Split-and-merge algorithms define a class of image segmentation methods. Topological maps are a mathematical model that represents image subdivisions in 2D and 3D. This paper discusses a split-and-merge method for 3D image data based on the topological map model. This model allows representations of states of segmentations and of merge and split operations. Indeed, it can be used as data structure for dynamic changes of segmentation. The paper details such an algorithmic approach and analyzes its time complexity. A general introduction into combinatorial and topological maps is given to support the understanding of the proposed algorithms.