Topological consistency plays a crucial role in the task of boundary segmentation for reticular images, such as cell membrane segmentation in neuron electron microscopic images, grain boundary segmentation in material microscopic images and road segmentation in aerial images. In these fields, topological changes in segmentation results have a serious impact on the downstream tasks, which can even exceed the misalignment of the boundary itself. To enhance the topology accuracy in segmentation results, we propose the Skea-Topo Aware loss, which is a novel loss function that takes into account the shape of each object and topological significance of the pixels. It consists of two components. First, a skeleton-aware weighted loss improves the segmentation accuracy by better modeling the object geometry with skeletons. Second, a boundary rectified term effectively identifies and emphasizes topological critical pixels in the prediction errors using both foreground and background skeletons in the ground truth and predictions. Experiments prove that our method improves topological consistency by up to 7 points in VI compared to 13 state-of-art methods, based on objective and subjective assessments across three different boundary segmentation datasets. The code is available at https://github.com/clovermini/Skea_topo.

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