A Branch Cut Algorithm for 180-Degree Ambiguity Resolution in 2D Vector Fields and Its Application to Single-Frame Fringe Projection Profilometry

The 180-degree ambiguity resolution is an estimation problem of correct signs of discrete samples of a two-dimensional (2D) vector field. To estimate the correct signs at 2D lattice points, several optimization approaches are proposed. These approaches assume that the true vector felid changes smoothly between many neighboring lattice points, and solve a combinatorial optimization problem on sign matrices, where the objective function is given by the sum of costs for neighboring signs. This objective function is non-submodular, and hence the optimization problem is NP-hard. For this NP-hard problem, we propose a branch cut type solver which is inspired by Goldstein's approach for 2D phase unwrapping. In application to single-frame fringe projection profilometry, we show the effectiveness of the proposed branch cut algorithm.