The Geometric Deformable Model is developed for accurate colon lumen segmentation as part of an automatic Virtual Colonoscopy system. The deformable model refines the lumen surface found by an automatic seed location and thresholding procedure. The challenges to applying the deformable model are described, showing the definition of the stopping function as the key to accurate segmentation. The limitations of current stopping criteria are examined and a new definition, tailored to the task of colon segmentation, is given. First, a multiscale edge operator is used to locate high confidence boundaries. These boundaries are then integrated into the stopping function using a distance transform. The hypothesis is that the new stopping function results in a more accurate representation of the lumen surface compared to previous monotonic functions of the gradient magnitude. This hypothesis is tested using observer ratings of colon surface fidelity at 100,000 randomly selected locations in each of four datasets. The results show that the surfaces determined by the modified deformable model better represent the lumen surface overall.