The loss function is an important factor for the success of machine learning. This paper proposes a new loss function for deep learning-based image co-segmentation. It aims to maximize the inter-class difference between the foreground and the background and at the same time minimize the two intra-class variances. This idea has some similarity to the Fisher criterion in pattern recognition. We further embed an edge weighting strategy into this form of Fisher-like criterion to let the pixels near the foreground edges be paid more attentions in the training process for achieving the finer segmentation. The resultant loss function is called EW-Fisher (Edge-Weighted Fisher). We apply the proposed EW-Fisher loss to image co-segmentation and evaluate it on commonly used datasets. In the experiments, the EW-Fisher stably outperforms the most-widely used cross-entropy loss and Dice loss as well as the recently presented edge agreement loss and Hausdorff distance loss. The comparison results and the ablation studies prove the values of our Fisher-like learning criterion and edge weighting strategy.

损失函数是机器学习成功的重要因素。本文提出了一种新的基于深度学习的图像协同分割损失函数。它旨在最大化前景和背景之间的类间差异，同时最小化两个类内差异。这个想法与模式识别中的Fisher准则有些相似。我们进一步将边缘权重策略嵌入到这种形式的Fisher类准则中，以使前景边缘附近的像素在训练过程中获得更多关注，以实现更精细的分割。最终的损失函数称为EW-Fisher（Edge-Weighted Fisher）。我们将建议的EW-Fisher损失应用于图像共分割，并在常用数据集上对其进行评估。在实验中 EW-Fisher稳定地胜过了最广泛使用的交叉熵损失和Dice损失，以及最近出现的边缘一致性损失和Hausdorff距离损失。比较结果和消融研究证明了我们类似费舍尔学习准则和边缘加权策略的价值。