Abstract

We propose a three-dimensional phase unwrapping technique that uses the Hungarian algorithm to join together all the partial residual loops that may occur in a wrapped phase volume. Experimental results have shown that the proposed algorithm is more robust and reliable than other well-known three-dimensional phase unwrapping algorithms. Additionally, the proposed algorithm is fast in terms of computational complexity, which makes it suitable for practical applications.

© 2009 Optical Society of America

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References

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  1. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software (Wiley, 1998).
  2. R. Cusack and N. Papadakis, Neuroimage 16, 754 (2001).
    [CrossRef]
  3. H. S. Abdul-Rahman, M. A. Gdeisat, D. R. Burton, M. J. Lalor, F. Lilley, and C. Moore, Appl. Opt. 46, 6623 (2007).
    [CrossRef] [PubMed]
  4. M. Jenkinson, Magn. Reson. Med. 49, 193 (2003).
    [CrossRef] [PubMed]
  5. J. M. Huntley, Appl. Opt. 40, 3901 (2001).
    [CrossRef]
  6. M. F. Salfity, P. D. Ruiz, J. M. Huntley, M. J. Graves, R. Cusack, and D. A. Beauregard, J. R. Soc. Interface 3, 415 (2006).
    [CrossRef] [PubMed]
  7. A. Hooper and H. A. Zebker, J. Opt. Soc. Am. A 24, 2737 (2007).
    [CrossRef]
  8. “Phase unwrapping,” http://www.ljmu.ac.uk/GERI/90202.htm.

2007

2006

M. F. Salfity, P. D. Ruiz, J. M. Huntley, M. J. Graves, R. Cusack, and D. A. Beauregard, J. R. Soc. Interface 3, 415 (2006).
[CrossRef] [PubMed]

2003

M. Jenkinson, Magn. Reson. Med. 49, 193 (2003).
[CrossRef] [PubMed]

2001

J. M. Huntley, Appl. Opt. 40, 3901 (2001).
[CrossRef]

R. Cusack and N. Papadakis, Neuroimage 16, 754 (2001).
[CrossRef]

Abdul-Rahman, H. S.

Beauregard, D. A.

M. F. Salfity, P. D. Ruiz, J. M. Huntley, M. J. Graves, R. Cusack, and D. A. Beauregard, J. R. Soc. Interface 3, 415 (2006).
[CrossRef] [PubMed]

Burton, D. R.

Cusack, R.

M. F. Salfity, P. D. Ruiz, J. M. Huntley, M. J. Graves, R. Cusack, and D. A. Beauregard, J. R. Soc. Interface 3, 415 (2006).
[CrossRef] [PubMed]

R. Cusack and N. Papadakis, Neuroimage 16, 754 (2001).
[CrossRef]

Gdeisat, M. A.

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software (Wiley, 1998).

Graves, M. J.

M. F. Salfity, P. D. Ruiz, J. M. Huntley, M. J. Graves, R. Cusack, and D. A. Beauregard, J. R. Soc. Interface 3, 415 (2006).
[CrossRef] [PubMed]

Hooper, A.

Huntley, J. M.

M. F. Salfity, P. D. Ruiz, J. M. Huntley, M. J. Graves, R. Cusack, and D. A. Beauregard, J. R. Soc. Interface 3, 415 (2006).
[CrossRef] [PubMed]

J. M. Huntley, Appl. Opt. 40, 3901 (2001).
[CrossRef]

Jenkinson, M.

M. Jenkinson, Magn. Reson. Med. 49, 193 (2003).
[CrossRef] [PubMed]

Lalor, M. J.

Lilley, F.

Moore, C.

Papadakis, N.

R. Cusack and N. Papadakis, Neuroimage 16, 754 (2001).
[CrossRef]

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software (Wiley, 1998).

Ruiz, P. D.

M. F. Salfity, P. D. Ruiz, J. M. Huntley, M. J. Graves, R. Cusack, and D. A. Beauregard, J. R. Soc. Interface 3, 415 (2006).
[CrossRef] [PubMed]

Salfity, M. F.

M. F. Salfity, P. D. Ruiz, J. M. Huntley, M. J. Graves, R. Cusack, and D. A. Beauregard, J. R. Soc. Interface 3, 415 (2006).
[CrossRef] [PubMed]

Zebker, H. A.

Appl. Opt.

J. Opt. Soc. Am. A

J. R. Soc. Interface

M. F. Salfity, P. D. Ruiz, J. M. Huntley, M. J. Graves, R. Cusack, and D. A. Beauregard, J. R. Soc. Interface 3, 415 (2006).
[CrossRef] [PubMed]

Magn. Reson. Med.

M. Jenkinson, Magn. Reson. Med. 49, 193 (2003).
[CrossRef] [PubMed]

Neuroimage

R. Cusack and N. Papadakis, Neuroimage 16, 754 (2001).
[CrossRef]

Other

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software (Wiley, 1998).

“Phase unwrapping,” http://www.ljmu.ac.uk/GERI/90202.htm.

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Figures (4)

Fig. 1
Fig. 1

Closed singularity loops and partial singularity loops in the phase volume.

Fig. 2
Fig. 2

Example construction of a phase volume with two crossing loops that break at the opposite boundaries. (a) 2D phase map with two residues of different signs; (b) 3D phase map built by stacking together a pile of these 2D phase maps; (c) incomplete loops in the 3D volume.

Fig. 3
Fig. 3

Resulting branch cut surface when (a) each loop in Fig. 2c is closed on itself; (b) ends are allowed to connect to other incomplete loops.

Fig. 4
Fig. 4

(a) Source wrapped-phase maps, produced by Fourier fringe analysis of fringe patterns projected onto the head of a radiotherapy RANDO phantom; (b)–(f) show a selection of different unwrapped-phase maps that have been produced by application of the following respective unwrapping algorithms: (b) Cusack’s algorithm, (c) the Prelude algorithm, (d) Huntley’s algorithm, (e) the author M. Gdeisat’s best path algorithm, and (f) the proposed algorithm.

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