Abstract
Variational models are widely used in image segmentation, with various models designed to address different types of images by optimizing specific objective functionals. However, traditional segmentation models primarily focus on the visual attributes of the image, often neglecting the topological properties of the target objects. This limitation can lead to segmentation results that deviate from the ground truth, particularly in images with complex topological structures. In this paper, we introduce a topology-preserving constraint into the iterative convolution-thresholding method (ICTM), resulting in the topology-preserving ICTM (TP-ICTM). Extensive experiments demonstrate that, by explicitly preserving the topological properties of target objects-such as connectivity-the proposed algorithm achieves enhanced accuracy and robustness, particularly in images with intricate structures or noise.