Many loss functions have been derived from cross-entropy loss functions such as large-margin softmax loss and focal loss. The large-margin softmax loss makes the classification more rigorous and prevents overfitting. The focal loss alleviates class imbalance in object detection by down-weighting the loss of well-classified examples. Recent research has shown that these two loss functions derived from cross entropy have valuable applications in the field of image segmentation. However, to the best of our knowledge, there is no unified formulation that combines these two loss functions so that they can not only be transformed mutually, but can also be used to simultaneously address class imbalance and overfitting. To this end, we subdivide the entropy-based loss into the regularizer-based entropy loss and the focal-based entropy loss, and propose a novel optimized hybrid focal loss to handle extreme class imbalance and prevent overfitting for crack segmentation. We have evaluated our proposal in comparison with three crack segmentation datasets (DeepCrack-DB, CRACK500 and our private PanelCrack dataset). Our experiments demonstrate that the focal margin component can significantly increase the IoU of cracks by 0.43 on DeepCrack-DB and 0.44 on our PanelCrack dataset, respectively.

翻译：许多损失函数源自交叉熵损失，例如大间隔软最大化损失和焦点损失。大间隔软最大化损失使分类更加严格并防止过拟合。焦点损失通过降低分类良好样本的权重来缓解目标检测中的类别不平衡。最新研究表明，这两种源自交叉熵的损失函数在图像分割领域具有重要应用。然而，据我们所知，目前尚无统一的公式能够将这两种损失函数结合，使其既可相互转换，又能同时解决类别不平衡和过拟合问题。为此，我们将基于熵的损失细分为基于正则项的熵损失和基于焦点的熵损失，并提出一种新颖的优化混合焦点损失，以处理裂缝分割中的极端类别不平衡并防止过拟合。我们在三个裂缝分割数据集（DeepCrack-DB、CRACK500 及我们的私有 PanelCrack 数据集）上评估了所提方法。实验表明，焦点间隔组件在 DeepCrack-DB 和 PanelCrack 数据集上分别将裂缝的交并比显著提高了 0.43 和 0.44。