Minimization of distribution matching losses is a principled approach to domain adaptation in the context of image classification. However, it is largely 
overlooked in adapting segmentation networks, which is currently dominated by adversarial models. We propose a class of loss functions, which encourage direct kernel density matching in the network-output space, up to some geometric transformations
computed from unlabeled inputs.
Rather than using an intermediate domain discriminator, our direct approach unifies distribution matching and segmentation in a single loss. Therefore, 
it simplifies segmentation adaptation by avoiding extra adversarial steps, while improving quality, stability and efficiency of training. We juxtapose our approach to state-of-the-art segmentation adaptation 
via adversarial training in the network-output space. In the challenging task of adapting brain segmentation across different magnetic resonance imaging (MRI) modalities, our approach achieves significantly better results
both in terms of accuracy and stability.

