Circular fringe projection profilometry and 3D sensitivity analysis based on extended epipolar geometry

For fringe projection profilometry, the phase-shifting direction needs to fit the position layout of a camera and a projector, or the quality of 3D reconstruction will be poor. Two-direction fringe projection profilometry, i.e. scanning along both horizontal and vertical directions, achieves robust performance, while the number of patterns is doubled comparing with one-direction scanning. In this paper, based on the extended epipolar geometry, we propose circular fringe projection profilometry to overcome the direction issue without doubling the number of patterns. First, by introducing the farthest and nearest points to the epipole in projector space, we can robustly control the spatial frequency of circular fringes in patterns. Second, by analytically relating the circularly-shaped phase to 3D world coordinate, we naturally reduce the number of the equations from 6 down to 3 for the proposed algorithm, and compute 3D point clouds in real time. Finally, we propose 3D sensitivity to conveniently analyze the error of reconstruction point clouds. The experimental results show that, compared with two-direction fringe projection profilometry which is robust in accuracy, the proposed is of a little better quality while the number of the patterns is half.