Maximum Class Separability for Rough-Fuzzy C-Means Based Brain MR Image Segmentation

Image segmentation is an indispensable process in the visualization of human tissues, particularly during clinical analysis of magnetic resonance (MR) images. In this paper, the rough-fuzzy c-means (RFCM) algorithm is presented for segmentation of brain MR images. The RFCM algorithm comprises a judicious integration of the of rough sets, fuzzy sets, and c-means algorithm. While the concept of lower and upper approximations of rough sets deals with vagueness and incompleteness in class definition of brain MR images, the membership function of fuzzy sets enables efficient handling of overlapping classes. The crisp lower bound and fuzzy boundary of a class, introduced in the RFCM algorithm, enable efficient segmentation of brain MR images. One of the major issues of the RFCM based brain MR image segmentation is how to select initial prototypes of different classes or categories. The concept of discriminant analysis, based on the maximization of class separability, is used to circumvent the initialization and local minima problems of the RFCM. Some quantitative indices are introduced to extract local features of MR images for accurate segmentation. The effectiveness of the RFCM algorithm, along with a comparison with other related algorithms, is demonstrated on a set of brain MR images.