OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 44, Iss. 7 — Mar. 1, 2005
  • pp: 1129–1140

Agglomerative clustering-based approach for two-dimensional phase unwrapping

Miguel Arevalillo Herráez, Jesús G. Boticario, Michael J. Lalor, and David R. Burton  »View Author Affiliations

Applied Optics, Vol. 44, Issue 7, pp. 1129-1140 (2005)

View Full Text Article

Enhanced HTML    Acrobat PDF (2136 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We describe a novel algorithm for two-dimensional phase unwrapping. The technique combines the principles of agglomerative clustering and use of heuristics to construct a discontinuous quality-guided path. Unlike other quality-guided algorithms, which establish the path at the start of the unwrapping process, our technique constructs the path as the unwrapping process evolves. This makes the technique less prone to error propagation, although it presents higher execution times than other existing algorithms. The algorithm reacts satisfactorily to random noise and breaks in the phase distribution. A variation of the algorithm is also presented that considerably reduces the execution time without affecting the results significantly.

© 2005 Optical Society of America

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(150.6910) Machine vision : Three-dimensional sensing

Original Manuscript: July 29, 2004
Revised Manuscript: October 28, 2004
Manuscript Accepted: November 4, 2004
Published: March 1, 2005

Miguel Arevalillo Herráez, Jesús G. Boticario, Michael J. Lalor, and David R. Burton, "Agglomerative clustering-based approach for two-dimensional phase unwrapping," Appl. Opt. 44, 1129-1140 (2005)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. C. Ghiglia, M. D. Pritt, Two-dimensional Phase Unwrapping: Theory, Algorithm, and Software (Wiley, New York, 1998).
  2. R. W. Schafer, A. V. Oppenheim, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), pp. 507–511.
  3. D. Robinson, “Phase unwrapping methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, W. R. Robinson, T. Reid, eds. (Institute of Physics, Philadelphia, Pa., 1993), pp. 194–229.
  4. H. A. Vrooman, A. A. M. Maas, “Image processing algorithms for the analysis of phase-shifted speckle interference patterns,” Appl. Opt. 30, 1636–1641 (1991). [CrossRef] [PubMed]
  5. J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 28, 3268–3270 (1989). [CrossRef] [PubMed]
  6. R. M. Goldstein, H. A. Zebker, C. L. Werner, “Two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988). [CrossRef]
  7. K. M. Hung, T. Yamada, “Phase unwrapping by regions using least-squares approach,” Opt. Eng. 37, 2965–2970 (1998). [CrossRef]
  8. O. Y. Kwon, D. M. Shough, R. A. Williams, “Stroboscopic phase-shifting interferometry,” Opt. Lett. 12, 855–857 (1987). [CrossRef] [PubMed]
  9. J. Schörner, A. Ettemeyer, U. Neupert, H. Rottenkolber, C. Winter, P. Obermeier, “New approaches in interpreting holographic images,” Opt. Lasers Eng. 14, 283–291 (1991). [CrossRef]
  10. J. A. Quiroga, E. Bernabeu, “Phase-unwrapping algorithm for noisy phase-map processing,” Appl. Opt. 33, 6725–6731 (1994). [CrossRef] [PubMed]
  11. J. A. Quiroga, A. González-Cano, E. Bernabeu, “Phase-unwrapping algorithm based on an adaptive criterion,” Appl. Opt. 34, 2560–2563 (1995). [CrossRef] [PubMed]
  12. M. Arevalillo Herráez, D. R. Burton, M. J. Lalor, M. A. Gdeisat, “Fast two-dimensional phase unwrapping algorithm based on sorting by reliability following a noncontinuous path,” Appl. Opt. 41, 7437–7443 (2002). [CrossRef]
  13. D. C. Ghiglia, G. A. Mastin, L. A. Romero, “Cellular-automata method for phase unwrapping,” J. Opt. Soc. Am. A 4, 267–280 (1987). [CrossRef]
  14. D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, “A quasi heterodyne holographic technique and automatic algorithms for phase unwrapping,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. SPIE1163, 95–119 (1989). [CrossRef]
  15. M. Arevalillo Herráez, D. R. Burton, M. J. Lalor, D. B. Clegg, “Robust, simple and fast algorithm for phase unwrapping,” Appl. Opt. 35, 5847–5852 (1996). [CrossRef]
  16. A. Baldi, “Two-dimensional phase unwrapping by quad-tree decomposition,” Appl. Opt. 40, 1187–1194 (2001). [CrossRef]
  17. J. J. Gierloff, “Phase unwrapping by regions,” in Current Developments in Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. SPIE818, 2–9 (1987).
  18. M. Arevalillo Herráez, M. A. Gdeisat, D. R. Burton, M. J. Lalor, “Robust, fast, and effective two-dimensional automatic phase unwrapping algorithm based on image decomposition,” Appl. Opt. 41, 7445–7455 (2002). [CrossRef]
  19. M. Servin, R. Rodriguez-Vera, A. J. Moore, “A robust cellular processor for phase unwrapping,” J. Mod. Opt. 41, 119–127 (1994). [CrossRef]
  20. D. C. Ghiglia, 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]
  21. J. M. Huntley, “New methods for unwrapping noisy phase maps,” in Interferometry ’94: New Techniques and Analysis in Optical Measurements, M. Kujawinska, K. Przysztof, eds., Proc. SPIE, 2340, 110–122 (1994).
  22. J. M. Huntley, H. O. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993). [CrossRef] [PubMed]
  23. A. K. Jain, M. N. Murty, P. J. Flynn, “Data clustering: a review,” ACM Comput. Surveys 31, 264–323 (1999). [CrossRef]
  24. A. K. Jain, P. J. Flynn, Three-Dimensional Object Recognition Systems (Elsevier Science, New York, 1993).
  25. T. Kurita, “An efficient agglomerative clustering algorithm using a heap,” Pattern Recogn. 24, 205–209 (1991). [CrossRef]
  26. J. W. J. Williams, “Heapsort,” Commun. ACM 7, 347–348 (1964).
  27. P. H. A. Sneath, R. R. Sokal, Numerical Taxonomy (Freeman, London, 1973).
  28. B. King, “Step-wise clustering procedures,” J. Am. Stat. Assoc. 69, 86–101 (1967). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited