Split learning (SL) has been proposed to train deep learning models in a decentralized manner. For decentralized healthcare applications with vertical data partitioning, SL can be beneficial as it allows institutes with complementary features or images for a shared set of patients to jointly develop more robust and generalizable models. In this work, we propose "Split-U-Net" and successfully apply SL for collaborative biomedical image segmentation. Nonetheless, SL requires the exchanging of intermediate activation maps and gradients to allow training models across different feature spaces, which might leak data and raise privacy concerns. Therefore, we also quantify the amount of data leakage in common SL scenarios for biomedical image segmentation and provide ways to counteract such leakage by applying appropriate defense strategies.