m
p(x) probability density function of the random variable x
P dimension or number of elements in a multivariate pixel
Pr(x) probability of the event x
Pf (l) histogram of image f
PACS picture archival and communication system
PAL phase alternate line
PAS periodic acid Schiff
PASM periodic acid silver methenamine
PC personal computer
PCA principal component analysis
PCS profile connection space
PDF probability density function
PDF portable document format
PET positron emission tomography
PHz petahertz = 1015
Hz
PMT photomultiplier tube

xxvi Color Image Processing
PPV positive predictive value
PSF point spread function
PSNR peak signal-to-noise ratio
R the set of real numbers
R+
the set of nonnegative real numbers
RP
set of P-dimensional real numbers
[r, g, b] the [red, green, blue] vector of a pixel;
a variable in the RGB space
R, r red component
RADAR radio detection and ranging
RAM random access memory
RBF radial basis functions
RDM reduced ordering using distance to the mean
RF radio frequency
RGB [red, green, blue] color representation
RIMM reference input medium metric
RMS root mean-squared
RMSE root mean-squared error
ROC receiver operating characteristics
ROI region of interest
ROMM reference output medium metric
ROS region of support
RYK red-yellow-black model for dermatological lesions
s second
sr steradian (unit of solid angle)
sRGB standard RGB color space
S saturation component
SD standard deviation
SECAM Séquentiel Couleur à Mémoire
SI Système Internationale de Unités
(International System of Units)
SMPTE Society of Motion Picture and Television Engineers
SNR signal-to-noise ratio
SONAR sound navigation and ranging
SPD spectral power distribution
SPECT single-photon emission computed tomography
SSIM structural similarity (index)
STARE Structured Analysis of the Retina
STIR short-tau inversion recovery (sequence in MRI)
t time variable
T a threshold
T
as a superscript, vector or matrix transposition
Th threshold
THz terahertz = 1012
Hz

Symbols and Abbreviations xxvii
TIFF tagged image file format
TN true negative
TNF true-negative fraction
TP true positive
TPF true-positive fraction
Tr trace of a matrix
Tv camera exposure time setting
TV television
T1-W T1-weighted (MRI)
UCS uniform color space
UHF ultrahigh frequency
US United States (of America)
voxel volume cell or element
v volt
V value component
V (λ) spectral luminous efficiency or luminosity function
V ′
(λ) spectral luminous efficiency for scotopic vision
V D vector dispersion
V DED vector dispersion edge detector
VDF vector directional filter
VIBGYOR violet, indigo, blue, green, yellow, orange, red
VMF vector median filter
VOS vector order statistics
V R vector range
w filter tap weight; weighting function
w filter or weight vector
W watt
xi a sample pixel (vector) of a color image
(x, y) image coordinates in the continuous space domain
X a set of sample pixels (vector) from a color image
XY Z color representation with the CIE coordinates
yi a sample pixel (vector) of a color image
Y yellow component
Y intensity or luminance component
Y a set of sample pixels (vector) from a color image
Y IQ [luminance, in-phase, quadrature] color representation
zi a sample pixel (vector) of a color image
Z a set of sample pixels (vector) from a color image
Z the set of all integers
ZHz zettahertz = 1021
Hz
∅ null set
1D one-dimensional
2D two-dimensional
3D three-dimensional
4D four-dimensional

xxviii Color Image Processing
γ gamma (slope) of an imaging system or process
δ Dirac delta (impulse) function
η noise process
κ a kernel function
λ wavelength
µ the mean of a random variable
µm micrometer = 10−6
m
Π product
ρRG correlation between the R and G components
ρ(λ) reflectance of a surface
σ the standard deviation of a random variable
σ2
the variance of a random variable
Σ sum
Φ radiant flux
Φv luminous flux
ω solid angle (steradian)
∇ gradient operator
·, •, h, i dot product
′
modified or transformed version of a variable
′
, ′′
first and second derivatives of a variable
′′
inch
! factorial
∗ when in-line, convolution
∗
as a superscript, complex conjugation
# number of
average or normalized version of the variable
under the bar
ˆ estimate of the variable under the symbol
× cross product when the related entities are vectors
∀ for all
∈ belongs to or is in (the set)
{ } a set
⊂ subset
⊃ superset
T
intersection
S
union
set-theoretic difference between sets, except for
≡ equivalent to
| given, conditional upon
→ maps to
←, ⇐ obtains (updated as)
⇒ leads to
⇔ transform pair
[ ] closed interval, including the limits
( ) open interval, not including the limits

Symbols and Abbreviations xxix
| | absolute value or magnitude
| | determinant of a matrix
k k norm of a vector or matrix
⌈x⌉ ceiling operator; the smallest integer ≥ x
⌊x⌋ floor operator; the largest integer ≤ x

1
The Nature and Representation of Color
Images
Color is an important and often pleasant part of the visual domain; however,
color is not a physical quantity but a human sensation. Color is the visual
perception generated in the brain in response to the incidence of light, with
a particular spectral distribution of power, on the retina. The retina is com-
posed of photoreceptors sensitive to the visible range of the electromagnetic
(EM) spectrum [21,36–38]. In general, different spectral distributions of power
produce distinct responses in the photoreceptors, and therefore, different color
sensations in the brain. See Table 1.1 for a representation of the EM spectrum
and its parts related to various modalities of imaging, and Figure 1.1 for a
display of the visible color spectrum as a part of the EM spectrum [1,39]. The
diffraction of sunlight by water shows the visible color spectrum in the form
of a rainbow; see Figure 1.2 for an example.
When a surface is illuminated with a source of light, it absorbs some parts of
the incident energy and reflects the remaining parts. When a surface is identi-
fied with a particular color, for example, red, it means that the surface reflects
light energy in the particular range of the visible spectrum associated with
the sensation of red and absorbs the rest of the incident energy. Therefore,
the color of an object varies with the illumination. An object that reflects a
part of the light that is incident upon it may be considered a secondary source
of light.
To reproduce and describe a color, a color representation model or color
space is needed. Many color spaces have been proposed and designed so as to
Figure 1.1 The visible color spectrum and approximate naming of its constituent
colors. O: orange. Y: yellow. With the inclusion of indigo as a hue between violet
and blue, the sequence of colors violet, indigo, blue, green, yellow, orange, and red
is commonly referred to as VIBGYOR; the same sequence of colors is observed in
rainbows and similar patterns of diffraction of white light. See also Figure 1.2.
1

2 Color Image Processing
Table 1.1 Schematic representation of the EM wave spectrum and its bands used
in various imaging applications. Visible light is only a small portion of the EM
spectrum (the boxed part of the figure). The boundaries of some of the bands are
approximate and vary from one reference to another. Acoustic waves used in seismic
imaging, sonar, and ultrasonography are not part of the EM spectrum. Accelerated
electrons used in electron microscopy share some properties with EM waves but are
composed of particles. Cosmic rays are also composed of particles and not included
in the EM spectrum. See the list of symbols and abbreviations on page xxi for
details regarding the symbols and acronyms used.
DC 0 infinite
AC power 60 Hz 5000 km
Impedance
imaging, MRI
None
Radiowaves
600 kHz
− 750 MHz
500 m
− 0.4 m
Microwaves
750 MHz
− 1 THz
Radar, microwave
imaging, screening
for security
0.4 m
− 0.3 mm
Infrared
10 THz
− 300 THz
0.03 mm
− 1 µm
Night vision,
thermography,
photogrammetry
Visible
light
700 nm
− 400 nm
425 THz
− 750 THz
Photography,
microscopy,
transillumination,
photogrammetry
Ultraviolet
750 THz
− 60 PHz
400 nm
− 5 nm
X rays
60 PHz
− 75 EHz
5 nm
− 4 pm
Radiography, CT,
crystallography,
astronomy, industrial
nondestructive testing
Gamma
rays
Nuclear medicine,
PET, SPECT, astronomy
None
Astronomy,
lithography,
fluorescence microscopy
75 EHz
− 1 ZHz
4 pm
− 0.3 pm
Name of Band Frequency Wavelength Imaging Applications

The Nature and Representation of Color Images 3
Figure 1.2 The visible color spectrum displayed in the form of a double rainbow
over the Canadian Rocky Mountains in Kananaskis near Calgary, Alberta, Canada.
Image courtesy of Chris Pawluk.
reproduce the widest possible range of colors visible to or sensed by the human
visual system (HVS). The choice of a particular color space is determined by
the application.
1.1 Color Perception by the Human Visual System
Three factors are involved in color perception: the light source incident on
an object, the reflectance of the object, and finally, the color sensitivity of
the receptor (the human eye or a detector). The eye does not respond in
the same way to different levels of power of the light arriving at the retina.
Under low levels of illumination, the mode of vision is called scotopic vision;
in such a situation, humans cannot clearly perceive colors [21]. When the level
of illumination is increased to an adequate level, the eye is able to perceive
colors; in this case, the mode of vision is called photopic vision.

1.1.1 The radiant spectrum
Color is an attribute of visual perception as a response to a physical stimulus
referred to as light. Light is a form of EM radiation, with the wavelength
or frequency within the visible band of the spectrum; see Table 1.1 and Fig-
ure 1.1. EM radiation can be categorized into various bands by its wavelength
or frequency, as shown in Table 1.1. The visible spectrum is limited to a nar-
row range within the EM spectrum, typically specified by the wavelengths
between 400 nm and 700 nm; see Figure 1.1. Light stimulates retinal recep-
tors in the eye, which ultimately leads to the phenomenon of vision and the
perception of color by the HVS.
The spectral composition of light represents some of its main properties. In
this sense, any composite source of light can be decomposed into monochro-
matic light components, each of them being perceived as a particular color.
Monochromatic light is characterized by its wavelength [25,40]. Although the
visible spectrum is continuous, with no clear boundaries between colors, the
name of a color is assigned to or associated with a given range of wavelength
as presented in Figure 1.1 [41]. It should be noted that such naming or asso-
ciation of a color with a band of EM radiation assumes certain characteristics
of the receptor, such as a standard human subject or viewer; not all human
beings perceive a given band of EM radiation in the same manner.
When characterizing light by its spectral composition, such composition is
quantified through spectroradiometry. Spectroradiometry is the technique of
measuring radiometric quantities as a function of wavelength. Radiometric
quantities [22, 40] are used to specify the properties of a source of light and
represent measurements of the power of the light source. There is a wide
variety of radiometric quantities used in the literature; some of the important
quantities are listed in Table 1.2.
Radiant flux, Φ, is the power of light emitted from or received on a surface.
In other words, radiant flux, or radiant power, is radiant energy per unit
time. Radiant flux density is the radiant flux per unit area. When the flux
is arriving at a surface, the radiant flux density is referred to as irradiance.
The flux can arrive from any direction above the surface, as indicated by the
rays in Figure 1.3. Mathematically, the radiant flux density, E, is
E =
dΦ
dA
, (1.1)
where Φ is the radiant flux arriving at the point of interest and dA is the
differential area surrounding the point. Irradiance is measured in W m−2
.
When flux is leaving a surface due to emission and/or reflection, the radiant
flux density is called radiant exitance; exitance is also known as emittance.
Radiant exitance is the power emitted from a surface per unit area. As with
irradiance, flux can leave in any direction above the surface (see Figure 1.3).
In the same way as irradiance, radiant exitance, M, is defined as

Table 1.2 The definitions, symbols, and units of a few important radiometric
quantities [22,40].
Quantity Definition SI Unit
Radiant flux Φ Watt (W)
Radiant intensity I = dΦ
dω Watts per steradian (W sr−1
)
Irradiance E = dΦ
dA Watts per square meter (W m−2
)
Radiant exitance M = dΦ
dA Watts per square meter (W m−2
)
Radiance L = d2
Φ
cos θ dA dω Watts per steradian per square meter
(W sr−1
m−2
)
Spectral irradiance E(λ) = dE
dλ Watts per cubic meter (W m−3
)
Spectral radiance L(λ) = dL
dλ Watts per steradian per cubic meter
(W sr−1
m−3
)
(a) (b)
Figure 1.3 (a) Irradiance: flux can arrive from any direction. (b) Radiant exi-
tance or emittance: flux leaves in any direction.
M =
dΦ
dA
, (1.2)
where Φ is the radiant flux leaving the point of interest and dA is the differ-
ential area surrounding the point.
Radiance is a measure of the power emitted by a source per unit solid
angle (expressed in steradians, sr) and per unit projected source area. More
specifically, radiance is the infinitesimal amount of radiant flux contained in
a differential conical ray, covering a solid angle of dω, leaving a point with
area dA in a given direction θ with reference to the normal, n, to the surface

Figure 1.4 The definition of radiance.
at the point under consideration. The projected area is the cross-sectional
area, cos θ dA, representing the ray–surface intersection area dA; Figure 1.4
illustrates this definition. The mathematical definition of radiance is
L =
d2
Φ
cos θ dA dω
. (1.3)
Radiance is measured in W/(sr m2
).
When a radiometric quantity includes its dependence on wavelength, it is
referred to with the adjective “spectral.” In this sense, spectral irradiance,
E(λ), is the irradiance as a function of wavelength, and spectral radiance,
L(λ), is the radiance as a function of wavelength. The two functions men-
tioned above are mathematically defined as
E(λ) =
dE
dλ
(1.4)
and
L(λ) =
dL
dλ
. (1.5)
A spectral power distribution (SPD) is a graph or a table describing the
variation of the spectral concentration of a radiometric quantity as a function
of wavelength [23]. An SPD is usually normalized for the purpose of color
measurement; the normalized SPD is called relative spectral power distribu-
tion. The traditional approach is to normalize an SPD in such a way that its
value at 560 nm is set to unity. The wavelength of 560 nm has been chosen
because it is near the center of the visible spectrum [22]; see Figure 1.1. Thus,
relative SPDs are dimensionless.

1.1.2 Spectral luminous efficiency
The spectral responsivity of a photodetector is the ratio of the output power
of the photodetector as a function of wavelength, Φo(λ), to the input spectral
radiant flux, Φ(λ). When the photodetector is the HVS, the output, Φv(λ),
is not a physical measure, but the perceived brightness. In such a case, the
spectral responsivity is called the luminous efficacy. The spectral luminous
efficacy for photopic vision is denoted as K(λ), and is defined as the ratio of
the perceived brightness to the spectral radiant flux:
K(λ) =
Φv(λ)
Φ(λ)
. (1.6)
The maximum spectral luminous efficacy for photopic vision is 683 lm/W
at 555 nm and is denoted as Km. (Lumen, abbreviated as lm, is the unit of
luminous flux, defined in Section 1.1.3.) On this basis, the spectral luminous
efficiency, V (λ), or luminosity function, is defined as
V (λ) =
K(λ)
Km
; (1.7)
by definition, the function has the value of unity at λ = 555 nm. In 1924,
the International Commission of Illumination (Commission Internationale de
l’Eclairage, or CIE) established the spectral luminous efficiency function for
photopic vision, V (λ). In 1951, the CIE published the spectral luminous
efficiency for scotopic vision, V ′
(λ). The two spectral luminous efficiency
functions are shown in Figure 1.5.
It has been shown that the CIE 1924 function V (λ) includes underesti-
mates of the spectral luminous efficiency at wavelengths below 460 nm. Judd
and Wyszecki [42], Vos [43], and Sharpe et al. [44] proposed modifications
to attempt to overcome this concern. Nevertheless, the CIE 1924 function
continues to be used as the luminous efficiency function that relates measured
radiometric quantities to perceived photometric quantities; see Section 1.1.3.
1.1.3 Photometric quantities
Photometry is the science of measuring visible light in terms of its perceived
brightness by a human observer. Photometric quantities can be obtained
from radiometric measures by weighting them with the spectral luminous
efficiency of the HVS; that is, a photometric quantity can be derived from its
corresponding radiometric quantity as
Xv = Km
Z ∞
0
X(λ) V (λ) dλ, (1.8)
where X(λ) represents a spectral radiometric quantity, Xv is its photometric
counterpart, and Km is a scaling factor, as defined in Section 1.1.2.

350 400 450 500 550 600 650 700 750 800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Wavelength (nm)
Spectral
luminous
efficiency
Figure 1.5 Spectral luminous efficiency functions for photopic vision, V (λ), in
solid line, and for scotopic vision, V ′
(λ), in dashed line.
The luminous flux, Φv, is a photometric quantity related to the radiant
flux through Equation 1.8. The lumen (lm) is the unit used to measure and
represent luminous flux; it is a derived unit in the International System of
Units (Système Internationale de Unités or SI). The lumen is derived from
the candela (cd) and represents the luminous flux emitted into a unit solid
angle (1 sr) by an isotropic point source having a luminous intensity of 1 cd.
Luminous intensity is analogous to radiant intensity, differing only by the
weighting related to the response of the eye, as specified in Equation 1.8.
Luminous intensity can be derived from the luminous flux as
Iv =
dΦv
dω
. (1.9)
Luminous intensity is measured in candelas (cd). Candela is the SI base unit
for photometric quantities; its definition has evolved over the years. In 1979,
during the 16th meeting of the Conférence Générale des Poids et Mesures,
the candela was redefined as the “luminous intensity in a given direction of a
source that emits monochromatic radiation of 540 × 1012
Hz and that has a
radiant intensity in that direction of 1/683 watt per steradian.” The frequency
of 540 × 1012
Hz for EM radiation or light corresponds to the wavelength of
555 nm, for which V (λ) is unity.

Table 1.3 The definitions, symbols, and units of a few commonly used photomet-
ric quantities. eq. = equivalent.
Quantity Symbol SI unit Radiometric eq.
Luminous flux Φv Lumens (lm) Radiant flux
Luminous intensity Iv Candela (cd = lm sr−1
) Radiant intensity
Illuminance Ev lm m−2
Irradiance
Luminous exitance Mv lm m−2
Radiant exitance
Luminance Lv nit = lm sr−1
m−2
Radiance
Illuminance is another photometric quantity that denotes luminous flux
density. Illuminance is the photometric counterpart of the radiometric quan-
tity called irradiance, E, and is represented with the symbol Ev. It may be
defined based on the luminous flux as
Ev =
dΦv
dA
. (1.10)
Illuminance is measured in lux (lx), another derived SI unit, which is ex-
pressed in lumens per square meter (lm/m2
). Most light meters measure this
quantity because it is important in illumination engineering. The Illuminat-
ing Engineering Society of North America (IESNA) Lighting Handbook [45]
has about 16 pages of recommended illuminance values for various activities
and localities, ranging from morgues to museums. Typical values range from
100, 000 lx for direct sunlight to 20 − 50 lx for hospital corridors at night.
Luminous exitance, Mv, is related to radiant exitance through Equation 1.8.
Luminance, with the symbol Lv, is analogous to radiance, being derived as
Lv =
d2
Φv
cos θ dA dω
. (1.11)
The unit of luminance is the nit, expressed in cd/m2
or lm/(sr m2
). It is
most often used to characterize the “brightness” of flat emitting or reflecting
surfaces; that is, luminance is the photometric quantity corresponding best to
the brightness perceived by the eye [40,46]. A typical laptop computer screen
has luminance between 100 and 250 nits. Typical cathode-ray tube (CRT)
monitors have luminance between 50 and 125 nits.
Table 1.3 gives a summary of the commonly used photometric quanti-
ties [46].

350 400 450 500 550 600 650 700 750 800
0
50
100
150
200
250
Wavelength (nm)
SPD
D50
D65
A
Figure 1.6 The relative SPD of a few different CIE standard illuminants.
1.1.4 Effects of light sources and illumination
The spectral radiance, L(λ), is affected by the spectral irradiance, E(λ), and
the reflectance of the surface, ρ(λ), with the relationship between them given
as
L(λ) = E(λ) ρ(λ). (1.12)
Therefore, the perceived color of an object is strongly affected by the light
under which it is observed. For colorimetric purposes, the CIE has standard-
ized the SPD of a few different illuminating sources. The standard SPDs do
not correspond to specific existing sources but represent ideal sources within
a typical group of sources [29]. The idealized sources are called illuminants,
and the CIE has defined a number of such sources. Each illuminant is charac-
terized by its relative SPD; however, it may also be defined with a correlated
color temperature. The correlated color temperature of a light source is the
color temperature at which the heated blackbody radiator best matches the
human-perceived color of the light source [22]. Figure 1.6 shows the relative
SPD of a few different CIE illuminants.
Illuminants A, B, and C were introduced by the CIE in 1931 with the inten-
tion of representing average incandescent light, direct sunlight, and average
daylight, respectively. Illuminant A, redefined in 2006, is intended to rep-

Table 1.4 Chromaticity coordinates of the white points of a few standard illumi-
nants.
Illuminant x y Type of illumination represented
A 0.44757 0.40745 Incandescent or tungsten filament lamp
D50 0.34567 0.35850 Sunlight at the horizon
D65 0.31271 0.32902 Sunlight at noon
resent typical, domestic, tungsten filament (incandescent) lighting. The CIE
states that the standard illuminant A should be used in all applications of col-
orimetry involving the use of incandescent lighting, unless there are specific
reasons for using a different illuminant [47]. The correlated color temperature
of illuminant A is 2856 Kelvin (K). With the advent of the D series of the
CIE illuminants, the B and C illuminants have become obsolete.
The illuminants in the D series of the CIE have been statistically defined
based upon a large number of measurements of real daylight [22]; they were
derived by Judd et al. [48] from spectral distributions of 622 samples of day-
light. Illuminant D65 is intended to represent average daylight. The CIE
standard illuminant D65 is recommended for use in all colorimetric calcu-
lations requiring representative daylight, unless there are specific reasons for
using a different illuminant [49]. Variations in the relative SPD of daylight are
known to occur, particularly in the ultraviolet spectral region, as a function
of season, time of day, and geographic location. However, the CIE standard
illuminant D65 is recommended for use pending the availability of additional
information on such variations [47]. The correlated color temperature of the
CIE standard illuminant D65 is 6504 K.
The CIE F illuminants include 12 illuminants representing various types
of fluorescent lighting. CIE F2 represents the typical cool white fluorescent
source, with a correlated color temperature of 4230 K.
The CIE E illuminant is the equal-energy illuminant. It is defined with a
relative SPD of 100 at all wavelengths.
An illuminant may also be characterized by its white point. The white
point of an illuminant is defined by its chromaticity coordinates or the chro-
maticity coordinates of a perfect diffuser illuminated with the illuminant (see
Section 1.2.1.1 for an explanation of chromaticity coordinates). A perfect dif-
fuser is a theoretical surface that does not absorb light; its apparent brightness
to an observer is the same regardless of the observer’s angle of view.
The chromaticity coordinates of a few standard illuminants are listed in
Table 1.4.

1.1.5 Color perception and trichromacy
Two types of photoreceptors are involved in sensing light in the HVS [21,36–
38]. Rods, being extremely sensitive to light, are responsible for vision under
low levels of illumination, that is, scotopic vision. Cones are responsible for
color vision under conditions of sufficiently high levels of illumination, known
as photopic vision.
The trichromatic theory of color vision, also referred to as the Young–
Helmholtz three-component theory, was proposed by Young (see MacAdam
[50]) and further developed by von Helmholtz [51]. The theory postulates the
existence of three independent types of cones with different spectral sensitiv-
ities. When excited by light, the cones produce three signals, one from each
type of cone, that are transmitted to the brain and cause a color sensation
directly correlated to the three signals [23].
Biological experiments have corroborated the trichromatic theory. There is
scientific evidence that observers with normal color vision have three types of
cones, which are commonly known as the L, M, and S cones [52]. The labels
L, M, and S stand for long, medium, and short wavelength, respectively. Each
cone has a spectral sensitivity of Si(λ), i = L, M, and S, and has peaks at the
wavelengths of about 555, 525, and 450 nm, respectively. The L, M, and S
cones are also referred to as red, green, and blue cones, because light of these
colors activates mainly the corresponding cones. The spectral sensitivities of
the three cones, as determined by Stockman et al. [53, 54], are represented
in Figure 1.7. As shown in Figure 1.7, there is substantial overlap in the
wavelength ranges of sensitivity of the three types of cones.
If Φ(λ) is the SPD of the incident light, the responses of the three cones
can be modeled as
ci =
Z
λ
Si(λ) Φ(λ) dλ. (1.13)
As a consequence, color sensation can be completely described with a three-
component vector, c, with each component being ci, i = L, M, and S.
1.1.6 Color attributes
Three quantities — hue, saturation, and brightness — are considered to be
the three basic attributes of color. The three quantities are used to describe
a color in common language as well as in technical terms, and are defined as
follows.
Hue is the attribute associated with the dominant wavelength of a source
of colored light. The name associated with a color is directly related to its
wavelength. In this sense, a stimulus at 540 nm is termed as green and a
stimulus at 580 nm is named as yellow (see Figure 1.1). Notwithstanding
this meaning of hue, color and hue are not interchangeable: color is a much
broader term that includes hue, saturation, and brightness [46].

350 400 450 500 550 600 650 700 750 800 850
−8
−7
−6
−5
−4
−3
−2
−1
0
1
Wavelength (nm)
Log
quantal
sensitivity
L
M
S
Figure 1.7 Spectral sensitivities of the L (red), M (green), and S (blue) cones.
Saturation refers to the quality of a color in terms of not being mixed with
white. As suggested by Sharma [25], saturation can be defined as the “color-
fulness” of an area judged in proportion to its brightness. Saturated colors are
pure colors in that they appear to be full of color. However, the perception
of saturation is dependent on the hue; specifically, a monochromatic stimulus
of 570 nm appears to be less saturated than other monochromatic light [55].
Brightness is a perceptual attribute closely associated with the physical
attribute of luminance, measured in cd/m2
, or nits. Brightness is defined as
the attribute of visual sensation according to which a source appears to emit
more light or less than another.
Chroma is another perceptual attribute related to the perceived colorful-
ness. Chroma is the colorfulness of an area judged as a proportion of the
brightness of a similarly illuminated white area. Therefore, a stimulus seen
in complete isolation can have a saturation value because it is judged in re-
lation to its own brightness, but chroma is relative to other colors; see also
Section 2.2.2.
Lightness is a relative perceptual attribute of a color related to the percep-
tual brightness. Lightness can be defined as the brightness of an area relative
to the brightness of an equally illuminated white area. Lightness is defined
mathematically in the CIE L∗
u∗
v∗
and L∗
a∗
b∗
color spaces (see Section 1.2.1).

The attributes of hue, lightness, and saturation (HLS) collectively form
the basis for the HLS family of color spaces; see Section 1.2.2.6 for details.
1.1.7 Color-matching functions
Consider three monochromatic sources of light with radiance Lj(λ), j = 1, 2,
and 3, as
L1(λ) = δ(λ − λ1), (1.14)
L2(λ) = δ(λ − λ2), (1.15)
L3(λ) = δ(λ − λ3), (1.16)
where δ represents the Dirac delta function; thus, the three sources of light
have an amount of power equal to unity. If Equation 1.13 is applied, due
to the fact that the three sources of light are Dirac delta functions in λ, the
responses of the three types of cones to the three sources of monochromatic
light can be calculated as
Z
λ
Si(λ) Lj(λ) dλ = Si(λj), (1.17)
for i = L, M, and S, and j = 1, 2, and 3.
Let us denote the three sources of monochromatic light as the primaries.
Three colors, usually monochromatic, are denoted as primaries when they are
employed together to obtain a wide range of colors [23,56].
Suppose that we want to create the same color sensation as that produced
by a source of monochromatic light at wavelength λm, Lm(λ) = δ(λ − λm),
with a linear combination of the three primaries as
α1L1(λ) + α2L2(λ) + α3L3(λ). (1.18)
In other words,
Z
λ
Si(λ) Lm(λ) dλ =
Z
λ
Si(λ) [α1L1(λ) + α2L2(λ) + α3L3(λ)] dλ
= α1Si(λ1) + α2Si(λ2) + α3Si(λ3). (1.19)
It is straighforward to infer that
Z
λ
Si(λ) Lm(λ) dλ = Si(λm). (1.20)
If the wavelength λm of the monochromatic light Lm(λ) is varied so that
a source of monochromatic light L(λ) of wavelength λ is analyzed, three
λ-dependent parameters, αi(λ), are obtained so that they define the linear

combination of the three primaries to obtain the monochromatic light at λ.
Therefore, we have


SL(λ)
SM (λ)
SS(λ)

 =


SL(λ1) SL(λ2) SL(λ3)
SM (λ1) SM (λ2) SM (λ3)
SS(λ1) SS(λ2) SS(λ3)




α1(λ)
α2(λ)
α3(λ)

 . (1.21)
In other words, the response of a photoreceptor i at a given wavelength λ
is equivalent to the response of the photoreceptor to a linear combination of
the three monochromatic primary colors. The three multipliers αi(λ) in the
linear combination are those used to obtain the same color perception as that
produced by a monochromatic stimulus at λ with a linear combination of the
three color primaries.
As a consequence, the responses of the L, M, and S cones to any light L(λ),
now not necessarily monochromatic, can be expressed as follows, by applying
Equation 1.21:


R
λ
SL(λ)L(λ)dλ
R
λ
SM (λ)L(λ)dλ
R
λ
SS(λ)L(λ)dλ

 =


SM (λ1) SM (λ2) SM (λ3)




R
λ
α1(λ)L(λ)dλ
R
λ
α2(λ)L(λ)dλ
R
λ
α3(λ)L(λ)dλ

 .(1.22)
If we define
A1 =
Z
α1(λ) L(λ) dλ, (1.23)
A2 =
Z
α2(λ) L(λ) dλ, (1.24)
A3 =
Z
α3(λ) L(λ) dλ, (1.25)
and use Equation 1.17, Equation 1.22 can be rewritten as


R
λ
SL(λ)L(λ)dλ
R
λ
SM (λ)L(λ)dλ
R
λ
SS(λ)L(λ)dλ

 =


SM (λ1) SM (λ2) SM (λ3)




A1
A2
A3

 . (1.26)
This result shows that the three functions α1(λ), α2(λ), and α3(λ) can also be
utilized to derive the linear combination of the three primaries that produces
the same color sensation as any light L(λ), and that the coefficients of the
linear combination are Ai. The three functions αi(λ), i = 1, 2, and 3, are
thus denoted as color-matching functions, and the coefficients in the linear
combination, Ai, are denoted as the tristimulus values.
It is possible that two different sources of light, La(λ) and Lb(λ), produce
the same visual sensation. Then, the two sources of light are called metamers.
In a formal definition, metamers, or metameric color stimuli, are color stimuli

that have different radiant SPDs but match in color for a given observer [23].
In mathematical terms, we have
Z
λ
Si(λ) La(λ) dλ =
Z
λ
Si(λ) Lb(λ) dλ, for i = L, M, and S. (1.27)
Applying Equation 1.26, we have
A1aSi(λ1) + A2aSi(λ2) + A3aSi(λ3) = A1bSi(λ1) + A2bSi(λ2) + A3bSi(λ3),
(1.28)
for i = L, M, and S. In matrix notation, the relationship between the three
tristimulus values corresponding to the two metameric sources of light must
be


A1a
A2a
A3a

 =


SM (λ1) SM (λ2) SM (λ3)


−1 

SM (λ1) SM (λ2) SM (λ3)




A1b
A2b
A3b

 .
(1.29)
Then, we have


A1a
A2a
A3a

 =


A1b
A2b
A3b

 . (1.30)
As a consequence, two metamers have the same tristimulus values. As ex-
plained in Section 1.1.4, the color sensation perceived under the observation
of a colored surface A depends not only on the reflectance of the surface,
ρa(λ), but also on the SPD of the light incident on the surface, Ea(λ). Then,
two surfaces can reflect metameric stimuli under a particular illuminant, but
they would be perceived as being different under other illuminants.
In 1931, the CIE defined a set of imaginary primaries that can be added us-
ing only positive weights, X, Y , and Z, to create all possible colors. (Note that
Y is also used for yellow in other representations of color; see Sections 1.1.8.4
and 1.2.2.4.) With this aim, the CIE selected three primary monochromatic
light stimuli, with L1(λ) = δ(λ − λ1), λ1 = 700 nm; L2(λ) = δ(λ − λ2), λ2 =
546.1 nm; and L3(λ) = δ(λ − λ3), λ3 = 435.8 nm. A chromaticity-matching

procedure was then performed. In this experiment, carried out by Guild [57]
and Wright [58], an observer was required to match the stimulus obtained from
a linear combination of the three primaries to a given monochromatic stim-
ulus. From these coordinates, a set of weights r(λ) = α1(λ), g(λ) = α2(λ),
and b(λ) = α3(λ) is obtained. These weights, collectively denoted as the
color-matching function as explained above, are represented in Figure 1.8. As
observed in Figure 1.8, a negative proportion of the primary L1(λ) is needed to
obtain some monochromatic light stimuli over the range 450−550 nm. In the
experiment, a negative value for a primary meant that the same primary light
was shone on the target that was being matched. Therefore, the CIE defined
a linear transformation of the color-matching functions such that all values
are positive and the second coordinate corresponds to the spectral luminous
efficiency function for photopic vision. To create this set of color-matching
functions with nonnegative lobes (the motivation for which was to enable the
creation of a measuring instrument with nonnegative filter transmittances),
unrealizable primaries are required, and were defined. According to this linear
transformation, we have


x(λ)
y(λ)
z(λ)

 =


0.49000 0.31000 0.20000
0.17697 0.81240 0.01063
0.00000 0.01000 0.99000




r(λ)
g(λ)
b(λ)

 . (1.31)
Finally, the weights x(λ), y(λ), and z(λ) are calculated as follows:
x(λ) =
x(λ)
y(λ)
V (λ), (1.32)
y(λ) = V (λ) , (1.33)
z(λ) =
z(λ)
y(λ)
V (λ); (1.34)
see Equation 1.7 for the definition of V (λ). The weights given above are shown
in Figure 1.9 [25,59].
1.1.8 Factors affecting color perception
The trichromatic theory of color vision explains the color-sensing mechanisms
that take place in the three types of photoreceptors present in the retina, but it
is not adequate to explain all of the mechanisms involved in color perception.
Firstly, the HVS cannot be considered as a static system, because its response
is optimized to each particular viewing condition. Chromatic adaptation is
the mechanism that explains this effect.
Secondly, color opponency explains other color vision phenomena. The
trichromatic theory provides a representation of colors in terms of three inde-
pendent variables, but the HVS perceives four clearly distinct color sensations:

350 400 450 500 550 600 650 700 750 800
−0.1
−0.05
0
0.05
0.1
0.15
0 2
0.25
0 3
0.35
Wavelength (nm)
Color−matching
functions
r
g
b
Figure 1.8 The r, g, and b color-matching functions.
red, green, yellow, and blue. Yellow is produced by the addition of green and
red light stimuli, but it is clearly perceived as a hue that is different from
its two components. Recent findings have demonstrated that, although color
perception is due to the three known types of photoreceptors or cones, a sub-
sequent opponent process occurs in neurons that connect the cones to the
ganglions [46, 60–62]. Color opponency is explained in more detail in Sec-
tion 1.1.8.4.
1.1.8.1 Chromatic adaptation and color constancy
Color constancy is the property of human vision by which the colors of an
object under different light sources with widely varying intensity levels and
spectral distributions are perceived as the same or remain constant [25]. Chro-
matic adaptation refers to changes in the sensitivity of the HVS according to
varying lighting conditions [22]; this phenomenon explains color constancy.
Nevertheless, the invariance of color perception under varying lighting con-
ditions is not absolute. As lighting conditions vary, there are changes in
color appearance [63]; chromatic adaptation models attempt to predict such
changes.
Apart from chromatic adaptation, visual sensitivity is also adapted to the
overall amount or strength of illumination. Light adaptation is the decrease in

350 400 450 500 550 600 650 700 750 800
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Wavelength (nm)
Color−matching
functions
x
y
z
Figure 1.9 The x, y, and z color-matching functions.
visual sensitivity as illumination is increased. On the contrary, dark adapta-
tion is the increase in the sensitivity of the HVS as the amount of illumination
decreases.
Computational color constancy is a computational method to estimate the
spectral surface reflectance of objects from limited color information available
in a typically trichromatic representation of a color scene when the SPD of
the ambient light is not known [64].
Figure 1.10 shows four images of a sheet of homogeneous pink color pho-
tographed under four different conditions of illumination. Nevertheless, when
a human observes the same sheet under the four different light sources, its
color is perceived as being almost the same. The substantial differences be-
tween the photographs indicate that the camera used cannot perform chro-
matic adaptation as the HVS does.
1.1.8.2 Chromatic adaptation methods
1. The von Kries model: The first proposed model for chromatic adaptation is
the von Kries model; though very simple, it is astonishing how well it models
the phenomenon [22]. Although in his paper published in 1902 [65] von Kries
did not define a set of equations for chromatic adaptation, his ideas have been
used to establish the first color appearance model, known as the von Kries

(a) (b)
(c) (d)
Figure 1.10 A pink sheet of paper photographed under four different types of
illumination: (a) halogen lamp, (b) fluorescent lamp, (c) flashlight, (d) afternoon
sunlight.

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CODE GALANT,
OU
ART DE CONTER FLEURETTE.
DU MÊME AUTEUR.
Code civil.
Code épicurien.
Code conjugal.
Code de la toilette.
Code des honnêtes gens.
Histoire populaire de Napoléon, 10 vol.
—— de la Révolution française, 8 vol.
—— de la Garde Nationale, 1 v. in-8o
.
Marie Stuart, roman historique, 4 v. in-12.

Une Blonde, 1 vol. in-8o
.
Vie et Aventures de Pigault-Lebrun, 1 vol. in-8o
.
SOUS PRESSE.
Histoire pittoresque, anecdotique et biographique de la
Police de Paris, 1 vol. in-8o
.
Procès historiques, 2 vol. in-8o
.
PARIS.—Imprimerie de Gregoire et Compagnie,
rue du Croissant, n. 16.
Gravure par Alfred Johannot.

CODE GALANT,
OU
ART DE CONTER FLEURETTE.
PAR HORACE RAISSON,
AUTEUR DU CODE CIVIL, DU CODE CONJUGAL, ETC.
Nouvelle édition.
Dans cette courte vie, tout est compte
et mécompte.
Charron. De la Sagesse.
PARIS.
OLLIVIER, ÉDITEUR,
QUAI DES AUGUSTINS, N. 37.
DELAUNAY, AU PALAIS-ROYAL.
1837.
PROLÉGOMÈNES.

Jeune ou vieux, bien ou mal, sot ou sage, une fois au moins
l'homme doit aimer; et du hasard d'un premier amour dépend trop
souvent la somme de bonheur de la vie entière.
Ce serait un livre précieux que celui où seraient enseignées
toutes les délicates théories de l'amour, où l'art de plaire se
trouverait réduit en principes: la jeunesse, l'inexpérience, y
puiseraient de précieuses leçons; malheureusement un tel ouvrage
est impossible.
Un livre ne saurait donner qu'une idée bien pauvre de l'amour, de
cet amour qui occupe toute l'ame, la remplit d'images tour-à-tour
heureuses ou désespérantes, mais toujours sublimes, l'isole et la
concentre dans une série d'idées où se rattache le malheur ou la
félicité. Comment pouvoir rendre sensibles la simplicité de geste et
de caractère, le regard, peignant si juste et avec tant de candeur la
nuance de chaque sensation? Comment surtout exprimer cette
aimable non-curance pour tout ce qui n'est pas la personne aimée?
Aussi, que de romans, que d'histoires amoureuses, et combien peu
d'observations simples et vraies sur l'amour!
Au reste, par le temps qui court, l'amour n'est pas une des
affaires graves de la vie, et contre un fou qui se brûle la cervelle à
Montmorency, on compte vingt étourdis qui se ruinent dans les
coulisses de l'Opéra; notre temps est plutôt celui de la galanterie
que celui de l'amour, et l'on ne saurait, au vrai, trop dire s'il faut l'en
féliciter ou l'en plaindre.
Le Code Galant que nous publions aujourd'hui est donc en
quelque sorte un livre de circonstance, et à ce titre du moins nous
espérons pour lui, de la part du lecteur, un bienveillant accueil:
quant à son contenu, nous avouons en toute humilité n'en être en
quelque sorte que le compilateur; un petit ouvrage de ce genre
s'écrit beaucoup plus avec la mémoire qu'avec l'esprit, et nous nous
sommes avant tout appliqué à y rassembler surtout ce qui se
rattache à l'art de conter fleurette, les idées vives, les aperçus
ingénieux, les observations délicates, épars dans une foule de bons
ouvrages, et qui, ainsi réunis, forment en quelque sorte un corps

complet de doctrine, d'où l'on peut, à son gré, déduire de faciles et
précieux enseignemens.
Dans quelques parties de ce Code nous avons eu à aborder de
délicates matières: nous nous sommes appliqué à les traiter avec
beaucoup de ménagemens, nous avons même parfois mieux aimé
passer à côté de la difficulté que de heurter de front les idées
enracinées de l'usage reçu; aussi espérons-nous que la pruderie
nous saura gré de notre retenue. Quant aux lecteurs dont les idées
sympathisent avec les nôtres, nous sommes assuré d'avance d'être
compris par eux.
Peut-être nous reprochera-t-on, comme on a déjà fait pour
quelques bagatelles publiées antécédemment[1]
, la futilité de ce petit
livre: mais est-ce donc une obligation invariable d'employer un style
mâle, et n'est-il permis d'écrire que sur des sujets collets-montés? Il
y a cent façons de réformer et d'instruire, et les heures
n'appartiennent pas toutes aux pensers graves. On parle, à tout
propos, du positif de la génération nouvelle et de la tendance
sérieuse des esprits de la jeune France. Grace au ciel, maintes gens,
nos amis, qui ne sont pas tombés encore à l'état caduc, aiment
toujours la liberté, le plaisir, peut-être un peu même la licence; mais
leur gaîté, bien qu'elle ne se pince pas les lèvres, est tout autant
dans les mœurs constitutionnelles que le sérieux de nos philosophes
frais émoulus du collége.
[1] Code gourmand, Code civil, etc.
Il nous reste, en lançant ce livret dans le monde, à faire des
vœux pour sa fortune et à le recommander surtout à l'indulgence du
lecteur. Nous eussions dû sans doute le faire meilleur et plus hardi:
nous n'osons dire ce qui nous en a empêché. S'il ennuie, l'excuse ne
serait pas admise; s'il fait passer gaîment une heure, il est pardonné.
H. R.

En commençant ce petit livre, il y aurait, ce semble, ingratitude à
ne pas consacrer quelques pages à raconter l'histoire touchante de
la gentille enfant dont le nom a fourni à-la-fois le titre et le sujet.
L'origine et l'étymologie du vieux dicton conter fleurette sont
d'ailleurs bien plus authentiques que celles consacrées chaque jour
par la docte Académie, et ce n'est pas sans quelque plaisir que l'on
relit la peinture naïve des premières amours de ce roi dont le nom
seul réveille déjà des souvenirs de noblesse et de galanterie.
Henri IV avait à peine quinze ans lorsque Charles IX vint à Nérac
pour visiter la cour de Navarre[2]
. Le court séjour du roi fut marqué
par des jeux et des fêtes où le jeune Henri se fit surtout remarquer
par son élégance, son ardeur et sa dextérité.
[2] En 1566.
Charles aimait à tirer de l'arc; on s'empressa de lui en donner le
divertissement, et l'on pense bien qu'aucun des courtisans, pas
même le duc de Guise, qui excellait à cet exercice, n'eut la
maladresse de se montrer plus adroit que le roi. Mais le tour d'Henri
(que l'on appelait encore Henriot) vient de tirer: il s'avance, et du
premier coup enlève avec sa flèche l'orange qui servait de but. Les
lois de ce noble jeu veulent qu'un second but soit immédiatement
placé et que le vainqueur le tire le premier: Henri s'apprête donc à
tirer sa seconde flèche; mais Charles s'y oppose et le repousse avec
humeur; Henri s'indigne, recule quelques pas, et, bandant son arc,
dirige la pointe acérée contre la poitrine de Charles. Le prudent
monarque se mit bien vite à l'abri derrière le plus gros des courtisans
d'alors, et donna l'ordre qu'on éloignât de sa personne ce dangereux
petit-cousin.
La paix se fit: le tir de l'arc recommença le lendemain, mais
Charles trouva un prétexte pour n'y point paraître. Cette fois, le duc
de Guise enleva tout d'abord l'orange, qui se fendit en deux. On n'en
trouvait pas d'autre pour replacer au but; le jeune prince voit briller
une rose sur le sein d'une des jeunes filles qui entourent la barrière,

il s'en saisit et court la placer. Le duc tire le premier: son adresse est
en défaut, il n'atteint pas; Henri, qui lui succède, lance sa flèche au
milieu de la fleur, dont il se saisit galamment, puis il court la rendre à
la jolie villageoise, sans la détacher de la flèche qui lui sert de tige.
Un trouble naïf et touchant se peint sur les traits charmans de la
jeune fille. Henri sent s'arrêter le battement de son cœur, un doux
regard s'échange rapidement entre eux.
Henri, en retournant au château, apprend que cette aimable
enfant s'appelle Fleurette et qu'elle habite avec son père, jardinier
du château, un petit pavillon qui se trouve à l'extrémité du bâtiment
des écuries[3]
.
[3] Ce pavillon existe encore; il sert à renfermer des instrumens aratoires.
Dès le lendemain, le jardinage est devenu la passion dominante
de Henri; il choisit un terrain de quelques toises aux environs de la
fontaine de la Garenne, où il sait que Fleurette se rend plusieurs fois
chaque jour; il l'entoure d'un treillage, y fait des plantations et
travaille avec d'autant plus d'ardeur qu'il est aidé par le père de
Fleurette et qu'il a vingt fois par jour l'occasion ou le prétexte de la
voir.
Si, comme madame de Genlis, j'écrivais un roman historique,
j'aurais beau jeu à arranger une série d'insignifians détails; mais je
raconte une anecdote, et, pour établir l'étymologie de mon vieux
dicton, il suffit, je pense, de rapporter les simples traditions du fait
touchant sur lesquelles elle repose.
Depuis près d'un mois, le sensible Henriot en contait à Fleurette;
tous deux s'aimaient éperdument, sans trop savoir encore ce qu'ils
se voulaient: ils l'apprirent un soir à la fontaine.
Fleurette s'y était rendue un peu tard; l'air était pur; le murmure
de la source, le chant plaintif du rossignol, enchantaient le silence de
la feuillée, et la lune éclairait de son jour touchant cette retraite où
la nature est déjà la volupté. Que se passa-t-il dans cette soirée à la

fontaine de la Garenne, entre le petit prince de quinze ans et la
bergerette de quatorze! plus est aisé de l'imaginer que de le dire;
toujours est-il qu'au retour de la fontaine, Fleurette avait pris le bras
du prince de Béarn et que celui-ci portait allègrement la cruche sur
sa tête. Ils se séparèrent à l'entrée du parc; l'un retourna gaîment
au château, l'autre pleurait en rentrant dans son modeste réduit.
Le père de Fleurette ne s'aperçut pas que sa fille, depuis ce jour,
allait plus tard à la fontaine; mais le précepteur du prince, le
vertueux Lagaucherie, remarqua que son royal élève avait toujours
un prétexte pour s'échapper durant la soirée, et que, par le plus
beau temps du monde, la forme de son chapeau se trouvait mouillée
au retour. Une fois sa prudence éveillée, il suivit de loin le jeune
prince; et, sans être vu, arriva assez tôt et assez près pour
s'apercevoir qu'il était venu trop tard. Convaincu de cette vérité que
la fuite est le seul remède à l'amour, il annonça au prince que le
lendemain ils se mettraient en route vers Pau, pour, de là, se rendre
à l'entrevue de Baïonne[4]
.
[4] Où fut résolu le massacre des protestans.
L'instinct de la gloire, peut-être aussi celui de l'inconstance,
parlaient déjà au cœur de Henri; cette nécessité d'une première
séparation, qu'il courut en larmes annoncer à Fleurette, trouvait à
son insu quelque adoucissement au fond de son ame; mais
comment peindre le désespoir de la naïve et sensible Fleurette: dans
les derniers instans d'un bonheur près de lui échapper, elle
pressentait tous les maux de l'avenir.
«Vous me quittez, Henri, disait la tendre enfant, étouffée par ses
pleurs, vous me quittez, vous m'oublierez, et je n'aurai plus qu'à
mourir!» Henri la rassurait et lui faisait le serment d'un amour
éternel que Fleurette seule devait acquitter.
«Voyez-vous cette fontaine de la Garenne,» disait-elle au
moment où la cloche du château rappelait le prince pour le signal du

départ: «absent, présent, vous me trouverez là!....... toujours
là!.......[5]
»
[5] Notice sur Nérac, par M. le comte de Villeneuve-Bargemont.
Les quinze mois qui s'écoulèrent jusqu'au retour d'Henri au
château d'Agen, avaient développé dans l'ame du jeune prince des
vertus incompatibles avec l'innocence des premières amours, et les
filles d'honneur de Catherine de Médicis s'étaient chargées du soin
d'effacer de son souvenir l'image de la pauvre petite Fleurette. Elle,
plus affligée que surprise d'un changement dont sa raison précoce
l'avait dès long-temps avertie, ne lutta pas contre un malheur prévu,
et ne songea qu'à s'y soustraire.
Plusieurs fois elle avait vu le prince de Béarn se promener dans
les bosquets de la Garenne avec mademoiselle d'Ayelle: elle n'avait
pu résister au désir de se trouver un jour sur leurs pas. La vue de
Fleurette, plus belle encore de sa tristesse et de sa pâleur, réveilla
dans le cœur du jeune Henri un tendre et cruel souvenir: il courut le
lendemain matin au pavillon, et la pria de se trouver encore une fois
du moins à la fontaine de la Garenne. «J'y serai à huit heures,»
répondit la jeune fille sans lever les yeux. Henri s'éloigna plein
d'espoir, et attendit avec cette impatience du premier amour, que
Fleurette d'un regard avait ranimée dans son sein, l'heure qui devait
la lui rendre. Huit heures sonnent: il s'esquive du château, il traverse
le taillis du parc et arrive à la fontaine. Fleurette ne s'y trouvait pas.
Il attend quelques minutes: le plus léger bruissement des feuilles fait
tressaillir son cœur; il va, vient, s'arrête..... Mais il aperçoit près de
la fontaine une petite baguette fichée sur l'endroit même où tant de
fois il s'est assis près de Fleurette. C'est une flèche: il la reconnaît: la
rose fanée y tient encore; un papier est attaché à la pointe; il le
prend, essaie de le lire; mais le jour s'est éteint. Palpitant, troublé, il
vole au château, ouvre le fatal billet... le voici: «Je vous ai dit que
vous me trouveriez à la fontaine: j'y suis. Peut-être êtes-vous passé
bien près de moi. Retournez-y, cherchez mieux... Vous ne m'aimiez
plus... il le fallait bien..... Mon Dieu! pardonnez-moi!...»

Henri a compris le sens cruel de ce billet: des valets munis de
flambeaux courent sur ses pas à la Garenne.....
Le corps de l'adorable enfant fut retiré du fond du bassin où
s'épanchent les eaux de la fontaine, et déposé entre les deux arbres
que l'on y voit encore. Des regrets déchirans, une douleur
poignante, furent du moins la punition de Henri.
Fleurette fut, de toutes les maîtresses du Béarnais, la seule qui
l'ait aimé sincèrement, la seule qui lui resta fidèle. Mais la pauvre
petite ne fit pas des ministres, ne travailla pas avec des confesseurs,
ne donna à la France ni bâtards, ni légitimés; aussi l'histoire ne fait-
elle aucune mention de Fleurette, et nul éditeur ne s'avise
d'annoncer pompeusement ses Mémoires. Par une heureuse
compensation toutefois, la galanterie a pris son joli nom sous ses
auspices et s'est chargée de perpétuer la gracieuse mémoire de la
jolie et tendre enfant, à qui l'on ne saurait se défendre de donner un
doux souvenir, chaque fois que l'on tente de conter fleurette.

TITRE PREMIER.
Avant.
CHAPITRE PREMIER.
De l'Amour.
ARTICLE PREMIER.
L'amour prend sa source dans les deux sentimens les plus purs,
l'admiration et l'espérance[6]
.
[6] Qui s'avise de devenir amoureux d'une reine, à moins qu'elle ne fasse des
avances?
ART. 2.
Il est difficile de définir l'amour: ce qu'on peut en dire est que
dans l'ame, c'est une passion de régner; dans l'esprit, c'est une
sympathie, et dans le corps, ce n'est qu'une envie cachée et délicate
de posséder ce que l'on aime, après beaucoup de mystères. (La
Rochefoucauld.)
ART. 3.

L'amour est comme la fièvre, il naît et s'éteint sans que la volonté
y ait la moindre part. Aussi ne peut-on s'applaudir des belles qualités
de ce qu'on aime que comme d'un hasard heureux.
ART. 4.
Les grandes passions se trahissent surtout par des preuves
ridicules, l'extrême timidité, par exemple, et même la mauvaise
honte.
ART. 5.
L'amant est bien près d'être heureux qui commence à douter du
bonheur qu'il se promettait et devient sévère sur les motifs d'espérer
qu'il a cru voir.
ART. 6.
Dans l'amour, au rebours de la plupart des autres passions, le
souvenir de ce que l'on a perdu paraît toujours au-dessus de ce
qu'on peut attendre de l'avenir.
ART. 7.
Le moment le plus déchirant de l'amour est celui où il s'aperçoit
qu'il s'est mépris et qu'il lui faut, de ses propres mains, détruire la
belle chimère de bonheur qu'il s'était bâtie à grand'peine.
ART. 8.
L'amour est de tous les âges: Horace Walpole inspira la passion la
plus vive à madame du Deffand, septuagénaire, et les belles
personnes de la cour du vieux roi Louis XIV étaient éprises de cette
ombre.
ART. 9.

Avant la naissance de l'amour, la beauté est nécessaire comme
enseigne; elle prédispose à cette passion par les louanges que l'on
entend donner à celle que l'on aimera. Une admiration très vive rend
la plus petite espérance décisive.
ART. 10.
L'amant trouve dans l'objet de son adoration toutes les
perfections, même celles des genres les plus opposés. Voilà la raison
morale pour laquelle l'amour est la plus violente des passions. Dans
les autres, les désirs doivent s'accommoder aux froides réalités; dans
celle-ci, ce sont les réalités qui s'empressent de se modeler sur les
désirs.
ART. 11.
Du moment qu'il aime, l'homme, même le plus sage, ne voit plus
aucun objet sous son jour vrai. Il s'exagère en moins ses propres
avantages, et en plus les moindres faveurs de l'objet aimé. La
crainte, l'espoir, donnent pour lui de la réalité aux fictions de son
esprit; il perd enfin le sentiment de la probabilité.
ART. 12.
Dans l'amour, les femmes ne pardonnent pas ce qu'elles
appellent un manque de délicatesse. Ce mot, inventé par l'orgueil,
n'est pas très clair; il a l'air d'exprimer quelque chose de semblable à
ce que les rois appellent lèse-majesté, crime d'autant plus
dangereux qu'on y tombe sans s'en douter.

CHAPITRE II.
De l'Attachement.
ARTICLE PREMIER.
L'attachement est une modification de l'amour et une nuance de
l'amitié.
ART. 2.
Un rapport d'humeur, de caractère, de position, l'insouciance, le
hasard, forment parfois des liens qui durent sans trouble toute la
vie.
ART. 3.
Dans l'attachement il faut plus d'abnégation que dans l'amour,
car on y est privé des douces compensations de l'amour-propre.
ART. 4.
Un attachement sincère prend nécessairement sa source dans un
vrai mérite et s'appuie sur quelque vertu. On blâme dans le monde
de semblables liaisons, et pourtant il y a mille à parier contre un que
la femme qui fait naître un durable attachement est plus estimable
que celle qui inspire un violent amour.
ART. 5.
Chez quelques hommes d'infiniment d'esprit, un attachement
n'est le résultat ni de la passion, ni de la convenance, ni du
désœuvrement: c'est en quelque sorte un besoin de société passive.

Cette situation se peint très bien par le mot de M. de Talleyrand, qui
venant de quitter la femme la plus célèbre de France par son génie
brillant et ses ouvrages admirables, prit pour maîtresse une belle
sotte: «Cela repose!» disait-il, et il n'a jamais rompu cet
attachement.
CHAPITRE III.
Du Goût.
ARTICLE PREMIER.
Le goût est à l'amour ce qu'une estampe est à un tableau: copie
exacte, moins la couleur.
ART. 2.
L'homme d'esprit prévoit d'avance toutes les phases d'une liaison
de goût; comme il y apporte plus de délicatesse que de passion, il
s'y montre constamment aimable.
ART. 3.
Les moralistes réprouvent l'amour-goût: ils ont tort. A quelque
genre d'affection en effet que l'on doive les plaisirs, dès qu'il y a
exaltation de l'ame, ils sont vifs, et leur souvenir doit être pur.
ART. 4.
Quelquefois le goût se change en amour durable. Il est alors
plein de charmes, car il est basé sur l'expérience, l'habitude et la
certitude de ne pouvoir trouver mieux.

ART. 5.
Le mal, c'est que dans l'amour-goût on tient plus de compte de la
manière dont les autres voient la personne à qui on s'attache que de
la manière dont on la voit soi-même.
ART. 6.
La grace de la nouveauté est à l'amour-goût ce que la fleur est
sur les fruits: elle y répand un lustre qui s'efface aisément et qui ne
revient jamais.
ART. 7.
Aussi une liaison de goût ne saurait-elle durer lorsque chez l'une
des deux parties seulement vient à naître l'amour-passion.
CHAPITRE IV.
Du Caprice.
ARTICLE PREMIER.
Le caprice est l'amour de ceux qui n'en ont pas.
ART. 2.
Les organisations trop faibles pour comprendre ou pour
supporter les délicieux tourmens de l'amour, se rejettent sur le
caprice: là, s'ils ne trouvent pas le bonheur, ils rencontrent du moins
le plaisir.

ART. 3.
On confond trop communément le caprice avec l'inconstance;
rien de plus dissemblable pourtant: l'une est un vice du cœur, l'autre
un calcul de l'esprit.
ART. 4.
Le caprice est assurément la source de mille petites félicités: il
butine en amour sur tout ce qu'il y a de vif, de gracieux, de gai.
Malheureusement son règne est court, et s'il laisse quelques
souvenirs, il laisse encore plus de regrets.
ART. 5.
«Le caprice, dit La Bruyère, est dans les femmes tout proche de
la beauté pour être son contre-poison et afin qu'elle nuise moins aux
hommes, qui n'en guériraient pas sans ce remède.»

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