Abstract

Image filtering is an essential image processing task for almost
every computer vision system where images are used for automatic
analysis or, even, for human inspection. In fact, noise
contaminating an image may be a grave drawback for most other
image processing tasks as, for instance, image ana\-lysis, edge
detection or pattern and/or object recognition and hence, it
should be reduced.

In the last years, the interest in using colour images has
impressively grown in a variety of applications. Therefore, colour
image filtering became an interesting area of research. It has
been widely observed that colour images have to be processed
taking into account the existing correlation among the image
channels. Probably, the most well-known approach in this sense is
the vector approach. Earliest vector filtering solutions as, for
instance, the vector median filter (VMF) or the vector directional
filter (VDF), are based on the theory of robust statistics and as
a consequence, they are able to perform a robust filtering.
Unfortunately, these techniques are non-adaptive to local image
statistics what implies that the processed images are usually
blurred in edges and image details. To overcome this drawback, a
number of adaptive vector processing solutions have been recently
proposed.

In the presented PhD dissertation two main tasks have been carried
out: (i) the study of fuzzy metrics applicability in colour image
filtering tasks and (ii) the design of new colour image filtering
solutions that take advantage of the observed interesting fuzzy
metrics and fuzzy logic properties. Extensive experimental results
presented in this dissertation have shown that fuzzy metrics and
fuzzy logic are useful to design both non-adaptive and adaptive
filtering techniques which are competitive with respect to recent
state-of-the-art filters. Moreover, as it is demonstrated in
several filter designs introduced in this dissertation, an
interesting advantage of fuzzy metrics is that they provide a
simple mechanism to simultaneously handle multiple distance
criteria.