Phase Unwrapping via Graph Cuts

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.

Full-field strain measurements at high rate on notched composites tested with a tensile Hopkinson bar

“…A second set of images was taken during the loading and the displacement between the initial (still) and the actual states have thus been calculated sensor by sensor from these two sets. This approach is only possible if the global strain remains low and by using a phase unwrapping algorithm in order to get "absolute" values of the displacements [2]. With this approach, one can obtain a displacement resolution equal to approximately 3 % of the grid pitch (6 µm).…”

MR elastography and diffusion‐weighted imaging of ex vivo prostate cancer: quantitative comparison to histopathology

“…Prior to inversion, displacements were unwrapped (17) and then aligned in time and space to ensure no phase jumps were present. Then, the displacements were filtered by a 3×3×3 spatial Gaussian filter with a 0.5 mm standard deviation.…”

Full-Field Strain Measurement and Identification of Composites Moduli at High Strain Rate with the Virtual Fields Method

“…A phase unwrapping algorithm had to be used to fix this problem but is not explained since it is not the aim of the present paper. More details about it can be found in [35]. To ensure that the absolute value of displacement obtained after phase unwrapping is the right one (as it could be affected by a constant value equal to k × p), each displacement map has been checked manually using the hole or some grid defect as the feature to follow.…”