# A Generalized Surface Loss for Reducing the Hausdorff Distance in Medical Imaging Segmentation

arXiv: https://arxiv.org/abs/2302.03868 · HTML: https://mlsanity.com/paper/2302.03868/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 50 references that are in the map.
- First posted on arXiv 8 Feb 2023.

## Builds on (most cited first, 25 of 25)

- [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)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [The Medical Segmentation Decathlon](https://mlsanity.com/paper/2106.05735/) (2021)
- [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)
- [The Liver Tumor Segmentation Benchmark (LiTS)](https://mlsanity.com/paper/1901.04056/) (2019)
- [MONAI: An open-source framework for deep learning in healthcare](https://mlsanity.com/paper/2211.02701/) (2022)
- [Normalized Loss Functions for Deep Learning with Noisy Labels](https://mlsanity.com/paper/2006.13554/) (2020)
- [Tversky loss function for image segmentation using 3D fully convolutional deep networks](https://mlsanity.com/paper/1706.05721/) (2017)
- [A survey of loss functions for semantic segmentation](https://mlsanity.com/paper/2006.14822/) (2020)
- [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)
- [A Novel Focal Tversky loss function with improved Attention U-Net for lesion segmentation](https://mlsanity.com/paper/1810.07842/) (2018)
- [Reducing the Hausdorff Distance in Medical Image Segmentation with Convolutional Neural Networks](https://mlsanity.com/paper/1904.10030/) (2019)
- [nnU-Net for Brain Tumor Segmentation](https://mlsanity.com/paper/2011.00848/) (2020)
- [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)
- [AnatomyNet: Deep Learning for Fast and Fully Automated Whole-volume Segmentation of Head and Neck Anatomy](https://mlsanity.com/paper/1808.05238/) (2018)
- [3D Segmentation with Exponential Logarithmic Loss for Highly Unbalanced Object Sizes](https://mlsanity.com/paper/1809.00076/) (2018)
- [Data augmentation and loss normalization for deep noise suppression](https://mlsanity.com/paper/2008.06412/) (2020)
- [Do We Really Need Dice? The Hidden Region-Size Biases of Segmentation Losses](https://mlsanity.com/paper/2104.08717/) (2021)
- [PocketNet: A Smaller Neural Network for Medical Image Analysis](https://mlsanity.com/paper/2104.10745/) (2021)
- [Reduce Noise in Computed Tomography Image using Adaptive Gaussian Filter](https://mlsanity.com/paper/1902.05985/) (2019)

## Built on by (most cited first, 13 of 13)

- [The TopCoW Challenge -- Topology-Aware Circle of Willis Segmentation for CT and MR Angiography](https://mlsanity.com/paper/2312.17670/) (2023)
- [Anomaly Detection and Generation with Diffusion Models: A Survey](https://mlsanity.com/paper/2506.09368/) (2025)
- [MIST: A Simple and Scalable End-To-End 3D Medical Imaging Segmentation Framework](https://mlsanity.com/paper/2407.21343/) (2024)
- [A Multimodal Feature Distillation with Mamba-Transformer Network for Brain Tumor Segmentation with Incomplete Modalities](https://mlsanity.com/paper/2404.14019/) (2024)
- [Model Agnostic Preference Optimization for Medical Image Segmentation](https://mlsanity.com/paper/2512.15009/) (2025)
- [TransGUNet: Transformer Meets Graph-based Skip Connection for Medical Image Segmentation](https://mlsanity.com/paper/2502.09931/) (2025)
- [ROIsGAN: A Region Guided Generative Adversarial Framework for Murine Hippocampal Subregion Segmentation](https://mlsanity.com/paper/2505.10687/) (2025)
- [Dual Teacher-Student Learning for Semi-supervised Medical Image Segmentation](https://mlsanity.com/paper/2505.11018/) (2025)
- [Pre- and Post-Treatment Glioma Segmentation with the Medical Imaging Segmentation Toolkit](https://mlsanity.com/paper/2507.19626/) (2025)
- [XAG-Net: A Cross-Slice Attention and Skip Gating Network for 2.5D Femur MRI Segmentation](https://mlsanity.com/paper/2508.06258/) (2025)
- [AD-SAM: Adapting the Segment Anything Model for Semantic Segmentation in Autonomous Driving](https://mlsanity.com/paper/2510.27047/) (2025)
- [FALCON: Few-Shot Adversarial Learning for Cross-Domain Medical Image Segmentation](https://mlsanity.com/paper/2601.01687/) (2026)
- [Mamba-driven MRI-to-CT Synthesis for MRI-only Radiotherapy Planning](https://mlsanity.com/paper/2603.23295/) (2026)

## Abstract (arXiv)

Within medical imaging segmentation, the Dice coefficient and Hausdorff-based metrics are standard measures of success for deep learning models. However, modern loss functions for medical image segmentation often only consider the Dice coefficient or similar region-based metrics during training. As a result, segmentation architectures trained over such loss functions run the risk of achieving high accuracy for the Dice coefficient but low accuracy for Hausdorff-based metrics. Low accuracy on Hausdorff-based metrics can be problematic for applications such as tumor segmentation, where such benchmarks are crucial. For example, high Dice scores accompanied by significant Hausdorff errors could indicate that the predictions fail to detect small tumors. We propose the Generalized Surface Loss function, a novel loss function to minimize Hausdorff-based metrics with more desirable numerical properties than current methods and with weighting terms for class imbalance. Our loss function outperforms other losses when tested on the LiTS and BraTS datasets using the state-of-the-art nnUNet architecture. These results suggest we can improve medical imaging segmentation accuracy with our novel loss function.