## 2 Related Work  
The application of photogrammetry in port machinery is still relatively rare. [PERSON] [17] tried to use photogrammetry to measure the data of gantry cranes, but the effect was not good. [PERSON] [18] developed the calibration method of camera effective focal length for port cranes. He proposed a new position and attitude estimation method to solve the problem of low measurement accuracy when the attitude angle is large. [PERSON] [19] developed a multi-line intersection point-fitting optimization algorithm for crane structure characteristics. Most of the corners on the crane are the intersections of three straight lines. Taking advantage of this feature, [PERSON] solved the problem that some key corners cannot be directly measured due to occlusion. The structure of port machinery has obvious characteristics, and a suitable photogrammetry algorithm can be developed according to its structural characteristics.  
Taking gantry crane [20] as the representative of port machinery, after a long period of high-intensity work, its supporting cylinder will be deformed, the center of the circle will be offset, and the safety will be reduced. The coordinates of the center of the circle and other key points play a crucial role in the safety evaluation of mechanical structures [21; 22]. Therefore, it is very important to measure the coordinates of the center of the circle. However, it is usually impossible to measure the center of a circle directly. In general, the coordinates of multiple points on a circle are measured first, and the center of a circle is fitted according to the spatial coordinates of each point [23]. In mathematical theory, the intersection point of midperpendicular of multiple strings on a circle is the center of the circle, but due to the existence of error, the multiple midperpendicular cannot strictly intersect at one point [19]. Therefore, an approximate model of image point distortion [24; 25] is established in the image plane. The Hough transform [26; 27; 28] is used to determine the similarity between the actual and ideal midperpendicular, and then the weight of each midperpendicular is determined according to the similarity, and more accurate coordinates of the center of the circle are obtained through the above process.  
Few scholars combine photogrammetry with the fitting of the center of the circle in space. This paper has made relevant research in this direction because of the need to provide supporting data for crane safety assessment. Compared with the previous research work conducted by scholars on the measurement of cranes, this paper has the following innovations: (i) A new approximate model of image point distortion is proposed; (ii) An iterative optimization method based on reprojection is proposed; and (iii) The midperpendicular is weighted by using the Hough transform. The research in this paper solves the problem of poor fitting accuracy of the measurement of the center of a port crane.  
The rest of this paper is structured as follows. The circle center fitting theory based on equal weight midperpendicular is proposed in Section 3.1; on the basis of Section 3.1, the circle center fitting theory based on weighted midperpendicular is proposed in Section 3.2. Section 4 introduces the experimental process. Section 5 analyzes the experimental results. And Section 6 summarizes the whole paper and prospective future research.