Image Segmentation with Homotopy Warping

Besides per-pixel accuracy, topological correctness is also crucial for the segmentation of images with fine-scale structures, e.g., satellite images and biomedical images. In this paper, by leveraging the theory of digital topology, we identify locations in an image that are critical for topology. By focusing on these critical locations, we propose a new homotopy warping loss to train deep image segmentation networks for better topological accuracy. To efficiently identity these topologically critical locations, we propose a new algorithm exploiting the distance transform. The proposed algorithm, as well as the loss function, naturally generalize to different topological structures in both 2D and 3D settings. The proposed loss function helps deep nets achieve better performance in terms of topology-aware metrics, outperforming state-of-the-art topology-preserving segmentation methods.