  Image segmentation is to extract meaningful objects from a given image. For
degraded images due to occlusions, obscurities or noises, the accuracy of the
segmentation result can be severely affected. To alleviate this problem, prior
information about the target object is usually introduced. In [10], a
topology-preserving registration-based segmentation model was proposed, which
is restricted to segment 2D images only. In this paper, we propose a novel 3D
topology-preserving registration-based segmentation model with the hyperelastic
regularization, which can handle both 2D and 3D images. The existence of the
solution of the proposed model is established. We also propose a converging
iterative scheme to solve the proposed model. Numerical experiments have been
carried out on the synthetic and real images, which demonstrate the
effectiveness of our proposed model.
