Accurate segmentation of 3-D cell nuclei in microscopy images is an essential task in many biological studies. Traditional image segmentation methods are challenged by the complexity and variability of microscope images, so there is a need to improve segmentation accuracy and reliability, as well as the level of automation. In this paper we present a novel automated algorithm for robust segmentation of 3-D cell nuclei using a combination of ideas. Our algorithm includes the following steps: image denoising, binarization, seed detection using the fast radial symmetric transform (FRST), initial segmentation using the random walker algorithm and the 3-D watershed algorithm, and final refinements using 3-D active contours. We show that our algorithm provides improved accuracy compared to existing segmentation algorithms.