The problem of automated segmenting and tracking of the outlines of cells in microscope images is the subject of active research. While great progress has been made on recognizing cells that are of high contrast and of predictable shape, many situations arise in practice where these properties do not exist and thus many interesting potential studies - such as the migration patterns of astrocytes to scratch wounds - have been relegated to being largely qualitative in nature. Here we analyse a select number of recent developments in this area, and offer an algorithm based on parametric active contours and formulated by taking into account cell movement dynamics. This Cell-Derived Active Contour (CDAC) method is compared with two state-of-the-art segmentation methods for phase-contrast microscopy. Specifically, we tackle a very difficult segmentation problem: human astrocytes that are very large, thin, and irregularly-shaped. We demonstrate quantitatively better results for CDAC as compared to similar segmentation methods, and we also demonstrate the reliable segmentation of qualitatively different data sets that were not possible using existing methods. We believe this new method will enable new and improved automatic cell migration and movement studies to be made.