# Region-wise Loss for Biomedical Image Segmentation

arXiv: https://arxiv.org/abs/2108.01405 · HTML: https://mlsanity.com/paper/2108.01405/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 49 references that are in the map.
- First posted on arXiv 3 Aug 2021.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [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)
- [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)
- [Deeply-Supervised Nets](https://mlsanity.com/paper/1409.5185/) (2014)
- [Tversky loss function for image segmentation using 3D fully convolutional deep networks](https://mlsanity.com/paper/1706.05721/) (2017)
- [Improved Texture Networks: Maximizing Quality and Diversity in Feed-forward Stylization and Texture Synthesis](https://mlsanity.com/paper/1701.02096/) (2017)
- [Boundary loss for highly unbalanced segmentation](https://mlsanity.com/paper/1812.07032/) (2018)
- [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)
- [The KiTS19 Challenge Data: 300 Kidney Tumor Cases with Clinical Context, CT Semantic Segmentations, and Surgical Outcomes](https://mlsanity.com/paper/1904.00445/) (2019)
- [Reducing the Hausdorff Distance in Medical Image Segmentation with Convolutional Neural Networks](https://mlsanity.com/paper/1904.10030/) (2019)
- [Combo Loss: Handling Input and Output Imbalance in Multi-Organ Segmentation](https://mlsanity.com/paper/1805.02798/) (2018)
- [Optimizing the Dice Score and Jaccard Index for Medical Image Segmentation: Theory & Practice](https://mlsanity.com/paper/1911.01685/) (2019)
- [Active Boundary Loss for Semantic Segmentation](https://mlsanity.com/paper/2102.02696/) (2021)
- [An Exploration of 2D and 3D Deep Learning Techniques for Cardiac MR Image Segmentation](https://mlsanity.com/paper/1709.04496/) (2017)
- [Distance Map Loss Penalty Term for Semantic Segmentation](https://mlsanity.com/paper/1908.03679/) (2019)
- [RV-GAN: Segmenting Retinal Vascular Structure in Fundus Photographs using a Novel Multi-scale Generative Adversarial Network](https://mlsanity.com/paper/2101.00535/) (2021)
- [A distance-based loss for smooth and continuous skin layer segmentation in optoacoustic images](https://mlsanity.com/paper/2007.05324/) (2020)
- [RatLesNetv2: A Fully Convolutional Network for Rodent Brain Lesion Segmentation](https://mlsanity.com/paper/2001.09138/) (2020)

## Built on by (most cited first, 7 of 7)

- [Loss Functions in the Era of Semantic Segmentation: A Survey and Outlook](https://mlsanity.com/paper/2312.05391/) (2023)
- [Enhancing Boundary Segmentation for Topological Accuracy with Skeleton-based Methods](https://mlsanity.com/paper/2404.18539/) (2024)
- [Optimizing against Infeasible Inclusions from Data for Semantic Segmentation through Morphology](https://mlsanity.com/paper/2408.14672/) (2024)
- [TopoMortar: A dataset to evaluate image segmentation methods focused on topology accuracy](https://mlsanity.com/paper/2503.03365/) (2025)
- [Disconnect to Connect: A Data Augmentation Method for Improving Topology Accuracy in Image Segmentation](https://mlsanity.com/paper/2503.05541/) (2025)
- [Towards High-Quality Image Segmentation: Improving Topology Accuracy by Penalizing Neighbor Pixels](https://mlsanity.com/paper/2603.18671/) (2026)
- [Component-Adaptive and Lesion-Level Supervision for Improved Small Structure Segmentation in Brain MRI](https://mlsanity.com/paper/2604.08015/) (2026)

## Abstract (arXiv)

We propose Region-wise (RW) loss for biomedical image segmentation. Region-wise loss is versatile, can simultaneously account for class imbalance and pixel importance, and it can be easily implemented as the pixel-wise multiplication between the softmax output and a RW map. We show that, under the proposed RW loss framework, certain loss functions, such as Active Contour and Boundary loss, can be reformulated similarly with appropriate RW maps, thus revealing their underlying similarities and a new perspective to understand these loss functions. We investigate the observed optimization instability caused by certain RW maps, such as Boundary loss distance maps, and we introduce a mathematically-grounded principle to avoid such instability. This principle provides excellent adaptability to any dataset and practically ensures convergence without extra regularization terms or optimization tricks. Following this principle, we propose a simple version of boundary distance maps called rectified Region-wise (RRW) maps that, as we demonstrate in our experiments, achieve state-of-the-art performance with similar or better Dice coefficients and Hausdorff distances than Dice, Focal, weighted Cross entropy, and Boundary losses in three distinct segmentation tasks. We quantify the optimization instability provided by Boundary loss distance maps, and we empirically show that our RRW maps are stable to optimize. The code to run all our experiments is publicly available at: https://github.com/jmlipman/RegionWiseLoss.