04
Multisource Image Fusion Algorithm Based On A New Evidential Reasoning Approach
Mickaél Germain! , Matthieu Voorons!, Jean-Marc Boucher?, Goze B. Bénié! et Éric Beaudry!
(1) Centre d'applications et de recherches en télédétection (CARTEL);
Université de Sherbrooke, Canada, Email : mickael.germain@usherbrooke.ca
tél. : (1-819)821-7180
(2) École Nationale Supérieure des Télécommunications de Bretagne,
France, Email : jm.boucher(@enst-bretagne. fr
tel. : 33 (0)2 29 00 11 11
Abstract— 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 Statis-
tical 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 Algo-
rithm, 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 Proces-
sing). 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 of-
ten necessary to associate additional and/or redundant informa-
tion, 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 as-
sistance 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 impor-
tance 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 antago-
nist 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 in-
creases.
One of the most known non-probabilistic techniques is the
fuzzy theory. This technique, introduced by Zadeh [13], repre-
sents information in the form of explicit functions of member-
ship. 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 re-
present 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 af-
fect a degree of confidence which is called mass function to all
simple and composed classes, and to take into account the igno-
rance of the information. However, there is no generic method
to define the mass functions. Most of the time, they are compu-
ted 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 Demps-
ter [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 confi-
dence 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
Jrame of discernment. It represents a set of mutually exclusive
and exhaustive propositions.
Let us note the hypotheses set © composed of single mutually
exclusive subset 0;. The DS fusion works on a single hypothe-
sis, 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 :
ms 929 — l0, 1] (1)
3. m(A) =1 (2)
Ac29
m(¢p) = 0 (3)
By using this representation model one can assign a confi-
dence value to a set of composed hypotheses. This value shows
