Table of Contents

Preface

Chapter 1: Definitions

1.1. Introduction

1.2. Choosing a definition

1.3. General characteristics of the data

1.4. Numerical/symbolic

1.5. Fusion systems

1.6. Fusion in signal and image processing and fusion in other fields

1.7. Bibliography

Chapter 2: Fusion in Signal Processing

2.1. Introduction

2.2. Objectives of fusion in signal processing

2.3. Problems and specificities of fusion in signal processing

2.4. Bibliography

Chapter 3: Fusion in Image Processing

3.1. Objectives of fusion in image processing

3.2. Fusion situations

3.3. Data characteristics in image fusion

3.4. Constraints

3.5. Numerical and symbolic aspects in image fusion

3.6. Bibliography

Chapter 4: Fusion in Robotics

4.1. The necessity for fusion in robotics

4.2. Specific features of fusion in robotics

4.3. Characteristics of the data in robotics

4.4. Data fusion mechanisms

4.5. Bibliography

Chapter 5: Information and Knowledge Representation in Fusion Problems

5.1. Introduction

5.2. Processing information in fusion

5.3. Numerical representations of imperfect knowledge

5.4. Symbolic representation of imperfect knowledge

5.5. Knowledge-based systems

5.6. Reasoning modes and inference

5.7. Bibliography

Chapter 6: Probabilistic and Statistical Methods

6.1. Introduction and general concepts

6.2. Information measurements

6.3. Modeling and estimation

6.4. Combination in a Bayesian framework

6.5. Combination as an estimation problem

6.6. Decision

6.7. Other methods in detection

6.8. An example of Bayesian fusion in satellite imagery

6.9. Probabilistic fusion methods applied to target motion analysis

6.10. Discussion

6.11. Bibliography

Chapter 7: Belief Function Theory

7.1. General concept and philosophy of the theory

7.2. Modeling

7.3. Estimation of mass functions

7.4. Conjunctive combination

7.5. Other combination modes

7.6. Decision

7.7. Application example in medical imaging

7.8. Bibliography

Chapter 8: Fuzzy Sets and Possibility Theory

8.1. Introduction and general concepts

8.2. Definitions of the fundamental concepts of fuzzy sets

8.3. Fuzzy measures

8.4. Elements of possibility theory

8.5. Combination operators

8.6. Linguistic variables

8.7. Fuzzy and possibilistic logic

8.8. Fuzzy modeling in fusion

8.9. Defining membership functions or possibility distributions

8.10. Combining and choosing the operators

8.11. Decision

8.12. Application examples

8.13. Bibliography

Chapter 9: Spatial Information in Fusion Methods

9.1. Modeling

9.2. The decision level

9.3. The combination level

9.4. Application examples

9.5. Bibliography

Chapter 10: Multi-Agent Methods: An Example of an Architecture and its Application for the Detection, Recognition and Identification of Targets

10.1. The DRI function

10.2. Proposed method: towards a vision system

10.3. The multi-agent system: platform and architecture

10.4. The control scheme

10.5. The information handled by the agents

10.6. The results

10.7. Bibliography

Chapter 11: Fusion of Non-Simultaneous Elements of Information: Temporal Fusion

11.1. Time variable observations

11.2. Temporal constraints

11.3. Fusion

11.4. Dating measurements

11.5. Evolutionary models

11.6. Single sensor prediction-combination

11.7. Multi-sensor prediction-combination

11.8. Conclusion

11.9. Bibliography

Chapter 12: Conclusion

12.1. A few achievements

12.2. A few prospects

12.3. Bibliography

Appendix A: Probabilities: A Historical Perspective

A.1. Probabilities through history

A.2. Objectivist and subjectivist probability classes

A.3. Fundamental postulates for an inductive logic

A.4. Bibliography

Appendix B: Axiomatic Inference of the Dempster-Shafer Combination Rule

B.1. Smets’s axioms

B.2. Inference of the combination rule

B.3. Relation with Cox’s postulates

B.4. Bibliography

List of Authors

Index

First published in France in 2003 by Hermes Science/Lavoisier entitled “Fusion d’informations en traitement du signal et des images”

First published in Great Britain and the United States in 2008 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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© ISTE Ltd, 2008

© LAVOISIER, 2003

The rights of Isabelle Bloch to be identified as the author of this work have been asserted by her in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Cataloging-in-Publication Data

[Fusion d’informations en traitement du signal et des images English] Information fusion in signal and image processing / edited by Isabelle Bloch.

p. cm.

Includes index.

ISBN 978-1-84821-019-6

1. Signal processing. 2. Image processing. I. Bloch, Isabelle.

TK5102.5.I49511 2008

621.382'2--dc22

2007018231

British Library Cataloguing-in-Publication Data

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

ISBN: 978-1-84821-019-6

Preface

Over the past few years, the field of information fusion has gone through considerable and rapid change. While it is difficult to write a book in such a dynamic environment, this book is justified by the fact that the field is currently at a turning point. After a phase of questions, debates, and even mistakes, during which the field of fusion in signal and image processing was not well defined, we are now able to efficiently use basic tools (often imported from other fields) and it is now possible to both design entire applications, and develop more complex and sophisticated tools. Nevertheless, there remains much theoretical work to be done in order to broaden the foundations of these methods, as well as experimental work to validate their use.

The objectives of this book are to present, on the one hand, the general ideas of fusion and its specificities in signal and image processing and in robotics, and on the other hand, the major methods and tools, which are essentially numerical. This book does not intend, of course, to compete with those devoted entirely to one of these tools, or one of these applications, but instead tries to underline the assets of the different theories in the intended application fields.

With a book like this one, we cannot aspire to be comprehensive. We will not discuss methods based on expert or multi-agent systems (however, an example will be given to illustrate them), on neural networks and all of the symbolic methods expressed in logical formalism. Several teams work on developing such methods, for example, in France, the IRIT in Toulouse and the CRIL in Lens on logical methods, the LAAS in Toulouse on neuromimetic methods, the IMAG in Grenoble on multi-agent systems, and many others. Likewise, among the methods we will discuss, many interesting aspects will have to be left aside, whether theoretical, methodological or regarding applications because they would bring the reader beyond the comparative context we want him to stay in, but we hope that the cited references will help complete this presentation for readers who would wish to study these aspects further.

This book is meant essentially for PhD students, researchers or people in the industry, who wish to familiarize themselves with the concepts of fusion and discover its main theories. It can also serve as a guide to understanding theories and methodologies, developing new applications, discovering new research subjects, for example, those suggested by the problems and prospects mentioned in this book.

The structure is organized in two sets of chapters. The first deals with definitions (Chapter 1) and the specificities of the fields that are discussed: signal processing in Chapter 2, image processing in Chapter 3 and robotics in Chapter 4. The second part is concerned with the major theories of fusion. After an overview of the modes of knowledge representation used in fusion (Chapter 5), we present the principles of probabilistic and statistical fusion in Chapter 6, of belief function theory in Chapter 7, of fuzzy and possibilistic fusion in Chapter 8. The specificities of fusion in image processing and in certain robotics problems require taking into account spatial information. This is discussed in Chapter 9, since the fusion methods developed in other fields do not consider it naturally. An example of an application that relies on a multi-agent architecture is given in Chapter 10. The specific methods of temporal fusion, finally, are described in Chapter 11.

This book owes a great deal to the GDR-PRC ISIS and to their directors, Odile Macchi and Jean-Marc Chassery. Its authors were the coordinators of the workgroup on information fusion and the related actions. The GDR was the first initiative that led to bringing together the French community of people working on information fusion in signal and image processing, to build ties with other communities (man-machine communications, robotics and automation, artificial intelligence), to enrich ideas and it thus became the preferred place for discussion. This book would not have existed without the maturity acquired in this group. This book is also indebted to the comments and discussions of the FUSION Working Group (a European project) directed by Professor Philippe Smets (IRIDIA, Université Libre de Bruxelles), aimed at summarizing the problems and methods of data fusion in different fields, from artificial intelligence to image processing, from regulations to financial analysis, etc. It grouped together researchers from the IRIT in Toulouse, the IRIDIA in Brussels, Télécom-Paris, the CNR in Padua, the University of Granada, the University of Tunis, the University of Magdeburg, the ONERA, Thomson-CSF, Delft University, University College London. Chapter 1 in particular owes much to this group. Finally, the trust bestowed on us by Bernard Dubuisson, his motivation and his encouragements also helped a great deal in the completion of this book. This book is dedicated to the memory of Philippe Smets.

Isabelle BLOCH

Chapter 1

Definitions ¹

1.1. Introduction

Fusion has become an important aspect of information processing in several very different fields, in which the information that needs to be fused, the objectives, the methods, and hence the terminology, can vary greatly, even if there are also many analogies. The objective of this chapter is to specify the context of fusion in the field of signal and image processing, to specify the concepts and to draw definitions. This chapter should be seen as a guide for the entire book. It should help those with another vision of the problem to find their way.

1.2. Choosing a definition

In this book, the word “information” is used in a broad sense. In particular, it covers both data (for example, measurements, images, signals, etc.) and knowledge (regarding the data, the subject, the constraints, etc.) that can be either generic or specific.

The definition of information fusion that we will be using throughout this book is given below.

DEFINITION 1.1 (Fusion of information). Fusion of information consists of combining information originating from several sources in order to improve decision making.

This definition, which is largely the result of discussions led within the GDR-PRC ISIS¹ workgroup on information fusion, is general enough to encompass the diversity of fusion problems encountered in signal and image processing. Its appeal lies in the fact that it focuses on the combination and decision phases, i.e. two operations that can take different forms depending on the problems and applications.

For each type of problem and application, this definition can be made more specific by answering a certain number of questions: what is the objective of the fusion? what is the information we wish to fuse? where does it come from? what are its characteristics (uncertainty, relation between the different pieces of information, generic or factual, static or dynamic, etc.)? what methodology should we choose? how can we assess and validate the method and the results? what are the major difficulties, the limits?, etc.

Let us compare this definition with those suggested by other workgroups that have contributed to forming the structure of the field of information fusion.

Definition 1.1 is a little more specific than that suggested by the European work-group FUSION [BLO 01], which worked on fusion in several fields from 1996 to 1999². The general definition retained in this project is the following: gathering information originating from different sources and using the gathered information to answer questions, make decisions, etc. In this definition, which also focuses on the combination and on the goals, the goals usually stop before the decision process, and are not restricted to improving the overall information. They include, for example, obtaining a general perspective, typically in problems related to fusing the opinions or preferences of people, which is one of the themes discussed in this project, but this goes beyond the scope of this book. Here, improving knowledge refers to the world as it is and not to the world as we would like it to be, as is the case with preference fusion.

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