Weighted and Mumford-Shah losses for weakly supervised semantic segmentation

In weakly supervised semantic segmentation (WSSS) tasks, the noise in pseudo labels poses a significant challenge to the training of segmentation networks. However, the widely used cross-entropy loss, which only considers individual pixel information in the images, is insufficient to address this issue. In order to effectively train segmentation networks using noisy labels, we propose a Weakly Supervised Semantic Segmentation method (WMS) based on weighted loss and Mumford-Shah loss. Firstly, we introduce a weighted loss with confidence weights for pseudo labels. This loss assigns weights to each pseudo label by incorporating a confidence indicator, enhancing the network's ability to resist noise interference. Additionally, we propose a Mumford-Shah (MS) loss based on variational segmentation. By leveraging the similarity between pixels in the original image, this loss introduces additional noise-free self-supervised information to assist in the training of the segmentation network, further suppressing the interference caused by noisy labels. Extensive experiments on the PASCAL VOC 2012 dataset demonstrate that the proposed method significantly improves WSSS performance.