An adaptive fuzzy C-means algorithm for image segmentation in the presence of intensity inhomogeneities

We present a novel algorithm for obtaining fuzzy segmentations of images that are subject to multiplicative intensity inhomogeneities, such as magnetic resonance images. The algorithm is formulated by modifying the objective function in the fuzzy C-means algorithm to include a multiplier field, which allows the centroids for each class to vary across the image. First and second order regularization terms ensure that the multiplier field is both slowly varying and smooth. An iterative algorithm that minimizes the objective function is described, and its efficacy is demonstrated on several test images.