  The Dice score is widely used for binary segmentation due to its robustness
to class imbalance. Soft generalisations of the Dice score allow it to be used
as a loss function for training convolutional neural networks (CNN). Although
CNNs trained using mean-class Dice score achieve state-of-the-art results on
multi-class segmentation, this loss function does neither take advantage of
inter-class relationships nor multi-scale information. We argue that an
improved loss function should balance misclassifications to favour predictions
that are semantically meaningful. This paper investigates these issues in the
context of multi-class brain tumour segmentation. Our contribution is
threefold. 1) We propose a semantically-informed generalisation of the Dice
score for multi-class segmentation based on the Wasserstein distance on the
probabilistic label space. 2) We propose a holistic CNN that embeds spatial
information at multiple scales with deep supervision. 3) We show that the joint
use of holistic CNNs and generalised Wasserstein Dice scores achieves
segmentations that are more semantically meaningful for brain tumour
segmentation.
