For liver surgical planning, the structure and morphology of the hepatic vessels and their relationship to tumors are of major interest. To achieve a fast and robust assistance with optimal quantitative and visual information, we present methods for a geometrical and structural analysis of vessel systems. Starting from the raw image data a sequence of image processing steps has to be carried out until a three-dimensional representation of the relevant anatomic and pathologic structures is generated. Based on computed tomography (CT) scans, the following steps are performed. 1) The volume data is preprocessed and the vessels are segmented. 2) The skeleton of the vessels is determined and transformed into a graph enabling a geometrical and structural shape analysis. Using this information the different intrahepatic vessel systems are identified automatically. 3) Based on the structural analysis of the branches of the portal vein, their vascular territories are approximated with different methods. These methods are compared and validated anatomically by means of corrosion casts of human livers. 4) Vessels are visualized with graphics primitives fitted to the skeleton to provide smooth visualizations without aliasing artifacts. The image analysis techniques have been evaluated in the clinical environment and have been used in more than 170 cases so far to plan interventions and transplantations.