This thesis deals with the development of a fast three-dimensional segmentation algorithm based on hierarchical island structures, which can be used for different application areas providing improved segmentation results. The so-called 3D-GSC (Grey Value Structure Code) is based on the CSC (Color Structure Code), introduced by Rehrmann in 1994, and realises an isotropic inspection of the 3D dataset. Both merge local precision and global view, by re-evaluating homogeneity decisions taken on a lower hierarchical level on the basis of the global view by subsequently splitting originally merged regions. The 3D-GSC is based on a three-dimensional island structure, which has to fulfil certain criteria established in this thesis thus allowing the implementation of the algorithm. To identify these island structures, all 14 three-dimensional translation lattices (Bravais lattices) were analysed with regard to their possible convex neighbourhoods and the latticecovering and overlapping properties of their edge-to-edge tiling. As a result, only the 14 neighbours of the non-primitive lattices are suitable for covering the corresponding lattices in a single overlapping manner and describe the neighbourhood structure of a rhombic dodecahedron, which defines the logical lat tice for the algorithm. But, in contrast to the 2D case, there is no ideal hierarchical solution for the complete single overlapping property in 3D due to the semi-regularity of the rhombic dodecahedron. The generation of the 3D-GSC takes place in the following phases. In the coding phase neigh bouring an d similar voxels are combined to local regions of the lowest hierarchical level. During the following linking phase these regions are linked hierarchically to global segments up to the highest hierarchical level. A region of a hierarchical level consists of contiguous and similar regions of the hierarchical level underneath and the grey-value of this region is calculated by the grey value mean of the participating regions weighted according to their region sizes. During the linking ph ase two regions can be non-similar and over lapping. Therefore, in order to obtain a disjoint segmentation result, the overlapping area must be separated afterwards. This procedure is carried out recursively down to the lowest hierarchical level during the splitting phase, which is initiated after the linking of an island. Finally this 3D segmentat ion method was examined empirically. Suitable error measures were determined and the segmentation results of different test data sets blurred with different amounts of noise were analysed. It appeared that irrespective of the noise intensity conside red the 3D-GSC provides better segmentat ion results than the 2D-GSC when applied to layers. The evaluation of runtime and memory requirements reinforces the wide applicability of the algorithm
