Anatomical landmark correspondences in medical images can provide additional guidance information for the alignment of two images, which, in turn, is crucial for many medical applications. However, manual landmark annotation is labor-intensive. Therefore, we propose an end-to-end deep learning approach to automatically detect landmark correspondences in pairs of two-dimensional (2D) images. Our approach consists of a Siamese neural network, which is trained to identify salient locations in images as landmarks and predict matching probabilities for landmark pairs from two different images. We trained our approach on 2D transverse slices from 168 lower abdominal Computed Tomography (CT) scans. We tested the approach on 22,206 pairs of 2D slices with varying levels of intensity, affine, and elastic transformations. The proposed approach finds an average of 639, 466, and 370 landmark matches per image pair for intensity, affine, and elastic transformations, respectively, with spatial matching errors of at most 1 mm. Further, more than 99% of the landmark pairs are within a spatial matching error of 2 mm, 4 mm, and 8 mm for image pairs with intensity, affine, and elastic transformations, respectively. To investigate the utility of our developed approach in a clinical setting, we also tested our approach on pairs of transverse slices selected from follow-up CT scans of three patients. Visual inspection of the results revealed landmark matches in both bony anatomical regions as well as in soft tissues lacking prominent intensity gradients.