A refractive three-dimensional reconstruction method for fringe projection with a planar medium

Abstract In special measurement situations, a vision measurement system needs to measure objects through a viewing observation window made of a planar transparent medium. The refraction at the interface between a medium and air leads to large measurement errors in the pin-hole imaging model. Most existing solutions require complex processes of calculating refracted light equations and/or matching stereo images. Here, we propose a refractive three-dimensional (3D) reconstruction method for fringe projection with a planar medium. We derive a coordinate conversion relationship from a pseudo-object point caused by light refraction to a real-object point based on flat refractive geometry. Then, we integrate the relationship into regular fringe projection framework for unbiased 3D reconstruction. Two experiments, including 3D shape measurements of a step and a regular sphere are performed. The results verify the effectiveness and accuracy of the proposed refractive 3D reconstruction method.