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In this paper we propose an automatic trajectory data reconciliation to correct common errors in vision-based vehicle trajectory data. Given "raw" vehicle detection and tracking information from automatic video processing algorithms, we propose a pipeline including (a) an online data association algorithm to match fragments that describe the same object (vehicle), which is formulated as a min-cost network circulation problem of a graph, and (b) a one-step trajectory rectification procedure formulated as a quadratic program to enhance raw detection data. The pipeline leverages vehicle dynamics and physical constraints to associate tracked objects when they become fragmented, remove measurement noises and outliers and impute missing data due to fragmentations. We assess the capability of the proposed two-step pipeline to reconstruct three benchmarking datasets: (1) a microsimulation dataset that is artificially downgraded to replicate upstream errors, (2) a 15-min NGSIM data that is manually perturbed, and (3) tracking data consists of 3 scenes from collections of video data recorded from 16-17 cameras on a section of the I-24 MOTION system, and compare with the corresponding manually-labeled ground truth vehicle bounding boxes. All of the experiments show that the reconciled trajectories improve the accuracy on all the tested input data for a wide range of measures. Lastly, we show the design of a software architecture that is currently deployed on the full-scale I-24 MOTION system consisting of 276 cameras that covers 4.2 miles of I-24. We demonstrate the scalability of the proposed reconciliation pipeline to process high-volume data on a daily basis.