## 1 Introduction  
With the development of the modern manufacturing industry, the requirements for the contour inspection of complex flat parts are becoming higher than ever, and the traditional dimensional inspection methods can hardly meet the requirements of measurement accuracy and speed. Rapid and accurate dimensional measurement methods have become an urgent problem. The application of machine vision to measure the sizes of parts has been a research hotspot and a major direction of development in the machinery precision machining and manufacturing industry [1]. Part size measurement based on machine vision mainly includes three technical points: part image contour extraction, graphic element segmentation point detection, and graphic element fitting. To date, numerous scholars have conducted research on these topics. Research on the direction of image contour extraction started early, and early studies mainly exploited the feature that contour points are discontinuous in the gray intensity in an image. An image was convolved using a local filter to determine the contour pixel point with the largest local gradient. Several linear filters [2; 3; 4] have been widely used, such as the Sobel, Perwitt, and Canny operators. However, [PERSON] and [PERSON] [5] pointed out that the real image contours are usually not step functions but a combination of step, peak, and roof situations. To cope with this situation, the grayscale gradient features were combined with other gradient features, including color and texture gradients, to obtain a probabilistic detector (Pb) [6]. [PERSON] [7] significantly improved the detection accuracy of Pb using sparse coded gradient (SCG) features instead of hand-designed gradients in Pb. SCG features can be automatically learned from image data using sparse coding, making the contour detection closer to that of humans. In recent years, many researchers have introduced deep learning techniques to the contour detection problem, with deep features instead of traditional hand-designed features. [PERSON] [8] proposed holistically nested edge detection (HED) based on deeply supervised nets (DSN) [9], which implemented holistic image training and prediction, and multi-scale and multi-level feature learning. In the scenario of part size measurement, the influence of complex background environments and textures was circumvented in image acquisition, which made contour extraction less difficult. Therefore, mature algorithms were usually adopted. [PERSON] et al. [10] used the algorithm proposed by [PERSON] [11] for contour extraction while measuring the lengths of plastic part notches in a video. This algorithm was adopted in this paper. The detection of the segmentation point of the graphic element is the most critical part of the entire dimensional measurement system, and the detection accuracy directly determines the accuracy of the graphic element fitting and even the final dimensional measurement. This research can be divided into four directions: the approximate curvature method, the Hough transform and its improvement algorithm, the contour approximation method, and the auxiliary detection method. [PERSON] et al. [12] proposed a curvature scale space (CSS) corner point detector that employed local curvatures in different directions for corner point detection and improved localization accuracy. Subsequently, many studies have been conducted based on the approximate curvature for graphic element segmentation point detection. For instance, [PERSON] et al. [13] proposed an eleven-point method to approximate the contour curvature, which improved the noise resistance of the traditional three-point method. [PERSON] et al. [14] adopted the eleven-point method to find the approximate locations of feature points and then calculated the curvature differences for feature points within those locations to find the accurate locations of feature points. The Hough transform was proposed by [PERSON] in 1962 to detect the features of specific shapes (such as lines or circles) in digitized images.