The performance of computer assisted systems for presentation, manipulation and quantitation of objects obtained from multidimensional image data depends critically on the ability to segment and describe structures in images. We describe the development of a prototype system that extracts three-dimensional (3-D) curvilinear structures from volume image data and converts them into a symbolic description which is more appropriate to assess features of tree-like, filamentous objects. The initial segmentation is performed by 3-D line filtering and/or 3-D hysteresis thresholding. A skeletal structure is derived by 3-D binary thinning, approximating the center-line by pseudo-parallel erosion while fully preserving the 3-D topology. The final graph datastructure encodes the spatial course of line sections, the estimate of the local diameter, and the topology at important key locations like branchings and end-points. The system is applied to analyze the cerebral vascular system resulting from magnetic resonance angiography (MRA).