Mark bars drawn on the surfaces of bolted joints are widely used to indicate the severity of loosening. The automatic and accurate determination of the loosening angle of mark bolted joints is a challenging issue that has not been investigated previously. This determination will release workers from heavy workloads. This study proposes an automated method for detecting the loosening angle of mark bolted joints by integrating computer vision and geometric imaging theory. This novel method contained three integrated modules. The first module used a Keypoint Regional Convolutional Neural Network (Keypoint-RCNN)-based deep learning algorithm to detect five keypoints and locate the region of interest (RoI). The second module recognised the mark ellipse and mark points using the transformation of the five detected keypoints and several image processing technologies such as dilation and expansion algorithms, a skeleton algorithm, and the least square method. In the last module, according to the geometric imaging theory, we derived a precise expression to calculate the loosening angle using the information for the mark points and mark ellipse. In lab-scale and real-scale environments, the average relative detection error was only 3.5%. This indicated that our method could accurately calculate the loosening angles of marked bolted joints even when the images were captured from an arbitrary view. In the future, some segmentation algorithms based on deep learning, distortion correction, accurate angle and length measuring instruments, and advanced transformation methods can be applied to further improve detection accuracy.

在螺栓接头表面绘制的标记条被广泛用于指示松动的严重程度。自动和准确地确定标记螺栓接头的松动角度是一个以前没有研究过的具有挑战性的问题。这一决定将使工人摆脱繁重的工作量。本研究结合计算机视觉和几何成像理论，提出了一种自动检测标记螺栓接头松动角度的方法。这种新颖的方法包含三个集成模块。第一个模块使用基于关键点区域卷积神经网络 (Keypoint-RCNN) 的深度学习算法来检测五个关键点并定位感兴趣区域 (RoI)。第二个模块使用五个检测到的关键点的变换以及膨胀和扩展算法、骨架算法和最小二乘法等多种图像处理技术来识别标记椭圆和标记点。在最后一个模块中，我们根据几何成像理论，利用标记点和标记椭圆的信息推导出了一个精确的表达式来计算松动角度。在实验室规模和实际规模环境中，平均相对检测误差仅为 3.5%。这表明即使从任意视图捕获图像，我们的方法也可以准确计算标记螺栓接头的松动角度。未来一些基于深度学习、畸变校正、精确角度和长度测量仪器的分割算法，