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• A cascade framework is proposed for automatic lung segmentation in CXRs. • An adaptive closed polyline searching method is used to obtain data sequence. • An improved machine learning model is proposed to express a mathematical model. • The explainability-guided mathematical model is used to denote lung contour. • Performance of the proposed method is evaluated on public multi-site datasets. Large variations in anatomical shape and size, too much overlap between anatomical structures, and inconsistent anatomical shapes make accurate lung segmentation in chest x-rays (CXR) a challenging problem. In this paper, we propose an automatic method called A-LugSeg that consists of two subnetworks for lung segmentation in CXRs. The first is a segmentation subnetwork based on a deep learning model (i.e., Mask-RCNN), which completes a coarse segmentation for each input CXR image. The second is a refinement subnetwork designed to optimize the coarse segmentation result by combining an improved closed principal curve method and an enhanced machine learning, where the lung contour's explainability-guided mathematical model is expressed by the machine learning's parameters. The performance of the proposed method is evaluated on three public datasets, namely the ShenZhen hospital Chest X-ray dataset (SZCX), Japanese Society of Radiological Technology dataset (JSRT), and Montgomery County chest x-ray dataset (MC), which contain the 662 CXRs, 247 CXRs, and 138 CXRs, respectively. We used different datasets for training/validation (SZCX) and testing (SZCX/JSRT/MC). Furthermore, we used six evaluation metrics to evaluate the performance of our proposed method, including Dice Similarity Coefficient (DSC), Jaccard Similarity Coefficient (Ω), Accuracy (ACC), Precision, Sensitivity, and Specificity. The obtained results (DSC = 0.973, Ω = 0.958, ACC = 0.972, and p -value for DSC < 0.001) for JSRT, (DSC = 0.971, Ω = 0.955, ACC = 0.97, and p -value for DSC < 0.001) for MC, (DSC = 0.972, Ω = 0.956, and ACC = 0.97) for hybrid datasets (JSRT + MC), and (Precision, Sensitivity, and Specificity are higher than 0.98) show the superior performance of the proposed dual subnetwork segmentation algorithm compared to the existing state of the art approaches. [ABSTRACT FROM AUTHOR]