Uniform estimation of orientation using local and nonlocal 2-D energy operators

M. Felsberg and E. Jonsson, “Energy tensors: Quadratic phase invariant image operators,” DAGM Symposium, Mustererkennung, Wien, (2005),

M. Felsberg and G. H. Granlund, “Detection using Channel Clustering and the 2D Energy Tensor,” Pattern Recognition: 26th DAGM Symposium, Tübingen, Germany, (2004), pp. 103–110.

J. Bigun, T. Bigun, and K. Nilsson., “Recognition by symmetry derivatives and the generalized structure tensor,” IEEE Trans. Pattern Anal. Mach. Intell. 26, (2004).
[Crossref] [PubMed]

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, and N. I. Smith, et al., “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7–12 (2004).
[Crossref] [PubMed]

B. Forster, T. Blu, and M. Unser., “A New Family of Complex Rotation-Covariant Multiresolution Bases in 2D,” Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing X, San Diego CA, USA, (2003), 475–479.

J. M. Huntley, “Fringe analysis today and tomorrow,” Speckle Metrology 2003, Trondheim, Norway, (2003), 167–174.

M. Servin, J. A. Quiroga, and J. L. Marroquin, “General n-dimensional quadrature transform and its application to interferogram demodulation,” J. Opt. Soc. Am. A 20, 925–934 (2003).
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J. A. Quiroga, M. Servin, and F. Cuevas, “Modulo two pi fringe orientation angle estimation by phase unwrapping with a regularized phase tracking algorithm,” J. Opt. Soc. Am. A 19, 1524–1531 (2002).
[Crossref]

M. Felsberg, “Low-Level Image Processing with the Structure Multivector,” PhD thesis. Christian-Albrechts-University of Kiel, 2002. http://www.isy.liu.se/~mfe/Diss.ps.gz

P. A. Fletcher and K. G. Larkin, “Direct Embedding and Detection of RST Invariant Watermarks,” IH2002, Fifth International Workshop on Information Hiding, Noordwijkerhout, The Netherlands, (2002), 129–144.

P.-E. Danielsson, Q. Lin, and Q.-Z. Ye, “Efficient detection of second degree variations in 2D and 3D images,” Journal of Vis. Commun. Image Represent. 12, 255–305 (2001).
[Crossref]

J. P. Da Costa, F. Le Pouliquen, C. Germain, and P. Baylou, “New operators for optimized orientation estimation,” ICIP 2001, Thessaloniki, Greece, (2001).

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J. V. d. Weijer, L. J. v. Vliet, P. W. Verbeek, and M. v. Ginkel, “Curvature estimation in oriented patterns using curvilinear models applied to gradient vector fields,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 1035–1042 (2001).
[Crossref]

K. G. Larkin, D. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns: I. General background to the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18, pp.1862–1870 (2001).
[Crossref]

K. G. Larkin, “Natural demodulation of two-dimensional fringe patterns: II. Stationary phase analysis of the spiral phase quadrature transform.,” J. Opt. Soc. Am. A 18, pp.1871–1881 (2001).
[Crossref]

K. G. Larkin, “A self-calibrating phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns,” Opt. Express 9, 236–253 (2001). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-5-236
[Crossref] [PubMed]

M. Alonso and G. W. Forbes, “Measures of spread for periodic distributions and the associated uncertainty relations,” Am. J. Phys. 69, 340–347 (2000).

P. Kovesi, “Image Features From Phase Congruency,” Videre: A Journal of Computer Vision Research, MIT Press 1, (1999). http://mitpress.mit.edu/e-journals/Videre/001/v13.html

X. Zhou, J. P. Baird, and J. F. Arnold, “Fringe-Orientation Estimation by use of a Gaussian Gradient Filter and Neighboring-Direction Averaging,” Appl. Opt. 38, 795–804 (1999).
[Crossref]

R. Hamila, J. Astola, M. A. Cheikh, and M. Gabbouj, et al., “Teager energy and the ambiguity function,” IEEE Trans. Signal Process. 47, 260–262 (1999).
[Crossref]

L. Hong, Y. F. Wan, and A. Jain, “Fingerprint Image Enhancement - Algorithm and Performance Evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 777–789 (1998).
[Crossref]

J. Burke and H. Helmers, “Complex Division as a Common Basis for Calculating Phase Differences in Electronic Speckle Pattern Interferometry in One Step,” Appl. Opt. 37, 2589–2590 (1998).
[Crossref]

H. Canabal, J. A. Quiroga, and E. Bernabeu, “Automatic processing in moire deflectometry by local fringe direction calculation,” Appl. Opt. 37, 5894–5901 (1998).
[Crossref]

J. P. Havlicek, D. S. Harding, and A. C. Bovik, “Multicomponent Multidimensional Signals,” Multidimens. Syst. Signal Process.  9, 391–398 (1998).
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J. L. Marroquin, R. Rodriguez-Vera, and M. Servin, “Local phase from local orientation by solution of a sequence of linear systems,” J. Opt. Soc. Am. A 15, 1536–1544 (1998).
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A. C. Bovik, J. Havlicek, M. Desai, and D. Harding, “Limits on discrete modulated signals,” IEEE Trans. Signal Process.  45, 867–879 (1997).
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B. Jahne, Practical handbook on Image processing for Scientific applications, CRC Press, Boca Raton, Florida, 1997.

J. P. Havlicek, “AM-FM Image models,” PhD thesis. University of Texas, 1996. http://hotnsour.ou.edu/joebob/PdfPubs/JPHavlicekDiss.pdf

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J. G. Daugman and C. J. Downing, “Demodulation, predictive coding, and spatial vision,” J. Opt. Soc. Am. A 12, 641–660 (1995).
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P. Maragos and A. C. Bovik, “Image Demodulation Using Multidimensional Energy Separation” J. Opt. Soc. Am. A 12, pp.1867–1876 (1995).
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H. Knutsson and M. Andersson, “Robust N-Dimensional Orientation Estimation using Quadrature Filters and Tensor Whitening,” ICASSP ′94, Adelaide, Australia, (1994). http://www.cvl.isy.liu.se/ScOut/Publications/PaperInfo/ka94.html

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P. Maragos, J. F. Kaiser, and T. F. Quatieri, “On amplitude and frequency demodulation using energy operators,” IEEE Trans. Sig. Process.  41, 1532–1550 (1993).
[Crossref]

A. C. Bovik, P. Maragos, and T. F. Quatieri, “AM-FM energy detection and separation in noise using multiband energy operators,” IEEE Trans. Sig. Process. 41, 3245–3265 (1993).
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P. Maragos, T. F. Quatieri, and J. F. Kaiser, “On separating amplitude from frequency modulations using energy operators,” Proc IEEE Int. Conf. ASSP, San Francisco, CA, (1992), 1–4.

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M. Alonso and G. W. Forbes, “Measures of spread for periodic distributions and the associated uncertainty relations,” Am. J. Phys. 69, 340–347 (2000).

H. Knutsson and M. Andersson, “Robust N-Dimensional Orientation Estimation using Quadrature Filters and Tensor Whitening,” ICASSP ′94, Adelaide, Australia, (1994). http://www.cvl.isy.liu.se/ScOut/Publications/PaperInfo/ka94.html

Q. Yu and K. Andresen, “Fringe-orientation maps and fringe skeleton extraction by the two-dimensional derivative-sign binary-fringe method,” Appl. Opt. 33, 6873–6878 (1994).
[Crossref] [PubMed]

K. Andresen and Q. Yu, “Robust Phase Unwrapping By Spin Filtering Combined With a Phase Direction Map,” Optik 94, pp.145–149 (1993).

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, and N. I. Smith, et al., “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7–12 (2004).
[Crossref] [PubMed]

X. Zhou, J. P. Baird, and J. F. Arnold, “Fringe-Orientation Estimation by use of a Gaussian Gradient Filter and Neighboring-Direction Averaging,” Appl. Opt. 38, 795–804 (1999).
[Crossref]

R. Hamila, J. Astola, M. A. Cheikh, and M. Gabbouj, et al., “Teager energy and the ambiguity function,” IEEE Trans. Signal Process. 47, 260–262 (1999).
[Crossref]

X. Zhou, J. P. Baird, and J. F. Arnold, “Fringe-Orientation Estimation by use of a Gaussian Gradient Filter and Neighboring-Direction Averaging,” Appl. Opt. 38, 795–804 (1999).
[Crossref]

J. P. Da Costa, F. Le Pouliquen, C. Germain, and P. Baylou, “New operators for optimized orientation estimation,” ICIP 2001, Thessaloniki, Greece, (2001).

E. H. Adelson and J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).
[Crossref] [PubMed]

H. Canabal, J. A. Quiroga, and E. Bernabeu, “Automatic processing in moire deflectometry by local fringe direction calculation,” Appl. Opt. 37, 5894–5901 (1998).
[Crossref]

J. Bigun, T. Bigun, and K. Nilsson., “Recognition by symmetry derivatives and the generalized structure tensor,” IEEE Trans. Pattern Anal. Mach. Intell. 26, (2004).
[Crossref] [PubMed]

J. Bigun, T. Bigun, and K. Nilsson., “Recognition by symmetry derivatives and the generalized structure tensor,” IEEE Trans. Pattern Anal. Mach. Intell. 26, (2004).
[Crossref] [PubMed]

B. Forster, T. Blu, and M. Unser., “A New Family of Complex Rotation-Covariant Multiresolution Bases in 2D,” Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing X, San Diego CA, USA, (2003), 475–479.

K. G. Larkin, D. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns: I. General background to the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18, pp.1862–1870 (2001).
[Crossref]

J. P. Havlicek, D. S. Harding, and A. C. Bovik, “Multicomponent Multidimensional Signals,” Multidimens. Syst. Signal Process.  9, 391–398 (1998).
[Crossref]

A. C. Bovik, J. Havlicek, M. Desai, and D. Harding, “Limits on discrete modulated signals,” IEEE Trans. Signal Process.  45, 867–879 (1997).
[Crossref]

P. Maragos and A. C. Bovik, “Image Demodulation Using Multidimensional Energy Separation” J. Opt. Soc. Am. A 12, pp.1867–1876 (1995).
[Crossref]

A. C. Bovik and P. Maragos, “Conditions for positivity of an energy operator,” IEEE Trans. Sig. Process. 42, 469–471 (1994).
[Crossref]

A. C. Bovik, P. Maragos, and T. F. Quatieri, “AM-FM energy detection and separation in noise using multiband energy operators,” IEEE Trans. Sig. Process. 41, 3245–3265 (1993).
[Crossref]

P. Maragos, A. C. Bovik, and T. F. Quatieri, “A multidimensional energy operator for image processing,” SPIE Conference on Visual Communications and Image Processing, Boston, MA, (1992), pp. 177–186.

J. P. Havlicek, J. W. Havlicek, and A. C. Bovik, “The Analytic Image,” IEEE International Conference on Image Processing, Santa Barbara,California, (1997), 446–449.

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J. Burke and H. Helmers, “Complex Division as a Common Basis for Calculating Phase Differences in Electronic Speckle Pattern Interferometry in One Step,” Appl. Opt. 37, 2589–2590 (1998).
[Crossref]

M. C. Morrone and D. C. Burr, “Feature detection in human vision: a phase-dependent energy model,” Proceedings of the Royal Society of London, B 235, 221–245 (1988).
[Crossref]

H. Canabal, J. A. Quiroga, and E. Bernabeu, “Automatic processing in moire deflectometry by local fringe direction calculation,” Appl. Opt. 37, 5894–5901 (1998).
[Crossref]

R. Hamila, J. Astola, M. A. Cheikh, and M. Gabbouj, et al., “Teager energy and the ambiguity function,” IEEE Trans. Signal Process. 47, 260–262 (1999).
[Crossref]

J. A. Quiroga, M. Servin, and F. Cuevas, “Modulo two pi fringe orientation angle estimation by phase unwrapping with a regularized phase tracking algorithm,” J. Opt. Soc. Am. A 19, 1524–1531 (2002).
[Crossref]

J. P. Da Costa, F. Le Pouliquen, C. Germain, and P. Baylou, “New operators for optimized orientation estimation,” ICIP 2001, Thessaloniki, Greece, (2001).

P.-E. Danielsson, Q. Lin, and Q.-Z. Ye, “Efficient detection of second degree variations in 2D and 3D images,” Journal of Vis. Commun. Image Represent. 12, 255–305 (2001).
[Crossref]

J. G. Daugman and C. J. Downing, “Demodulation, predictive coding, and spatial vision,” J. Opt. Soc. Am. A 12, 641–660 (1995).
[Crossref]

J. G. Daugman, “Image analysis and compact coding by oriented Gabor primitives,” Image Understanding and Man Machine interface, 19–30, (1987).

A. C. Bovik, J. Havlicek, M. Desai, and D. Harding, “Limits on discrete modulated signals,” IEEE Trans. Signal Process.  45, 867–879 (1997).
[Crossref]

J. G. Daugman and C. J. Downing, “Demodulation, predictive coding, and spatial vision,” J. Opt. Soc. Am. A 12, 641–660 (1995).
[Crossref]

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M. Felsberg and E. Jonsson, “Energy tensors: Quadratic phase invariant image operators,” DAGM Symposium, Mustererkennung, Wien, (2005),

M. Felsberg and G. H. Granlund, “Detection using Channel Clustering and the 2D Energy Tensor,” Pattern Recognition: 26th DAGM Symposium, Tübingen, Germany, (2004), pp. 103–110.

M. Felsberg, “Low-Level Image Processing with the Structure Multivector,” PhD thesis. Christian-Albrechts-University of Kiel, 2002. http://www.isy.liu.se/~mfe/Diss.ps.gz

M. Felsberg and G. Sommer, “The monogenic signal,” Institut fur informatik, Chritian-Albrechts-Universitat, 2001.

M. Felsberg and U. Köthe, “Get: The connection between monogenic scale-space and gaussian derivatives,” Scale Space and PDE Methods in Computer Vision, ed. R. Kimmel, N. Sochen, and J. Weickert, LNCS, Springer, 2005) 3459: 192–203.
[Crossref]

M. Felsberg, “The GET Operator,” Dept. EE, Linkoping University, 2004.http://www.cvl.isy.liu.se/ScOut/Publications/

P. A. Fletcher and K. G. Larkin, “Direct Embedding and Detection of RST Invariant Watermarks,” IH2002, Fifth International Workshop on Information Hiding, Noordwijkerhout, The Netherlands, (2002), 129–144.

M. Alonso and G. W. Forbes, “Measures of spread for periodic distributions and the associated uncertainty relations,” Am. J. Phys. 69, 340–347 (2000).

B. Forster, T. Blu, and M. Unser., “A New Family of Complex Rotation-Covariant Multiresolution Bases in 2D,” Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing X, San Diego CA, USA, (2003), 475–479.

R. Hamila, J. Astola, M. A. Cheikh, and M. Gabbouj, et al., “Teager energy and the ambiguity function,” IEEE Trans. Signal Process. 47, 260–262 (1999).
[Crossref]

D. Gabor, “Theory of communications,” Journal of the IEE,  93, 429–457 (1947).

J. P. Da Costa, F. Le Pouliquen, C. Germain, and P. Baylou, “New operators for optimized orientation estimation,” ICIP 2001, Thessaloniki, Greece, (2001).

J. V. d. Weijer, L. J. v. Vliet, P. W. Verbeek, and M. v. Ginkel, “Curvature estimation in oriented patterns using curvilinear models applied to gradient vector fields,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 1035–1042 (2001).
[Crossref]

M. Felsberg and G. H. Granlund, “Detection using Channel Clustering and the 2D Energy Tensor,” Pattern Recognition: 26th DAGM Symposium, Tübingen, Germany, (2004), pp. 103–110.

G. H. Granlund and H. Knutsson, Signal processing for computer vision, Kluwer, Dordrecht, Netherlands, 1995.

H. Knutsson, R. Wilson, and G. H. Granlund, “Anisotropic Non-Stationary Image Estimation and its Applications ┅ Part I: Restoration of Noisy Images,” IEEE Trans. Commun. 31, 388╌397 (1983).
[Crossref]

R. Hamila, J. Astola, M. A. Cheikh, and M. Gabbouj, et al., “Teager energy and the ambiguity function,” IEEE Trans. Signal Process. 47, 260–262 (1999).
[Crossref]

A. C. Bovik, J. Havlicek, M. Desai, and D. Harding, “Limits on discrete modulated signals,” IEEE Trans. Signal Process.  45, 867–879 (1997).
[Crossref]

J. P. Havlicek, D. S. Harding, and A. C. Bovik, “Multicomponent Multidimensional Signals,” Multidimens. Syst. Signal Process.  9, 391–398 (1998).
[Crossref]

V. Havin and B. Joricke, The uncertainty principle in harmonic analysis, Springer-Verlag, Berlin, 1994.

A. C. Bovik, J. Havlicek, M. Desai, and D. Harding, “Limits on discrete modulated signals,” IEEE Trans. Signal Process.  45, 867–879 (1997).
[Crossref]

J. P. Havlicek, D. S. Harding, and A. C. Bovik, “Multicomponent Multidimensional Signals,” Multidimens. Syst. Signal Process.  9, 391–398 (1998).
[Crossref]

J. P. Havlicek, “AM-FM Image models,” PhD thesis. University of Texas, 1996. http://hotnsour.ou.edu/joebob/PdfPubs/JPHavlicekDiss.pdf

J. P. Havlicek, J. W. Havlicek, and A. C. Bovik, “The Analytic Image,” IEEE International Conference on Image Processing, Santa Barbara,California, (1997), 446–449.

J. P. Havlicek, J. W. Havlicek, and A. C. Bovik, “The Analytic Image,” IEEE International Conference on Image Processing, Santa Barbara,California, (1997), 446–449.

J. Burke and H. Helmers, “Complex Division as a Common Basis for Calculating Phase Differences in Electronic Speckle Pattern Interferometry in One Step,” Appl. Opt. 37, 2589–2590 (1998).
[Crossref]

L. Hong, Y. F. Wan, and A. Jain, “Fingerprint Image Enhancement - Algorithm and Performance Evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 777–789 (1998).
[Crossref]

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J. M. Huntley, “Fringe analysis today and tomorrow,” Speckle Metrology 2003, Trondheim, Norway, (2003), 167–174.

B. Jahne, Practical handbook on Image processing for Scientific applications, CRC Press, Boca Raton, Florida, 1997.

L. Hong, Y. F. Wan, and A. Jain, “Fingerprint Image Enhancement - Algorithm and Performance Evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 777–789 (1998).
[Crossref]

C. F. Shu and R. C. Jain, “Direct Estimation and Error Analysis For Oriented Patterns,” CVGIP-Image Understanding 58, 383–398 (1993).
[Crossref]

M. Felsberg and E. Jonsson, “Energy tensors: Quadratic phase invariant image operators,” DAGM Symposium, Mustererkennung, Wien, (2005),

V. Havin and B. Joricke, The uncertainty principle in harmonic analysis, Springer-Verlag, Berlin, 1994.

P. Maragos, J. F. Kaiser, and T. F. Quatieri, “On amplitude and frequency demodulation using energy operators,” IEEE Trans. Sig. Process.  41, 1532–1550 (1993).
[Crossref]

P. Maragos, T. F. Quatieri, and J. F. Kaiser, “On separating amplitude from frequency modulations using energy operators,” Proc IEEE Int. Conf. ASSP, San Francisco, CA, (1992), 1–4.

P. Maragos, T. F. Quatieri, and J. F. Kaiser, “Speech nonlinearities, modulations, and energy operators,” Proc IEEE Int. Conf. ASSP, Toronto, Canada, (1991), 421–424.

J. F. Kaiser, “On a simple algorithm to calculate the 'energy' of a signal,” Proc IEEE Int. Conf. Acoust. Speech, Signal Processing, Albuquerque, NM, (1990), pp. 381–384.

M. Kass and A. Witkin, “Analyzing oriented patterns,” CVGIP 37, 362–385 (1987).

G. H. Granlund and H. Knutsson, Signal processing for computer vision, Kluwer, Dordrecht, Netherlands, 1995.

H. Knutsson and M. Andersson, “Robust N-Dimensional Orientation Estimation using Quadrature Filters and Tensor Whitening,” ICASSP ′94, Adelaide, Australia, (1994). http://www.cvl.isy.liu.se/ScOut/Publications/PaperInfo/ka94.html

H. Knutsson, R. Wilson, and G. H. Granlund, “Anisotropic Non-Stationary Image Estimation and its Applications ┅ Part I: Restoration of Noisy Images,” IEEE Trans. Commun. 31, 388╌397 (1983).
[Crossref]

H. Knutsson, “Filtering and Reconstruction in Image Processing,” PhD. Linkoping University, 1982.

J. J. Koenderink and W. Richards, “Two-dimensional curvature operators,” J. Opt. Soc. Am. A 5, 1136–1141 (1988).
[Crossref]

M. Felsberg and U. Köthe, “Get: The connection between monogenic scale-space and gaussian derivatives,” Scale Space and PDE Methods in Computer Vision, ed. R. Kimmel, N. Sochen, and J. Weickert, LNCS, Springer, 2005) 3459: 192–203.
[Crossref]

P. Kovesi, “Image Features From Phase Congruency,” Videre: A Journal of Computer Vision Research, MIT Press 1, (1999). http://mitpress.mit.edu/e-journals/Videre/001/v13.html

G. Krieger and C. Zetzche, “Nonlinear image operators for evaluation of local intrinsic dimension,” IEEE Trans. Image Process. 5, 1026–1042 (1996).
[Crossref] [PubMed]

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, and N. I. Smith, et al., “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7–12 (2004).
[Crossref] [PubMed]

P. A. Fletcher and K. G. Larkin, “Direct Embedding and Detection of RST Invariant Watermarks,” IH2002, Fifth International Workshop on Information Hiding, Noordwijkerhout, The Netherlands, (2002), 129–144.

K. G. Larkin, “A self-calibrating phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns,” Opt. Express 9, 236–253 (2001). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-5-236
[Crossref] [PubMed]

K. G. Larkin, D. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns: I. General background to the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18, pp.1862–1870 (2001).
[Crossref]

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