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 talk, we will talk about the registration-based 3D segmentation, convexity segmentation, star-shape segmentation, and interactive segmentation.