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

Adrian Celaya, Beatrice Riviere, David Fuentes

TL;DR

The paper addresses the mismatch between Dice-centric training losses and Hausdorff-distance-based evaluation in medical image segmentation. It introduces Generalized Surface Loss (GSL), a bounded, normalized boundary-focused loss with precomputed class weights and flexible scheduling to combine with a region-based loss such as Dice-CE. Empirical results on LiTS and BraTS show that GSL reduces HD-based metrics (HD95 and ASD) while preserving Dice, using the nnUNet framework. This approach offers a practical, robust route to improve clinically critical boundary accuracy in tumor and organ segmentation tasks.

Abstract

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.

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

TL;DR

The paper addresses the mismatch between Dice-centric training losses and Hausdorff-distance-based evaluation in medical image segmentation. It introduces Generalized Surface Loss (GSL), a bounded, normalized boundary-focused loss with precomputed class weights and flexible scheduling to combine with a region-based loss such as Dice-CE. Empirical results on LiTS and BraTS show that GSL reduces HD-based metrics (HD95 and ASD) while preserving Dice, using the nnUNet framework. This approach offers a practical, robust route to improve clinically critical boundary accuracy in tumor and organ segmentation tasks.

Abstract

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.
Paper Structure (17 sections, 15 equations, 4 figures, 2 tables)

This paper contains 17 sections, 15 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Previous Work
  3. Region-Based Losses
  4. Dice Loss
  5. Generalized Dice Loss
  6. Boundary-Based Losses
  7. Hausdorff Loss
  8. Boundary Loss
  9. Materials and Methods
  10. Generalized Surface Loss
  11. Network Architecture
  12. Data
  13. Training and Testing
  14. Results
  15. Discussion
  16. ...and 2 more sections

Figures (4)

  • Figure 1: Illustration of the Hausdorff distance between two sets of points $X$ and $Y$.
  • Figure 2: (Left) Example segmentation. (Right) DTM for example segmentation. Here, the values in the DTM are positive on the exterior, zero on the boundary, or negative in the object's interior.
  • Figure 3: From left to right, ground truth and predictions from the nnUNet architecture trained on LiTS data with Dice-CE, BL, and GSL functions for a spectrum of easier to more difficult test cases. Here, we see that, even for more difficult cases, the GSL produces visually superior predictions than the Dice-CE and BL functions.
  • Figure 4: From left to right, ground truth and predictions from the nnUNet architecture trained on BraTS data with Dice-CE, BL, and GSL functions for a spectrum of easier to more difficult test cases. Here, we see that, even for more difficult cases, the GSL produces visually superior predictions than the Dice-CE and BL functions.