# Theoretical analysis and experimental validation of volume bias of soft Dice optimized segmentation maps in the context of inherent uncertainty

arXiv: https://arxiv.org/abs/2211.04161 · HTML: https://mlsanity.com/paper/2211.04161/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 49 references that are in the map.
- First posted on arXiv 8 Nov 2022.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Generalised Dice overlap as a deep learning loss function for highly unbalanced segmentations](https://mlsanity.com/paper/1707.03237/) (2017)
- [Identifying the Best Machine Learning Algorithms for Brain Tumor Segmentation, Progression Assessment, and Overall Survival Prediction in the BRATS Challenge](https://mlsanity.com/paper/1811.02629/) (2018)
- [A large annotated medical image dataset for the development and evaluation of segmentation algorithms](https://mlsanity.com/paper/1902.09063/) (2019)
- [A Probabilistic U-Net for Segmentation of Ambiguous Images](https://mlsanity.com/paper/1806.05034/) (2018)
- [Efficient Multi-Scale 3D CNN with Fully Connected CRF for Accurate Brain Lesion Segmentation](https://mlsanity.com/paper/1603.05959/) (2016)
- [Bayesian SegNet: Model Uncertainty in Deep Convolutional Encoder-Decoder Architectures for Scene Understanding](https://mlsanity.com/paper/1511.02680/) (2015)
- [PHiSeg: Capturing Uncertainty in Medical Image Segmentation](https://mlsanity.com/paper/1906.04045/) (2019)
- [The Importance of Skip Connections in Biomedical Image Segmentation](https://mlsanity.com/paper/1608.04117/) (2016)
- [Standardized Assessment of Automatic Segmentation of White Matter Hyperintensities and Results of the WMH Segmentation Challenge](https://mlsanity.com/paper/1904.00682/) (2019)
- [Learning in an Uncertain World: Representing Ambiguity Through Multiple Hypotheses](https://mlsanity.com/paper/1612.00197/) (2016)
- [TernausNet: U-Net with VGG11 Encoder Pre-Trained on ImageNet for Image Segmentation](https://mlsanity.com/paper/1801.05746/) (2018)
- [Assessing Reliability and Challenges of Uncertainty Estimations for Medical Image Segmentation](https://mlsanity.com/paper/1907.03338/) (2019)
- [Optimizing the Dice Score and Jaccard Index for Medical Image Segmentation: Theory & Practice](https://mlsanity.com/paper/1911.01685/) (2019)
- [No New-Net](https://mlsanity.com/paper/1809.10483/) (2018)
- [Optimization for Medical Image Segmentation: Theory and Practice when evaluating with Dice Score or Jaccard Index](https://mlsanity.com/paper/2010.13499/) (2020)
- [Analysis and Optimization of Loss Functions for Multiclass, Top-k, and Multilabel Classification](https://mlsanity.com/paper/1612.03663/) (2016)
- [Prediction of final infarct volume from native CT perfusion and treatment parameters using deep learning](https://mlsanity.com/paper/1812.02496/) (2018)
- [Optimization with soft Dice can lead to a volumetric bias](https://mlsanity.com/paper/1911.02278/) (2019)

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

- [A review of uncertainty quantification in medical image analysis: probabilistic and non-probabilistic methods](https://mlsanity.com/paper/2310.06873/) (2023)
- [Jaccard Metric Losses: Optimizing the Jaccard Index with Soft Labels](https://mlsanity.com/paper/2302.05666/) (2023)
- [Dice Semimetric Losses: Optimizing the Dice Score with Soft Labels](https://mlsanity.com/paper/2303.16296/) (2023)
- [Encoding Enhanced Complex CNN for Accurate and Highly Accelerated MRI](https://mlsanity.com/paper/2306.11977/) (2023)
- [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)

## Abstract (arXiv)

The clinical interest is often to measure the volume of a structure, which is typically derived from a segmentation. In order to evaluate and compare segmentation methods, the similarity between a segmentation and a predefined ground truth is measured using popular discrete metrics, such as the Dice score. Recent segmentation methods use a differentiable surrogate metric, such as soft Dice, as part of the loss function during the learning phase. In this work, we first briefly describe how to derive volume estimates from a segmentation that is, potentially, inherently uncertain or ambiguous. This is followed by a theoretical analysis and an experimental validation linking the inherent uncertainty to common loss functions for training CNNs, namely cross-entropy and soft Dice. We find that, even though soft Dice optimization leads to an improved performance with respect to the Dice score and other measures, it may introduce a volume bias for tasks with high inherent uncertainty. These findings indicate some of the method's clinical limitations and suggest doing a closer ad-hoc volume analysis with an optional re-calibration step.