## 1 Introduction  
In the field of mechanical processing, concentricity is an important technical indicator for evaluating the alignment accuracy of cylindrical workpieces. The quality of concentricity directly affects the assembly quality, performance, operational stability, and lifespan of the entire mechanical system. The most crucial step in concentricity detection is circle fitting, and scholars at home and abroad have conducted extensive research on circle fitting algorithms. [PERSON] from Nanchang University proposed an edge point screening method [1] and combined sub-pixel edge detection with circle center positioning. This algorithm has high detection accuracy and anti-noise ability. [PERSON] et al. achieved real-time measurement and adjustment of the coaxiality of parts by improving methods such as one-dimensional measurement of rectangles to find boundary points [2]. This method has the characteristics of high speed, high robustness, and high precision. [PERSON] et al. proposed an image edge detection method using sinusoidal moving fitting [3], which has the characteristics of high measurement accuracy and good stability compared to the traditional random Hough transform. [PERSON] et al. proposed a multi-bottle mouth positioning algorithm based on DBSCAN random circle detection [4], which has high accuracy and real-time performance. [PERSON] et al. proposed an optimization method for circle center fitting based on photogrammetry and Hough transform [5], which effectively solved the problem of the inability to directly measure the circle center on construction machinery. [PERSON] et al. proposed an iterative method for robust circle fitting [6], and the proposed iterative procedure can reduce the impact of abnormal values on the estimation of circle parameters. [PERSON] et al. combined Hough transform, the de-noising process, and the robust least squares circle fitting method [7] to extract the position of tree stem segments from terrestrial laser scanning data. [PERSON] et al. proposed a fast circle detection algorithm based on information compression [8]. [PERSON] et al. proposed a new circle detection MFLS algorithm based on model fitting and the least squares technique [9], which has strong anti-interference ability. [PERSON] et al. addressed the issue of circular projections becoming elliptical in optical CCD detection and proposed a circle detection algorithm based on ellipse de-noising [10]. At present, modern methods based on image processing, laser measurement, and three-coordinate detection have become research hotspots, but they have certain limitations. For example, algorithms based on Canny edge detection and Hough transform are susceptible to noise interference and require a large amount of computation. Laser measuring instruments [11] have high precision but expensive costs and poor environmental adaptability. Although the coordinate measuring machine (CMM) [12] has excellent accuracy, it has low detection efficiency and complex operation. The existing concentricity detection of piston components mostly adopts manual eye inspection, which has low efficiency and large subjective error. Therefore, how to optimize existing methods or explore new detection techniques to achieve high precision, high efficiency, and low-cost concentricity measurement is still an urgent problem to be solved.  
Aiming at the problems of low efficiency and large subjective error of manual eye inspection in concentricity detection of piston components, this study proposes an improved Canny algorithm for non-contact detection of the concentricity of the spring in the first piston component. The improved Canny algorithm can effectively suppress false edges and retain more edge information, and, at the same time, the improved Canny algorithm reduces the concentricity error by 4%, resulting in an effective non-contact measurement of the spring concentricity of the first piston component.