Image filtering is an essential image processing task for almost every computer vision system where images are used for automatic analysis or for human inspection. In fact, noise contaminating an image may be a major drawback for most other image processing tasks like, for instance, image analysis,edge detection or pattern and/or object recognition and hence, it should be reduced. Similarly, increasing of resolution and image size conduces to high computational requirements, that should been decrease, especially for real time applications and so.
In the last years, the interest in using colour images has grown dramatically in a variety of applications. Therefore, colour image filtering has become an interesting area of research. It has been widely observed that colour images have to be processed taking into account the existing correlation among 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). Unfortunately, these techniques are non-adaptive to local image statistics which 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, and a well-down approach are the peer group techniques. In last years, the theory of fuzzy sets (topologies, metrics and logic) has been developed, and they are a good mathematical tool to use in image filtering.
This PhD dissertation main goals are: (i) the study of fuzzy metrics applicability in colour image filtering tasks and computational improvement; (ii) the design of new colour image filtering solutions that take advantage of the observed interesting fuzzy metrics and fuzzy logic properties and obtain a good computational perform and (iii) implement parallel versions of the filters designed with MPI to test the performance with parallel computing. Extensive experimental results presented in this dissertation have shown that fuzzy metrics are useful to design filtering techniques with low computational cost which are competitive with respect to recent state-of-the-art filters.