EW-Fisher: A Novel Loss Function for Deep Learning-Based Image Co-Segmentation

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.