Topology-preserving geometric deformable models (TGDMs) are used to segment objects that have a known topology. Their accuracy is inherently limited, however, by the resolution of the underlying computational grid. Although this can be overcome by using fine-resolution grids, both the computational cost and the size of the resulting surface increase dramatically. In order to maintain computational efficiency and to keep the surface mesh size manageable, we have developed a new framework, termed OTGDMs, for topology-preserving geometric deformable models on balanced octree grids (BOGs). In order to do this, definitions and concepts from digital topology on regular grids were extended to BOGs so that characterization of simple points could be made. Other issues critical to the implementation of OTGDMs are also addressed. We demonstrate the performance of the proposed method using both mathematical phantoms and real medical images.