# Polynomial Dice Loss for Medical Image Segmentation

arXiv: https://arxiv.org/abs/2606.23373 · HTML: https://mlsanity.com/paper/2606.23373/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 18 references that are in the map.
- First posted on arXiv 22 Jun 2026.

## Builds on (most cited first, 11 of 11)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [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)
- [Tversky loss function for image segmentation using 3D fully convolutional deep networks](https://mlsanity.com/paper/1706.05721/) (2017)
- [A Novel Focal Tversky loss function with improved Attention U-Net for lesion segmentation](https://mlsanity.com/paper/1810.07842/) (2018)
- [Combo Loss: Handling Input and Output Imbalance in Multi-Organ Segmentation](https://mlsanity.com/paper/1805.02798/) (2018)
- [PolyLoss: A Polynomial Expansion Perspective of Classification Loss Functions](https://mlsanity.com/paper/2204.12511/) (2022)
- [AnatomyNet: Deep Learning for Fast and Fully Automated Whole-volume Segmentation of Head and Neck Anatomy](https://mlsanity.com/paper/1808.05238/) (2018)
- [Taylor Outlier Exposure](https://mlsanity.com/paper/2412.07219/) (2024)

## Abstract (arXiv)

Medical image segmentation is a fundamental task for medical image processing and computer-assisted intervention, yet data imbalance and small lesion detection pose significant challenges. Dice Loss, which measures the overlap between predicted and ground truth regions, is widely used to mitigate these issues. To further emphasize its properties, we propose Polynomial Dice Loss, a polynomial extension of Dice Loss. Specifically, by leveraging the geometric characteristics of Dice Loss and formulating the loss function as a polynomial representation via Taylor expansion, we enable the adjustment of the contribution of higher-order components to the loss function. In our experiments, we evaluate the proposed method against loss functions derived from conventional Dice and Tversky coefficients. Experimental results and further analysis show that the polynomial formulation provides a simple way to control the loss shape and achieves competitive performance across multiple segmentation settings.