Encoder-decoder networks become a popular choice for various medical image segmentation tasks. When they are trained with a standard loss function, these networks are not explicitly enforced to preserve the shape integrity of an object in an image. However, this ability of the network is important to obtain more accurate results, especially when there is a low-contrast difference between the object and its surroundings. In response to this issue, this work introduces a new shape-aware loss function, which we name FourierLoss. This loss function relies on quantifying the shape dissimilarity between the ground truth and the predicted segmentation maps through the Fourier descriptors calculated on their objects, and penalizing this dissimilarity in network training. Different than the previous studies, FourierLoss offers an adaptive loss function with trainable hyperparameters that control the importance of the level of the shape details that the network is enforced to learn in the training process. This control is achieved by the proposed adaptive loss update mechanism, which end-to-end learns the hyperparameters simultaneously with the network weights by backpropagation. As a result of using this mechanism, the network can dynamically change its attention from learning the general outline of an object to learning the details of its contour points, or vice versa, in different training epochs. Working on 2879 computed tomography images of 93 subjects, our experiments revealed that the proposed adaptive shape-aware loss function led to statistically significantly better results for liver segmentation, compared to its counterparts.

翻译：编码器-解码器网络已成为多种医学图像分割任务的流行选择。当使用标准损失函数训练时，这些网络并未被明确强制保持图像中对象的形状完整性。然而，网络的这一能力对于获得更准确的结果至关重要，尤其是在对象与背景之间对比度较低的情况下。为解决这一问题，本文提出了一种新的形状感知损失函数，我们称之为FourierLoss。该损失函数通过计算对象上的傅里叶描述子来量化真实分割图与预测分割图之间的形状差异性，并在网络训练中惩罚这种差异性。与以往研究不同，FourierLoss提供了一种具有可训练超参数的自适应损失函数，这些超参数控制网络在训练过程中被强制学习的形状细节重要程度。这种控制通过所提出的自适应损失更新机制实现，该机制通过反向传播与网络权重同时端到端地学习超参数。使用该机制的结果是，网络可以在不同训练周期内动态地将注意力从学习对象的整体轮廓转移到学习其轮廓点的细节，或反之。基于对93名受试者的2879张计算机断层扫描图像进行的实验表明，与同类方法相比，所提出的自适应形状感知损失函数在肝脏分割任务中取得了统计上显著更优的结果。