Belief Function Theory - Information Fusion in Signal and Image Processing - page 95

Chapter 7
Belief Function Theory
7.1. General concept and philosophy of the theory
Belief function theory (or Dempster-Shafer theory) dates back to the 1970s but its
use in signal and image fusion is relatively recent. Nevertheless, the first applications
show some promise and in this chapter we will point out the characteristics of this
theory that deserve our attention, both from the perspectives of representing knowl-
edge and its imperfections (imprecision, uncertainty, ambiguity, absence of knowl-
edge, conflict) and of combining it.
Although this theory is inspired by concepts of superior and inferior probabilities,
and therefore often considered from a probabilistic point of view, it can be interpreted
in a more general way, from a subjective point of view, as a quantitative formal model
of degrees of confidence [SME 90a]. One of the main assets of this theory is that it
deals with subsets rather than singletons, making it very flexible for modeling many
of the situations we come across in signal and image fusion. It also provides us with
representations of uncertainty, imprecision, as well as of the absence of knowledge.
For this purpose, several functions are used to model the information and manipulate
it, instead of simply the probabilities used in the previous chapter. This theory can
be used to measure conflicts between sources and to interpret them in terms of the
reliability of the sources, of an open world or of contradicting observations. Although
several combination modes are possible, conjunctive combination is the most com-
monly used in the fields we are concerned with here and we will focus mostly on
this mode. This means that the essential part of the user's work will be transferred to