# Do We Really Need Dice? The Hidden Region-Size Biases of Segmentation Losses

arXiv: https://arxiv.org/abs/2104.08717 · HTML: https://mlsanity.com/paper/2104.08717/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 54 references that are in the map.
- First posted on arXiv 18 Apr 2021.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Pyramid Scene Parsing Network](https://mlsanity.com/paper/1612.01105/) (2016)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Panoptic Segmentation](https://mlsanity.com/paper/1801.00868/) (2018)
- [Generalised Dice overlap as a deep learning loss function for highly unbalanced segmentations](https://mlsanity.com/paper/1707.03237/) (2017)
- [Kvasir-SEG: A Segmented Polyp Dataset](https://mlsanity.com/paper/1911.07069/) (2019)
- [Segmentation Transformer: Object-Contextual Representations for Semantic Segmentation](https://mlsanity.com/paper/1909.11065/) (2019)
- [PraNet: Parallel Reverse Attention Network for Polyp Segmentation](https://mlsanity.com/paper/2006.11392/) (2020)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [Tversky loss function for image segmentation using 3D fully convolutional deep networks](https://mlsanity.com/paper/1706.05721/) (2017)
- [Boundary loss for highly unbalanced segmentation](https://mlsanity.com/paper/1812.07032/) (2018)
- [Hierarchical Multi-Scale Attention for Semantic Segmentation](https://mlsanity.com/paper/2005.10821/) (2020)
- [DoubleU-Net: A Deep Convolutional Neural Network for Medical Image Segmentation](https://mlsanity.com/paper/2006.04868/) (2020)
- [Deep learning to achieve clinically applicable segmentation of head and neck anatomy for radiotherapy](https://mlsanity.com/paper/1809.04430/) (2018)
- [Combo Loss: Handling Input and Output Imbalance in Multi-Organ Segmentation](https://mlsanity.com/paper/1805.02798/) (2018)
- [Optimization for Medical Image Segmentation: Theory and Practice when evaluating with Dice Score or Jaccard Index](https://mlsanity.com/paper/2010.13499/) (2020)
- [3D Segmentation with Exponential Logarithmic Loss for Highly Unbalanced Object Sizes](https://mlsanity.com/paper/1809.00076/) (2018)
- [Learn to Segment Retinal Lesions and Beyond](https://mlsanity.com/paper/1912.11619/) (2019)
- [Cardiac Segmentation from LGE MRI Using Deep Neural Network Incorporating Shape and Spatial Priors](https://mlsanity.com/paper/1906.07347/) (2019)
- [The Devil is in the Decoder: Classification, Regression and GANs](https://mlsanity.com/paper/1707.05847/) (2017)
- [Bridging Category-level and Instance-level Semantic Image Segmentation](https://mlsanity.com/paper/1605.06885/) (2016)

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

- [A Generalized Surface Loss for Reducing the Hausdorff Distance in Medical Imaging Segmentation](https://mlsanity.com/paper/2302.03868/) (2023)
- [On the Optimal Combination of Cross-Entropy and Soft Dice Losses for Lesion Segmentation with Out-of-Distribution Robustness](https://mlsanity.com/paper/2209.06078/) (2022)
- [Merging Context Clustering with Visual State Space Models for Medical Image Segmentation](https://mlsanity.com/paper/2501.01618/) (2025)
- [Towards Fairness under Label Bias in Image Segmentation: Impact, Measurement and Mitigation](https://mlsanity.com/paper/2605.06891/) (2026)
- [CT evaluation of 2D and 3D holistic deep learning methods for the volumetric segmentation of airway lesions](https://mlsanity.com/paper/2403.08042/) (2024)
- [A Multimodal Feature Distillation with Mamba-Transformer Network for Brain Tumor Segmentation with Incomplete Modalities](https://mlsanity.com/paper/2404.14019/) (2024)
- [Adaptive Voxel-Weighted Loss Using L1 Norms in Deep Neural Networks for Detection and Segmentation of Prostate Cancer Lesions in PET/CT Images](https://mlsanity.com/paper/2502.02756/) (2025)
- [Pioneering Precision in Lumbar Spine MRI Segmentation with Advanced Deep Learning and Data Enhancement](https://mlsanity.com/paper/2409.06018/) (2024)
- [Cross-Task Pretraining for Cross-Organ Cross-Scanner Adenocarcinoma Segmentation](https://mlsanity.com/paper/2410.07124/) (2024)
- [ContextLoss: Context Information for Topology-Preserving Segmentation](https://mlsanity.com/paper/2506.11134/) (2025)
- [JParc: Joint cortical surface parcellation with registration](https://mlsanity.com/paper/2512.22485/) (2025)
- [Towards Investigating Residual Hearing Loss: Quantification of Fibrosis in a Novel Cochlear OCT Dataset](https://mlsanity.com/paper/2608.21189/) (2026)

## Abstract (arXiv)

Most segmentation losses are arguably variants of the Cross-Entropy (CE) or Dice losses. On the surface, these two categories of losses seem unrelated, and there is no clear consensus as to which category is a better choice, with varying performances for each across different benchmarks and applications. Furthermore, it is widely argued within the medical-imaging community that Dice and CE are complementary, which has motivated the use of compound CE-Dice losses. In this work, we provide a theoretical analysis, which shows that CE and Dice share a much deeper connection than previously thought. First, we show that, from a constrained-optimization perspective, they both decompose into two components, i.e., a similar ground-truth matching term, which pushes the predicted foreground regions towards the ground-truth, and a region-size penalty term imposing different biases on the size of the predicted regions. Then, we provide bound relationships and an information-theoretic analysis, which uncover hidden region-size biases: Dice has an intrinsic bias towards specific extremely imbalanced solutions, whereas CE implicitly encourages the ground-truth region proportions. Our theoretical results explain the wide experimental evidence in the medical-imaging literature, whereby Dice losses bring improvements for imbalanced segmentation. Based on our theoretical analysis, we propose a principled and simple solution, which enables to control explicitly the region-size bias. The proposed method integrates CE with explicit terms based on L1 or the KL divergence, which encourage segmenting region proportions to match target class proportions, thereby mitigating class imbalance but without losing generality. Comprehensive experiments and ablation studies over different losses and applications validate our theoretical analysis, as well as the effectiveness of explicit and simple region-size terms.