## 1 Introduction  
With the rapid development of Chinese high-speed railway construction and the continuous expansion of the international market, the demand for China Railway Track System (CRTSIII) track slabs with completely independent intellectual property rights continues to grow rapidly. The dimensional accuracy directly affects the stability, smoothness of the track and the safety of the train operation. Therefore, it is necessary to carry out a strict inspection on the external dimensions of the track slab before the delivery, and the higher requirements should also be put forward for the detection efficiency and detection accuracy of the track slab. At present, the detection of the deviation of the track slab external dimensions is mainly based on the manual inspection and contact-type measurement devices. It takes 40 min to detect a track slab, and the detection efficiency and repeatability of which are rather low, which cannot bring greater benefits to actual production [1]. With the advancement of computer science and information technology, the rapid development of industrial photography and machine vision, 3D scanning technology has become a widely used measurement technology with its fast scanning speed, non-contact, and high measurement accuracy [2; 3; 4; 5]. Compared with other non-contact measurement methods [6; 7; 8; 9], 3D scanning technology has the advantages of convenient integration with the computer, real-time processing and high flexibility of 3D reconstruction. It is widely applied in various fields, especially in industrial measurement, and it has great prospects. The data acquired by the 3D scanning system is point cloud data with three-dimensional information, which are usually defined by \(X\), \(Y\), and \(Z\) coordinates, and are often used to represent the external surface information of the object being scanned. In the last decade, capture technologies that can generate 3D point cloud data are becoming mature and usable for more accurate point cloud data acquisition. As point cloud data acquisition technology is gradually maturing, the demand for 3D scanning technology in workpiece positioning and inspection, vehicle detection, and aircraft and shipbuilding manufacturing in industrial measurement is also increasing. [PERSON] [10] reported an automatic welding robot path planning system based on 3D vision technology and the successfully applied 3D scanning technology to the measurement and welding of complex geometric workpieces. [PERSON] et al. [11] studied an edge and corner detection method for unstructured 3D point clouds for unorganized point clouds and its application in robot welding. [PERSON] and [PERSON] et al. [12] presented a systematic and practical approach for dimensional and surface quality assessment of precast concrete elements using building information modeling (BIM) and 3D laser scanning technology, and the approach has the potential to produce an automated and reliable dimensional and surface quality assessment for precast concrete elements. [PERSON] et al. [13] investigated a new solution to the high-quality 3D reverse modeling problem of complex surfaces for fine workpieces by using a laser line-scanning sensor. The surface of the measured object was reconstructed completely and accurately, and the measurement accuracy of the workpiece reconstruction was relatively high. [PERSON] and [PERSON] [14] used a 3D scanner to detect the surface of the car and proposed a new algorithm for various defects in the context of industrial surface inspection of free-form metallic pieces of cars. [PERSON] and [PERSON] et al. [15] used three-dimensional scanning technology to automatically detect defects on the airplane exterior surface, and the result shows that their work is robust, effective, and promising for industrial applications. [PERSON] and [PERSON] et al. [16] also used 3D scanning technology to measure and evaluate surface damage of honeycomb sandwich panels, and the results showed that this method is more efficient and reliable compared to manual methods.