We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divide-and-conquer approach to generate inter-slice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scan-line order and calculates triangle vertices using linear interpolation. We find the gradient of the original data, normalize it, and use it as a basis for shading the models. The detail in images produced from the generated surface models is the result of maintaining the inter-slice connectivity, surface data, and gradient information present in the original 3D data. Results from computed tomography (CT), magnetic resonance (MR), and single-photon emission computed tomography (SPECT) illustrate the quality and functionality of marching cubes. We also discuss improvements that decrease processing time and add solid modeling capabilities.

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 3D representation of the relevant anatomic and pathologic structures is generated. Based on aT scans the following steps are performed: (1) The volume data is preprocessed and the vessels are segmented. (2) The skeleton of the ves- sels is determined and transformed into a graph enabling a geometrical and structural shape analysis. Using this information the different intrahepatic vessel systems are iden- tified 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 cor- rosion 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.

this report, the reconstruction and modeling of cerebral vascular structures are addressed. The main contributions brought are the following:

This paper proposes a new representation scheme of the cerebral blood vessels. This model provides information on the semantics of the vascular structure: the topological relationships between vessels and the labeling of vascular accidents such as aneurysms and stenoses. In addition, the model keeps information of the inner surface geometry as well as of the vascular map volume properties, i.e. the tissue density, the blood flow velocity and the vessel wall elasticity.

this report, the visualization of cerebral blood vessels is analyzed and a new visualization method is proposed which enhances the blood vessels while keeping a lower computational cost than other existing methods.