# Dice Semimetric Losses: Optimizing the Dice Score with Soft Labels

arXiv: https://arxiv.org/abs/2303.16296 · HTML: https://mlsanity.com/paper/2303.16296/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 56 references that are in the map.
- First posted on arXiv 28 Mar 2023.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Generalised Dice overlap as a deep learning loss function for highly unbalanced segmentations](https://mlsanity.com/paper/1707.03237/) (2017)
- [The Liver Tumor Segmentation Benchmark (LiTS)](https://mlsanity.com/paper/1901.04056/) (2019)
- [Tversky loss function for image segmentation using 3D fully convolutional deep networks](https://mlsanity.com/paper/1706.05721/) (2017)
- [Knowledge Distillation from A Stronger Teacher](https://mlsanity.com/paper/2205.10536/) (2022)
- [Metrics reloaded: Recommendations for image analysis validation](https://mlsanity.com/paper/2206.01653/) (2022)
- [The state of the art in kidney and kidney tumor segmentation in contrast-enhanced CT imaging: Results of the KiTS19 Challenge](https://mlsanity.com/paper/1912.01054/) (2019)
- [Dice Loss for Data-imbalanced NLP Tasks](https://mlsanity.com/paper/1911.02855/) (2019)
- [A Novel Focal Tversky loss function with improved Attention U-Net for lesion segmentation](https://mlsanity.com/paper/1810.07842/) (2018)
- [Local Temperature Scaling for Probability Calibration](https://mlsanity.com/paper/2008.05105/) (2020)
- [Who Said What: Modeling Individual Labelers Improves Classification](https://mlsanity.com/paper/1703.08774/) (2017)
- [Optimization for Medical Image Segmentation: Theory and Practice when evaluating with Dice Score or Jaccard Index](https://mlsanity.com/paper/2010.13499/) (2020)
- [A Consistent and Differentiable Lp Canonical Calibration Error Estimator](https://mlsanity.com/paper/2210.07810/) (2022)
- [Efficient Medical Image Segmentation Based on Knowledge Distillation](https://mlsanity.com/paper/2108.09987/) (2021)
- [Meta-Cal: Well-controlled Post-hoc Calibration by Ranking](https://mlsanity.com/paper/2105.04290/) (2021)
- [Spatially Varying Label Smoothing: Capturing Uncertainty from Expert Annotations](https://mlsanity.com/paper/2104.05788/) (2021)
- [SoftSeg: Advantages of soft versus binary training for image segmentation](https://mlsanity.com/paper/2011.09041/) (2020)
- [Masked Distillation with Receptive Tokens](https://mlsanity.com/paper/2205.14589/) (2022)
- [Post Training Uncertainty Calibration of Deep Networks For Medical Image Segmentation](https://mlsanity.com/paper/2010.14290/) (2020)
- [Using Soft Labels to Model Uncertainty in Medical Image Segmentation](https://mlsanity.com/paper/2109.12622/) (2021)

## Built on by (most cited first, 5 of 5)

- [SiNGR: Brain Tumor Segmentation via Signed Normalized Geodesic Transform Regression](https://mlsanity.com/paper/2405.16813/) (2024)
- [3DDX: Bone Surface Reconstruction from a Single Standard-Geometry Radiograph via Dual-Face Depth Estimation](https://mlsanity.com/paper/2409.16702/) (2024)
- [RAPID-Net: Accurate Pocket Identification for Binding-Site-Agnostic Docking](https://mlsanity.com/paper/2502.02371/) (2025)
- [RankSEG-RMA: An Efficient Segmentation Algorithm via Reciprocal Moment Approximation](https://mlsanity.com/paper/2510.15362/) (2025)
- [Image-level Regression for Uncertainty-aware Retinal Image Segmentation](https://mlsanity.com/paper/2405.16815/) (2024)

## Abstract (arXiv)

The soft Dice loss (SDL) has taken a pivotal role in numerous automated segmentation pipelines in the medical imaging community. Over the last years, some reasons behind its superior functioning have been uncovered and further optimizations have been explored. However, there is currently no implementation that supports its direct utilization in scenarios involving soft labels. Hence, a synergy between the use of SDL and research leveraging the use of soft labels, also in the context of model calibration, is still missing. In this work, we introduce Dice semimetric losses (DMLs), which (i) are by design identical to SDL in a standard setting with hard labels, but (ii) can be employed in settings with soft labels. Our experiments on the public QUBIQ, LiTS and KiTS benchmarks confirm the potential synergy of DMLs with soft labels (e.g. averaging, label smoothing, and knowledge distillation) over hard labels (e.g. majority voting and random selection). As a result, we obtain superior Dice scores and model calibration, which supports the wider adoption of DMLs in practice. The code is available at https://github.com/zifuwanggg/JDTLosses