For many medical segmentation tasks, the contrast along most of the boundary of the target object is high, allowing simple thresholding or region growing approaches to provide nearly sufficient solutions for the task. However, the regions recovered by these techniques frequently leak through bottlenecks in which the contrast is low or nonexistent. We propose a new approach based on a novel speed-up of the isoperimetric algorithm [1] that can solve the problem of leaks through a bottleneck. The speed enhancement converts the isoperimetric segmentation algorithm to a fast, linear-time computation by using a tree representation as the underlying graph instead of a standard lattice structure. In this paper, we show how to create an appropriate tree substrate for the segmentation problem and how to use this structure to perform a lineartime computation of the isoperimetric algorithm. This approach is shown to overcome common problems with watershed-based techniques and to provide fast, high...