## 1 Introduction
They utilized laser displacement sensors and a weighted least squares fitting method to obtain the geometric center point of the workpieces. Subsequently, they used the obtained geometric center point to calculate the concentricity between the forging billets and upsetting rod or piercing rod. [PERSON] et al. [7] proposed a non-contact coaxiality measurement system based on laser alignment with laser displacement sensors at its core. They utilized high-precision laser displacement sensors to measure the internal dimensions of small holes. They utilized the least squares method and particle swarm optimization algorithm (PSO) to fit the centers of the small holes, subsequently calculating the coaxiality error values. The problem of coaxiality measurement of a large span small hole system was solved. [PERSON] et al. [8] proposed a method for measuring the coaxiality of stepped shafts based on line-structured light vision. They established a world coordinate system based on the optical planes corresponding to each position. Then, the center point coordinates of the intercept line were determined by fitting an ellipse in the coordinate system, and the equation of the reference axis was calculated using the least squares method. Finally, the coaxiality error of each axis segment relative to the reference axis segment was solved via the principle of least containment. [PERSON] et al. [9] proposed a method for measuring the coaxiality error of a distant non-connected axis based on the principle of laser collimation. First, the laser spot was obtained by rotating the laser module and the four-quadrant photodetector module. Finally, they calculated the angular deviation and parallel deviation using the center and radius formed by the laser spot. After analyzing the current situation of coaxiality measurement both domestically and abroad, it was found that the optical measurement technology proposed by researchers has been widely applied in the process of coaxiality measurement of parts. Although these measurement techniques boast high precision, they are not suitable for the coaxiality measurement of automobile brake piston components. As shown in Figure 1, due to the spring structure of the part itself, during a rotating movement the laser beam emitted by the laser sensor will sometimes irradiate inside the spring coils, and sometimes irradiate on the spring, which causes the laser sensor to fail to obtain accurate measurement values. Although capacitive sensors are widely used for displacement and angle measurements,their accuracy and sensitivity are relatively low. During the rotational motion of automobile brake piston components, the variation of the spring relative to the reference axis is very small, rendering capacitive sensors unable to provide accurate feedback information. Additionally, while coordinate measuring machines are high-precision instruments, they have low detection efficiency and high costs, and thus are unable to meet the automated testing needs of enterprises. In recent years, with the rapid development of computer technology and wavelet analysis in the field of image processing and computer vision, many researchers have used machine vision technology to realize non-contact detection and online detection. Images can be decomposed into sub-images of different scales and frequencies by means of wavelet transform, and then edge detection, image denoising, and feature point extraction can be realized [10; 11; 12; 13; 14; 15; 16]. In addition, compared with traditional measurement technology, machine vision technology has high precision, high efficiency, and a low cost, and avoids the risk of damaging the surface of parts, so it has been widely studied [17; 18; 19; 20; 21]. Many researchers have studied shaft parts based on machine vision technology. [PERSON] et al. [22] proposed a geometric measurement system for shaft parts based on machine vision. The system first utilized industrial cameras to capture images of the parts.