Abstract

Fringe patterns with noise and discontinuity are often encountered but difficult to analyze. Discontinuity-detectable and boundary-aware processing techniques are demanded. A local orientation coherence based fringe segmentation (LOCS) method and its cooperation with boundary-aware coherence enhancing diffusion (BCED) for discontinuous fringe pattern denoising are proposed in this paper. The LOCS method has three steps. First, as orientation coherence indicated by structure tensors is informative to describe fringe structures, it is selected for discontinuity recognition. Due to the complexity of the discontinuity problem, the detected boundary often has missing parts and is not very accurate. Boundary completion by cubic splines and boundary refinement based on partial structure tensors are further performed as the second and third steps, respectively. Subsequently, the BCED method is developed to adapt the original CED to fringe segments with irregular boundaries. Simulated and experimental fringe patterns are tested and successful results have been obtained.

© 2016 Optical Society of America

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Corrections

3 August 2016: A correction was made to the author affiliations.


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References

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  1. D. W. Robinson and G. T. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics, 1993).
  2. Q. Kemao, Windowed Fringe Pattern Analysis (SPIE, 2013).
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    [Crossref]
  4. C. Galvan and M. Rivera, “Second-order robust regularization cost function for detecting and reconstructing phase discontinuities,” Appl. Opt. 45(2), 353–359 (2006).
    [Crossref] [PubMed]
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    [Crossref]
  6. B. Li, C. Tang, X. Zhu, Y. Su, and W. Xu, “Shearlet transform for phase extraction in fringe projection profilometry with edges discontinuity,” Opt. Lasers Eng. 78, 91–98 (2016).
    [Crossref]
  7. M. Rivera and J. L. Marroquin, “Half-quadratic cost functions for phase unwrapping,” Opt. Lett. 29(5), 504–506 (2004).
    [Crossref] [PubMed]
  8. H. Cui, W. Liao, N. Dai, and X. Cheng, “Reliability-guided phase-unwrapping algorithm for the measurement of discontinuous three-dimensional objects,” Opt. Eng. 50(6), 063602 (2011).
    [Crossref]
  9. M. Zhao, H. Wang, and Q. Kemao, “Snake-assisted quality-guided phase unwrapping for discontinuous phase fields,” Appl. Opt. 54(24), 7462–7470 (2015).
    [Crossref] [PubMed]
  10. W. Ju, D. Xiang, B. Zhang, L. Wang, I. Kopriva, and X. Chen, “Random walk and graph cut for co-segmentation of lung tumor on PET-CT images,” IEEE Trans. Image Process. 24(12), 5854–5867 (2015).
    [Crossref] [PubMed]
  11. V. Estellers, D. Zosso, S. Rongjie Lai, J. Osher, Thiran, and X. Bresson, “Efficient algorithm for level set method preserving distance function,” IEEE Trans. Image Process. 21(12), 4722–4734 (2012).
    [Crossref] [PubMed]
  12. J. Chen, G. Zhao, M. Salo, E. Rahtu, and M. Pietikäinen, “Automatic dynamic texture segmentation using local descriptors and optical flow,” IEEE Trans. Image Process. 22(1), 326–339 (2013).
    [Crossref] [PubMed]
  13. H. Wang, Q. Kemao, W. Gao, F. Lin, and H. S. Seah, “Fringe pattern denoising using coherence-enhancing diffusion,” Opt. Lett. 34(8), 1141–1143 (2009).
    [Crossref] [PubMed]
  14. C. Tang, L. Wang, H. Yan, and C. Li, “Comparison on performance of some representative and recent filtering methods in electronic speckle pattern interferometry,” Opt. Lasers Eng. 50(8), 1036–1051 (2012).
    [Crossref]
  15. S. Fu and C. Zhang, “Fringe pattern denoising via image decomposition,” Opt. Lett. 37(3), 422–424 (2012).
    [Crossref] [PubMed]
  16. J. C. Estrada, M. Servin, and J. A. Quiroga, “Noise robust linear dynamic system for phase unwrapping and smoothing,” Opt. Express 19(6), 5126–5133 (2011).
    [Crossref] [PubMed]
  17. I. Iglesias, “Phase estimation from digital holograms without unwrapping,” Opt. Express 22(18), 21340–21346 (2014).
    [Crossref] [PubMed]
  18. Z. Cheng, D. Liu, Y. Yang, T. Ling, X. Chen, L. Zhang, J. Bai, Y. Shen, L. Miao, and W. Huang, “Practical phase unwrapping of interferometric fringes based on unscented Kalman filter technique,” Opt. Express 23(25), 32337–32349 (2015).
    [Crossref] [PubMed]
  19. B. Jahne, Spatio-Temporal Image Processing: Theory and Scientific Applications (Springer-Verlag, 1993).
  20. L. Piegl and W. Tiller, The NURBS Book (Springer-Verlag, 1997).
  21. J. Weickert, Anisotropic Diffusion in Image Processing (Teubner-Verlag, 1998).
  22. H. Wang, Q. Kemao, R. Liang, H. Wang, and X. He, “Oriented boundary padding for iterative and oriented fringe pattern denoising techniques,” Signal Process. 102, 112–121 (2014).
    [Crossref]
  23. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16(8), 2080–2095 (2007).
    [Crossref] [PubMed]

2016 (1)

B. Li, C. Tang, X. Zhu, Y. Su, and W. Xu, “Shearlet transform for phase extraction in fringe projection profilometry with edges discontinuity,” Opt. Lasers Eng. 78, 91–98 (2016).
[Crossref]

2015 (4)

M. Zhao and K. Qian, “WFF-BM3D: a hybrid denoising scheme for fringe patterns,” Proc. SPIE 9524, 952423 (2015).
[Crossref]

M. Zhao, H. Wang, and Q. Kemao, “Snake-assisted quality-guided phase unwrapping for discontinuous phase fields,” Appl. Opt. 54(24), 7462–7470 (2015).
[Crossref] [PubMed]

W. Ju, D. Xiang, B. Zhang, L. Wang, I. Kopriva, and X. Chen, “Random walk and graph cut for co-segmentation of lung tumor on PET-CT images,” IEEE Trans. Image Process. 24(12), 5854–5867 (2015).
[Crossref] [PubMed]

Z. Cheng, D. Liu, Y. Yang, T. Ling, X. Chen, L. Zhang, J. Bai, Y. Shen, L. Miao, and W. Huang, “Practical phase unwrapping of interferometric fringes based on unscented Kalman filter technique,” Opt. Express 23(25), 32337–32349 (2015).
[Crossref] [PubMed]

2014 (2)

H. Wang, Q. Kemao, R. Liang, H. Wang, and X. He, “Oriented boundary padding for iterative and oriented fringe pattern denoising techniques,” Signal Process. 102, 112–121 (2014).
[Crossref]

I. Iglesias, “Phase estimation from digital holograms without unwrapping,” Opt. Express 22(18), 21340–21346 (2014).
[Crossref] [PubMed]

2013 (1)

J. Chen, G. Zhao, M. Salo, E. Rahtu, and M. Pietikäinen, “Automatic dynamic texture segmentation using local descriptors and optical flow,” IEEE Trans. Image Process. 22(1), 326–339 (2013).
[Crossref] [PubMed]

2012 (4)

C. Tang, L. Wang, H. Yan, and C. Li, “Comparison on performance of some representative and recent filtering methods in electronic speckle pattern interferometry,” Opt. Lasers Eng. 50(8), 1036–1051 (2012).
[Crossref]

S. Fu and C. Zhang, “Fringe pattern denoising via image decomposition,” Opt. Lett. 37(3), 422–424 (2012).
[Crossref] [PubMed]

V. Estellers, D. Zosso, S. Rongjie Lai, J. Osher, Thiran, and X. Bresson, “Efficient algorithm for level set method preserving distance function,” IEEE Trans. Image Process. 21(12), 4722–4734 (2012).
[Crossref] [PubMed]

S. Li, X. Su, and W. Chen, “Hilbert assisted wavelet transform method of optical fringe pattern phase reconstruction for optical profilometry and interferometry,” Optik (Stuttg.) 123(1), 6–10 (2012).
[Crossref]

2011 (2)

H. Cui, W. Liao, N. Dai, and X. Cheng, “Reliability-guided phase-unwrapping algorithm for the measurement of discontinuous three-dimensional objects,” Opt. Eng. 50(6), 063602 (2011).
[Crossref]

J. C. Estrada, M. Servin, and J. A. Quiroga, “Noise robust linear dynamic system for phase unwrapping and smoothing,” Opt. Express 19(6), 5126–5133 (2011).
[Crossref] [PubMed]

2009 (1)

2007 (1)

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16(8), 2080–2095 (2007).
[Crossref] [PubMed]

2006 (1)

2004 (1)

Bai, J.

Bresson, X.

V. Estellers, D. Zosso, S. Rongjie Lai, J. Osher, Thiran, and X. Bresson, “Efficient algorithm for level set method preserving distance function,” IEEE Trans. Image Process. 21(12), 4722–4734 (2012).
[Crossref] [PubMed]

Chen, J.

J. Chen, G. Zhao, M. Salo, E. Rahtu, and M. Pietikäinen, “Automatic dynamic texture segmentation using local descriptors and optical flow,” IEEE Trans. Image Process. 22(1), 326–339 (2013).
[Crossref] [PubMed]

Chen, W.

S. Li, X. Su, and W. Chen, “Hilbert assisted wavelet transform method of optical fringe pattern phase reconstruction for optical profilometry and interferometry,” Optik (Stuttg.) 123(1), 6–10 (2012).
[Crossref]

Chen, X.

W. Ju, D. Xiang, B. Zhang, L. Wang, I. Kopriva, and X. Chen, “Random walk and graph cut for co-segmentation of lung tumor on PET-CT images,” IEEE Trans. Image Process. 24(12), 5854–5867 (2015).
[Crossref] [PubMed]

Z. Cheng, D. Liu, Y. Yang, T. Ling, X. Chen, L. Zhang, J. Bai, Y. Shen, L. Miao, and W. Huang, “Practical phase unwrapping of interferometric fringes based on unscented Kalman filter technique,” Opt. Express 23(25), 32337–32349 (2015).
[Crossref] [PubMed]

Cheng, X.

H. Cui, W. Liao, N. Dai, and X. Cheng, “Reliability-guided phase-unwrapping algorithm for the measurement of discontinuous three-dimensional objects,” Opt. Eng. 50(6), 063602 (2011).
[Crossref]

Cheng, Z.

Cui, H.

H. Cui, W. Liao, N. Dai, and X. Cheng, “Reliability-guided phase-unwrapping algorithm for the measurement of discontinuous three-dimensional objects,” Opt. Eng. 50(6), 063602 (2011).
[Crossref]

Dabov, K.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16(8), 2080–2095 (2007).
[Crossref] [PubMed]

Dai, N.

H. Cui, W. Liao, N. Dai, and X. Cheng, “Reliability-guided phase-unwrapping algorithm for the measurement of discontinuous three-dimensional objects,” Opt. Eng. 50(6), 063602 (2011).
[Crossref]

Egiazarian, K.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16(8), 2080–2095 (2007).
[Crossref] [PubMed]

Estellers, V.

V. Estellers, D. Zosso, S. Rongjie Lai, J. Osher, Thiran, and X. Bresson, “Efficient algorithm for level set method preserving distance function,” IEEE Trans. Image Process. 21(12), 4722–4734 (2012).
[Crossref] [PubMed]

Estrada, J. C.

Foi, A.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16(8), 2080–2095 (2007).
[Crossref] [PubMed]

Fu, S.

Galvan, C.

Gao, W.

He, X.

H. Wang, Q. Kemao, R. Liang, H. Wang, and X. He, “Oriented boundary padding for iterative and oriented fringe pattern denoising techniques,” Signal Process. 102, 112–121 (2014).
[Crossref]

Huang, W.

Iglesias, I.

Ju, W.

W. Ju, D. Xiang, B. Zhang, L. Wang, I. Kopriva, and X. Chen, “Random walk and graph cut for co-segmentation of lung tumor on PET-CT images,” IEEE Trans. Image Process. 24(12), 5854–5867 (2015).
[Crossref] [PubMed]

Katkovnik, V.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16(8), 2080–2095 (2007).
[Crossref] [PubMed]

Kemao, Q.

Kopriva, I.

W. Ju, D. Xiang, B. Zhang, L. Wang, I. Kopriva, and X. Chen, “Random walk and graph cut for co-segmentation of lung tumor on PET-CT images,” IEEE Trans. Image Process. 24(12), 5854–5867 (2015).
[Crossref] [PubMed]

Li, B.

B. Li, C. Tang, X. Zhu, Y. Su, and W. Xu, “Shearlet transform for phase extraction in fringe projection profilometry with edges discontinuity,” Opt. Lasers Eng. 78, 91–98 (2016).
[Crossref]

Li, C.

C. Tang, L. Wang, H. Yan, and C. Li, “Comparison on performance of some representative and recent filtering methods in electronic speckle pattern interferometry,” Opt. Lasers Eng. 50(8), 1036–1051 (2012).
[Crossref]

Li, S.

S. Li, X. Su, and W. Chen, “Hilbert assisted wavelet transform method of optical fringe pattern phase reconstruction for optical profilometry and interferometry,” Optik (Stuttg.) 123(1), 6–10 (2012).
[Crossref]

Liang, R.

H. Wang, Q. Kemao, R. Liang, H. Wang, and X. He, “Oriented boundary padding for iterative and oriented fringe pattern denoising techniques,” Signal Process. 102, 112–121 (2014).
[Crossref]

Liao, W.

H. Cui, W. Liao, N. Dai, and X. Cheng, “Reliability-guided phase-unwrapping algorithm for the measurement of discontinuous three-dimensional objects,” Opt. Eng. 50(6), 063602 (2011).
[Crossref]

Lin, F.

Ling, T.

Liu, D.

Marroquin, J. L.

Miao, L.

Osher, J.

V. Estellers, D. Zosso, S. Rongjie Lai, J. Osher, Thiran, and X. Bresson, “Efficient algorithm for level set method preserving distance function,” IEEE Trans. Image Process. 21(12), 4722–4734 (2012).
[Crossref] [PubMed]

Pietikäinen, M.

J. Chen, G. Zhao, M. Salo, E. Rahtu, and M. Pietikäinen, “Automatic dynamic texture segmentation using local descriptors and optical flow,” IEEE Trans. Image Process. 22(1), 326–339 (2013).
[Crossref] [PubMed]

Qian, K.

M. Zhao and K. Qian, “WFF-BM3D: a hybrid denoising scheme for fringe patterns,” Proc. SPIE 9524, 952423 (2015).
[Crossref]

Quiroga, J. A.

Rahtu, E.

J. Chen, G. Zhao, M. Salo, E. Rahtu, and M. Pietikäinen, “Automatic dynamic texture segmentation using local descriptors and optical flow,” IEEE Trans. Image Process. 22(1), 326–339 (2013).
[Crossref] [PubMed]

Rivera, M.

Rongjie Lai, S.

V. Estellers, D. Zosso, S. Rongjie Lai, J. Osher, Thiran, and X. Bresson, “Efficient algorithm for level set method preserving distance function,” IEEE Trans. Image Process. 21(12), 4722–4734 (2012).
[Crossref] [PubMed]

Salo, M.

J. Chen, G. Zhao, M. Salo, E. Rahtu, and M. Pietikäinen, “Automatic dynamic texture segmentation using local descriptors and optical flow,” IEEE Trans. Image Process. 22(1), 326–339 (2013).
[Crossref] [PubMed]

Seah, H. S.

Servin, M.

Shen, Y.

Su, X.

S. Li, X. Su, and W. Chen, “Hilbert assisted wavelet transform method of optical fringe pattern phase reconstruction for optical profilometry and interferometry,” Optik (Stuttg.) 123(1), 6–10 (2012).
[Crossref]

Su, Y.

B. Li, C. Tang, X. Zhu, Y. Su, and W. Xu, “Shearlet transform for phase extraction in fringe projection profilometry with edges discontinuity,” Opt. Lasers Eng. 78, 91–98 (2016).
[Crossref]

Tang, C.

B. Li, C. Tang, X. Zhu, Y. Su, and W. Xu, “Shearlet transform for phase extraction in fringe projection profilometry with edges discontinuity,” Opt. Lasers Eng. 78, 91–98 (2016).
[Crossref]

C. Tang, L. Wang, H. Yan, and C. Li, “Comparison on performance of some representative and recent filtering methods in electronic speckle pattern interferometry,” Opt. Lasers Eng. 50(8), 1036–1051 (2012).
[Crossref]

Thiran,

V. Estellers, D. Zosso, S. Rongjie Lai, J. Osher, Thiran, and X. Bresson, “Efficient algorithm for level set method preserving distance function,” IEEE Trans. Image Process. 21(12), 4722–4734 (2012).
[Crossref] [PubMed]

Wang, H.

M. Zhao, H. Wang, and Q. Kemao, “Snake-assisted quality-guided phase unwrapping for discontinuous phase fields,” Appl. Opt. 54(24), 7462–7470 (2015).
[Crossref] [PubMed]

H. Wang, Q. Kemao, R. Liang, H. Wang, and X. He, “Oriented boundary padding for iterative and oriented fringe pattern denoising techniques,” Signal Process. 102, 112–121 (2014).
[Crossref]

H. Wang, Q. Kemao, R. Liang, H. Wang, and X. He, “Oriented boundary padding for iterative and oriented fringe pattern denoising techniques,” Signal Process. 102, 112–121 (2014).
[Crossref]

H. Wang, Q. Kemao, W. Gao, F. Lin, and H. S. Seah, “Fringe pattern denoising using coherence-enhancing diffusion,” Opt. Lett. 34(8), 1141–1143 (2009).
[Crossref] [PubMed]

Wang, L.

W. Ju, D. Xiang, B. Zhang, L. Wang, I. Kopriva, and X. Chen, “Random walk and graph cut for co-segmentation of lung tumor on PET-CT images,” IEEE Trans. Image Process. 24(12), 5854–5867 (2015).
[Crossref] [PubMed]

C. Tang, L. Wang, H. Yan, and C. Li, “Comparison on performance of some representative and recent filtering methods in electronic speckle pattern interferometry,” Opt. Lasers Eng. 50(8), 1036–1051 (2012).
[Crossref]

Xiang, D.

W. Ju, D. Xiang, B. Zhang, L. Wang, I. Kopriva, and X. Chen, “Random walk and graph cut for co-segmentation of lung tumor on PET-CT images,” IEEE Trans. Image Process. 24(12), 5854–5867 (2015).
[Crossref] [PubMed]

Xu, W.

B. Li, C. Tang, X. Zhu, Y. Su, and W. Xu, “Shearlet transform for phase extraction in fringe projection profilometry with edges discontinuity,” Opt. Lasers Eng. 78, 91–98 (2016).
[Crossref]

Yan, H.

C. Tang, L. Wang, H. Yan, and C. Li, “Comparison on performance of some representative and recent filtering methods in electronic speckle pattern interferometry,” Opt. Lasers Eng. 50(8), 1036–1051 (2012).
[Crossref]

Yang, Y.

Zhang, B.

W. Ju, D. Xiang, B. Zhang, L. Wang, I. Kopriva, and X. Chen, “Random walk and graph cut for co-segmentation of lung tumor on PET-CT images,” IEEE Trans. Image Process. 24(12), 5854–5867 (2015).
[Crossref] [PubMed]

Zhang, C.

Zhang, L.

Zhao, G.

J. Chen, G. Zhao, M. Salo, E. Rahtu, and M. Pietikäinen, “Automatic dynamic texture segmentation using local descriptors and optical flow,” IEEE Trans. Image Process. 22(1), 326–339 (2013).
[Crossref] [PubMed]

Zhao, M.

Zhu, X.

B. Li, C. Tang, X. Zhu, Y. Su, and W. Xu, “Shearlet transform for phase extraction in fringe projection profilometry with edges discontinuity,” Opt. Lasers Eng. 78, 91–98 (2016).
[Crossref]

Zosso, D.

V. Estellers, D. Zosso, S. Rongjie Lai, J. Osher, Thiran, and X. Bresson, “Efficient algorithm for level set method preserving distance function,” IEEE Trans. Image Process. 21(12), 4722–4734 (2012).
[Crossref] [PubMed]

Appl. Opt. (2)

IEEE Trans. Image Process. (4)

W. Ju, D. Xiang, B. Zhang, L. Wang, I. Kopriva, and X. Chen, “Random walk and graph cut for co-segmentation of lung tumor on PET-CT images,” IEEE Trans. Image Process. 24(12), 5854–5867 (2015).
[Crossref] [PubMed]

V. Estellers, D. Zosso, S. Rongjie Lai, J. Osher, Thiran, and X. Bresson, “Efficient algorithm for level set method preserving distance function,” IEEE Trans. Image Process. 21(12), 4722–4734 (2012).
[Crossref] [PubMed]

J. Chen, G. Zhao, M. Salo, E. Rahtu, and M. Pietikäinen, “Automatic dynamic texture segmentation using local descriptors and optical flow,” IEEE Trans. Image Process. 22(1), 326–339 (2013).
[Crossref] [PubMed]

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16(8), 2080–2095 (2007).
[Crossref] [PubMed]

Opt. Eng. (1)

H. Cui, W. Liao, N. Dai, and X. Cheng, “Reliability-guided phase-unwrapping algorithm for the measurement of discontinuous three-dimensional objects,” Opt. Eng. 50(6), 063602 (2011).
[Crossref]

Opt. Express (3)

Opt. Lasers Eng. (2)

B. Li, C. Tang, X. Zhu, Y. Su, and W. Xu, “Shearlet transform for phase extraction in fringe projection profilometry with edges discontinuity,” Opt. Lasers Eng. 78, 91–98 (2016).
[Crossref]

C. Tang, L. Wang, H. Yan, and C. Li, “Comparison on performance of some representative and recent filtering methods in electronic speckle pattern interferometry,” Opt. Lasers Eng. 50(8), 1036–1051 (2012).
[Crossref]

Opt. Lett. (3)

Optik (Stuttg.) (1)

S. Li, X. Su, and W. Chen, “Hilbert assisted wavelet transform method of optical fringe pattern phase reconstruction for optical profilometry and interferometry,” Optik (Stuttg.) 123(1), 6–10 (2012).
[Crossref]

Proc. SPIE (1)

M. Zhao and K. Qian, “WFF-BM3D: a hybrid denoising scheme for fringe patterns,” Proc. SPIE 9524, 952423 (2015).
[Crossref]

Signal Process. (1)

H. Wang, Q. Kemao, R. Liang, H. Wang, and X. He, “Oriented boundary padding for iterative and oriented fringe pattern denoising techniques,” Signal Process. 102, 112–121 (2014).
[Crossref]

Other (5)

D. W. Robinson and G. T. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics, 1993).

Q. Kemao, Windowed Fringe Pattern Analysis (SPIE, 2013).

B. Jahne, Spatio-Temporal Image Processing: Theory and Scientific Applications (Springer-Verlag, 1993).

L. Piegl and W. Tiller, The NURBS Book (Springer-Verlag, 1997).

J. Weickert, Anisotropic Diffusion in Image Processing (Teubner-Verlag, 1998).

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Figures (11)

Fig. 1
Fig. 1 LOCS method. (a) A noisy fringe pattern; (b) the histogram of λ 2 ; (c) the discontinuous region; (d) the discontinuous boundary; (e) the complete boundary shown in white and the ground truth shown in red for comparison; (f) the refined boundary shown in white and the ground truth shown in red for comparison.
Fig. 2
Fig. 2 BCED principle. (a) Fringe orientations; (b) fringe directions.
Fig. 3
Fig. 3 Denoising results of Fig. 1(a). (a) CED denoising result; (b) BCED denoising result.
Fig. 4
Fig. 4 Simulated fringe patterns. (a) Noiseless; (b) additive noise (STD 1.5); (c) speckle noise.
Fig. 5
Fig. 5 Segmentation results. (a) Noiseless; (b) additive noise (STD 1.5); (c) speckle noise.
Fig. 6
Fig. 6 Simulated fringe patterns. (a) Noiseless; (b) additive noise (STD 1.5); (c) speckle noise.
Fig. 7
Fig. 7 Segmentation results. (a) Noiseless; (b) additive noise (STD 1.5); (c) speckle noise.
Fig. 8
Fig. 8 Denoising results. (a) Result of Fig. 4(b) with BCED; (b) result of Fig. 4(b) with BM3D; (c) result of Fig. 4(c) with BCED; (d) result of Fig. 4(c) with BM3D.
Fig. 9
Fig. 9 Denoising results. (a) Result of Fig. 6(b) with BCED; (b) result of Fig. 6(b) with BM3D; (c) result of Fig. 6(c) with BCED; (d) result of Fig. 6(c) with BM3D.
Fig. 10
Fig. 10 Results of an experimental fringe pattern from fringe projection profilometry. (a) An experimental fringe pattern; (b) LOCS result; (c) BCED result.
Fig. 11
Fig. 11 Results of an experimental fringe pattern from phase-shifting electronic speckle pattern shearing interferometer. (a) An experimental fringe pattern; (b) LOCS result; (c) BCED result.

Tables (1)

Tables Icon

Table 1 Mean absolute errors of denoising results

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

S ( x , y ) = [ u , v ω ( u , v ) f x σ 2 ( u , v ) u , v ω ( u , v ) f x σ ( u , v ) f y σ ( u , v ) u , v ω ( u , v ) f x σ ( u , v ) f y σ ( u , v ) u , v ω ( u , v ) f y σ 2 ( u , v ) ] ,
M ( x , y ) = [ λ 2 ( x , y ) > t h r ] ,
t h r 0 = arg max t [ δ h f ( t ) δ h b ( t ) ] ,
x ( k ) = l = 1 L ϖ l ( k ) P x l ,
P x l ' = P x l + 0 .15 s i g n ( x A x B ) [ M p ( x A , y A ) M p ( x B , y B ) ] ϖ l ( k x A ) ,
f ( x , y ; t + 1 ) = f ( x , y ; t ) + ε × f t ( x , y ; t ) , f ( x , y ; 0 ) = f 0 ( x , y ) ,
f t = ( D f )
D = χ 1 [ sin 2 θ sin θ cos θ sin θ cos θ cos 2 θ ] + χ 2 [ cos 2 θ sin θ cos θ sin θ cos θ sin 2 θ ] ,
f t ( x , y ) = i = 1 1 j = 1 1 a ( i , j ) f ( x + i , y + j ) ,
f t ( ϑ ) ( x , y ) = a ( 1 , 0 ) [ f ( x + 1 , y ) f ( x , y ) ] + a ( 0 , 1 ) [ f ( x , y + 1 ) f ( x , y ) ] + 2 a ( 1 , 1 ) [ f ( x + 1 , y + 1 ) f ( x , y ) ]

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