Image segmentation aims to extract the target objects or to identify the corresponding boundaries. For corrupted images due to occlusions, obscurities or noises, to get an accurate segmentation result is very difficult. To overcome this issue, the prior information is often introduced and particularly, the convex prior attracts more and more attentions recently. In this paper, we propose a topology- and convexity-preserving registration-based segmentation model, which can be suitable for both 2D and 3D cases. By incorporating the level set representation and imposing the constraints on the suitable regions, we can explicitly force the fully convex segmentation results or the partially convex segmentation results. To solve the proposed model, we employ the alternating direction method of multipliers and numerical experiments on 2/3D synthetic and real images demonstrate that the proposed model can indeed lead to the accurately topology- and convexity-preserving segmentation.

图像分割旨在提取目标对象或识别相应的边界。对于由于遮挡、模糊或噪声而损坏的图像，要获得准确的分割结果是非常困难的。为了克服这个问题，经常引入先验信息，特别是凸先验最近吸引了越来越多的关注。在本文中，我们提出了一种基于拓扑和凸性保留注册的分割模型，该模型适用于 2D 和 3D 情况。通过结合水平集表示并对合适的区域施加约束，我们可以明确地强制完全凸分割结果或部分凸分割结果。为了解决所提出的模型，