Second-order robust regularization cost function for detecting and reconstructing phase discontinuities

We propose a robust method for computing discontinuous phase maps from a fringe pattern with carrier frequency. Our algorithm is based on the minimization of an edge-preserving regularized cost function, specifically, on a robust regularized potential that uses a paradigm called the plate with adaptive rest condition, i.e., a second-order edge-preserving potential. Given that the proposed cost function is not convex, our method uses as its initial point an overly smoothed phase computed with a standard fringe analysis method and then reconstructs the phase discontinuities. Although the method is general purpose, it is introduced in the context of interferometric gauge-block calibration. The performance of the algorithm is demonstrated by numerical experiments with both synthetic and real data.