This paper proposes and compares methods for designing hierarchical 2D meshes for representation of object-based video and hierarchical 3D meshes for 3D objects used in telemedicine and multimedia applications. The same approach has been applied both in 2D and 3D but with different constraints. This representation consists of a hierarchy of Delaunay meshes, obtained by recursive simplification of the initial fine level-of-detail mesh geometry. There is no guarantee of an optimal mesh in 3D that uses a specific given set of node points whereas in 2D it is guaranteed that there is a unique 2D Delaunay mesh which uses all the node points for a specific set. To solve this problem an optimized alpha value is used in 3D Delaunay triangulation in the proposed algorithm. Mesh simplification entails removal of mesh nodes to reduce the level of detail. The selection of nodes to be removed is achieved by associating a cost with each mesh node. The Delaunay topology constraint on each mesh level not only helps to design meshes with desired geometric properties, but also enables efficient compression of the mesh data for multimedia applications.