Information Fusion in Signal and Image Processing: Major Probabilistic and Non-Probabilistic Numerical Approaches

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 knowledge and its imperfections (imprecision, uncertainty, ambiguity, absence of knowledge, 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 ...