The purpose of our work is to outline objects on images in an interactive environment. We use an improved method based on energy minimizing active contours or `snakes.' Kass et al., proposed a variational technique; Amini used dynamic programming; and Williams and Shah introduced a fast, greedy algorithm. We combine the advantages of the latter two methods in a two-stage algorithm. The first stage is a greedy procedure that provides fast initial convergence. It is enhanced with a cost term that extends over a large number of points to avoid oscillations. The second stage, when accuracy becomes important, uses dynamic programming. This step is accelerated by the use of alternating search neighborhoods and by dropping stable points from the iterations. We have also added several features for user interaction. First, the user can define points of high confidence. Mathematically, this results in an extra cost term and, in that way, the robustness in difficult areas (e.g., noisy edges, sharp corners) is improved. We also give the user the possibility of incremental contour tracking, thus providing feedback on the refinement process. The algorithm has been tested on numerous photographic clip art images and extensive tests on medical images are in progress.