Skyline plays a pivotal role in mountainous visual geo-localization and localization/navigation of planetary rovers/UAVs and virtual/augmented reality applications. We present a novel mountainous skyline detection approach where we adapt a shallow learning approach to learn a set of filters to discriminate between edges belonging to sky-mountain boundary and others coming from different regions. Unlike earlier approaches, which either rely on extraction of explicit feature descriptors and their classification, or fine-tuning general scene parsing deep networks for sky segmentation, our approach learns linear filters based on local structure analysis. At test time, for every candidate edge pixel, a single filter is chosen from the set of learned filters based on pixel's structure tensor, and then applied to the patch around it. We then employ dynamic programming to solve the shortest path problem for the resultant multistage graph to get the sky-mountain boundary. The proposed approach is computationally faster than earlier methods while providing comparable performance and is more suitable for resource constrained platforms e.g., mobile devices, planetary rovers and UAVs. We compare our proposed approach against earlier skyline detection methods using four different data sets. Our code is available at \url{https://github.com/TouqeerAhmad/skyline_detection}.