Why Fuzzy Image Processing?

Many colleagues (not only the opponents of fuzzy logic) ask why we should use fuzzy techniques in image processing. There are many reasons to do this. The most important of them are as follows:

1. Fuzzy techniques are powerful tools for knowledge represenation and processing

2. Fuzzy techniques can manage the vagueness and ambiguity efficiently

In many image processing applications, we have to use expert knowledge to overcome the difficulties (e.g. object recognition, scene analysis). Fuzzy set theory and fuzzy logic offer us powerful tools to represent and process human knowledge in form of fuzzy if-then ruels. On the other side, many difficulties in image processing arise because the data/tasks/results are uncertain. This uncertainty, however, is not always due to the randomness but to the ambiguity and vagueness. Beside randomness which can be managed by probability theory we can distiguish between three other kinds of imperfection in the image processing (see Fig.1):

• Grayness ambiguity

• Geometrical fuzziness

• Vague (complex/ill-defiend) knowledge

These problems are fuzzy in the nature. The question whether a pixel should become darker or brighter than it already is, the question where is the boundary between two image segments, and the question what is a tree in a scene analysis problem, all of these and other similar questions are examples for situations that a fuzzy approach can be the more suitable way to manage the imperfection.

Fig.1. Uncertainty/imperfect knowledge in image processing
(Adapted from: Tizhoosh, Fuzzy Image Processing, © CopyRight Springer,1997)

As an example, we can regard the variable colour as a fuzzy set. It can be described with the subsets yellow, orange, red, violet and blue:

colour = {yellow, orange, red, violet, blue}

The non-crisp boundaries between the colours can be represented much better. A soft computing becomes possible (see Fig.2).

Fig.2. Representation of colours as fuzzy subsets.