Abstract

An evaluation of the suitability of eight existing phase unwrapping algorithms to be used in a real-time optical body surface sensor based on Fourier fringe profilometry is presented. The algorithms are assessed on both the robustness of the results they give and their speed of execution. The algorithms are evaluated using four sets of real human body surface data, each containing five-hundred frames, obtained from patients undergoing radiotherapy, where fringe discontinuity is significant. We also present modifications to an existing algorithm, noncontinuous quality-guided path algorithm (NCQUAL), in order to decrease its execution time by a factor of 4 to make it suitable for use in a real-time system. The results obtained from the modified algorithm are compared with those of the existing algorithms. Three suitable algorithms were identified: two-stage noncontinuous quality-guided path algorithm (TSNCQUAL)—the modified algorithm presented here—for online processing and Flynn’s minimum discontinuity algorithm (FLYNN) and preconditioned conjugate gradient method (PCG) algorithms for enhanced accuracy in off-line processing.

© 2011 Optical Society of America

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References

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  1. C. J. Moore, F. Lilley, V. Sauret, M. J. Lalor, and D. R. Burton, “Opto-electronic sensing of body surface topology changes during radiotherapy for rectal cancer,” Int. J. Radiat. Oncol. Biol. Phys. 56, 248–258 (2003).
    [CrossRef] [PubMed]
  2. G. J. Price, P. J. Sharrock, T. E. Marchant, J. M. Parkhurst, D. J. Burton, P. Jain, P. Price, and C. J. Moore, “An analysis of breast motion using high-frequency, dense surface points captured by an optical sensor during radiotherapy treatment delivery,” Phys. Med. Biol. 54, 6515–6533(2009).
    [CrossRef] [PubMed]
  3. G. J. Price, T. E. Marchant, J. M. Parkhurst, P. J. Sharrock, G. Whitfield, and C. J. Moore, “Design of, and some clinical experience with, a novel optical surface measurement system in radiotherapy,” Proc. SPIE 7822, 76224B (2010).
    [CrossRef]
  4. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160(1982).
    [CrossRef]
  5. M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1983).
    [CrossRef] [PubMed]
  6. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  7. J. Strand and T. Taxt, “Performance evaluation of two-dimensional phase unwrapping algorithms,” Appl. Opt. 38, 4333–4344 (1999).
    [CrossRef]
  8. E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46, 106–116 (2008).
    [CrossRef]
  9. 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]
  10. R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
    [CrossRef]
  11. T. J. Flynn, “Consistent 2-D phase unwrapping guided by a quality map,” in Proceedings of the International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, 1996), pp. 2057–2059.
  12. T. J. Flynn, “Two-dimensional phase unwrapping with minimum weighted discontinuity,” J. Opt. Soc. Am. A 14, 2692–2701 (1997).
    [CrossRef]
  13. M. D. Pritt, “Multigrid phase unwrapping for interferometric SAR,” in Proceedings of the International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, 1995), pp. 562–564.
  14. D. C. Ghiglia and L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. A 11, 107–117 (1994).
    [CrossRef]
  15. D. C. Ghiglia and L. A. Romero, “Minimum Lp-norm two-dimensional phase unwrapping,” J. Opt. Soc. Am. A 13, 1999–2013 (1996).
    [CrossRef]
  16. G. J. Price, J. M. Parkhurst, P. J. Sharrock, T. E. Marchant, and C. J. Moore, “A real-time robust Fourier profilometry system for use in image guided radiotherapy,” Phys. Med. Biol. (posted August 2011, submitted).
    [PubMed]
  17. F. Lilley, M. J. Lalor, and D. R. Burton, “Robust fringe analysis system for human body shape measurement,” Opt. Eng. 39, 187–195 (2000).
    [CrossRef]

2010

G. J. Price, T. E. Marchant, J. M. Parkhurst, P. J. Sharrock, G. Whitfield, and C. J. Moore, “Design of, and some clinical experience with, a novel optical surface measurement system in radiotherapy,” Proc. SPIE 7822, 76224B (2010).
[CrossRef]

2009

G. J. Price, P. J. Sharrock, T. E. Marchant, J. M. Parkhurst, D. J. Burton, P. Jain, P. Price, and C. J. Moore, “An analysis of breast motion using high-frequency, dense surface points captured by an optical sensor during radiotherapy treatment delivery,” Phys. Med. Biol. 54, 6515–6533(2009).
[CrossRef] [PubMed]

2008

E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46, 106–116 (2008).
[CrossRef]

2003

C. J. Moore, F. Lilley, V. Sauret, M. J. Lalor, and D. R. Burton, “Opto-electronic sensing of body surface topology changes during radiotherapy for rectal cancer,” Int. J. Radiat. Oncol. Biol. Phys. 56, 248–258 (2003).
[CrossRef] [PubMed]

2002

2000

F. Lilley, M. J. Lalor, and D. R. Burton, “Robust fringe analysis system for human body shape measurement,” Opt. Eng. 39, 187–195 (2000).
[CrossRef]

1999

1997

1996

1994

1988

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

1983

1982

Burton, D. J.

G. J. Price, P. J. Sharrock, T. E. Marchant, J. M. Parkhurst, D. J. Burton, P. Jain, P. Price, and C. J. Moore, “An analysis of breast motion using high-frequency, dense surface points captured by an optical sensor during radiotherapy treatment delivery,” Phys. Med. Biol. 54, 6515–6533(2009).
[CrossRef] [PubMed]

Burton, D. R.

C. J. Moore, F. Lilley, V. Sauret, M. J. Lalor, and D. R. Burton, “Opto-electronic sensing of body surface topology changes during radiotherapy for rectal cancer,” Int. J. Radiat. Oncol. Biol. Phys. 56, 248–258 (2003).
[CrossRef] [PubMed]

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]

F. Lilley, M. J. Lalor, and D. R. Burton, “Robust fringe analysis system for human body shape measurement,” Opt. Eng. 39, 187–195 (2000).
[CrossRef]

Busca, G.

E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46, 106–116 (2008).
[CrossRef]

Flynn, T. J.

T. J. Flynn, “Two-dimensional phase unwrapping with minimum weighted discontinuity,” J. Opt. Soc. Am. A 14, 2692–2701 (1997).
[CrossRef]

T. J. Flynn, “Consistent 2-D phase unwrapping guided by a quality map,” in Proceedings of the International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, 1996), pp. 2057–2059.

Gdeisat, M. A.

Ghiglia, D. C.

Goldstein, R. M.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Herráez, M. A.

Ina, H.

Jain, P.

G. J. Price, P. J. Sharrock, T. E. Marchant, J. M. Parkhurst, D. J. Burton, P. Jain, P. Price, and C. J. Moore, “An analysis of breast motion using high-frequency, dense surface points captured by an optical sensor during radiotherapy treatment delivery,” Phys. Med. Biol. 54, 6515–6533(2009).
[CrossRef] [PubMed]

Kobayashi, S.

Lalor, M. J.

C. J. Moore, F. Lilley, V. Sauret, M. J. Lalor, and D. R. Burton, “Opto-electronic sensing of body surface topology changes during radiotherapy for rectal cancer,” Int. J. Radiat. Oncol. Biol. Phys. 56, 248–258 (2003).
[CrossRef] [PubMed]

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]

F. Lilley, M. J. Lalor, and D. R. Burton, “Robust fringe analysis system for human body shape measurement,” Opt. Eng. 39, 187–195 (2000).
[CrossRef]

Lilley, F.

C. J. Moore, F. Lilley, V. Sauret, M. J. Lalor, and D. R. Burton, “Opto-electronic sensing of body surface topology changes during radiotherapy for rectal cancer,” Int. J. Radiat. Oncol. Biol. Phys. 56, 248–258 (2003).
[CrossRef] [PubMed]

F. Lilley, M. J. Lalor, and D. R. Burton, “Robust fringe analysis system for human body shape measurement,” Opt. Eng. 39, 187–195 (2000).
[CrossRef]

Marchant, T. E.

G. J. Price, T. E. Marchant, J. M. Parkhurst, P. J. Sharrock, G. Whitfield, and C. J. Moore, “Design of, and some clinical experience with, a novel optical surface measurement system in radiotherapy,” Proc. SPIE 7822, 76224B (2010).
[CrossRef]

G. J. Price, P. J. Sharrock, T. E. Marchant, J. M. Parkhurst, D. J. Burton, P. Jain, P. Price, and C. J. Moore, “An analysis of breast motion using high-frequency, dense surface points captured by an optical sensor during radiotherapy treatment delivery,” Phys. Med. Biol. 54, 6515–6533(2009).
[CrossRef] [PubMed]

G. J. Price, J. M. Parkhurst, P. J. Sharrock, T. E. Marchant, and C. J. Moore, “A real-time robust Fourier profilometry system for use in image guided radiotherapy,” Phys. Med. Biol. (posted August 2011, submitted).
[PubMed]

Moore, C. J.

G. J. Price, T. E. Marchant, J. M. Parkhurst, P. J. Sharrock, G. Whitfield, and C. J. Moore, “Design of, and some clinical experience with, a novel optical surface measurement system in radiotherapy,” Proc. SPIE 7822, 76224B (2010).
[CrossRef]

G. J. Price, P. J. Sharrock, T. E. Marchant, J. M. Parkhurst, D. J. Burton, P. Jain, P. Price, and C. J. Moore, “An analysis of breast motion using high-frequency, dense surface points captured by an optical sensor during radiotherapy treatment delivery,” Phys. Med. Biol. 54, 6515–6533(2009).
[CrossRef] [PubMed]

C. J. Moore, F. Lilley, V. Sauret, M. J. Lalor, and D. R. Burton, “Opto-electronic sensing of body surface topology changes during radiotherapy for rectal cancer,” Int. J. Radiat. Oncol. Biol. Phys. 56, 248–258 (2003).
[CrossRef] [PubMed]

G. J. Price, J. M. Parkhurst, P. J. Sharrock, T. E. Marchant, and C. J. Moore, “A real-time robust Fourier profilometry system for use in image guided radiotherapy,” Phys. Med. Biol. (posted August 2011, submitted).
[PubMed]

Mutoh, K.

Parkhurst, J. M.

G. J. Price, T. E. Marchant, J. M. Parkhurst, P. J. Sharrock, G. Whitfield, and C. J. Moore, “Design of, and some clinical experience with, a novel optical surface measurement system in radiotherapy,” Proc. SPIE 7822, 76224B (2010).
[CrossRef]

G. J. Price, P. J. Sharrock, T. E. Marchant, J. M. Parkhurst, D. J. Burton, P. Jain, P. Price, and C. J. Moore, “An analysis of breast motion using high-frequency, dense surface points captured by an optical sensor during radiotherapy treatment delivery,” Phys. Med. Biol. 54, 6515–6533(2009).
[CrossRef] [PubMed]

G. J. Price, J. M. Parkhurst, P. J. Sharrock, T. E. Marchant, and C. J. Moore, “A real-time robust Fourier profilometry system for use in image guided radiotherapy,” Phys. Med. Biol. (posted August 2011, submitted).
[PubMed]

Price, G. J.

G. J. Price, T. E. Marchant, J. M. Parkhurst, P. J. Sharrock, G. Whitfield, and C. J. Moore, “Design of, and some clinical experience with, a novel optical surface measurement system in radiotherapy,” Proc. SPIE 7822, 76224B (2010).
[CrossRef]

G. J. Price, P. J. Sharrock, T. E. Marchant, J. M. Parkhurst, D. J. Burton, P. Jain, P. Price, and C. J. Moore, “An analysis of breast motion using high-frequency, dense surface points captured by an optical sensor during radiotherapy treatment delivery,” Phys. Med. Biol. 54, 6515–6533(2009).
[CrossRef] [PubMed]

G. J. Price, J. M. Parkhurst, P. J. Sharrock, T. E. Marchant, and C. J. Moore, “A real-time robust Fourier profilometry system for use in image guided radiotherapy,” Phys. Med. Biol. (posted August 2011, submitted).
[PubMed]

Price, P.

G. J. Price, P. J. Sharrock, T. E. Marchant, J. M. Parkhurst, D. J. Burton, P. Jain, P. Price, and C. J. Moore, “An analysis of breast motion using high-frequency, dense surface points captured by an optical sensor during radiotherapy treatment delivery,” Phys. Med. Biol. 54, 6515–6533(2009).
[CrossRef] [PubMed]

Pritt, M. D.

M. D. Pritt, “Multigrid phase unwrapping for interferometric SAR,” in Proceedings of the International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, 1995), pp. 562–564.

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

Romero, L. A.

Sauret, V.

C. J. Moore, F. Lilley, V. Sauret, M. J. Lalor, and D. R. Burton, “Opto-electronic sensing of body surface topology changes during radiotherapy for rectal cancer,” Int. J. Radiat. Oncol. Biol. Phys. 56, 248–258 (2003).
[CrossRef] [PubMed]

Sharrock, P. J.

G. J. Price, T. E. Marchant, J. M. Parkhurst, P. J. Sharrock, G. Whitfield, and C. J. Moore, “Design of, and some clinical experience with, a novel optical surface measurement system in radiotherapy,” Proc. SPIE 7822, 76224B (2010).
[CrossRef]

G. J. Price, P. J. Sharrock, T. E. Marchant, J. M. Parkhurst, D. J. Burton, P. Jain, P. Price, and C. J. Moore, “An analysis of breast motion using high-frequency, dense surface points captured by an optical sensor during radiotherapy treatment delivery,” Phys. Med. Biol. 54, 6515–6533(2009).
[CrossRef] [PubMed]

G. J. Price, J. M. Parkhurst, P. J. Sharrock, T. E. Marchant, and C. J. Moore, “A real-time robust Fourier profilometry system for use in image guided radiotherapy,” Phys. Med. Biol. (posted August 2011, submitted).
[PubMed]

Strand, J.

Takeda, M.

Taxt, T.

Werner, C. L.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Whitfield, G.

G. J. Price, T. E. Marchant, J. M. Parkhurst, P. J. Sharrock, G. Whitfield, and C. J. Moore, “Design of, and some clinical experience with, a novel optical surface measurement system in radiotherapy,” Proc. SPIE 7822, 76224B (2010).
[CrossRef]

Zappa, E.

E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46, 106–116 (2008).
[CrossRef]

Zebker, H. A.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Appl. Opt.

Int. J. Radiat. Oncol. Biol. Phys.

C. J. Moore, F. Lilley, V. Sauret, M. J. Lalor, and D. R. Burton, “Opto-electronic sensing of body surface topology changes during radiotherapy for rectal cancer,” Int. J. Radiat. Oncol. Biol. Phys. 56, 248–258 (2003).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

F. Lilley, M. J. Lalor, and D. R. Burton, “Robust fringe analysis system for human body shape measurement,” Opt. Eng. 39, 187–195 (2000).
[CrossRef]

Opt. Lasers Eng.

E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46, 106–116 (2008).
[CrossRef]

Phys. Med. Biol.

G. J. Price, P. J. Sharrock, T. E. Marchant, J. M. Parkhurst, D. J. Burton, P. Jain, P. Price, and C. J. Moore, “An analysis of breast motion using high-frequency, dense surface points captured by an optical sensor during radiotherapy treatment delivery,” Phys. Med. Biol. 54, 6515–6533(2009).
[CrossRef] [PubMed]

G. J. Price, J. M. Parkhurst, P. J. Sharrock, T. E. Marchant, and C. J. Moore, “A real-time robust Fourier profilometry system for use in image guided radiotherapy,” Phys. Med. Biol. (posted August 2011, submitted).
[PubMed]

Proc. SPIE

G. J. Price, T. E. Marchant, J. M. Parkhurst, P. J. Sharrock, G. Whitfield, and C. J. Moore, “Design of, and some clinical experience with, a novel optical surface measurement system in radiotherapy,” Proc. SPIE 7822, 76224B (2010).
[CrossRef]

Radio Sci.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Other

T. J. Flynn, “Consistent 2-D phase unwrapping guided by a quality map,” in Proceedings of the International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, 1996), pp. 2057–2059.

M. D. Pritt, “Multigrid phase unwrapping for interferometric SAR,” in Proceedings of the International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, 1995), pp. 562–564.

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

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Figures (6)

Fig. 1
Fig. 1

(a) Possible configuration of regions resulting from the initial unwrap for an 8 × 8 array of pixels; the connections between pixels are shown by the black arrows; the head pixel of each region is marked with a black circle. (b) A typical wrapped phase map and (c) the regions created in it by unwrapping each pixel with respect to its best quality neighbor. (d) The final unwrapped phase map.

Fig. 2
Fig. 2

Flow chart describing operation of the TSNCQUAL algorithm.

Fig. 3
Fig. 3

Diagram showing the layout of the optical sensors heads relative to the treatment couch. The three camera/projector pairs are filtered in the red, green, and blue bands and each capture a portion of the patient body surface, the partial surfaces combine to create a full ‘wrap-around’ surface.

Fig. 4
Fig. 4

Human body surface data. From left to right the figures show, for each dataset, the fringe image captured by the central camera in the optical system, the intensity of the fringes, a mask created by applying a threshold to the fringe intensity image, the wrapped phase map and the (subjectively determined) correctly unwrapped phase map. Figures (a)–(e) are for dataset 1, (f)–(j) dataset 2, (k)–(o) dataset 3, and (p)–(t) dataset 4.

Fig. 5
Fig. 5

Incorrectly unwrapped phase maps produced using the GOLD, MCUT, and MGRID algorithms. Images (a–d) show examples from the GOLD and MCUT algorithms which show similar behavior; images; (e–h) show examples from the MGRID algorithm.

Fig. 6
Fig. 6

(a, e) Incorrectly unwrapped phase maps produced by the QUAL, NCQUAL, TSNQUAL, (b, f) FLYNN, (c, g) PCG, and (d, h) LPNORM algorithms for datasets 2 and 4 (a–d and e–h, respectively).

Tables (3)

Tables Icon

Table 1 Number of Discontinuities in the Unwrapped Phase Maps, Averaged for each Five-Hundred Frame Dataset, for Each of the Phase Unwrapping Algorithms Investigated

Tables Icon

Table 2 Percentage Area of the Masked Area of the Phase Map to be Unwrapped Without Any Discontinuities, Averaged for Each Five-Hundred Frame Dataset, for Each of the Phase Unwrapping Algorithms

Tables Icon

Table 3 Average Execution Time Required for Each of the Datasets for Each of the Phase Unwrapping Algorithms

Metrics