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 Chan et al. (J Math Imaging Vis 60(3):401–421, 2018), 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.

图像分割是从给定图像中提取有意义的对象。对于由于遮挡，模糊或噪点而导致的降级图像，会严重影响分割结果的准确性。为了减轻这个问题，通常引入有关目标对象的先验信息。在Chan等人中。（J Math Imaging Vis 60（3）：401–421，2018），提出了一种基于拓扑保留配准的分割模型，该模型仅限于分割2D图像。在本文中，我们提出了一种具有超弹性正则化的，基于3D拓扑保留，基于配准的分割模型，该模型可以处理2D和3D图像。建立了所提出模型的解的存在性。我们还提出了一种收敛的迭代方案来解决所提出的模型。