A precise measurement method for tube endpoints based on spatial geometry and perspective projection model

Abstract

Tubes are widely used in the aerospace field for such things as engines, fuel pipelines, cooling systems, etc. To improve manufacturing efficiency and accuracy, researchers develop multi-camera vision methods for measuring tube geometry parameters. However, these methods cannot measure the exact position of the endpoints of the tube, because the projection points of the tube endpoints have no obvious texture features in the image. To solve the above problem, a precise measurement method for tube endpoints based on spatial geometry and perspective projection model is proposed in this paper. First, we establish a Plücker coordinate system, which treats the end of the tube as a cylinder. Then, several line equations parallel to the center line are calculated on the surface of the cylinder and their intersections with the end face are obtained on these lines, which refers to the optical center of the camera, the radius of the tube, and etc. These intersections are projected onto the centerline and optimized to get the endpoint. Finally, we build a multi-camera vision measurement system consisting of ten industrial cameras to verify the effectiveness of the proposed method. Extensive experiments have shown that the average error of this method is within 0.1 mm, and the standard deviation is within 0.08 mm, which proves the superiority of our proposed method.