Multi-modal remote sensing images exhibit complex discrepancies and diverse contents, posing significant challenges for precise matching tasks. While traditional local self-similarity (LSS) descriptors can capture salient structures and contours, their ability to establish accurate feature correspondences remains limited due to these intricate variations. To address this, we propose an enhanced LSS (ELSS) descriptor incorporating graph-based feature selection during descriptor construction. The method models LSS features at different angles within local patches as graph nodes, with edges representing their similarity relationships. By recording correlation ranking indices and generating ranking frequency histograms, we reconstruct LSS to retain only the most relevant features, thereby reducing its dependency on intensity information. Experiments on three public datasets (encompassing four cross-modal scenarios with 250 test images) validate the effectiveness of our enhanced LSS. When combined with four representative feature detectors, ELSS achieves state-of-the-art results: 276.92 for number correct matches (NCM) and 2.08 for root mean square error (RMSE), outperforming six competing methods. These results validate ELSS's effectiveness in mitigating radiometric and geometric variations for robust multimodal image matching.