Digital Color Imaging E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 491

Veröffentlichungsjahr: 2013

Beschreibung

This collective work identifies the latest developments in the field of the automatic processing and analysis of digital color images.

For researchers and students, it represents a critical state of the art on the scientific issues raised by the various steps constituting the chain of color image processing.

It covers a wide range of topics related to computational color imaging, including color filtering and segmentation, color texture characterization, color invariant for object recognition, color and motion analysis, as well as color image and video indexing and retrieval.

Leseprobe

Table of Contents

Foreword

Chapter 1. Color Representation and Processing in Polar Color Spaces

1.1. Introduction

1.2. The HSI triplet

1.3. Processing of hue: a variable on the unit circle

1.4. Color morphological filtering in the HSI space

1.5. Morphological color segmentation in the HSI space

1.6. Conclusion

1.7. Bibliography

Chapter 2. Adaptive Median Color Filtering

2.1. Introduction

2.2. Noise

2.3. Nonlinear filtering

2.4. Median filter: methods derived from vector methods

2.5. Adaptive filters

2.6. Performance comparison

2.7. Conclusion

2.8. Bibliography

Chapter 3. Anisotropic Diffusion PDEs for Regularization of Multichannel Images: Formalisms and Applications

3.1. Introduction

3.2. Preliminary concepts

3.3. Local geometry in multi-channel images

3.4. PDEs for multi-channel image smoothing: overview

3.5. Regularization and curvature preservation

3.6. Numerical implementation

3.7. Some applications

3.8. Conclusion

3.9. Bibliography

Chapter 4. Linear Prediction in Spaces with Separate Achromatic and Chromatic Information

4.1. Introduction

4.2. Complex vector 2D linear prediction

4.3. Spectral analysis in the IHLS and L*a*b* color spaces

4.4. Application to segmentation of textured color images

4.5. Conclusion

4.6. Bibliography

Chapter 5. Region Segmentation

5.1. Introduction

5.2. Compact histograms

5.3. Spatio-colorimetric classification

5.4. Segmentation by graph analysis

5.5. Evaluation of segmentation methods against a “ground truth”

5.6. Conclusion

5.7. Bibliography

Chapter 6. Color Texture Attributes

6.1. Introduction

6.2. Statistical features

6.3. Spatio-frequential features

6.4. Stochastic modeling

6.5. Color texture classification

6.6. Conclusion

6.7. Bibliography

Chapter 7. Photometric Color Invariants for Object Recognition

7.1. Introduction

7.2. Basic assumptions

7.3. Color invariant characteristics

7.4. Conclusion

7.5. Bibliography

Chapter 8. Color Key Point Detectors and Local Color Descriptors

8.1. Introduction

8.2. Color key point and region detectors

8.3. Local color descriptors

8.4. Conclusion

8.4. Conclusion

Chapter 9. Motion Estimation in Color Image Sequences

9.1. Introduction

9.2. Extension of classical motion estimation techniques to color image spaces

9.3. Apparent motion and vector images

9.4. Conclusion

9.5. Bibliography

Appendix A. Appendix to Chapter 7: Summary of Hypotheses and Color Characteristic Invariances

A.1.Bibliography

List of Authors

Index

First published 2012 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USA

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© ISTE Ltd 2012

The rights of Christine Fernandez-Maloigne, Frédérique Robert-Inacio and Ludovic Macaire to be identified as the author of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Cataloging-in-Publication Data

Numerical color imaging / edited by Christine Fernandez-Maloine, Frederique Robert-Inacio, [and] Ludovic Macaire.

p. cm.

Includes bibliographical references and index.

ISBN 978-1-84821-347-0

1. Color--Mathematics--Research. 2. Image processing--Mathematics--Research. 3. Color vision-- Research. I. Fernández-Maloine, Christine. II. Robert-Inacio, Frédérique. III. Macaire, Ludovic.

QC496.N86 2012

35.601'51--dc23

2012008577

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN: 978-1-84821-347-0

Foreword

The relationship that scientists have with color is one that is particularly worthy of examination. The study of color has its roots in physics, and more specifically in optics, and to a lesser extent in biology, in the context of the physiology of perception. Due to this double connection both with physical science and life science, the study of color holds a unique position in physics that is shared only with the field of acoustics (for exactly the same reasons). We will however see that scientists have approached these two fields very differently.

Other fields associated with the human perception of physical phenomena could also benefit from the same approach, but so far at least this has not been followed through. Other senses – touch, taste, and smell – do not seem to have achieved the same theoretical underpinnings and methodology, or the same body of experimental research to put them firmly into the realm of physics.

As with acoustics, and more specifically musical acoustics, when studying color, the scientist is faced with a highly demanding task. Not only must he understand how the signals are generated and propagated, but he must also explain the interpretation that ultimately occurs in the body of the listener or viewer. In caude venenum! This final stage proves to be the most intractable in the face of a rigorous approach. The researcher must contend with uncertainty and imprecision, with the variable and the relative and, worst of all, the subjective. He must attempt to justify beauty, harmony, ugliness, and disharmony. Curiously, while it is primarily mathematicians who have attempted to bring order and harmony to sound, it is the physicists who have dealt with the problem of color. Maybe this can be explained in retrospect by the large spectral range occupied by sound (over ten octaves), compared to the visible spectrum, which barely covers a single octave, and by the selectiveness of the sensors.

The ear is an instrument that is near linear in frequency that transmits all the signals it receives, while the retina is a three-channel projector where a great deal of mixing takes place. Thus, sound provides a huge diversity of signals that can be used to extract order and rules, which is the natural domain of the mathematician. Colors however must be explained and the means by which they are reduced to such a compact form is in the domain of the physicist.

Great men of physics have been fascinated by this problem, starting with Newton who was the first (1666) to separate white light into its component colors and then recombine them to recreate the original light, thereby demonstrating that white light consists of different colors. After him, Young (1777), Dalton (1794), and Helmholtz (1850), among others, carried out a wide range of studies in color perception, leading in particular to the identification of the three components of color vision and the identification of color blindness within the population. Lord Rayleigh, Lorentz, Mie, and Planck dedicated themselves to explaining the colors of natural phenomena, including the sky and clouds as well as powders and metals. Maxwell not only built the foundations of the wave approach to radiation, but he also showed how the visible spectrum fits into the broader electromagnetic spectrum. Playing with spinning tops, he showed the laws of color balancing that are the basis of metamerism and used this insight to discover the color perception space (1857). Finally, it is less widely known that he was also responsible for producing the first color photograph by superimposing three black and white photographs taken with appropriate filters.

These approaches on the nature of color taken by famous physicists, as well as a large number of less famous and unknown researchers, were not taken in the absence of any psychological or even philosophical consideration, which in any case is incredibly subjective. Long before this, the ancient philosophers had already placed color at the center of their visions of harmony, in interpretations that were built around an intimate mixture of reality and mathematics. In the same way as with music, color was given a key role in the harmony of the universe.

Aristotle had adopted a vision based around the antagonism between “light” and ”darkness”, between which there lay seven carefully chosen gradings ranging from white to black. This antagonism of conflicting colors persisted in representations up until the 20th Century and contributed on a large-scale to the antagonism of complementary colors used by painters and photographers. Aristotle chose the seven colors of the rainbow as the basis for his decomposition, which he placed between white and black. Plato distanced himself from this approach, confining the effects of color to within the eye, and proposing his own primary colors with different hues and saturation. Later, Pythagoras looked for other harmonies within the positions of the planets, which led to a more universal equilibrium within which colors and music both played roles.

Fifteen centuries later, in the classical era and in parallel with the work of physicists, a concurrent trend toward physical analysis started to develop. This was led largely by philosophers, attempting to bring color within the sphere of human experience, in terms of perception, sensitivity, and subjectivity. This began with the postulates of Locke, who in the 17th Century separated color from the object it was associated with, and was followed by the writings of Goethe that drew on a spectrum of experimental work to “prove” the limitations of Newton’s approach, which was too physical in that it ignored the role of the individual and the context in color perception, and was not subtle enough to describe simultaneous contrast and variations in hue; finally, Schopenhauer refused to ascribe any objective qualities to color, viewing it simply as the result of subjective antagonism between light and darkness in the perception of the observer, whose retina becomes fatigued from overstimulation.

It was from these often divergent works, which at times led to conflict between physicists and philosophers, that the artists of the 19th Century drew inspiration for their palettes: first Turner and the adherents of the English school of painting, followed by Seurat and the entire Impressionist family, and especially the works of Chevreul (1839).

When approaching an academic text such as the present work, the reader should keep in mind the complexity of the representation and modeling of color, models that are the pinnacle of twenty-five centuries of historical study. We encourage the reader to examine the impact of ancient theories of color on modern day practices in digital processing of color images, in their filtering and restoration, the extraction of significant components, lines, shapes, and textures, their compression and transformation. This book will help the reader to grasp the importance of the mathematical tools that are required for the treatment of this complex data: differential equations, graphs, Markov fields, spectral analysis, etc. It will also draw attention to the importance of a suitable choice of color space for color representation: RGB, L*a*b, HSV, etc. This choice is determined both by physical constraints and by the requirements of psycho-physiology; the reader will discover the importance of metrics associated with similarity and confusion, or alternatively with contrasts.

The reader will also be struck, on reading these chapters, by the role of experimentation, the relevance of experiment and empirical approaches, and the importance of the ultimate adjudicator, the human observer, who is required to classify and categorize, above and beyond what can be achieved with scores and norms. The book will reveal why operations that the human eye has no difficulty at all with, discrimination and detection, today require a vast and complex arsenal if they are to be automated, and why their results still often remain limited or conditional. Finally, through this, the reader will understand why the compelling avenues of research presented here are still ripe for further exploration, challenges that still inspire the authors of this work.

Henri MaîtreApril 2012

Chapter 1

Color Representation and Processing in Polar Color Spaces1

1.1. Introduction

A wide range of technological representations for color have been established over the last few decades. We recommend some classic references to the reader interested in developing a thorough appreciation of this multiplicity [CAR 95, POY 03, SHI 95, TRE 04]. Today, it is widely accepted that no single color space is suitable for all fields and all applications. We will, however, show that the specific choice of representation has a strong impact on the image processing methods and algorithms that we will discuss. In particular, this chapter will focus on the processing of color images represented in polar coordinates. The hue, saturation, intensity (HSI) triplet is very closely related to how the human vision system operates, and this makes it highly intuitive. We, therefore, intend to work in a geometric framework whereby the RGB (red, green, blue) color cube is transformed into polar coordinates, and this will require us to adapt our subsequent processing of these color coordinates.

We will begin by recalling intuitively the three variables represented by this triplet, and will then show a sample calculation for the geometric transformation of Cartesian RGB coordinates into polar HSI coordinates. The manipulation of hue and associated operators is particularly important. We will treat in detail various examples of filtering and segmentation methods that can be used to best exploit the HSI triplet form. These image processing approaches are largely nonlinear techniques or extensions of color images of operators and transformations with their roots in concepts of mathematical morphology.

Notations used in this chapter

Throughout this chapter, we will use a different notation for the color axes, which will be denoted in capital letters (RGB, HSI, etc.), from that used for coordinates of color points c (the latter being a vector), which will be represented by lowercase letters: r, g, b, h, s, i,

Recall also that the (,) pair, where corresponds to the natural order of scalar values is a complete totally ordered lattice or chain. The family of gray level images, written as (E,), also forms a complete lattice.