When performing manual segmentations, experts heavily rely on prior anatomical knowledge. Topology is an important prior information due to its stability across patients. Recently, several losses based on persistent homology were proposed to constrain topology. However, such approaches are computationally expensive and complex to implement, in particular in 3D. In this paper, we propose a novel loss function to introduce topological priors in deep learning-based segmentation, which is fast to compute and easy to implement. Our approach was evaluated in several medical datasets (spleen, heart, hippocampus, red nucleus). It allowed reducing topological errors and, in some cases, improving voxel-level accuracy.
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