Variational image decomposition model TGV-Hilbert-BM3D for phase retrieval in FPP and its application for an on-site...

Mass loss from wall surface bulge deformation can be used to estimate the strength loss of reinforcement, bond reduction, and ductility degradation, so it is very important to accurately measure the three-dimensional (3D) shape of on-site wall surface bulge. In this paper, we try to solve the problem by use of fringe projection profilometry. In the fringe projection patterns of wall surface bulge, the contrast of the fringes is very weak, and there are sometimes cracks in patterns. We first present a preprocessing method to inpaint fringes if there are damaged fringes caused by cracks. Then we propose a new, to the best of our knowledge, image decomposition model, total generalized variation (TGV)-Hilbert-block-matching (BM)3D, to effectively extract the fringe component. Finally, we use Fourier transform, phase unwrapping, and carrier-removal methods to obtain the unwrapped phase. We test the proposed method on a simulated fringe projection pattern and two real fringe projection patterns of wall surface bulge. We compare our method with the advanced total variation space-generalized functions space-BM3D, TV-Hilbert-L₂, and Beppo-Levi-space-Hilbert-BM3D methods. In addition, we perform ablation experiments to prove that our preprocessing method is necessary. The experimental results demonstrate that our method can effectively measure the 3D shape of wall surface bulge from a single fringe projection pattern for the first time, to our knowledge.