Multisource Image Fusion Algorithm Based On A New Evidential Reasoning Approach

We propose a new way to initialize the mass function of the Dempster-Shafer theory of evidence. The new initialization process is based on a fuzzy statistical approach and uses the FSEM algorithm (Fuzzy Statistical Estimation Maximization). This allows to classify image in "pure" and "fuzzy" regions, and thus enable an optimal estimation of the inaccuracy and uncertainty of the classification. We apply our new evidential reasoning approach for the fusion of a Landsat multispectral image with vegetation indices and a digital elevation model. Keywords— Remote Sensing, Classification Algorithm, Fusion Algorithm, Evidential Reasoning, Fuzzy Logic INTRODUCTION This article describes a new data fusion algorithm which is a part of the SITI project (Intelligent System of Image Processing). The purpose of this project is to design and develop new algorithms for analysing, segmenting and extracting information based on an expert fusion process of optical, radar or auxiliary data. Data fusion related to a same object or a same scene becomes more and more essential in remote sensing applications. It is often necessary to associate additional and/or redundant information, in order to reject, confirm or create a decision. A definition of data fusion was formulated by Bloch and Maître [3] : “data fusion is the joint use of heterogeneous information for the assistance with the decision-making”. This definition emphasizes the essential points of a fusion process : the heterogeneity of the data makes it possible to provide additional information for sources of similar or different nature ; the joint use of information enables to specify the importance of the final decision. Indeed, if a decision is made for each kind of data separately, then the process can not be considered as a fusion process anymore ; the goal of fusion is to provide an aid in the decision-making process. There are mainly three models of fusion operators cited in the scientific literature : probabilistic bayesian models , fuzzy models and models resulting from the Dempster-Shafer theory of evidence. The probabilistic bayesian models are the most cited models ; the concept of fusion is deduced from the Bayes rule. However, in the bayesian models there is a confusion between two antagonist concepts : the uncertainty and the inaccuracy. Moreover, we have to note that the performances of the bayesian data fusion tend to be decrease when the number of information sources increases. One of the most known non-probabilistic techniques is the fuzzy theory. This technique, introduced by Zadeh [13], represents information in the form of explicit functions of membership. The disadvantage of the fuzzy theory is that it characterizes the uncertainty in an implicit way, only the inaccurate property of information is represented [3]. The Demspter-Shafer (DS) theory of evidence allows to represent at the same time the inaccuracy and uncertainty using confidence, plausibility and credibility functions. It defines a framework of understanding representing all the subsets of the classes space. The principal advantage of this theory is to affect a degree of confidence which is called mass function to all simple and composed classes, and to take into account the ignorance of the information. However, there is no generic method to define the mass functions. Most of the time, they are computed using an empirical method which depend on the nature of the information. Thus, we will present, in the next sections, a new global solution with a more rigorous way to deal with the concepts of uncertainty and inaccuracy in the DS theory. THE DEMPSTER-SHAFER THEORY OF EVIDENCE The DS theory of evidence was first introduced by Dempster [6] and formalized by Shafer [11]. This mathematical theory is composed of three distinct parts : the definition of the mass functions, the combination process and the decision-making. The definition of the mass definition A mass function can be compared with a degree of confidence one can have in the studied data. It have to be set between values 0 and 1, where 1 stands for a total confidence and 0 for no confidence at all. In the terminology of Dempster and Shafer, we do not define anymore data or classes, but only "hypotheses". Then, a mass function will be defined on a hypotheses set, called the frame of discernment. It represents a set of mutually exclusive and exhaustive propositions. Let us note the hypotheses set Θ composed of single mutually exclusive subset θi. The DS fusion works on a single hypothesis, but it works also on all subset composed of several single hypotheses. So the DS fusion process is based on 2 elements called propositions. A mass function for one source and for one proposition is defined as follows : m : 2 → [0, 1] (1) ∑