Traditional segmentation techniques do not quite meet the challenges posed by inherently fuzzy medical images. Image segmentation based on fuzzy connectedness addresses this problem by attempting to capture both closeness, based on characteristic intensity, and "hanging togetherness," based on intensity homogeneity, of image elements to the target object. This paper presents a modification and extension of previously published image segmentation algorithms based on fuzzy connectedness, which is computed as a linear combination of an object-feature-based and a homogeneity-based component using fixed weights. We provide a method, called fuzzy connectedness using dynamic weights (DyW), to introduce directional sensitivity to the homogeneity-based component and to dynamically adjust the linear weights in the functional form of fuzzy connectedness. Dynamic computation of the weights relieves the user of the exhaustive search process to find the best combination of weights suited to a particular application. This is critical in applications such as analysis of cardiac cine magnetic resonance (MR) images, where the optimal combination of affinity component weights can vary for each slice, each phase, and each subject, in spite of data being acquired from the same MR scanner with identical protocols. We present selected results of applying DyW to segment phantom images and actual MR, computed tomography, and infrared data. The accuracy of DyW is assessed by comparing it to two different formulations of fuzzy connectedness. Our method consistently achieves accuracy of more than 99.15% for a range of image complexities: contrast 5%-65%, noise-to-contrast ratio of 6%-18%, and bias field of four types with maximum gain factor of up to 10%.