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Midline shift (MLS) is a well-established factor used for outcome prediction in traumatic brain injury, stroke and brain tumors. The importance of automatic estimation of MLS was recently highlighted by ACR Data Science Institute. In this paper we introduce a novel deep learning based approach for the problem of MLS detection, which exploits task-specific structural knowledge. We evaluate our method on a large dataset containing heterogeneous images with significant MLS and show that its mean error approaches the inter-expert variability. Finally, we show the robustness of our approach by validating it on an external dataset, acquired during routine clinical practice.