Markov random field based phase demodulation of interferometric images

• Published in: Computer vision and image understanding Vol. 115; no. 6; pp. 759 - 770
• Main Authors: Wu, Dijia, Boyer, Kim L.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.06.2011; Elsevier
• Subjects: 2 π ambiguity; Algorithms; Ambiguity; Applied sciences; Artificial intelligence; Computer science; control theory; systems; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Fringe pattern analysis; Information, signal and communications theory; Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Interferometers; Interferometric imaging; Markov processes; Mathematical models; Minimization; Optical instruments, equipment and techniques; Optimization; Pattern recognition. Digital image processing. Computational geometry; Phase demodulation; Phase unwrapping; Physics; Sign ambiguity; Signal and communications theory; Signal, noise; Telecommunications and information theory; Sign ambiguity; Interferometric imaging; Phase unwrapping; Phase demodulation; Fringe pattern analysis; 2 π ambiguity; Markov process; Random phase; Path following; Submodular function; Multigrid; Robustness; Growth of error; Pattern analysis; Mathematical programming; Light interferometry; Probabilistic approach; 2π ambiguity; Minimization; Orientation; Hierarchized structure; Optimal solution; Heuristic method; NP hard problem; Objective function; Ambiguity
• ISSN: 1077-3142; 1090-235X
• DOI: 10.1016/j.cviu.2011.02.001

► We propose a Markov random field based sign ambiguity resolution method in interferometry (MSRAI). ► MSARI outperforms traditional path following phase demodulation methods. ► We propose the use of Multilevel Quadratic Pseudo-Boolean Optimization method. ► It better approximates optimal solution of non-submodular problems than LBP and traditional QPBO. We present a novel method to solve the sign ambiguity for phase demodulation from a single interferometric image that possibly contains closed fringes. The problem is formulated in a Markov random field (MRF) energy minimization framework with the assumption of phase gradient orientation continuity. The binary pairwise objective function is non-submodular and therefore its minimization is an NP-hard problem, for which we devise a multigrid hierarchy of quadratic pseudoboolean optimization problems that can be improved iteratively to approximate the optimal solution. We name the method MSARI algorithm, for Markov based sign ambiguity resolution in interferometry. Compared with traditional path-following phase demodulation methods, the new approach does not require any heuristic scanning strategy, is not subject to the propagation of error, and the extension to three dimensional fringe patterns is straightforward. A set of experiments with synthetic data and real prelens tear film interferometric images of the human eye demonstrate the effectiveness and robustness of the proposed algorithm as compared with existing state-of-the-art phase demodulation methods.