In this paper, a novel technique for rapid and automatic computation of flight paths for guiding virtual endoscopic exploration of three-dimensional medical images is described. While manually planning flight paths is a tedious and time consuming task, our algorithm is automated and fast. Our method for positioning the virtual camera is based on the medial axis transform but is much more computationally efficient. By iteratively correcting a path toward the medial axis, the necessity of evaluating simple point criteria during morphological thinning is eliminated. The virtual camera is also oriented in a stable viewing direction, avoiding sudden twists and turns. We tested our algorithm on volumetric data sets of eight colons, one aorta and one bronchial tree. The algorithm computed the flight paths in several minutes per volume on an inexpensive workstation with minimal computation time added for multiple paths through branching structures (10%-13% per extra path). The results of our algorithm are smooth, centralized paths that aid in the task of navigation in virtual endoscopic exploration of three-dimensional medical images.