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In this study, we investigate the detection of cardiomegaly on frontal chest radiographs through two alternative deep-learning approaches - via anatomical segmentation and via image-level classification. We used the publicly available ChestX-ray14 dataset, and obtained heart and lung segmentation annotations for 778 chest radiographs for the development of the segmentation-based approach. The classification-based method was trained with 65k standard chest radiographs with image-level labels. For both approaches, the best models were found through hyperparameter searches where architectural, learning, and regularization related parameters were optimized systematically. The resulting models were tested on a set of 367 held-out images for which cardiomegaly annotations were hand-labeled by two independent expert radiologists. Sensitivity, specificity, positive predictive value, negative predictive value, and area under the receiver operating characteristic curve (AUC) were calculated. The performance of the segmentation-based system with an AUC of 0.977 is significantly better for classifying cardiomegaly than the classification-based model which achieved an AUC of 0.941. Only the segmentation-based model achieved comparable performance to an independent expert reader (AUC of 0.978). We conclude that the segmentation-based model requires 100 times fewer annotated chest radiographs to achieve a substantially better performance, while also producing more interpretable results.