Imaging model and vision measurement method considering refraction effect of flat glass windows in tunnel construction

Vision measurement has become an indispensable technology in tunnel construction. However, the harsh construction environment necessitates the provision of a certain thickness of flat glass windows to protect the vision system. This, in turn, leads to an obvious refraction effect, rendering the pinhole model and traditional vision measurement methods inadequate. As such, this paper offers a comprehensive solution to this problem. Firstly, the imaging model under the refraction of flat glass is shown based on the virtual camera and virtual space point, respectively. Secondly, a three-parameter calibration method for flat glass was proposed, which could determine the refractive index, unit normal vector, and light path normal distance. A practical dynamic interval constraint was introduced to address the failure of the epipolar constraint in refraction image pairs. Lastly, a new binocular disparity method is presented to avoid the impact of refraction distortion on the solution accuracy of three-dimensional coordinates. Effectiveness experiments are conducted, showing a refractive index relative error within ±1%, a miniaturized and efficient dynamic interval constraint, a maximum reconstruction error of 0.120 mm, and a maximum measurement error of only 0.093 mm. A series of stability experiments are also performed under different target attitudes, glass attitudes, working distances, and pollution conditions. The results demonstrate the robustness of the proposed solution. Although the scheme is developed for the vision system in harsh tunnel construction environments, it can serve as a reference for any vision measurement applications under glass protection windows.