Self-supervised visual assessment of railway track curvature via homography learning based on projective curvilinear geometry model

Railway track curvature monitoring is crucial for ensuring operational safety and passenger comfort. As a robust complement to the single-point physical sensor approaches, vision-based methods have recently gained increasing adoption. However, existing approaches frequently neglect the systematic exploitation of railway ego-vision geometry in two critical aspects: (1) the rail-camera kinematic coupling that relates the rail appearance in camera’s view and the track curvature during curvilinear motion, and (2) the potential of self-supervised learning to overcome annotation scarcity in this domain. This geometric oversight limits their accuracy in real-world dynamic scenarios. To address these gaps, this study proposes a novel vision-based framework that systematically exploits the railway ego vision geometry. Our methodology comprises two key innovations: First, a projective curvilinear geometry model that mathematically relates the ground-planes-induced homography to actual track curvature, thereby establishing a mapping from curvature and its variation to rail imaging curves. Second, a self-supervised curvature prediction network trained using automatically generated labels from our geometric model, eliminating the need for manual curve annotations. The self-supervision is achieved through a cyclic consistency mechanism between predicted curvatures and reprojected image features. Experimental validation using real-world railway footage demonstrates significant improvements: Our method reduces the average root mean squared error by 23.31% compared to state-of-the-art vision-based curvature estimation methods. These results underscore the effectiveness of geometry-aware computer vision for railway geometry monitoring • A homography model incorporates curvature-constrained curvilinear motion in railway. • Flow trajectory of expansion (FTOE) models railway geometry in vehicle vision. • The envelope of FTOE determined by rail curvature simplifies track curve detection. • A neural network learns to predict rail curvature using self-supervised labels.