Table 4.

Comparison of the theory and limitations of different methods.

Method	Method Principle	Limitations
Tunnel axis + Profile Radius [37]	Comparing the difference between the distance from the real arch profile to the tunnel axis and the distance from the standard arch profile to the tunnel axis.	The method is sensitive to the interference resulted from the steel mesh as well as the errors in the tunnel axis calibration, and the arch installation are inevitable.
Harris3D [38], SIFT3D [39]	These feature points were extended from the feature description method of 2D images, and are widely used for point cloud registration, recognition, and classification.	They are not applicable to distinguish steel arches from steel grids since steel arches arranged longitudinally and steel grids arranged horizontally have similar Harris3D and SIFT3D characteristics.
NARF [40]	The method can be used to take the center of the tunnel point cloud as the observation point and expand it into a range image for edge detection.	The recognition effect of the NARF method is unstable and needs to be improved.
Boundary detection [10]	Based on the given Euclidean distance and k-tree search method, the boundary of the hole is detected after the point cloud is triangulated.	The shielding effect of steel arches on laser results in multiple types of banded holes in the point cloud behind the arch.
region-growing	The seed points keep growing according to the characteristics of the surface until the seed points reach the boundary.	The segmentation effect depends on the given parameters and has poor adaptability to rough and complex surfaces.
MVCNN [41], GVCNN [42]	The 3D point cloud is projected into 2D images from multiple views, and CNN is used to extract features for each view in combination with the image processing method.	The projection method will lead to the loss of the key geometric spatial information of the arch structure, which will affect the segmentation accuracy of the point cloud.
Voxnet [41], PointGrid [44]	The disordered point cloud is voxelized into a regular structure, and then the neural network architecture is used to learn its characteristics.	Low efficiency of voxel grid arrangement; large memory occupied in the calculation process; time consuming; information loss.
Pointnet [41]	This method extracts the feature description of each independent point and the description of global point cloud features. Therefore, the point cloud of the steel arch area should be segmented into independent individuals to form a data set.	The relationship between points and neighborhood information is not considered, resulting in information loss when dealing with large-scale point cloud data. It can be used to detect the areas instead of the edge of the steel arches.