Image Processing Reference
In-Depth Information
Chapter 8
Fuzzy Sets and Possibility Theory
8.1. Introduction and general concepts
As we have seen in the first chapters of this topic, imprecisions and uncertainties
are inherent to the data handled in the application fields that concern us.
The advantages of fuzzy sets and possibility theory for information processing,
particularly in image and vision [KRI 92], fall into the four following categories:
- the ability of fuzzy sets to represent spatial information in images as well as
its imprecision, on several levels (local, regional, or global) and in different forms
(numerical, symbolic, quantitative, qualitative);
- the possibility of representing very heterogenous information, directly extracted
from images or obtained from outside knowledge, such as expert or generic knowledge
in a field or about a problem;
- the possibility of generalizing to fuzzy sets operations for manipulating spatial
- the various possible semantics;
- the flexibility of the combination operators, which makes it possible to fuse ele-
ments of information that are different in nature, in very different situations.
We will particularly insist on this last point.
In this chapter, we will first of all present the basic elements of fuzzy set and
possibility theory. Their use in the more specific context of fusion will be discussed
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