Fuzzy Clustering Algorithms and Their Application to Medical Image Analysis

The general problem of data clustering is concerned with the discovery of a grouping structure within a finite number of data points. Fuzzy Clustering algorithms provide a fuzzy description of the discovered structure. The main advantage of this description is that it captures the imprecision encountered when describing real-life data. Thus, the user is provided with more information about the structure in the data compared to a crisp, non-fuzzy scheme. During the early part of our research, we investigated the popular Fuzzy c-Means (FCM) algorithm and in particular its problem of being unable to correctly identify clusters with grossly different populations. We devised a suite of benchmark data sets to investigate the reasons for this shortcoming. We found that the shortcoming originates from the formulation of the objective function of FCM which allows clusters with relatively large population and extent to dominate the solution. This led to a search for a new objective function, which we have indeed formulated. Subsequently, we derived a new so-called Population Diameter Independent (PDI) algorithm. PDI was tested on the same benchmark data used to study FCM and was found to perform better than FCM. We have also analysed PDI’s behaviour and identified how it can be further improved. Since image segmentation is fundamentally a clustering problem, the next step was to investigate the use of fuzzy clustering techniques for image segmentation. We have identified the main decision points in this process. Furthermore, we have used fuzzy clustering to detect the left ventricular blood pool in cardiac cine images. Specifically, the images were of the Magnetic Resonance (MR) modality, containing blood velocity data as well as tissue density data. We have analysed the relative impact of the velocity data in the goal of achieving better accuracy. Our work would be typically used for qualitative analysis of anatomical structures and quantitative analysis of anatomical measures.