Stereo vision reconstruction method for variable-diameter bent pipes based on 2D-3D cyclic mapping

Stereo vision has been widely applied to the 3D reconstruction of industrial pipes for external shape quality control, owing to its high accuracy, non-contact operation, and low cost. However, most existing stereo vision-based studies focus on constant-diameter pipes, whereas variable-diameter ones have received limited attention. To address this issue, we model variable-diameter bent pipes (VDBPs) as bent truncated cones (BTCs) and propose a holistic cross-sectional circle reconstruction method based on 2D-3D cyclic mapping. A perspective projection model of the BTC is first established and a reconstruction auxiliary line is introduced. Then, by exploiting the structural characteristics of the BTC and the constraint imposed by the reconstruction auxiliary line, the normals and projected centers of the cross-sectional circles are determined. From these, the corresponding 3D circle centers and radii are estimated. Finally, these circles are reconstructed and combined to form the outer surface of the BTC, thereby enabling the 3D reconstruction of VDBPs. To validate the method, a multi-view stereo vision system is developed, and both simulations and experiments are conducted. The experimental reconstruction results are evaluated using both ATOS Q scanning and Leitz PMM-C contact measurement. For a VDBP with an axis bend radius of 270 mm, a central angle of 90°, and radii of 15 mm and 40 mm at the two ends, the system achieves a repeatability error of 0.026 mm and a reconstruction error of 0.098 mm, demonstrating the method's reliability and high accuracy.