# Dual Attention Equivariant Network for Weakly Supervised Semantic Segmentation
## 1 Introduction  
Semantic segmentation is a fundamental and critical task in the field of computer vision [1], and its purpose is to make accurate pixel-level classification prediction of images. With the rapid development of deep learning in recent years, the semantic segmentation model has made great progress and has been widely applied in fields of intelligent driving, intelligent security, satellite remote sensing image, medical image analysis, and so on [2, 3, 4, 5]. However, fully supervised semantic segmentation requires manual labeling for each pixel, which is not only expensive but also time-consuming.  
Recently, many studies have adopted weakly supervised semantic segmentation to address the problem of manual pixel-by-pixel annotation by using weak supervision such as boundary boxes [6, 7, 8], doodling [9, 10], and image-level classification labels [11, 12, 13, 14, 15]. Among these methods, weakly supervised semantic segmentation using image-level classification labels has garnered significant attention from academia and industry due to the following reasons: (1) by providing high-level semantic information and semantic categories of images, it is easy to interpret and understand the semantic segmentation results;(2) it can be applied into large-scale semantic segmentation scenarios by only using a small amount of annotation information; (3) it highly correlates with image-level labels and can result in more intuitive outcomes. Therefore, we focus on weakly supervised semantic segmentation based on image-level classification labels in this paper.  
Many weakly supervised semantic segmentation based on image-level classification labels use CAM to generate initial pseudo-labels [16, 17, 18, 19, 20]. However, CAM utilizes global average pooling to convert feature maps into class activation values and will cause the loss of some pixel-level spatial information. As a result, the generated CAM fails to accurately capture the boundaries and details of the target objects. Some work [21, 22] has been carried out on the improvement of CAM by taking account of the cross-image relationship, the equivariance across various transformed images, and pixel correlation. However, these works mainly focus on discriminative regions provided by the classification network, and do not fully consider correlation between features in the channel and spatial dimensions; this may mean that they overlook some important features and lead to the underactivation of target objects.  
Motivated by the above, in this paper, we investigate the improvement in the accuracy of CAM by considering the correlation between different feature maps in the channel and spatial dimensions provided by classification networks. Specifically, we propose a DAEN model to improve CAM accuracy by using a channel-spatial attention module that accurately extracts categorical features from both spatial and channel dimensions, and a pixel-correlation module that calculates the normalized feature similarity between pixels in different feature maps. To further improve CAM, DAEN also carries out equivariance regularization to the transformed images to generate additional supervision. The contribution of DAEN can be summarized as follows:  
* We propose a dual attention equivariant network model that combines the channel-spatial attention module, equivariance regularization, and pixel-correlation module to effectively improve the accuracy of CAM by considering both channel and spatial information of different feature maps.
* We design a channel-spatial attention module for DAEN to extract accurately features of target objects by considering the correlation among feature maps in different channels.
* Extensive experiments on PASCAL VOC 2012 and LUAD-HistoSeg datasets demonstrate that our proposed model outperforms existing state-of-the-art models for image-level weakly supervised semantic segmentation.