Automated segmentation of medical images is a challenging problem. The number of segments in a medical image may be unknown a priori, due to the presence or absence of pathological anomalies. Some unsupervised learning techniques founded in information theory concepts may provide a solid approach to this problem's solution. We have developed the Improved "Jump" Method (IJM), a technique that efficiently finds a suitable number of clusters representing different tissue characteristics in a medical image. IJM works by optimizes an objective function that quantifies the quality of particular cluster configurations. Recent developments involving interesting relationships between Spectral Clustering (SC) and kernel Principal Component Analysis (kPCA) are used to extend IJM to the non-linear domain. This novel SC approach maps the data to a new space where the points belonging to the same cluster are collinear if the parameters of a Radial Basis Function (RBF) kernel are adequately selected. After projecting these points onto the unit sphere, IJM measures the quality of different cluster configurations, yielding an algorithm that simultaneously selects the number of clusters, and the RBF kernel parameter. Validation of this method is sought via segmentation of MR brain images in a combination of all major modalities. Such labeled MRI datasets serve as benchmarks for any segmentation algorithm. The effectiveness of the nonlinear IJM is demonstrated in the segmentation of uterine cervix color images for early identification of cervical neoplasia, as an aid to cervical cancer diagnosis. Studies are in progress in segmentation and detection of multiple sclerosis lesions.