# Optimization Method of Square Hole Measurement Based on Generalized Point Photogrammetry
## 1 Introduction
Laser Radar determines the spatial information of targets by receiving reflected signals, but its accuracy cannot meet engineering requirements [24; 25; 26; 27]. Laser scanning has high stability and is suitable for extremely large objects. The generated large point clouds require complex post-processing to complete the extraction of key information. Laser scanners are suitable for measuring static objects, but are not suitable for engineering projects that require real-time performance, as they have low efficiency and high cost. [28; 29] Therefore, an efficient and fast measurement method is needed to complete the field measurement. In the process of completing the assembly of the segmental beam, it is necessary to lift the segmental beam with the square rod first. In this process, whether the square rod and the square hole can be accurately aligned is very important. As shown in Figure 1, there are six square rods on the lifting tool. After achieving precise alignment of the holes and rods, the control system will insert the six suspension rods into the square holes, and then the lifting tool can lift the beam. The cross sections of the rod and the hole are both square. In order to ensure that the square rod can be placed in the square hole, the side length of the square hole is usually 10 mm longer than the side length of the square rod. Before aligning the square hole and the square rods, the accurate position of the square hole and the square rod should be calculated to ensure that six square rods are placed in the six square hole simultaneously and then lifted. The above process requires high accuracy. The traditional alignment method mainly relies on manual operation, and the operator needs to manually adjust the position of the square rod to ensure accurate alignment between the hole and the rod. This manual adjustment method has low efficiency and poor safety. Traditional photogrammetry can calculate the space coordinates of key points, but the premise is that the image plane coordinates of the point can be accurately extracted from the image. In engineering environments, the features of points are usually not obvious, and the error in extracting the image plane coordinates of points is usually large. Compared to point features [30; 31; 32], the extraction of line features [33; 34; 35; 36] should be more stable. Therefore, this paper proposes an optimization method of square hole measurement based on generalized point photogrammetry. The structure of this article is arranged as follows. Section 2 introduces the mathematical principles of generalized point photogrammetry. On the basis of Section 2, Section 3 introduces the Lagrange multiplier method into general photogrammetry and provides detailed mathematical derivation. On the basis of Section 3, Section 4 has added geometric constraints for square holes and derived optimization methods. On the theoretical basis of the previous chapters, experiments are conducted in Section 6. In order to better verify the robustness and engineering applicability of the algorithm, the experiments are divided into simulation experiments and engineering experiments. This article has the following innovative points. A generalized point photogrammetric mathematical model based on the Lagrange multiplier method is proposed. A square hole optimization method based on constraint conditions is proposed. This article combines image processing technology with photogrammetry technology and is used to solve practical engineering problems.