The precision and efficiency of rail inspection are of vital importance to the operation and safety of railway systems. However, because of vibrations that occur in the rail inspection vehicle and installation error of the line laser sensor, the collected rail profile is distorted. As a result, the accuracy and robustness of conventional registration and inspection methods cannot be guaranteed. In this paper, an accurate and robust calibration method for measuring rail profile distortion is proposed. In this study, the impact of vibration on the rail profile, which was obtained with a laser sensor, was analyzed. Then, the collected rail profile was divided into two segments according to the actual condition where only the upper part of the rail was subjected to wear. An accurate and robust reweighted-scaling iterative closest point algorithm was proposed to calibrate the distorted rail profile, and the upper and lower boundaries of the scale ratio were used as constraints to solve the registration problem effectively and efficiently. Finally, the Hausdorff distance method was introduced to clearly visualize the rectified rail profile and wear. The experimental results demonstrated that the proposed method can realize the affine transformation of the distorted rail profile with a high precision and robustness. Additionally, it can achieve an online dynamic calibration and inspection of the rail by comparing the data with the conventional iterative closest point, scaling iterative closest point, and Calipri.

It is a challenge for the dynamic inspection of railway route for freight car transporting cargo that out-of-gauge. One possible way is using the inspection frame installed in the inspection train to simulate the whole procedure for cargo transportation, which costs a lot of manpower and material resources as well as time. To overcome the above problem, this paper proposes an augmented reality (AR) based dynamic inspection method for visualized railway routing of freight car with out-of-gauge. First, the envelope model of the dynamic moving train with out-of-gauge cargo is generated by using the orbital spectrum of the railway, and the envelope model is matched with a piece of homemade calibration equipment located on the position of the railway that needs to be inspected. Then, the structure from motion (SFM) algorithm is used to reconstruct the environment where the virtual envelope model occludes the buildings or equipment along the railway. Finally, the distance function is adopted to calculate the distance between the obstacle and the envelope of the freight car with out-of-gauge, determining whether the freight car can pass a certain line. The experimental results show that the proposed method performs well for the route selection of out-of-gauge cargo transportation with low cost, high precision, and high efficiency. Moreover, the digital data of the environments along the railway and the envelope of the freight car can be reused, which will increase the digitalization and intelligence for route selection of out-of-gauge cargo transportation.