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 Weighted Normalized Boundary Loss, 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 BraTS dataset using a standard 3D U-Net and the state-of-the-art nnUNet architectures. These results suggest we can improve segmentation accuracy with our novel loss function.

翻译：在医学影像分割领域，Dice系数和基于豪斯多夫（Hausdorff）的度量是评估深度学习模型成功与否的标准指标。然而，当前的医学影像分割损失函数在训练过程中往往仅关注Dice系数或类似的区域度量指标。因此，使用这类损失函数训练的分割架构可能面临Dice系数精度高但豪斯多夫度量精度低的潜在风险。基于豪斯多夫的度量精度低下可能对肿瘤分割等应用造成困扰——此类基准指标至关重要。例如，高Dice分数伴随显著豪斯多夫误差可能表明预测结果未能检测到小体积肿瘤。我们提出了加权归一化边界损失函数（Weighted Normalized Boundary Loss），这是一种新型损失函数，旨在最小化基于豪斯多夫的度量，其数值性质优于现有方法，并包含针对类别不平衡的权重项。通过在BraTS数据集上使用标准3D U-Net和当前最先进的nnUNet架构进行测试，该损失函数的表现优于其他损失函数。这些结果表明，我们的新型损失函数能够有效提升分割精度。