Abstract: Combining the properties of conformal geometry and graph-based topological information, a non-rigid 3D object retrieval methodology is proposed, which is both robust and efficient in terms of retrieval accuracy and computation speed. While graph-based methods are robust to non-rigid object deformations, they require intensive computation which can be reduced by the use of appropriate representations, addressed through geometry-based methods. In this respect, we present a 3D object retrieval methodology, which combines the above advantages in a unified manner. Furthermore, we propose a string matching strategy for the comparison of graphs which describe 3D objects.