Edge-based and region-based active contours are frequently used in image segmentation. While edges characterize small neighborhoods of pixels, region descriptors characterize entire image regions that may have overlapping probability densities. In this paper, we propose to characterize image regions locally by defining Local Region Descriptors (LRDs). These are essentially feature statistics from pixels located within windows centered on the evolving contour, and they may reduce the overlap between distributions. LRDs are used to define general-form energies based on level sets. In general, a particular energy is associated with an active contour by means of the logarithm of the probability density of features conditioned on the region. In order to reduce the number of local minima of such energies, we introduce two novel functions for constructing the energy functional which are both based on the assumption that local densities are approximately Gaussian. The first uses a similarity measure between features of pixels that involves confidence intervals. The second employs a local Markov Random Field (MRF) model. By minimizing the associated energies, we obtain active contours that can segment objects that have largely overlapping global probability densities. Our experiments show that the proposed method can accurately segment natural large images in very short time when using a fast level-set implementation.