This paper details the development of a geometrical-based displacement extraction framework capable of automatically extracting critical infrastructure measurements in one sequence. The framework is a novel rail viaduct bearing inspection pipeline implemented on BINOv2: Bearing Inspector for Narrow-space Observation Version 2. BINOv2 is a tethered custom Unmanned Aerial Vehicle (UAV) system utilized to supplant labor-intensive pipelines and enhance inspection accuracy of infrastructure conditions in confined remote locations. The algorithm accepts stereoscopic images taken from a single monocular camera on a bi-directional cascaded linear actuator system in a rack-and-pinion configuration. A point cloud model generated from the image sets then runs through a hierarchical neural network for 3D segmentation to extract targeted regions of interest. Our training pipeline generates and forms the full model's training data set using only a small sample of real point clouds. The point cloud generated is inadequate to form the full bearing geometry profile. Therefore, the proposed framework projects best-fit circles based on the point cloud curvature to form the full bearing geometry profile so that the required displacement measurement is available for extraction. Several experiments were conducted on a mock-up and actual operational site to validate the proposed framework's accuracy, its robustness and comparison with other state-of-the-art alternatives.