# Optimizing the Dice Score and Jaccard Index for Medical Image Segmentation: Theory & Practice

arXiv: https://arxiv.org/abs/1911.01685 · HTML: https://mlsanity.com/paper/1911.01685/

## Key facts

- Cited by 71 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2019.

## Built on by (most cited first, 30 of 71)

- [Self-Paced Contrastive Learning for Semi-supervised Medical Image Segmentation with Meta-labels](https://mlsanity.com/paper/2107.13741/) (2021)
- [A Survey on Training Challenges in Generative Adversarial Networks for Biomedical Image Analysis](https://mlsanity.com/paper/2201.07646/) (2022)
- [Tracking through Containers and Occluders in the Wild](https://mlsanity.com/paper/2305.03052/) (2023)
- [Towards a vision foundation model for comprehensive assessment of Cardiac MRI](https://mlsanity.com/paper/2410.01665/) (2024)
- [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)
- [OysterNet: Enhanced Oyster Detection Using Simulation](https://mlsanity.com/paper/2209.08176/) (2022)
- [SGSeg: Enabling Text-free Inference in Language-guided Segmentation of Chest X-rays via Self-guidance](https://mlsanity.com/paper/2409.04758/) (2024)
- [Fit Pixels, Get Labels: Meta-learned Implicit Networks for Image Segmentation](https://mlsanity.com/paper/2510.04021/) (2025)
- [Improved 3D Whole Heart Geometry from Sparse CMR Slices](https://mlsanity.com/paper/2408.07532/) (2024)
- [Generative AI Enables Medical Image Segmentation in Ultra Low-Data Regimes](https://mlsanity.com/paper/2408.17421/) (2024)
- [Region-wise Loss for Biomedical Image Segmentation](https://mlsanity.com/paper/2108.01405/) (2021)
- [On Image Segmentation With Noisy Labels: Characterization and Volume Properties of the Optimal Solutions to Accuracy and Dice](https://mlsanity.com/paper/2206.06484/) (2022)
- [Theoretical analysis and experimental validation of volume bias of soft Dice optimized segmentation maps in the context of inherent uncertainty](https://mlsanity.com/paper/2211.04161/) (2022)
- [Meta-Polyp: a baseline for efficient Polyp segmentation](https://mlsanity.com/paper/2305.07848/) (2023)
- [MRI Scan Synthesis Methods based on Clustering and Pix2Pix](https://mlsanity.com/paper/2312.05176/) (2023)
- [DRAC: Diabetic Retinopathy Analysis Challenge with Ultra-Wide Optical Coherence Tomography Angiography Images](https://mlsanity.com/paper/2304.02389/) (2023)
- [Structure Preserving Cycle-GAN for Unsupervised Medical Image Domain Adaptation](https://mlsanity.com/paper/2304.09164/) (2023)
- [DopUS-Net: Quality-Aware Robotic Ultrasound Imaging based on Doppler Signal](https://mlsanity.com/paper/2305.08938/) (2023)
- [M^2UNet: MetaFormer Multi-scale Upsampling Network for Polyp Segmentation](https://mlsanity.com/paper/2306.08600/) (2023)
- [Can Foundation Models Really Segment Tumors? A Benchmarking Odyssey in Lung CT Imaging](https://mlsanity.com/paper/2505.01239/) (2025)
- [Improving Classification Model Performance on Chest X-Rays through Lung Segmentation](https://mlsanity.com/paper/2202.10971/) (2022)
- [DOMINO: Domain-aware Model Calibration in Medical Image Segmentation](https://mlsanity.com/paper/2209.06077/) (2022)
- [Computed tomography coronary angiogram images, annotations and associated data of normal and diseased arteries](https://mlsanity.com/paper/2211.01859/) (2022)
- [Whale Detection Enhancement through Synthetic Satellite Images](https://mlsanity.com/paper/2308.07766/) (2023)
- [SiNGR: Brain Tumor Segmentation via Signed Normalized Geodesic Transform Regression](https://mlsanity.com/paper/2405.16813/) (2024)
- [USE-Evaluator: Performance Metrics for Medical Image Segmentation Models with Uncertain, Small or Empty Reference Annotations](https://mlsanity.com/paper/2209.13008/) (2022)
- [DOMINO++: Domain-aware Loss Regularization for Deep Learning Generalizability](https://mlsanity.com/paper/2308.10453/) (2023)
- [Deep Learning-Driven Segmentation of Ischemic Stroke Lesions Using Multi-Channel MRI](https://mlsanity.com/paper/2501.02287/) (2025)
- [Image-free single-pixel segmentation](https://mlsanity.com/paper/2108.10617/) (2021)

## Abstract (arXiv)

The Dice score and Jaccard index are commonly used metrics for the evaluation of segmentation tasks in medical imaging. Convolutional neural networks trained for image segmentation tasks are usually optimized for (weighted) cross-entropy. This introduces an adverse discrepancy between the learning optimization objective (the loss) and the end target metric. Recent works in computer vision have proposed soft surrogates to alleviate this discrepancy and directly optimize the desired metric, either through relaxations (soft-Dice, soft-Jaccard) or submodular optimization (Lov'asz-softmax). The aim of this study is two-fold. First, we investigate the theoretical differences in a risk minimization framework and question the existence of a weighted cross-entropy loss with weights theoretically optimized to surrogate Dice or Jaccard. Second, we empirically investigate the behavior of the aforementioned loss functions w.r.t. evaluation with Dice score and Jaccard index on five medical segmentation tasks. Through the application of relative approximation bounds, we show that all surrogates are equivalent up to a multiplicative factor, and that no optimal weighting of cross-entropy exists to approximate Dice or Jaccard measures. We validate these findings empirically and show that, while it is important to opt for one of the target metric surrogates rather than a cross-entropy-based loss, the choice of the surrogate does not make a statistical difference on a wide range of medical segmentation tasks.