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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 32 — Nov. 10, 2009
  • pp: 6313–6323

Hybrid robust and fast algorithm for three-dimensional phase unwrapping

Miguel Arevalillo-Herráez, Munther A. Gdeisat, and David R. Burton  »View Author Affiliations


Applied Optics, Vol. 48, Issue 32, pp. 6313-6323 (2009)
http://dx.doi.org/10.1364/AO.48.006313


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Abstract

We present a hybrid three-dimensional (3D) unwrapping algorithm that combines the strengths of two other fast and robust existing techniques. In particular, a branch-cut surface algorithm and a path- following method have been integrated in a symbiotic way, still keeping execution times within a range that permits their use in real-time applications that need a relatively fast solution to the problem. First, branch-cut surfaces are calculated, disregarding partial residue loops that end at the boundary of the 3D phase volume. These partial loops are then used to define a quality for each image voxel. Finally, unwrapping proceeds along a path determined by a minimum spanning tree (MST). The MST is built according to the quality of the voxels and avoids crossing the branch-cut surfaces determined at the first step. The resulting technique shows a higher robustness than any of the two methods used in isolation. On the one hand, the 3D MST algorithm benefits from the branch-cut surfaces, which endows it with a higher robustness to noise and open-ended wraps. On the other hand, incorrectly placed surfaces due to open loops at the boundaries in the branch-cut surface approach disappear.

© 2009 Optical Society of America

OCIS Codes
(100.5070) Image processing : Phase retrieval
(100.5088) Image processing : Phase unwrapping

ToC Category:
Image Processing

History
Original Manuscript: July 13, 2009
Revised Manuscript: August 25, 2009
Manuscript Accepted: September 15, 2009
Published: November 6, 2009

Citation
Miguel Arevalillo-Herráez, Munther A. Gdeisat, and David R. Burton, "Hybrid robust and fast algorithm for three-dimensional phase unwrapping," Appl. Opt. 48, 6313-6323 (2009)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-48-32-6313


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References

  1. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  2. M. Costantini, F. Malvarosa, F. Minati, L. Pietranera, and G. Milillo, “A three-dimensional phase unwrapping algorithm for processing of multitemporal sar interferometric measurements,” in Geoscience and Remote Sensing Symposium, 2002 (IEEE, 2002), Vol. 3, pp. 1741-1743.
  3. R. Cusack and N. Papadakis, “New robust 3-d phase unwrapping algorithms: Application to magnetic field mapping and undistorting echoplanar images,” NeuroImage 16, 754-764(2002). [CrossRef] [PubMed]
  4. D. C. Ghiglia and L. A. Romero, “Minimum lp-norm two-dimensional phase unwrapping,” J. Opt. Soc. Am. A 13, 1999-2013 (1996). [CrossRef]
  5. R. Cusack, J. M. Huntley, and H. T. Goldrein, “Improved noise-immune phase-unwrapping algorithm,” Appl. Opt. 34, 781-789 (1995). [CrossRef] [PubMed]
  6. M. Pritt and J. Shipman, “Least-squares two-dimensional phase unwrapping using FFT's,” IEEE Trans. Geosci. Remote Sens. , 32, 706-708 (1994). [CrossRef]
  7. J. M. B. Dias and J. M. N. Leitão, “The ZπM algorithm: a method for interferometric image reconstruction in SAR/SAS,” IEEE Trans. Image Process. 11, 408-422 (2002). [CrossRef]
  8. L. Aiello, D. Riccio, P. Ferraro, S. Grilli, L. Sansone, G. Coppola, S. D. Nicola, and A. Finizio, “Green's formulation for robust phase unwrapping in digital holography,” Opt. Lasers Eng. 45, 750-755 (2007). [CrossRef]
  9. L. Ying, Z. Liang, D. Munson, R. Koetter, and B. Frey, “Unwrapping of MR phase images using a Markov random field model,” IEEE Trans. Med. Imaging 25, 128-136(2006). [CrossRef] [PubMed]
  10. J. Bioucas-Dias and G. Valadao, “Phase unwrapping via graph cuts,” IEEE Trans Image Process. 16, 698-709 (2007). [CrossRef]
  11. J. M. Huntley, “Three-dimensional noise-immune phase unwrapping algorithm,” Appl. Opt. 40, 3901-3908 (2001). [CrossRef]
  12. M. A. Herráez, J. G. Boticario, M. J. Lalor, and D. R. Burton, “Agglomerative clustering-based approach for two-dimensional phase unwrapping,” Appl. Opt. 44, 1129-1140 (2005). [CrossRef] [PubMed]
  13. A. Baldi, “Two-dimensional phase unwrapping by quad-tree decomposition,” Appl. Opt. 40, 1187-1194 (2001). [CrossRef]
  14. M. Jenkinson, “A fast, automated, n-dimensional phase unwrapping algorithm,” Magn. Reson. Med. 49, 193-197(2003). [CrossRef] [PubMed]
  15. M. A. Herráez, D. R. Burton, M. J. Lalor, and M. A. Gdeisat, “Robust, fast and effective two dimensional automatic phase unwrapping algorithm based on image decomposition,” Appl. Opt. 41, 7445-7455 (2002). [CrossRef] [PubMed]
  16. N. H. Ching, D. Rosenfeld, and M. Braun, “Two-dimensional phase unwrapping using a minimum spanning tree algorithm,” IEEE Trans. Image Process. 1, 355-365(1992). [CrossRef]
  17. L. An, Q.-S. Xiang, and S. Chavez, “A fast implementation of the minimum spanning tree method for phase unwrapping,” IEEE Trans. Med. Imaging 19, 805-808(2000). [CrossRef] [PubMed]
  18. M. A. Herráez, D. R. Burton, M. J. Lalor, and M. A. Gdeisat, “Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path,” Appl. Opt. 41, 7437-7444 (2002). [CrossRef] [PubMed]
  19. H. S. Abdul-Rahman, M. A. Gdeisat, D. R. Burton, M. J. Lalor, F. Lilley, and C. J. Moore, “Fast and robust three-dimensional best path phase unwrapping algorithm,” Appl. Opt. 46, 6623-6635 (2007). [CrossRef] [PubMed]
  20. R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713-720 (1988). [CrossRef]
  21. H. W. Kuhn, “The Hungarian method for the assignment problem,” Naval Res. Log. Q. 2, 83-97 (1955). [CrossRef]
  22. “Extending the dynamic range of phase contrast magnetic resonance velocity imaging using advanced higher-dimensional phase unwrapping algorithms,” J. R. Soc. Interface 3, 415-427(2006). [CrossRef] [PubMed]
  23. M. F. Salfity, P. D. Ruiz, J. M. Huntley, M. J. Graves, R. Cusack, and D. A. Beauregard, “Branch cut surface placement for unwrapping of undersampled three-dimensional phase data: application to magnetic resonance imaging arterial flow mapping,” Appl. Opt. 45, 2711-2722 (2006). [CrossRef] [PubMed]
  24. O. Marklund, J. M. Huntley, and R. Cusack, “Robust unwrapping algorithm for three-dimensional phase volumes of arbitrary shape containing knotted phase singularity loops,” Opt. Eng. 46, (2007). [CrossRef]
  25. A. Hooper and H. A. Zebker, “Phase unwrapping in three dimensions with application to InSAR time series,” J. Opt. Soc. Am. A 24, 2737-2747 (2007). [CrossRef]
  26. K. Brakke, “The surface evolver,” Exp. Math. 1, 141-165 (1992).
  27. M. T. Goodrich and R. Tamassia, “Kruskal's algorithm,” in Data Structures and Algorithms in Java, 4th ed. (Wiley, 2006), Chap. 13, Section 13.7, p. 632.
  28. S. Chavez, Q.-S. Xiang, and L. An, “Understanding phase maps in mri: a new cutline phase unwrapping method,” IEEE Trans. Med. Imaging 21, 966-977 (2002). [CrossRef] [PubMed]
  29. B. W. Silverman, Density Estimation for Statistics and Data Analysis (CRC, 1986).

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