Topology-Preserving Image Segmentation by Beltrami Representation of Shapes

Abstract

A new approach using the Beltrami representation of a shape for topology-preserving image segmentation is proposed in this paper. Using the proposed model, the target object can be segmented from the input image by a region of user-prescribed topology. Given a target image I, a template image J is constructed and then deformed with respect to the Beltrami representation. The deformation on J is designed such that the topology of the segmented region is preserved as which the object is interior in J. The topology-preserving property of the deformation is guaranteed by imposing only one constraint on the Beltrami representation, which is easy to be handled. Introducing the Beltrami representation 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. 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 meet any practical need (e.g., medical imaging). High accuracy and stability of the proposed model to deal with different segmentation tasks are validated by numerical experiments on both artificial and real images.