GeoP2M-Speed: A Geometry-Aware Pixel-to-Metric Transformation Framework for Roadside Monocular Vehicle Speed Estimation

Vehicle speed estimation from roadside monocular videos offers the advantages of low cost, non-contact sensing, and convenient deployment, but its reliability is limited by the lack of explicit physical scale, monocular depth errors, cross-camera scale deviations, and temporal position fluctuations. To address these issues, this paper proposes a geometry-aware Pixel-to-Metric framework. A Geometry-Aware Multi-Scale Residual DETR (GeoMR-DETR) is developed for monocular 3D vehicle detection, together with a Geometry-Guided Scale-Adaptive Residual Refinement (GSAR) mechanism that adaptively fuses multi-scale signed depth residuals for target-level depth refinement. A nonlinear road-geometry-constrained metric mapping then transforms camera-coordinate 3D positions into road-space metric coordinates, followed by association-reliability weighting and robust temporal regression for speed recovery from continuous longitudinal trajectories. GeoMR-DETR achieves AP3DR40 values of 30.32%, 21.63%, and 18.05% on KITTI Easy, Moderate, and Hard, respectively, with consistent improvements on RoPE3D. On BrnoCompSpeed, the framework achieves a mean absolute error of 1.233 km/h, a median error of 0.981 km/h, and a 95th-percentile error of 2.253 km/h, demonstrating reliable vehicle speed estimation using fixed roadside monocular cameras.