FAST ALGORITHM FOR INTEGRATING INCONSISTENT GRADIENT FIELDS

A discrete Fourier transform (DFT) based algorithm for solving a quadr atic cost functional is proposed; this regularized functional allows o ne to obtain a consistent gradient field from an inconsistent one. The calculated consistent gradient may then be integrated by use of simpl e methods. The technique is presented in the context of the phase-unwr apping problem; however, it may be applied to other problems, such as shapes from shading (a robot-vision technique) when inconsistent gradi ent fields with irregular domains are obtained. The regularized functi onal introduced here has advantages over existing techniques; in parti cular, it is able to manage complex irregular domains and to interpola te over regions with invalid data without any smoothness assumptions o ver the rest of the lattice, so that the estimation error is reduced. Furthermore, there are no free parameters to adjust. The DFT is used t o compute a preconditioner because there is highly efficient hardware to perform the calculations and also because it may be computed by opt ical means. (C) 1997 Optical Society of America.