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Capturing the global topology of an image is essential for proposing an accurate segmentation of its domain. However, most of existing segmentation methods do not preserve the initial topology of the given input, which is detrimental for numerous downstream object-based tasks. This is all the more true for deep learning models which most work at local scales. In this paper, we propose a new topology-preserving deep image segmentation method which relies on a new leakage loss: the Pathloss. Our method is an extension of the BALoss [1], in which we want to improve the leakage detection for better recovering the closeness property of the image segmentation. This loss allows us to correctly localize and fix the critical points (a leakage in the boundaries) that could occur in the predictions, and is based on a shortest-path search algorithm. This way, loss minimization enforces connectivity only where it is necessary and finally provides a good localization of the boundaries of the objects in the image. Moreover, according to our research, our Pathloss learns to preserve stronger elongated structure compared to methods without using topology-preserving loss. Training with our topological loss function, our method outperforms state-of-the-art topology-aware methods on two representative datasets of different natures: Electron Microscopy and Historical Map.