Many modern medical imaging scanners produce high-resolution three-dimensional (3D) digital images of vascular trees. In this context, accurate definition of a vacular tree's central axes and associated branch points remains a problem. We propose a method for accurate sub-voxel-level central-axis definition and branch-point localization. The method starts by deriving a sub-voxel-level polygonal surface model of the vascular tree from a given 3D image; the polygonal surface model is derived from a combination of a segmented image and the original gray-scale image data. Next, topographic analysis, based on differential geometry concepts, is performed on the surface model to arrive at a set of axes and branch points. Using 3D micro-CT images, we apply the method to a graphics-based tree-analysis system and demonstrate the method's efficacy at defining a set of central axes and at accurately localizing branch points.