Information Fusion in Signal and Image Processing

Major Probabilistic and Non-Probabilistic Numerical Approaches

Isabelle Bloch

• Publisher: Wiley-ISTE
• Year: 2013
• Print ISBN: 9781848210196
• eBook ISBN: 9781118623855
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Signals & Signal Processing
• Index: Technology & Engineering

The area of information fusion has grown considerably during the last few years, leading to a rapid and impressive evolution. In such fast-moving times, it is important to take stock of the changes that have occurred. As such, this books offers an overview of the general principles and specificities of information fusion in signal and image processing, as well as covering the main numerical methods (probabilistic approaches, fuzzy sets and possibility theory and belief functions).

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.

Some of the first notable efforts in clarifying the field were made by the data fusion work group at the US Department of Defense’s Joint Directors of Laboratories (JDL). This group was created in 1986 and focused on specifying and codifying the terminology of data fusion in some sort of dictionary (Data Fusion Lexicon) [JDL 91]. The method suggested was exclusively meant for defense applications (such as automatically tracking, recognizing and identifying targets, battlefield surveillance) and focused on functionalities, by identifying processes, functions and techniques [HAL 97]. It emphasized the description of a hierarchy of steps in processing a system. The definition we use here contrasts with the JDL’s definition and chooses another perspective, focusing more on describing combination and decision methods rather than systems. It is better suited to the diversity of situations encountered in signal and image processing. In this sense, it is a broader definition.

Another European workgroup of the EARSeL (European Association of Remote Sensing Laboratories) extended the JDL’s definition to the broader field of satellite imagery [WAL 99]: the fusion of data constitutes a formal framework in which the data originating from different sources can be expressed; its goal is to obtain information of higher quality; the exact definition of “higher quality” will depend on the application. This definition encompasses most of the definitions suggested by several authors in satellite imagery, which are gathered in [WAL 99]. Definition 1.1 goes further and includes decisions.

The meaning of the word fusion can be understood on different levels. Other concepts, such as estimation, revision, association of data and data mining, can sometimes be considered as fusion problems in a broad sense of the word. Let us specify these concepts.

Fusion and estimation. The objective of estimation is to combine several values of a parameter or a distribution, in order to obtain a plausible value of this parameter. Thus, we have the same combination and decision steps, which are the two major ingredients of Definition 1.1. On the other hand, numerical fusion methods often require a preliminary step to estimate the distributions that are to be combined (see section 1.5) and the estimation is then interpreted as one of the steps of the fusion process.

Fusion and revision or updating. Revising or updating consists of completing or modifying an element of information based on new information. It can be considered as one of the fields of fusion. Sometimes, fusion is considered in a stricter sense, where combination is symmetric. As for revision, it is not symmetric and it draws a distinction between information known beforehand and new information. Here, we will be considering dynamic processes among others (particularly robotics), and it seems important for us to include revision and updating as part of fusion (for example, for applications such as helping a robot comprehend its environment). Revision involves the addition of new information that makes it possible to modify, or specify, the information previously available about the observed phenomenon, whereas updating involves a modification of the phenomenon that leads to modifying the information about it (typically in a time-based process).

Fusion and association. Data association is the operation that makes it possible to find among different signals originating from two sources or more those that are transmitted by the same object (source or target). According to Bar-Shalom and Fort-man [BAR 88], data association is the most difficult step in multiple target tracking. It consists of detecting and associating noisy measurements, the origins of which are unknown because of several factors, such as random false alarms in detections, clutter, interfering targets, traps and other countermeasures. The main models used in this field are either deterministic (based on classic hypothesis tests), or probabilistic models (essential Bayesian) [BAR 88, LEU 96, ROM 96]. The most common method [BAR 88] relies on the Kalman filter with a Gaussian hypothesis. More recently, other estimation methods have been suggested, such as the Interactive Multiple Model estimator (IMM), which can adapt to different types of motion and reduce noise, while preserving a good accuracy in estimating states [YED 97]. This shows how the problems we come across can be quite different from those covered by Definition 1.1.

Fusion and data mining. Data mining consists of extracting relevant parts of information and data, which can be, for example, special data (in the sense that it has specific properties), or rare data. It can be distinguished from fusion that tries to explain where the objective is to find general trends, or from fusion that tries to generalize and lead to more generic knowledge based on data. We will not be considering data mining as a fusion problem.

1.3. General characteristics of the data

In this section, we will briefly describe the general characteristics of the information we wish to fuse, characteristics that have to be taken into account in a fusion process. More detailed and specific examples will be given for each field in the following chapters.

A first characteristic involves the type of information we wish to fuse. It can consist of direct observations, results obtained after processing these observations, more generic knowledge, expressed in the form of rules for example, or opinions of experts. This information can be expressed either in numerical or symbolic form (see section 1.4). Particular attention is needed in choosing the scale used for representing the information. This scale should not necessarily have any absolute significance, but it at least has to be possible to compare information using the scale. In other words, scales induce an order within populations. This leads to properties of commensurability, or even of normalization.

The different levels of the elements of information we wish to fuse are also a very important aspect. Usually, the lower level (typically the original measurements) is distinguished from a higher level requiring preliminary steps, such as processing, extracting primitives or structuring the information. Depending on the level, the constraints can vary, as well as the difficulties. This will be illustrated, for example, in the case of image fusion in Chapter 3.

Other distinctions in the types of data should also be underlined, because they give rise to different models and types of processing. The distinction between common and rare data is one of them. Information can also be either factual or generic. Generic knowledge can be, for example, a model of the observed phenomenon, general rules, integrity constraints. Factual information is more directly related to the observations. Often, these two types of information have different specificities. Generic information is usually less specific (and serves as a “default”) than factual information, which is directly relevant to the particular phenomenon being observed. The default is considered if the specific information is not available or reliable, otherwise, and if the elements of information are contradictory, more specific information is preferred. Finally, information can be static or dynamic, and again, this leads to different ways of modeling and describing it.

The information handled in a fusion process is comprised, on the one hand, of the elements of information we wish to fuse together and, on the other hand, of additional information used to guide or assist the combination. It can consist of information regarding the information we wish to combine, such as information on the sources, on their dependences, their reliability, preferences, etc. It can also be contextual information regarding the field. This additional information is not necessarily expressed using the same formalism as the information we wish to combine (it usually is not), but it can be involved in choosing the model used for describing the elements of information we wish to fuse.

One of the important characteristics of information in fusion is its imperfection, which is always present (fusion would otherwise not be necessary). It can take different forms, which are briefly described below. Let us note that there is not always a consensus on the definition of these concepts in other works. The definitions we give here are rather intuitive and well suited to the problem of fusion, but are certainly not universal. The different possible nuances are omitted on purpose here because they will be discussed further and illustrated in the following chapters for each field of fusion described in this book.

Uncertainty. Uncertainty is related to the truth of an element of information and characterizes the degree to which it conforms with reality [DUB 88]. It refers to the nature of the object or fact involved, its quality, its essence, or its occurrence.

Imprecision. Imprecision involves the content of the information and therefore is a measurement of a quantitative lack of knowledge on a measurement [DUB 88]. It involves the lac...

Table of contents

• Cover
• Title Page
• Copyright
• Preface
• Chapter 1. Definitions
• Chapter 2. Fusion in Signal Processing
• Chapter 3. Fusion in Image Processing
• Chapter 4. Fusion in Robotics
• Chapter 5. Information and Knowledge Representation in Fusion Problems
• Chapter 6. Probabilistic and Statistical Methods
• Chapter 7. Belief Function Theory
• Chapter 8. Fuzzy Sets and Possibility Theory
• Chapter 9. Spatial Information in Fusion Methods
• Chapter 10. Multi-Agent Methods: An Example of an Architecture and its Application for the Detection, Recognition and Identification of Targets
• Chapter 11. Fusion of Non-Simultaneous Elements of Information: Temporal Fusion
• Chapter 12. Conclusion
• Appendix A: Probabilities: A Historical Perspective
• Appendix B: Axiomatic Inference of the Dempster-Shafer Combination Rule
• List of Authors
• Index