Approximately one-third of the U.S. rail network is owned and operated by shortline railroads (Class II and III), which often face challenges due to marginal infrastructure conditions, limited revenue, and a small workforce. To effectively manage their infrastructure, shortlines need a reliable and cost-effective inventory of their rail tracks. While significant advancements have been made in automatic rail extraction methods, these typically require high-density point cloud datasets with known sensor specifications, which are often unattainable for shortlines due to financial and technical constraints. To overcome these challenges, we propose a novel, configuration-independent coarse-to-fine extraction method designed specifically for low-density LiDAR data. This method leverages high-level geometric features of the rails, making it suitable for point clouds with unknown sensor properties. The integrated framework includes multiple AI methods and signal filter processing methods including slicing, peak-finding, isolation forest, DBSCAN, k-mean clustering, nearest neighbors, HLSF, and gaussian mixture model. We evaluated our framework using a grade-crossing dataset from the Federal Railroad Administration, characterized by a point cloud density of only 293 points/m². Our results demonstrate an average completeness of 96.97%, correctness of 99.71%, and quality of 96.67% across various extraction scenarios. These findings suggest that our method empowers shortlines to effectively extract rail geometry measurements from any available low-density LiDAR data.