A new approach using the Beltrami Signature of a shape to segment an object from an image with promised topology is proposed in this paper. Given a target image $I$, a template image $J$ called the topological prior image is deformed according to the newly proposed Beltrami Signature, such that the topology of the segmented region is preserved as that of the object interior in $J$. The topology preserving property of the deformation is guaranteed by imposing only one constraint on the Beltrami Signature, which is easy to be handled. Introducing the Beltrami Signature also allows large deformations on the topological prior $J$, so that it can be a very simple image, such as an image of disks, torus, disjoint disks, etc. Hence, prior shape information of $I$ is unnecessary for the proposed model. Additionally, the proposed model can be easily incorporated with selective segmentation, in which landmark constraints can be imposed interactively to facilitate any practical need (e.g. medical imaging). High accuracy and stability of the proposed model to deal with different segmentation tasks is validated by numerical experiments on both artificial and real images.