This paper introduces a technique for the automated description of tubular objects in 3D medical images. The goal of automated 3D object description is to extract a representation which consistently details the location, size, and structure of objects in 3D images using minimal user interaction. Such a representation provides a means which objects can be classified, quantifiably evaluated, and registered. It also serves as a region of interest specification for visualization processes.The technique presented in this paper is suited for generating representations of 3D objects with nearly circular cross sections which have, possibly as a result of a global operation (e.g., blurring), intensity extrema near their centers. Such tubular objects commonly occur within human anatomy (e.g., vessels and selected bones). The medial axis of each of these objects is well approximated its intensity ridge. The scales of the local maxima in medialness at all points along the ridge can be mapped to local width estimates. Together these measures capture the location, size, and structure of tubular objects.This paper covers the mathematical basis, the implementation issues, and the application of this technique to the extraction of vessels from 3D magnetic resonance angiographic images and bones from 3D X-ray computed tomographic images.