# On Image Segmentation With Noisy Labels: Characterization and Volume Properties of the Optimal Solutions to Accuracy and Dice

arXiv: https://arxiv.org/abs/2206.06484 · HTML: https://mlsanity.com/paper/2206.06484/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 50 references that are in the map.
- First posted on arXiv 13 Jun 2022.

## Builds on (most cited first, 22 of 22)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Generalised Dice overlap as a deep learning loss function for highly unbalanced segmentations](https://mlsanity.com/paper/1707.03237/) (2017)
- [Embracing Imperfect Datasets: A Review of Deep Learning Solutions for Medical Image Segmentation](https://mlsanity.com/paper/1908.10454/) (2019)
- [Data Programming: Creating Large Training Sets, Quickly](https://mlsanity.com/paper/1605.07723/) (2016)
- [Deep learning with noisy labels: exploring techniques and remedies in medical image analysis](https://mlsanity.com/paper/1912.02911/) (2019)
- [The Importance of Skip Connections in Biomedical Image Segmentation](https://mlsanity.com/paper/1608.04117/) (2016)
- [Deep Label Distribution Learning with Label Ambiguity](https://mlsanity.com/paper/1611.01731/) (2016)
- [Optimizing the Dice Score and Jaccard Index for Medical Image Segmentation: Theory & Practice](https://mlsanity.com/paper/1911.01685/) (2019)
- [Deep Learning from Noisy Image Labels with Quality Embedding](https://mlsanity.com/paper/1711.00583/) (2017)
- [Deep Convolutional Neural Networks with Spatial Regularization, Volume and Star-shape Priori for Image Segmentation](https://mlsanity.com/paper/2002.03989/) (2020)
- [SoftSeg: Advantages of soft versus binary training for image segmentation](https://mlsanity.com/paper/2011.09041/) (2020)
- [Learning to Segment Skin Lesions from Noisy Annotations](https://mlsanity.com/paper/1906.03815/) (2019)
- [Pick-and-Learn: Automatic Quality Evaluation for Noisy-Labeled Image Segmentation](https://mlsanity.com/paper/1907.11835/) (2019)
- [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)
- [Label fusion and training methods for reliable representation of inter-rater uncertainty](https://mlsanity.com/paper/2202.07550/) (2022)
- [Soft labeling by Distilling Anatomical knowledge for Improved MS Lesion Segmentation](https://mlsanity.com/paper/1901.09263/) (2019)
- [On the relationship between calibrated predictors and unbiased volume estimation](https://mlsanity.com/paper/2112.12560/) (2021)
- [Robustness study of noisy annotation in deep learning based medical image segmentation](https://mlsanity.com/paper/2003.06240/) (2020)
- [Superpixel-Guided Label Softening for Medical Image Segmentation](https://mlsanity.com/paper/2007.08897/) (2020)

## Built on by (most cited first, 6 of 6)

- [Label-Noise Robust Diffusion Models](https://mlsanity.com/paper/2402.17517/) (2024)
- [Noisy Annotations in Semantic Segmentation](https://mlsanity.com/paper/2406.10891/) (2024)
- [Noisy Image Segmentation With Soft-Dice](https://mlsanity.com/paper/2304.00801/) (2023)
- [Marginal Thresholding in Noisy Image Segmentation](https://mlsanity.com/paper/2304.04116/) (2023)
- [Modality-AGnostic Image Cascade (MAGIC) for Multi-Modality Cardiac Substructure Segmentation](https://mlsanity.com/paper/2506.10797/) (2025)
- [A Novel Method to Evaluate Models on Unreliable, Noisy and Inconsistent Labels: Adaptive Resolution Label Aggregation (ARLA)](https://mlsanity.com/paper/2607.11214/) (2026)

## Abstract (arXiv)

We study two of the most popular performance metrics in medical image segmentation, Accuracy and Dice, when the target labels are noisy. For both metrics, several statements related to characterization and volume properties of the set of optimal segmentations are proved, and associated experiments are provided. Our main insights are: (i) the volume of the solutions to both metrics may deviate significantly from the expected volume of the target, (ii) the volume of a solution to Accuracy is always less than or equal to the volume of a solution to Dice and (iii) the optimal solutions to both of these metrics coincide when the set of feasible segmentations is constrained to the set of segmentations with the volume equal to the expected volume of the target.