Journal of Electronic ImagingEfficient fuzzy c-means clustering for image data
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The clustering process can be quite slow when there is a large data set to be clustered. We investigate four efficient fuzzy c-means clustering methods qFCMs, based on the quad-tree application to multispectral image feature compression and/or an aggregation process to reduce the number of exemplars for image analysis. An image is first partitioned into multiresolution blocks with variable size to extract the representative ones by homogeneity criteria. The blocks can be represented by a mean or fuzzy number to represent the image information. The first algorithm qFCMb is performed by applying only the representative blocks to a weighted FCM, which can speed up the clustering. To further improve the clustering efficiency, the reduction is done by aggregating similar examples and using a weighted exemplar in the clustering process (qFCMba). Based on the same processes used in qFCMb and qFCMba, nonhomogeneous regions including pixel information can also be supplemented to refine the clustering results, which are termed qFCMp and qFCMpa, respectively. Because of the merit of higher efficiency with the aggregation process, we recommend qFCMba and qFCMpa. A set of 14 images is used for experiments, comparison, and discussion. Performances are reported by the mean reduction rate, speedup, mean correspondence rate, and root mean square error. Results show that the mean reduction rate of both qFCMba and qFCMpa can be as high as 98% reduction in sample size. Average speedups of as much as 40 to 150 times (100 to 200 times) a traditional implementation FCM are obtained using qFCMpa (qFCMba), while producing partitions that are equivalent to those produced by FCM. On the measure of root mean square error, qFCMba is the better choice, as indicated in the experiment of clustering a noisy image.