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Brain midline delineation can facilitate the clinical evaluation of brain midline shift, which plays an important role in the diagnosis and prognosis of various brain pathology. Nevertheless, there are still great challenges with brain midline delineation, such as the largely deformed midline caused by the mass effect and the possible morphological failure that the predicted midline is not a connected curve. To address these challenges, we propose a context-aware refinement network (CAR-Net) to refine and integrate the feature pyramid representation generated by the UNet. Consequently, the proposed CAR-Net explores more discriminative contextual features and a larger receptive field, which is of great importance to predict largely deformed midline. For keeping the structural connectivity of the brain midline, we introduce a novel connectivity regular loss (CRL) to punish the disconnectivity between adjacent coordinates. Moreover, we address the ignored prerequisite of previous regression-based methods that the brain CT image must be in the standard pose. A simple pose rectification network is presented to align the source input image to the standard pose image. Extensive experimental results on the CQ dataset and one inhouse dataset show that the proposed method requires fewer parameters and outperforms three state-of-the-art methods in terms of four evaluation metrics. Code is available at https://github.com/ShawnBIT/Brain-Midline-Detection.