Segmentation and visualization techniques have evolved to a point where high quality 3-D displays can be generated from medical image data sets. Clinical experience with computer assisted analysis demonstrates that the availability of pretty pictures is often not sufficient for diagnosis, surgical planning and image guided surgery, a promising new application field. The interactive analysis like the qualitative and quantitative exploration of image structures require an appropriate representation of shapes and their interrelationships. Further, symbolic object descriptions must be encoded by suitable data structures to ensure efficient generation and manipulation of graphical displays and to allow multimodality fusion and functional simulations. This paper presents a prototypical system for the comprehensive analysis of the cerebral vascularity. The shape of the blood vessels is segmented from 3-D image data. Although sufficient for providing clinical useful images by simple surface rendering, the raster representations of the blood vessel tree is converted into a symbolic graph description encoding vessels and vessel branchings as arcs and nodes, respectively. This representation of the global topology and local geometry is further enhanced by fusing additional information about local flow velocity and direction. Newly developed computer assisted tools make use of this rich model and of the object-oriented data structure. Regarding the whole system, the 3-D visualization and the 3D interaction have to be seen as the key components of the user interface, integrating the observer into the interactive analysis loop by providing immediate feedback to various types of manipulations and queries. Clinical examples demonstrate the versatility of the system to access, retrieve and navigate information that was not acessible with conventional visual interpretation. It will be clearly illustrated that this type of analysis goes by far beyond simple rendering of 3-D objects which is the today's state of the art in visualization of medical data.