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Deep Convolutional Neural Networks have proven effective in solving the task of semantic segmentation. However, their efficiency heavily relies on the pixel-level annotations that are expensive to get and often require domain expertise, especially in medical imaging. Weakly supervised semantic segmentation helps to overcome these issues and also provides explainable deep learning models. In this paper, we propose a novel approach to the semantic segmentation of medical chest X-ray images with only image-level class labels as supervision. We improve the disease localization accuracy by combining three approaches as consecutive steps. First, we generate pseudo segmentation labels of abnormal regions in the training images through a supervised classification model enhanced with a regularization procedure. The obtained activation maps are then post-processed and propagated into a second classification model-Inter-pixel Relation Network, which improves the boundaries between different object classes. Finally, the resulting pseudo-labels are used to train a proposed fully supervised segmentation model. We analyze the robustness of the presented method and test its performance on two distinct datasets: PASCAL VOC 2012 and SIIM-ACR Pneumothorax. We achieve significant results in the segmentation on both datasets using only image-level annotations. We show that this approach is applicable to chest X-rays for detecting an anomalous volume of air in the pleural space between the lung and the chest wall. Our code has been made publicly available.