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Deep neural networks have increased the accuracy of automatic segmentation,however, their accuracy depends on the availability of a large number of fullysegmented images. Methods to train deep neural networks using images for whichsome, but not all, regions of interest are segmented are necessary to makebetter use of partially annotated datasets. In this paper, we propose the firstaxiomatic definition of label-set loss functions that are the loss functionsthat can handle partially segmented images. We prove that there is one and onlyone method to convert a classical loss function for fully segmented images intoa proper label-set loss function. Our theory also allows us to define theleaf-Dice loss, a label-set generalization of the Dice loss particularly suitedfor partial supervision with only missing labels. Using the leaf-Dice loss, weset a new state of the art in partially supervised learning for fetal brain 3DMRI segmentation. We achieve a deep neural network able to segment whitematter, ventricles, cerebellum, extra-ventricular CSF, cortical gray matter,deep gray matter, brainstem, and corpus callosum based on fetal brain 3D MRI ofanatomically normal fetuses or with open spina bifida. Our implementation ofthe proposed label-set loss functions is available athttps://github.com/LucasFidon/label-set-loss-functions

Label-set Loss Functions for Partial Supervision: Application to Fetal Brain 3D MRI Parcellation