Despite the recent success of deep learning methods at achieving new state-of-the-art accuracy for medical image segmentation, some major limitations are still restricting their deployment into clinics. One major limitation of deep learning-based segmentation methods is their lack of robustness to variability in the image acquisition protocol and in the imaged anatomy that were not represented or were underrepresented in the training dataset. This suggests adding new manually segmented images to the training dataset to better cover the image variability. However, in most cases, the manual segmentation of medical images requires highly skilled raters and is time-consuming, making this solution prohibitively expensive. Even when manually segmented images from different sources are available, they are rarely annotated for exactly the same regions of interest. This poses an additional challenge for current state-of-the-art deep learning segmentation methods that rely on supervised learning and therefore require all the regions of interest to be segmented for all the images to be used for training. This thesis introduces new mathematical and optimization methods to mitigate those limitations.