# Robust Analysis and Laser Stripe Center Extraction for Rail Images
## 1 Introduction  
With the rapid development of high-speed railway systems, railway profile detection has become an important method by which to measure rail wear to guarantee the safety of railway transportation. Rather than the use of a manual detection method, line-structured light measurement is extensively applied due to its advantages of being non-contact, fast, and highly accurate [1; 2; 3]. A line-structured light sensor containing a camera and one laser projector is mounted on the inside of the rail. The sensor projects a laser onto the surface of the rail, and the camera then captures an image of the distorted laser stripe modulated by the rail surface. The architecture of this system is shown in Figure 1. Three-dimensional (3D) information about the profile of the rail can be obtained based on the laser stripe center and the calibrated results [4; 5; 6; 7]. Therefore, the light stripe center extraction of the rail image is a significant step in the measurement of rail wear. Figure 1: The architecture of the line-structured light sensor. The process of light stripe center extraction in rail wear measurement systems based on laser triangulation techniques is difficult. Different from the under-controlled conditions of the surrounding light, many factors, such as variable luminance and uneven surfaces, modulate the shape of the light stripe on a rail image captured in outdoor environments, and show up as image noise. While most noise can be filtered with the assistance of interferential filters, it usually cannot be removed completely, as shown in Figure 2. The light stripe in the rail image may be of different widths and luminance, and while some regions of the stripe appear dim, other regions are already saturated. Moreover, in some regions, the cross-sectional distribution of the light stripe no longer conforms to the Gaussian distribution. This results in the difficulty of light stripe center extraction in complex environments, and most traditional light stripe extraction methods cannot be directly applied to rail images. Most existing light stripe extraction methods are sensitive to noise, and therefore cannot work well in outdoor environments. The Center of Mass method detects the center-points in each column or row, whereas the correlations between columns and rows are not taken into account; thus, this method is sensitive to image noise. The Steger method [8; 9] is most commonly used for light stripe extraction because of its high accuracy; however, it is time-consuming, and it is difficult to select a proper scale factor when the widths of the light stripe vary over a large range. In addition, the Gaussian distribution is normally thought to be satisfied on the cross-section, which is impractical for rail images. [PERSON] et al. [10] evaluated the performances of five methods, including Gaussian approximation, the Center of Mass method, parabolic estimation, the Blais and Rioux detector, and linear approximation. The results showed that their accuracies were all on the sub-pixel level. Other works, such as that by [PERSON] et al. [11], have revealed that the Center of Mass method can be conducted in real time with strong robustness. In addition to these traditional methods, some novel robust laser stripe extraction methods have been proposed. In the work by [PERSON] et al. [12], a high-dynamic-range imaging system was constructed to measure an object partially highlighted or partially reflected in a specular manner; however, this method requires a sophisticated hardware setup. In the method developed by [PERSON] et al. [13], center of mass is used in rows only if the maximum grayscale of pixels in the row is larger than the adjacent background. Then, a laser peak linking process is applied to fill in the gaps generated in the previous step. In the method proposed by [PERSON] et al. [14], preprocessing, including self-adaptive convolution and threshold segmentation, is adopted to reduce the influence of noise before center of mass is determined.