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 Clu stering algorithms provide a fuzzy description of the discovered structure. The ma in advantage of this description is that it captures the imprecision encountered w hen describing real-life data. Thus, the user is provided with more information about the st ructure in the data compared to a crisp, non-fuzzy scheme. During the early part of our research, we investigated the po pular Fuzzy c-Means (FCM) algorithm and in particular its problem of being unabl e to correctly identify clusters with grossly different populations. We devised a s uite of benchmark data sets to investigate the reasons for this shortcoming. We fou nd that the shortcoming originates from the formulation of the objective function o f 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 for mulated. 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 id entified how it can be further improved. Since image segmentation is fundamentally a clustering pro blem, the next step was to investigate the use of fuzzy clustering techniques for im age segmentation. We have identified the main decision points in this process. Further more, we have used fuzzy clustering to detect the left ventricular blood pool in card i c cine images. Specifically, the images were of the Magnetic Resonance (MR) modality, con taini g blood velocity data as well as tissue density data. We have analysed the rela tive 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 quantit tive analysis of anatomical measures.

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