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

arXiv: https://arxiv.org/abs/2107.03846 · HTML: https://mlsanity.com/paper/2107.03846/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 27 references that are in the map.
- First posted on arXiv 8 Jul 2021.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Prior-aware Neural Network for Partially-Supervised Multi-Organ Segmentation](https://mlsanity.com/paper/1904.06346/) (2019)
- [Multi-organ Segmentation over Partially Labeled Datasets with Multi-scale Feature Abstraction](https://mlsanity.com/paper/2001.00208/) (2020)
- [Generalised Wasserstein Dice Score for Imbalanced Multi-class Segmentation using Holistic Convolutional Networks](https://mlsanity.com/paper/1707.00478/) (2017)
- [Learning joint segmentation of tissues and brain lesions from task-specific hetero-modal domain-shifted datasets](https://mlsanity.com/paper/2009.04009/) (2020)
- [Automatic brain tissue segmentation in fetal MRI using convolutional neural networks](https://mlsanity.com/paper/1906.04713/) (2019)
- [MONAIfbs: MONAI-based fetal brain MRI deep learning segmentation](https://mlsanity.com/paper/2103.13314/) (2021)
- [Efficient multi-class fetal brain segmentation in high resolution MRI reconstructions with noisy labels](https://mlsanity.com/paper/2009.06275/) (2020)
- [Joint Learning of Brain Lesion and Anatomy Segmentation from Heterogeneous Datasets](https://mlsanity.com/paper/1903.03445/) (2019)
- [Longitudinal analysis of fetal MRI in patients with prenatal spina bifida repair](https://mlsanity.com/paper/1911.06542/) (2019)

## Built on by (most cited first, 12 of 12)

- [MultiTalent: A Multi-Dataset Approach to Medical Image Segmentation](https://mlsanity.com/paper/2303.14444/) (2023)
- [Fetal Brain Tissue Annotation and Segmentation Challenge Results](https://mlsanity.com/paper/2204.09573/) (2022)
- [A Dempster-Shafer approach to trustworthy AI with application to fetal brain MRI segmentation](https://mlsanity.com/paper/2204.02779/) (2022)
- [Distributionally Robust Segmentation of Abnormal Fetal Brain 3D MRI](https://mlsanity.com/paper/2108.04175/) (2021)
- [The Dice loss in the context of missing or empty labels: Introducing Phi and ε](https://mlsanity.com/paper/2207.09521/) (2022)
- [Synthetic magnetic resonance images for domain adaptation: Application to fetal brain tissue segmentation](https://mlsanity.com/paper/2111.04737/) (2021)
- [Partial supervision for the FeTA challenge 2021](https://mlsanity.com/paper/2111.02408/) (2021)
- [OOD-SEG: Exploiting out-of-distribution detection techniques for learning image segmentation from sparse multi-class positive-only annotations](https://mlsanity.com/paper/2411.09553/) (2024)
- [Domain generalization in fetal brain MRI segmentation with multi-reconstruction augmentation](https://mlsanity.com/paper/2211.14282/) (2022)
- [Enhancing Corpus Callosum Segmentation in Fetal MRI via Pathology-Informed Domain Randomization](https://mlsanity.com/paper/2508.20475/) (2025)
- [Comparative evaluation of training strategies using partially labelled datasets for segmentation of white matter hyperintensities and stroke lesions in FLAIR MRI](https://mlsanity.com/paper/2601.20503/) (2026)
- [ImputeECG: Deep Learning Reconstruction of Complete 12-Lead Electrocardiograms from Incomplete Recordings for Cardiac Assessment](https://mlsanity.com/paper/2607.05009/) (2026)

## Abstract (arXiv)

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