Phase unwrapping is the inference of absolute phase from modulo-2pi phase. This paper introduces a new energy minimization framework for phase unwrapping. The considered objective functions are first-order Markov random fields. We provide an exact energy minimization algorithm, whenever the corresponding clique potentials are convex, namely for the phase unwrapping classical Lp norm, with p > or = 1. Its complexity is KT (n, 3n), where K is the length of the absolute phase domain measured in 2pi units and T (n, m) is the complexity of a max-flow computation in a graph with n nodes and m edges. For nonconvex clique potentials, often used owing to their discontinuity preserving ability, we face an NP-hard problem for which we devise an approximate solution. Both algorithms solve integer optimization problems by computing a sequence of binary optimizations, each one solved by graph cut techniques. Accordingly, we name the two algorithms PUMA, for phase unwrappping max-flow/min-cut. A set of experimental results illustrates the effectiveness of the proposed approach and its competitiveness in comparison with state-of-the-art phase unwrapping algorithms.

The paper presents a new max-flow/min-cut approach for recovering the absolute phase from modulo-2/spl pi/ phase, the so-called phase unwrapping (PU) problem. The adopted criterion is the minimization of the L/sup p/ norm of phase differences, leading to computationally demanding integer optimization problems. The unwrapped phase is computed iteratively through a sequence of binary optimizations, each one mapped onto a max-flow/min-cut problem on a certain graph. Accordingly, we name this new algorithm PUMF (for phase unwrapping max-flow). A set of experimental results illustrates the effectiveness of PUMF approach, namely for 0 < p < 1, where most competitors fail.