Abstract
Branch cut placement is an important issue in 2D phase unwrapping. The main requirement is to get the shortest branch cut placement with a minimum isolated area. We present a branch cut placement method that is based on hierarchical balanced partitioning (HBP) of the residue map. The method has two stages. In the first stage, the balanced residues which are one pixel or two pixels apart are connected. In the second stage, the remaining residues are processed via hierarchical and balanced partitioning of the residue map and subsequent serial connection. The method considers both local and global positioning of the residues and in this respect produces better results compared to the well-known conventional Goldstein method where the residue groups are connected based on local considerations only with respect to branch-cut length, and isolated area. The proposed method is also compared with the combined and extended methods based on residue searching, phase unwrapping max-flow method, exchange algorithm, minimum-cost matching theory, and hybrid genetic algorithm by using different types and sizes of wrapped input images. The implementation of the proposed method and the RMSE values are also comparable.
Similar content being viewed by others
Data availability
Code availability
The code is not publicly available.
References
Goldstein, R.M., Zebker, H.A., Werner, C.L.: Satellite radar interferometry: two-dimensional phase unwrapping. Radio Sci. 23(4), 713–720 (1988)
Rauscher, A., Barth, M., Reichenbach, J.R., Stollberger, R., Moser, E.: Automated unwrapping of MR phase images applied to BOLD MR-venography at 3 tesla. J. Magn. Reson. Imaging 18(2), 175–180 (2003)
Richards, M.A.: A Beginner’s Guide to Interferometric SAR Concepts and Signal Processing, IEEE Aerospace and Electronic Systems Magazine Vol. 22, No. 9, (September 2007)
Onat, E., Özkazanç, Y.: An Analysis on Path Following Phase Unwrapping Algorithms. IEEE - 28th Signal Processing and Communications Applications Conference (SIU), (2020)
Tofighi, M., Yorulmaz, O., Köse, K., Yıldırım, D.C., Çetin-Atalay, R., Çetin, A.E.: Phase and TV based convex sets for blind deconvolution of microscopic images. IEEE J. Select. Top. Signal Process. 10(1), 81–91 (2016)
Yu, H., Lan, Y., Yuan, Z., Xu, J., Lee, H.: Phase unwrapping in InSAR, IEEE Geosicence and RemoteSensing Mag., (2019)
Ghiglia, D.C., Pritt, M.D.: Two Dimensional Phase Unwrapping Theory, Algorithms and Software. John Wiley, New York, USA (1998)
Ghiglia, D.C., Romero, L.A.: Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods. Opt. Soc. Am. A 11(1), 107–117 (1994)
Ghiglia, D.C., Romero, L.A.: Minimum Lp-norm two-dimensional phase unwrapping. Opt. Soc. Am. A 13(10), 1999–2013 (1996)
Flynn, T.J.: Consistent 2-D Phase Unwrapping Guided by a Quality Map, Proc. of the International Geoscience and RemoteSensing Symp, (1996)
Roth, M.W.: Phase Unwrapping for Interferometric SAR by the Least-Error Path. John Hopkins Univ. App. Physics Laboratory Tech, Report (1995)
Flynn, T.J.: Two dimensional phase unwrapping with minimum weighted discontinuity. J. Opt. Soc. Am. 14(10), 2692–2701 (1997)
Zhou, L., Yu, H., Lan, Y.: Deep convolutional neural network-based robust phase gradient estimation for two-dimensional phase unwrapping using SAR interferograms. IEEE Trans. Geosci. Remote Sens. 58(7), 4653–4665 (2020)
Zhou, L., Yu, H., Pascazio, V., Xing, M.: PU-GAN: a one-step 2-D InSAR phase unwrapping based on conditional generative adversarial network. IEEE Trans. Geosci. Remote Sens. 60, 1–10 (2022)
Marhamati, R., Masnadi-Shirazi, M.A.: The principles of proper placement of branch cut in phase unwrapping using combined and extended methods based on residue searching, Signal, Image and Video Processing, Vol. 14, Is. 3, pp. 593-600 (2020)
Bioucas-Dias, J., Valadao, G.: Phase unwrapping via graph cuts. IEEE Trans. Image Process. 16(3), 698–709 (2007)
Zheng, D., Da, F.: A novel algorithm for branch cut phase unwrapping. Opt. Lasers Eng. 49(5), 609–617 (2011)
Buckland, J., Huntley, J., Turner, S.: Unwrapping noisy phase maps by use of a minimum-cost-matching algorithm. Appl. Opt. 34(23), 5100–5108 (1995)
Karout, S.A., Gdeisat, M.A., Burton, D.R., Lalor, M.J.: Two-dimensional phase unwrapping using a hybrid genetic algorithm. Appl. Opt. 46(5), 730–743 (2007)
Karout, S.A., Gdeisat, M.A., Burton, D.R., Lalor, M.J.: Residue vector, an approach to branch-cut placement in phase unwrapping: theoretical study. Appl. Opt. 46(21), 4712–4727 (2007)
Author information
Authors and Affiliations
Contributions
All of the authors contributed equally to this work and reviewed the manuscript.
Corresponding author
Ethics declarations
Conflict of interest
No competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Deprem, Z., Onat, E. Phase unwrapping via hierarchical and balanced residue partitioning. SIViP 18, 2895–2902 (2024). https://doi.org/10.1007/s11760-023-02958-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11760-023-02958-5