%0 Journal Article %1 Bioucas-dias07phaseunwrapping %A Bioucas dias, José %A Member, Senior %A Valadão, Gonçalo %D 2007 %J IEEE Transactions on Image Processing %K cuts graph phase unwrapping %P 2007 %T Phase unwrapping via graph cuts %U http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.141.2041 %X Abstract — Phase unwrapping is the inference of absolute phase from modulo-2π 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 L p norm, with p ≥ 1. Its complexity is KT(n, 3n), where K is the length of the absolute phase domain measured in 2π 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 unwrapping 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. Index Terms — Phase unwrapping, energy minimization, integer optimization, submodularity, graph cuts, image

@article{Bioucas-dias07phaseunwrapping, abstract = {Abstract — Phase unwrapping is the inference of absolute phase from modulo-2π 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 L p norm, with p ≥ 1. Its complexity is KT(n, 3n), where K is the length of the absolute phase domain measured in 2π 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 unwrapping 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. Index Terms — Phase unwrapping, energy minimization, integer optimization, submodularity, graph cuts, image}, added-at = {2014-08-28T12:14:31.000+0200}, author = {Bioucas dias, José and Member, Senior and Valadão, Gonçalo}, biburl = {https://www.bibsonomy.org/bibtex/2d0b7df6469df5d1d9bbb61d871195f08/icgrvlab}, description = {CiteSeerX — Phase unwrapping via graph cuts}, interhash = {222fc60fef797bf6f11a66750c2629ad}, intrahash = {d0b7df6469df5d1d9bbb61d871195f08}, journal = {IEEE Transactions on Image Processing}, keywords = {cuts graph phase unwrapping}, pages = 2007, timestamp = {2014-08-28T12:14:31.000+0200}, title = {Phase unwrapping via graph cuts}, url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.141.2041}, year = 2007 }