# Generalised Wasserstein Dice Score for Imbalanced Multi-class Segmentation using Holistic Convolutional Networks

arXiv: https://arxiv.org/abs/1707.00478 · HTML: https://mlsanity.com/paper/1707.00478/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2017.

## Built on by (most cited first, 21 of 21)

- [Unified Focal loss: Generalising Dice and cross entropy-based losses to handle class imbalanced medical image segmentation](https://mlsanity.com/paper/2102.04525/) (2021)
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- [Calibrating the Dice loss to handle neural network overconfidence for biomedical image segmentation](https://mlsanity.com/paper/2111.00528/) (2021)
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- [Modeling Multimodal Aleatoric Uncertainty in Segmentation with Mixture of Stochastic Experts](https://mlsanity.com/paper/2212.07328/) (2022)
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- [Distributionally Robust Segmentation of Abnormal Fetal Brain 3D MRI](https://mlsanity.com/paper/2108.04175/) (2021)
- [AMD-HookNet for Glacier Front Segmentation](https://mlsanity.com/paper/2302.02744/) (2023)
- [Generalized Wasserstein Dice Loss, Test-time Augmentation, and Transformers for the BraTS 2021 challenge](https://mlsanity.com/paper/2112.13054/) (2021)
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- [Double U-Net for Super-Resolution and Segmentation of Live Cell Images](https://mlsanity.com/paper/2212.02028/) (2022)
- [Tree-based Semantic Losses: Application to Sparsely-supervised Large Multi-class Hyperspectral Segmentation](https://mlsanity.com/paper/2506.21150/) (2025)
- [GEPAR3D: Geometry Prior-Assisted Learning for 3D Tooth Segmentation](https://mlsanity.com/paper/2508.00155/) (2025)
- [AMD-HookNet++: Evolution of AMD-HookNet with Hybrid CNN-Transformer Feature Enhancement for Glacier Calving Front Segmentation](https://mlsanity.com/paper/2512.14639/) (2025)
- [Size and Smoothness Aware Adaptive Focal Loss for Small Tumor Segmentation](https://mlsanity.com/paper/2407.09828/) (2024)
- [Label tree semantic losses for rich multi-class medical image segmentation](https://mlsanity.com/paper/2507.15777/) (2025)
- [Tracing 3D Anatomy in 2D Strokes: A Multi-Stage Projection Driven Approach to Cervical Spine Fracture Identification](https://mlsanity.com/paper/2601.15235/) (2026)

## Abstract (arXiv)

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.