Adaptive Fuzzy eMeans Segmentation

The adaptive fuzzy c-means algorithm (AFCM) [34] is an unsupervised technique that clusters data by iteratively computing a fuzzy membership function, mean value estimates for each tissue class, and an estimate of intensity inhomogen-eities present in the image. The fuzzy membership function, constrained to be between zero and one, reflects the degree of similarity between the data value at that location and the prototypical data value, or centroid, of its class. Thus, a high membership value near unity signifies that the data value at that location is "close" to the centroid for that particular class. AFCM generalizes the fuzzy c-means algorithm [20,33] to images with intensity inhomogeneities, which are modeled as a smoothly varying gain field. It is formulated as the minimization of the following objective function with respect to the membership functions u, the centroids v, and gain field g.

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