Skip to main content
Log in

Phase unwrapping via hierarchical and balanced residue partitioning

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Data availability

https://github.com/emrahonat/HBP

Code availability

The code is not publicly available.

References

  1. Goldstein, R.M., Zebker, H.A., Werner, C.L.: Satellite radar interferometry: two-dimensional phase unwrapping. Radio Sci. 23(4), 713–720 (1988)

    Article  ADS  Google Scholar 

  2. 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)

    Article  PubMed  Google Scholar 

  3. 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)

  4. Onat, E., Özkazanç, Y.: An Analysis on Path Following Phase Unwrapping Algorithms. IEEE - 28th Signal Processing and Communications Applications Conference (SIU), (2020)

  5. 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)

    Article  ADS  Google Scholar 

  6. Yu, H., Lan, Y., Yuan, Z., Xu, J., Lee, H.: Phase unwrapping in InSAR, IEEE Geosicence and RemoteSensing Mag., (2019)

  7. Ghiglia, D.C., Pritt, M.D.: Two Dimensional Phase Unwrapping Theory, Algorithms and Software. John Wiley, New York, USA (1998)

    Google Scholar 

  8. 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)

    Article  ADS  Google Scholar 

  9. Ghiglia, D.C., Romero, L.A.: Minimum Lp-norm two-dimensional phase unwrapping. Opt. Soc. Am. A 13(10), 1999–2013 (1996)

    Article  ADS  Google Scholar 

  10. Flynn, T.J.: Consistent 2-D Phase Unwrapping Guided by a Quality Map, Proc. of the International Geoscience and RemoteSensing Symp, (1996)

  11. Roth, M.W.: Phase Unwrapping for Interferometric SAR by the Least-Error Path. John Hopkins Univ. App. Physics Laboratory Tech, Report (1995)

  12. Flynn, T.J.: Two dimensional phase unwrapping with minimum weighted discontinuity. J. Opt. Soc. Am. 14(10), 2692–2701 (1997)

    Article  ADS  Google Scholar 

  13. 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)

    Article  ADS  Google Scholar 

  14. 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)

    Google Scholar 

  15. 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)

  16. Bioucas-Dias, J., Valadao, G.: Phase unwrapping via graph cuts. IEEE Trans. Image Process. 16(3), 698–709 (2007)

    Article  ADS  MathSciNet  PubMed  Google Scholar 

  17. Zheng, D., Da, F.: A novel algorithm for branch cut phase unwrapping. Opt. Lasers Eng. 49(5), 609–617 (2011)

    Article  Google Scholar 

  18. 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)

    Article  ADS  CAS  PubMed  Google Scholar 

  19. 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)

    Article  ADS  PubMed  Google Scholar 

  20. 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)

    Article  ADS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Contributions

All of the authors contributed equally to this work and reviewed the manuscript.

Corresponding author

Correspondence to Emrah Onat.

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.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-023-02958-5

Keywords

Navigation