The Hausdorff Distance (HD) is widely used in evaluating medical image segmentation methods. However, existing segmentation methods do not attempt to reduce HD directly. In this paper, we present novel loss functions for training convolutional neural network (CNN)-based segmentation methods with the goal of reducing HD directly. We propose three methods to estimate HD from the segmentation probability map produced by a CNN. One method makes use of the distance transform of the segmentation boundary. Another method is based on applying morphological erosion on the difference between the true and estimated segmentation maps. The third method works by applying circular/spherical convolution kernels of different radii on the segmentation probability maps. Based on these three methods for estimating HD, we suggest three loss functions that can be used for training to reduce HD. We use these loss functions to train CNNs for segmentation of the prostate, liver, and pancreas in ultrasound, magnetic resonance, and computed tomography images and compare the results with commonly-used loss functions. Our results show that the proposed loss functions can lead to approximately 18-45 % reduction in HD without degrading other segmentation performance criteria such as the Dice similarity coefficient. The proposed loss functions can be used for training medical image segmentation methods in order to reduce the large segmentation errors.

本文介绍使用不同的方法估算分割质量，提出三种新的损失函数，以使训练卷积神经网络(CNN)的分割方法能直接减少 Hausdorff 距离 (HD)，这三种方法分别是基于分割边界的距离变换、真实和估计分割图的形态学腐蚀，以及在不同半径的圆形/球形卷积核上应用分割概率图，结果表明，使用这些损失函数可以使 HD 减少约 18-45% 而不会降低其他分割性能。

卷积神经网络降低医学图像分割中的Hausdorff距离