Novel image processing methods based on fuzzy logic

This thesis incorporates three main topics. First, a hybrid c-means clustering model is proposed as a generalization of fuzzy, possibilistic, and hard c-means algorithms. Second, novel image processing methods are introduced, as applications of the hybrid clustering. Finally, a virtual endoscope model is proposed and implemented, based on the clustering and image segmentation results. The hybrid clustering model unifies the classical, fuzzy and possibilistic logics within a single objective function, introducing an infinite number of different clustering algorithms, which are obtained by varying the two tradeoff parameters. Based on several tests, some recommendations have been proposed for the optimal choice of the tradeoff parameters. Further on, an alternative formulation of the hybrid model is proposed: by dropping the partition matrices and computing a few sums instead, the memory requirements of the algorithm is drastically reduced, which makes it suitable for hardware implementation. We have analyzed the properties of the so-called suppressed FCM algorithm, and found an alternative optimal suppression, achieved as a special case of the proposed hybrid clustering model. Series of tests have been performed, which revealed the properties of the hybrid clustering: it is more robust, has quicker convergence and produces finer partition quality, than earlier c-means clustering methods. The proposed clustering method is universal, in the sense that it is suitable to classify any kind of vectorial data, for which the operation of weighted averaging is defined. Within the scope of image processing, our main goal was to create novel methods for accurate and efficient segmentation of MR brain images. In this order, we have proposed a new procedure for quick segmentation of MR images contaminated with high-frequency Gaussian and impulse noises, using histogram-based c-means clustering. Further on, a concept of multi-stage inhomogeneity compensation was introduced, that was involved into two different segmentation procedures. We have also proved that the efficiency and accuracy of these c-means based procedures are enhanced by the proposed hybrid clustering model. Based on our clustering and image segmentation methods, a novel concept of virtual endoscope was introduced, which was later implemented using 3-D surface models and 3-D computer graphics techniques.