A New Approach for Automatic Fuzzy Clustering Applied to Magnetic Resonance Image Clustering

Many clustering and segmentation algorithms suffer from the limitation that the number of clusters/segments is specified manually by human operators. It is often impractical to expect a human with sufficient domain knowledge to be available to select the number of clusters/segments to return. Thus, the estimation of optimal cluster number during the clustering process is our prime concern. In this paper, we introduce a new validity index method based on multi-degree entropy algorithm for determining the number of clusters automatically. This multi-degree entropy algorithm combines multi-degree immersion and entropy algorithms to partition an image into levels of intensity. The output of the multi-degree immersion processes are regions in which the interior does not contain any sharp grey value transitions, i.e. each level of intensity contains one or more regions of connected points or oversegmentation. These regions are passed to the entropy procedure to perform a suitable merging which produces the final number of clusters based on validity function criteria. Validity functions are used to find a relation between intra-cluster and inter-cluster variability, which is of course a reasonable principle. The latter process uses a region-based similarity representation of the image regions to decide whether regions can be merged. The proposed method is experimented on a discrete image example to prove its efficiency and applicability. The existing validation indices like PC, XB, and CE are evaluated and compared with the proposed index when applied on two simulation and one real life data. A direct benefit of this method is being able to determine the number of clusters for given application medical images.