Abstract

The fringe skeleton method is the most straightforward analysis method for phase extraction and widely used in dynamic measurement. Binarization is often required in this method. In the traditional binarization methods, filtering is often a necessary step prior to binarization due to the influence of intrinsic speckle noises in ESPI fringe patterns. In this paper, we propose a binarization method based on local entropy and fuzzy c-means (FCM) clustering algorithm. In this method, the pixels in the given ESPI fringe pattern are clustered into white fringes and black fringes according to their local entropy instead of the original intensity information. There is no need to perform the filtering preprocessing, because the intrinsic speckle noises are utilized as essentials. We evaluate the performance of our method by applying it to the computer-simulated and real fringe patterns. Experimental results demonstrate that the proposed method can achieve the desired binarization results, and the binarization results can give desired skeleton results.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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2019 (5)

M. Chen, C. Tang, M. Xu, and Z. Lei, “A clustering framework based on FCM and texture features for denoising ESPI fringe patterns with variable density,” Opt. Laser. Eng. 119, 77–86 (2019).
[Crossref]

F. Hao, C. Tang, M. Xu, and Z. Lei, “Batch denoising of ESPI fringe patterns based on convolutional neural network,” Appl. Opt. 58(13), 3338–3346 (2019).
[Crossref]

M. Chen, C. Tang, M. Xu, and Z. Lei, “Binarization of optical fringe patterns with intensity inhomogeneities based on modified FCM algorithm,” Opt. Laser. Eng. 123, 14–19 (2019).
[Crossref]

M. Chen, C. Tang, M. Xu, and Z. Lei, “The oriented bilateral filtering method for removal of speckle noise in electronic speckle pattern interferometry fringes,” Appl. Phys. B: Lasers Opt. 125(7), 121 (2019).
[Crossref]

B. Li, C. Tang, T. Zheng, and Z. Lei, “Fully automated extraction of the fringe skeletons in dynamic electronic speckle pattern interferometry using a U-Net convolutional neural network,” Opt. Eng. 58(2), 023105 (2019).
[Crossref]

2018 (7)

W. Huo, Y. Huang, J. Pei, Q. Zhang, Q. Gu, and J. Yang, “Ship Detection from Ocean SAR Image Based on Local Contrast Variance Weighted Information Entropy,” Sensors 18(4), 1196 (2018).
[Crossref]

H. Ren, J. Li, and X. Gao, “3-D shape measurement of rail achieved by a novel phase measurement profilometry based on virtual reference fringe generated by image interpolation,” Optik 161, 348–359 (2018).
[Crossref]

Q. Zhou, C. Tang, B. Li, and Z. Lei, “Adaptive oriented PDEs filtering methods based on new controlling speed function for discontinuous optical fringe patterns,” Opt. Laser. Eng. 100, 111–117 (2018).
[Crossref]

G. Tavera Ruiz, H. Manuel, M. Flores-Moreno, C. Frausto-Reyes, and M. Santoyo, “Cortical bone quality affectations and their strength impact analysis using holographic interferometry,” Biomed. Opt. Express 9(10), 4818–4833 (2018).
[Crossref]

C. Dong, K. Li, Y. Jiang, D. Arola, and D. Zhang, “Evaluation of thermal expansion coefficient of carbon fiber reinforced composites using electronic speckle interferometry,” Opt. Express 26(1), 531–543 (2018).
[Crossref]

S. Wang, M. Lu, L. M. Bilgeri, M. Jakobi, F. S. Bloise, and A. W. Koch, “Temporal electronic speckle pattern interferometry for real-time in-plane rotation analysis,” Opt. Express 26(7), 8744–8755 (2018).
[Crossref]

P. P. Padghan and K. M. Alti, “Quantification of nanoscale deformations using electronic speckle pattern interferometer,” Opt. Laser Technol. 107, 72–79 (2018).
[Crossref]

2017 (2)

B. Li, C. Tang, G. Gao, M. Chen, S. Tang, and Z. Lei, “General filtering method for electronic speckle pattern interferometry fringe images with various densities based on variational image decomposition,” Appl. Opt. 56(16), 4843–4853 (2017).
[Crossref]

X. Wang and C. Chen, “Ship Detection for Complex Background SAR Images Based on a Multiscale Variance Weighted Image Entropy Method,” IEEE Geosci. Remote Sensing Lett. 14(2), 184–187 (2017).
[Crossref]

2016 (4)

X. Chen, C. Tang, B. Li, and Y. Su, “Gradient vector fields based on variational image decomposition for skeletonization of electronic speckle pattern interferometry fringe patterns with variable density and their applications,” Appl. Opt. 55(25), 6893–6902 (2016).
[Crossref]

D. Manuel, H. Montes, J. M. Flores-Moreno, and F. M. Santoyo, “Laser speckle based digital optical methods in structural mechanics: A review,” Opt. Laser. Eng. 87, 32–58 (2016).
[Crossref]

M. Kumar, R. Agarwal, R. Bhutani, R. Bhutani, and C. Shakher, “Measurement of strain distribution in cortical bone around miniscrew implants used for orthodontic anchorage using digital speckle pattern interferometry,” Opt. Eng. 55(5), 054101 (2016).
[Crossref]

G. Pedrini, V. Martínez-García, P. Weidmann, M. Wenzdburger, A. Killinger, U. Weber, S. Schmauder, R. Gadow, and W. Osten, “Residual Stress Analysis of Ceramic Coating by Laser Ablation and Digital Holography,” Exp. Mech. 56(5), 683–701 (2016).
[Crossref]

2015 (3)

M. Kumar, K. Gaur, and C. Shakher, “Measurement of Material Constants (Young's Modulus and Poisson's Ratio) of Polypropylene Using Digital Speckle Pattern Interferometry (DSPI),” J. JSEM 15(special), 87–91 (2015).

M. Kumar and S. Chandra, “Measurement of temperature and temperature distribution in gaseous flames by digital speckle pattern shearing interferometry using holographic optical element,” Opt. Laser. Eng. 73, 33–39 (2015).
[Crossref]

F. Zhang, D. Wang, Z. Xiao, L. Geng, J. Wu, Z. Xu, J. Sun, K. Wang, and J. Tao, “Skeleton extraction and phase interpolation for single ESPI fringe pattern based on the partial differential equations,” Opt. Express 23(23), 29625–29638 (2015).
[Crossref]

2014 (1)

C. Qi, “Maximum entropy for image segmentation based on an adaptive particle swarm optimization,” Appl. Math. Inf. Sci. 8(6), 3129–3135 (2014).
[Crossref]

2013 (1)

2011 (2)

G. Wang, Y. J. Li, and H. C. Zhou, “Application of the radial basis function interpolation to phase extraction from a single electronic speckle pattern interferometric fringe,” Appl. Opt. 50(19), 3110–3117 (2011).
[Crossref]

A. L. Barbieri, G. F. Arruda, F. A. Rodrigues, O. M. Bruno, and L. D. Costa, “An entropy-based approach to automatic image segmentation of satellite images,” Phys. A (Amsterdam, Neth.) 390(3), 512–518 (2011).
[Crossref]

2010 (3)

2008 (3)

C. Tang, W. Lu, Y. Cai, L. Han, and G. Wang, “Nearly preprocessing-free method for skeletonization of gray-scale electronic speckle pattern interferometry fringe patterns via partial differential equations,” Opt. Lett. 33(2), 183–185 (2008).
[Crossref]

L. Wang, G. Leedham, and S. Y. Cho, “Minutiae feature analysis for infrared hand vein pattern biometrics,” Pattern Recognit. 41(3), 920–929 (2008).
[Crossref]

J. Wang, J. Kong, Y. Lu, M. Qi, and B. Zhang, “A modified FCM algorithm for MRI brain image segmentation using both local and non-local spatial constraints,” Comput. Med. Imag. Grap. 32(8), 685–698 (2008).
[Crossref]

2007 (1)

2006 (1)

2005 (1)

2003 (3)

W. An and T. Carlsson, “Speckle interferometry for measurement of continuous deformations,” Opt. Laser. Eng. 40(5-6), 529–541 (2003).
[Crossref]

C. Accadia, S. Mariani, M. Casaioli, A. Lavagnini, and A. Speranza, “Speranza. Sensitivity of Precipitation Forecast Skill Scores to Bilinear Interpolation and a Simple Nearest-Neighbor Average Method on High-Resolution Verification Grids,” Auk 133(2), 129–130 (2003).

C. Yan, N. Sang, and T. Zhang, “Local entropy-based transition region extraction and thresholding,” Pattern Recognit. Lett. 24(16), 2935–2941 (2003).
[Crossref]

1999 (1)

C. Studholme, D. L. G. Hill, and D. J. Hawkes, “An overlap invariant entropy measure of 3D medical image alignment,” Pattern Recognit. 32(1), 71–86 (1999).
[Crossref]

1989 (1)

B. Sharp, “Electronic speckle pattern interferometry (ESPI),” Opt. Laser. Eng. 11(4), 241–255 (1989).
[Crossref]

1984 (1)

C. Bezdek, R. Ehrlich, and W. Full, “FCM: The fuzzy c-means clustering algorithm,” Comput. Geosci. 10(2-3), 191–203 (1984).
[Crossref]

1979 (1)

N. Otsu, “A Threshold Selection Method from Gray-Level Histograms,” IEEE Trans. Syst., Man, Cybern. 9(1), 62–66 (1979).
[Crossref]

Accadia, C.

C. Accadia, S. Mariani, M. Casaioli, A. Lavagnini, and A. Speranza, “Speranza. Sensitivity of Precipitation Forecast Skill Scores to Bilinear Interpolation and a Simple Nearest-Neighbor Average Method on High-Resolution Verification Grids,” Auk 133(2), 129–130 (2003).

Agarwal, R.

M. Kumar, R. Agarwal, R. Bhutani, R. Bhutani, and C. Shakher, “Measurement of strain distribution in cortical bone around miniscrew implants used for orthodontic anchorage using digital speckle pattern interferometry,” Opt. Eng. 55(5), 054101 (2016).
[Crossref]

Alti, K. M.

P. P. Padghan and K. M. Alti, “Quantification of nanoscale deformations using electronic speckle pattern interferometer,” Opt. Laser Technol. 107, 72–79 (2018).
[Crossref]

An, W.

W. An and T. Carlsson, “Speckle interferometry for measurement of continuous deformations,” Opt. Laser. Eng. 40(5-6), 529–541 (2003).
[Crossref]

Arola, D.

Arruda, G. F.

A. L. Barbieri, G. F. Arruda, F. A. Rodrigues, O. M. Bruno, and L. D. Costa, “An entropy-based approach to automatic image segmentation of satellite images,” Phys. A (Amsterdam, Neth.) 390(3), 512–518 (2011).
[Crossref]

Barbieri, A. L.

A. L. Barbieri, G. F. Arruda, F. A. Rodrigues, O. M. Bruno, and L. D. Costa, “An entropy-based approach to automatic image segmentation of satellite images,” Phys. A (Amsterdam, Neth.) 390(3), 512–518 (2011).
[Crossref]

Bernsen, J.

J. Bernsen, “Dynamic thresholding of grey-level images,” In: 8th International Conference on Pattern Recognition, Paris France, 27-31 October, 1986, pp. 1251–1255.

Bezdek, C.

C. Bezdek, R. Ehrlich, and W. Full, “FCM: The fuzzy c-means clustering algorithm,” Comput. Geosci. 10(2-3), 191–203 (1984).
[Crossref]

Bhutani, R.

M. Kumar, R. Agarwal, R. Bhutani, R. Bhutani, and C. Shakher, “Measurement of strain distribution in cortical bone around miniscrew implants used for orthodontic anchorage using digital speckle pattern interferometry,” Opt. Eng. 55(5), 054101 (2016).
[Crossref]

M. Kumar, R. Agarwal, R. Bhutani, R. Bhutani, and C. Shakher, “Measurement of strain distribution in cortical bone around miniscrew implants used for orthodontic anchorage using digital speckle pattern interferometry,” Opt. Eng. 55(5), 054101 (2016).
[Crossref]

Bilgeri, L. M.

Bloise, F. S.

Bruno, O. M.

A. L. Barbieri, G. F. Arruda, F. A. Rodrigues, O. M. Bruno, and L. D. Costa, “An entropy-based approach to automatic image segmentation of satellite images,” Phys. A (Amsterdam, Neth.) 390(3), 512–518 (2011).
[Crossref]

Cai, Y.

Carlsson, T.

W. An and T. Carlsson, “Speckle interferometry for measurement of continuous deformations,” Opt. Laser. Eng. 40(5-6), 529–541 (2003).
[Crossref]

Casaioli, M.

C. Accadia, S. Mariani, M. Casaioli, A. Lavagnini, and A. Speranza, “Speranza. Sensitivity of Precipitation Forecast Skill Scores to Bilinear Interpolation and a Simple Nearest-Neighbor Average Method on High-Resolution Verification Grids,” Auk 133(2), 129–130 (2003).

Chandra, S.

M. Kumar and S. Chandra, “Measurement of temperature and temperature distribution in gaseous flames by digital speckle pattern shearing interferometry using holographic optical element,” Opt. Laser. Eng. 73, 33–39 (2015).
[Crossref]

Chen, C.

X. Wang and C. Chen, “Ship Detection for Complex Background SAR Images Based on a Multiscale Variance Weighted Image Entropy Method,” IEEE Geosci. Remote Sensing Lett. 14(2), 184–187 (2017).
[Crossref]

Chen, M.

M. Chen, C. Tang, M. Xu, and Z. Lei, “A clustering framework based on FCM and texture features for denoising ESPI fringe patterns with variable density,” Opt. Laser. Eng. 119, 77–86 (2019).
[Crossref]

M. Chen, C. Tang, M. Xu, and Z. Lei, “Binarization of optical fringe patterns with intensity inhomogeneities based on modified FCM algorithm,” Opt. Laser. Eng. 123, 14–19 (2019).
[Crossref]

M. Chen, C. Tang, M. Xu, and Z. Lei, “The oriented bilateral filtering method for removal of speckle noise in electronic speckle pattern interferometry fringes,” Appl. Phys. B: Lasers Opt. 125(7), 121 (2019).
[Crossref]

B. Li, C. Tang, G. Gao, M. Chen, S. Tang, and Z. Lei, “General filtering method for electronic speckle pattern interferometry fringe images with various densities based on variational image decomposition,” Appl. Opt. 56(16), 4843–4853 (2017).
[Crossref]

Chen, S.

Chen, X.

Chen, Z.

Cho, S. Y.

L. Wang, G. Leedham, and S. Y. Cho, “Minutiae feature analysis for infrared hand vein pattern biometrics,” Pattern Recognit. 41(3), 920–929 (2008).
[Crossref]

Costa, L. D.

A. L. Barbieri, G. F. Arruda, F. A. Rodrigues, O. M. Bruno, and L. D. Costa, “An entropy-based approach to automatic image segmentation of satellite images,” Phys. A (Amsterdam, Neth.) 390(3), 512–518 (2011).
[Crossref]

Deng, H.

Dong, C.

Ehrlich, R.

C. Bezdek, R. Ehrlich, and W. Full, “FCM: The fuzzy c-means clustering algorithm,” Comput. Geosci. 10(2-3), 191–203 (1984).
[Crossref]

Flores-Moreno, J. M.

D. Manuel, H. Montes, J. M. Flores-Moreno, and F. M. Santoyo, “Laser speckle based digital optical methods in structural mechanics: A review,” Opt. Laser. Eng. 87, 32–58 (2016).
[Crossref]

Flores-Moreno, M.

Frausto-Reyes, C.

Fritts, J. E.

H. Zhang, J. E. Fritts, and S. A. Goldman, “Entropy-based objective evaluation method for image segmentation,” In: Proceedings of SPIE - International Society for Optics and Photonics, San Jose, California, United States, 18 December 2003, pp. 38–50.

Full, W.

C. Bezdek, R. Ehrlich, and W. Full, “FCM: The fuzzy c-means clustering algorithm,” Comput. Geosci. 10(2-3), 191–203 (1984).
[Crossref]

Gadow, R.

G. Pedrini, V. Martínez-García, P. Weidmann, M. Wenzdburger, A. Killinger, U. Weber, S. Schmauder, R. Gadow, and W. Osten, “Residual Stress Analysis of Ceramic Coating by Laser Ablation and Digital Holography,” Exp. Mech. 56(5), 683–701 (2016).
[Crossref]

Gao, G.

Gao, T.

Gao, X.

H. Ren, J. Li, and X. Gao, “3-D shape measurement of rail achieved by a novel phase measurement profilometry based on virtual reference fringe generated by image interpolation,” Optik 161, 348–359 (2018).
[Crossref]

Gaur, K.

M. Kumar, K. Gaur, and C. Shakher, “Measurement of Material Constants (Young's Modulus and Poisson's Ratio) of Polypropylene Using Digital Speckle Pattern Interferometry (DSPI),” J. JSEM 15(special), 87–91 (2015).

Geng, L.

Goldman, S. A.

H. Zhang, J. E. Fritts, and S. A. Goldman, “Entropy-based objective evaluation method for image segmentation,” In: Proceedings of SPIE - International Society for Optics and Photonics, San Jose, California, United States, 18 December 2003, pp. 38–50.

Gu, Q.

W. Huo, Y. Huang, J. Pei, Q. Zhang, Q. Gu, and J. Yang, “Ship Detection from Ocean SAR Image Based on Local Contrast Variance Weighted Information Entropy,” Sensors 18(4), 1196 (2018).
[Crossref]

Guo, D.

J. Zong, T. Qiu, W. Li, and D. Guo, “Automatic ultrasound image segmentation based on local entropy and active contour model,” Comput. Math. Appl., (to be published).

Han, L.

Hao, F.

Hawkes, D. J.

C. Studholme, D. L. G. Hill, and D. J. Hawkes, “An overlap invariant entropy measure of 3D medical image alignment,” Pattern Recognit. 32(1), 71–86 (1999).
[Crossref]

Hill, D. L. G.

C. Studholme, D. L. G. Hill, and D. J. Hawkes, “An overlap invariant entropy measure of 3D medical image alignment,” Pattern Recognit. 32(1), 71–86 (1999).
[Crossref]

Huang, Y.

W. Huo, Y. Huang, J. Pei, Q. Zhang, Q. Gu, and J. Yang, “Ship Detection from Ocean SAR Image Based on Local Contrast Variance Weighted Information Entropy,” Sensors 18(4), 1196 (2018).
[Crossref]

Huntley, J. M.

Huo, W.

W. Huo, Y. Huang, J. Pei, Q. Zhang, Q. Gu, and J. Yang, “Ship Detection from Ocean SAR Image Based on Local Contrast Variance Weighted Information Entropy,” Sensors 18(4), 1196 (2018).
[Crossref]

Jakobi, M.

Jiang, Y.

Killinger, A.

G. Pedrini, V. Martínez-García, P. Weidmann, M. Wenzdburger, A. Killinger, U. Weber, S. Schmauder, R. Gadow, and W. Osten, “Residual Stress Analysis of Ceramic Coating by Laser Ablation and Digital Holography,” Exp. Mech. 56(5), 683–701 (2016).
[Crossref]

Koch, A. W.

Kong, J.

J. Wang, J. Kong, Y. Lu, M. Qi, and B. Zhang, “A modified FCM algorithm for MRI brain image segmentation using both local and non-local spatial constraints,” Comput. Med. Imag. Grap. 32(8), 685–698 (2008).
[Crossref]

Kumar, M.

M. Kumar, R. Agarwal, R. Bhutani, R. Bhutani, and C. Shakher, “Measurement of strain distribution in cortical bone around miniscrew implants used for orthodontic anchorage using digital speckle pattern interferometry,” Opt. Eng. 55(5), 054101 (2016).
[Crossref]

M. Kumar, K. Gaur, and C. Shakher, “Measurement of Material Constants (Young's Modulus and Poisson's Ratio) of Polypropylene Using Digital Speckle Pattern Interferometry (DSPI),” J. JSEM 15(special), 87–91 (2015).

M. Kumar and S. Chandra, “Measurement of temperature and temperature distribution in gaseous flames by digital speckle pattern shearing interferometry using holographic optical element,” Opt. Laser. Eng. 73, 33–39 (2015).
[Crossref]

Lavagnini, A.

C. Accadia, S. Mariani, M. Casaioli, A. Lavagnini, and A. Speranza, “Speranza. Sensitivity of Precipitation Forecast Skill Scores to Bilinear Interpolation and a Simple Nearest-Neighbor Average Method on High-Resolution Verification Grids,” Auk 133(2), 129–130 (2003).

Leedham, G.

L. Wang, G. Leedham, and S. Y. Cho, “Minutiae feature analysis for infrared hand vein pattern biometrics,” Pattern Recognit. 41(3), 920–929 (2008).
[Crossref]

Lei, Z.

B. Li, C. Tang, T. Zheng, and Z. Lei, “Fully automated extraction of the fringe skeletons in dynamic electronic speckle pattern interferometry using a U-Net convolutional neural network,” Opt. Eng. 58(2), 023105 (2019).
[Crossref]

M. Chen, C. Tang, M. Xu, and Z. Lei, “The oriented bilateral filtering method for removal of speckle noise in electronic speckle pattern interferometry fringes,” Appl. Phys. B: Lasers Opt. 125(7), 121 (2019).
[Crossref]

M. Chen, C. Tang, M. Xu, and Z. Lei, “Binarization of optical fringe patterns with intensity inhomogeneities based on modified FCM algorithm,” Opt. Laser. Eng. 123, 14–19 (2019).
[Crossref]

M. Chen, C. Tang, M. Xu, and Z. Lei, “A clustering framework based on FCM and texture features for denoising ESPI fringe patterns with variable density,” Opt. Laser. Eng. 119, 77–86 (2019).
[Crossref]

F. Hao, C. Tang, M. Xu, and Z. Lei, “Batch denoising of ESPI fringe patterns based on convolutional neural network,” Appl. Opt. 58(13), 3338–3346 (2019).
[Crossref]

Q. Zhou, C. Tang, B. Li, and Z. Lei, “Adaptive oriented PDEs filtering methods based on new controlling speed function for discontinuous optical fringe patterns,” Opt. Laser. Eng. 100, 111–117 (2018).
[Crossref]

B. Li, C. Tang, G. Gao, M. Chen, S. Tang, and Z. Lei, “General filtering method for electronic speckle pattern interferometry fringe images with various densities based on variational image decomposition,” Appl. Opt. 56(16), 4843–4853 (2017).
[Crossref]

Li, B.

B. Li, C. Tang, T. Zheng, and Z. Lei, “Fully automated extraction of the fringe skeletons in dynamic electronic speckle pattern interferometry using a U-Net convolutional neural network,” Opt. Eng. 58(2), 023105 (2019).
[Crossref]

Q. Zhou, C. Tang, B. Li, and Z. Lei, “Adaptive oriented PDEs filtering methods based on new controlling speed function for discontinuous optical fringe patterns,” Opt. Laser. Eng. 100, 111–117 (2018).
[Crossref]

B. Li, C. Tang, G. Gao, M. Chen, S. Tang, and Z. Lei, “General filtering method for electronic speckle pattern interferometry fringe images with various densities based on variational image decomposition,” Appl. Opt. 56(16), 4843–4853 (2017).
[Crossref]

X. Chen, C. Tang, B. Li, and Y. Su, “Gradient vector fields based on variational image decomposition for skeletonization of electronic speckle pattern interferometry fringe patterns with variable density and their applications,” Appl. Opt. 55(25), 6893–6902 (2016).
[Crossref]

C. Tang, W. Lu, S. Chen, , Z. Zhang, B. Li, W. Wang, and L. Han, “Denoising by coupled partial differential equations and extracting phase by backpropagation neural networks for electronic speckle pattern interferometry,” Appl. Opt. 46(30), 7475–7484 (2007).
[Crossref]

C. Tang, F. Zhang, B. Li, and H. Yan, “Performance evaluation of partial differential equation models in electronic speckle pattern interferometry and the delta-mollification phase map method,” Appl. Opt. 45(28), 7392–7400 (2006).
[Crossref]

Li, J.

H. Ren, J. Li, and X. Gao, “3-D shape measurement of rail achieved by a novel phase measurement profilometry based on virtual reference fringe generated by image interpolation,” Optik 161, 348–359 (2018).
[Crossref]

Li, K.

Li, W.

J. Zong, T. Qiu, W. Li, and D. Guo, “Automatic ultrasound image segmentation based on local entropy and active contour model,” Comput. Math. Appl., (to be published).

Li, Y. J.

Liu, J.

Lu, M.

Lu, W.

Lu, Y.

J. Wang, J. Kong, Y. Lu, M. Qi, and B. Zhang, “A modified FCM algorithm for MRI brain image segmentation using both local and non-local spatial constraints,” Comput. Med. Imag. Grap. 32(8), 685–698 (2008).
[Crossref]

Manuel, D.

D. Manuel, H. Montes, J. M. Flores-Moreno, and F. M. Santoyo, “Laser speckle based digital optical methods in structural mechanics: A review,” Opt. Laser. Eng. 87, 32–58 (2016).
[Crossref]

Manuel, H.

Mariani, S.

C. Accadia, S. Mariani, M. Casaioli, A. Lavagnini, and A. Speranza, “Speranza. Sensitivity of Precipitation Forecast Skill Scores to Bilinear Interpolation and a Simple Nearest-Neighbor Average Method on High-Resolution Verification Grids,” Auk 133(2), 129–130 (2003).

Martínez-García, V.

G. Pedrini, V. Martínez-García, P. Weidmann, M. Wenzdburger, A. Killinger, U. Weber, S. Schmauder, R. Gadow, and W. Osten, “Residual Stress Analysis of Ceramic Coating by Laser Ablation and Digital Holography,” Exp. Mech. 56(5), 683–701 (2016).
[Crossref]

Mi, Q.

Montes, H.

D. Manuel, H. Montes, J. M. Flores-Moreno, and F. M. Santoyo, “Laser speckle based digital optical methods in structural mechanics: A review,” Opt. Laser. Eng. 87, 32–58 (2016).
[Crossref]

Osten, W.

G. Pedrini, V. Martínez-García, P. Weidmann, M. Wenzdburger, A. Killinger, U. Weber, S. Schmauder, R. Gadow, and W. Osten, “Residual Stress Analysis of Ceramic Coating by Laser Ablation and Digital Holography,” Exp. Mech. 56(5), 683–701 (2016).
[Crossref]

Otsu, N.

N. Otsu, “A Threshold Selection Method from Gray-Level Histograms,” IEEE Trans. Syst., Man, Cybern. 9(1), 62–66 (1979).
[Crossref]

Padghan, P. P.

P. P. Padghan and K. M. Alti, “Quantification of nanoscale deformations using electronic speckle pattern interferometer,” Opt. Laser Technol. 107, 72–79 (2018).
[Crossref]

Pedrini, G.

G. Pedrini, V. Martínez-García, P. Weidmann, M. Wenzdburger, A. Killinger, U. Weber, S. Schmauder, R. Gadow, and W. Osten, “Residual Stress Analysis of Ceramic Coating by Laser Ablation and Digital Holography,” Exp. Mech. 56(5), 683–701 (2016).
[Crossref]

Pei, J.

W. Huo, Y. Huang, J. Pei, Q. Zhang, Q. Gu, and J. Yang, “Ship Detection from Ocean SAR Image Based on Local Contrast Variance Weighted Information Entropy,” Sensors 18(4), 1196 (2018).
[Crossref]

Qi, C.

C. Qi, “Maximum entropy for image segmentation based on an adaptive particle swarm optimization,” Appl. Math. Inf. Sci. 8(6), 3129–3135 (2014).
[Crossref]

Qi, M.

J. Wang, J. Kong, Y. Lu, M. Qi, and B. Zhang, “A modified FCM algorithm for MRI brain image segmentation using both local and non-local spatial constraints,” Comput. Med. Imag. Grap. 32(8), 685–698 (2008).
[Crossref]

Qiu, T.

J. Zong, T. Qiu, W. Li, and D. Guo, “Automatic ultrasound image segmentation based on local entropy and active contour model,” Comput. Math. Appl., (to be published).

Ren, H.

H. Ren, J. Li, and X. Gao, “3-D shape measurement of rail achieved by a novel phase measurement profilometry based on virtual reference fringe generated by image interpolation,” Optik 161, 348–359 (2018).
[Crossref]

C. Tang, H. Ren, L. Wang, Z. Wang, L. Han, and T. Gao, “Oriented couple gradient vector fields for skeletonization of gray-scale optical fringe patterns with high density,” Appl. Opt. 49(16), 2979–2984 (2010).
[Crossref]

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A. L. Barbieri, G. F. Arruda, F. A. Rodrigues, O. M. Bruno, and L. D. Costa, “An entropy-based approach to automatic image segmentation of satellite images,” Phys. A (Amsterdam, Neth.) 390(3), 512–518 (2011).
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Ruiz, P. D.

Sang, N.

C. Yan, N. Sang, and T. Zhang, “Local entropy-based transition region extraction and thresholding,” Pattern Recognit. Lett. 24(16), 2935–2941 (2003).
[Crossref]

Santoyo, F. M.

D. Manuel, H. Montes, J. M. Flores-Moreno, and F. M. Santoyo, “Laser speckle based digital optical methods in structural mechanics: A review,” Opt. Laser. Eng. 87, 32–58 (2016).
[Crossref]

Santoyo, M.

Schmauder, S.

G. Pedrini, V. Martínez-García, P. Weidmann, M. Wenzdburger, A. Killinger, U. Weber, S. Schmauder, R. Gadow, and W. Osten, “Residual Stress Analysis of Ceramic Coating by Laser Ablation and Digital Holography,” Exp. Mech. 56(5), 683–701 (2016).
[Crossref]

Shakher, C.

M. Kumar, R. Agarwal, R. Bhutani, R. Bhutani, and C. Shakher, “Measurement of strain distribution in cortical bone around miniscrew implants used for orthodontic anchorage using digital speckle pattern interferometry,” Opt. Eng. 55(5), 054101 (2016).
[Crossref]

M. Kumar, K. Gaur, and C. Shakher, “Measurement of Material Constants (Young's Modulus and Poisson's Ratio) of Polypropylene Using Digital Speckle Pattern Interferometry (DSPI),” J. JSEM 15(special), 87–91 (2015).

Sharp, B.

B. Sharp, “Electronic speckle pattern interferometry (ESPI),” Opt. Laser. Eng. 11(4), 241–255 (1989).
[Crossref]

Speranza, A.

C. Accadia, S. Mariani, M. Casaioli, A. Lavagnini, and A. Speranza, “Speranza. Sensitivity of Precipitation Forecast Skill Scores to Bilinear Interpolation and a Simple Nearest-Neighbor Average Method on High-Resolution Verification Grids,” Auk 133(2), 129–130 (2003).

Studholme, C.

C. Studholme, D. L. G. Hill, and D. J. Hawkes, “An overlap invariant entropy measure of 3D medical image alignment,” Pattern Recognit. 32(1), 71–86 (1999).
[Crossref]

Su, Y.

Sun, J.

Tang, C.

B. Li, C. Tang, T. Zheng, and Z. Lei, “Fully automated extraction of the fringe skeletons in dynamic electronic speckle pattern interferometry using a U-Net convolutional neural network,” Opt. Eng. 58(2), 023105 (2019).
[Crossref]

M. Chen, C. Tang, M. Xu, and Z. Lei, “Binarization of optical fringe patterns with intensity inhomogeneities based on modified FCM algorithm,” Opt. Laser. Eng. 123, 14–19 (2019).
[Crossref]

M. Chen, C. Tang, M. Xu, and Z. Lei, “The oriented bilateral filtering method for removal of speckle noise in electronic speckle pattern interferometry fringes,” Appl. Phys. B: Lasers Opt. 125(7), 121 (2019).
[Crossref]

M. Chen, C. Tang, M. Xu, and Z. Lei, “A clustering framework based on FCM and texture features for denoising ESPI fringe patterns with variable density,” Opt. Laser. Eng. 119, 77–86 (2019).
[Crossref]

F. Hao, C. Tang, M. Xu, and Z. Lei, “Batch denoising of ESPI fringe patterns based on convolutional neural network,” Appl. Opt. 58(13), 3338–3346 (2019).
[Crossref]

Q. Zhou, C. Tang, B. Li, and Z. Lei, “Adaptive oriented PDEs filtering methods based on new controlling speed function for discontinuous optical fringe patterns,” Opt. Laser. Eng. 100, 111–117 (2018).
[Crossref]

B. Li, C. Tang, G. Gao, M. Chen, S. Tang, and Z. Lei, “General filtering method for electronic speckle pattern interferometry fringe images with various densities based on variational image decomposition,” Appl. Opt. 56(16), 4843–4853 (2017).
[Crossref]

X. Chen, C. Tang, B. Li, and Y. Su, “Gradient vector fields based on variational image decomposition for skeletonization of electronic speckle pattern interferometry fringe patterns with variable density and their applications,” Appl. Opt. 55(25), 6893–6902 (2016).
[Crossref]

X. Zhu, Z. Chen, C. Tang, Q. Mi, and X. Yan, “Application of two oriented partial differential equation filtering models on speckle fringes with poor quality and their numerically fast algorithms,” Appl. Opt. 52(9), 1814–1823 (2013).
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C. Tang, T. Gao, S. Yan, L. Wang, and J. Wu, “The oriented spatial filter masks for electronic speckle pattern interferometry phase patterns,” Opt. Express 18(9), 8942–8947 (2010).
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C. Tang, H. Ren, L. Wang, Z. Wang, L. Han, and T. Gao, “Oriented couple gradient vector fields for skeletonization of gray-scale optical fringe patterns with high density,” Appl. Opt. 49(16), 2979–2984 (2010).
[Crossref]

C. Tang, W. Lu, Y. Cai, L. Han, and G. Wang, “Nearly preprocessing-free method for skeletonization of gray-scale electronic speckle pattern interferometry fringe patterns via partial differential equations,” Opt. Lett. 33(2), 183–185 (2008).
[Crossref]

C. Tang, W. Lu, S. Chen, , Z. Zhang, B. Li, W. Wang, and L. Han, “Denoising by coupled partial differential equations and extracting phase by backpropagation neural networks for electronic speckle pattern interferometry,” Appl. Opt. 46(30), 7475–7484 (2007).
[Crossref]

C. Tang, F. Zhang, B. Li, and H. Yan, “Performance evaluation of partial differential equation models in electronic speckle pattern interferometry and the delta-mollification phase map method,” Appl. Opt. 45(28), 7392–7400 (2006).
[Crossref]

Tang, S.

Tao, J.

Tavera Ruiz, G.

Wang, D.

Wang, G.

Wang, J.

J. Wang, J. Kong, Y. Lu, M. Qi, and B. Zhang, “A modified FCM algorithm for MRI brain image segmentation using both local and non-local spatial constraints,” Comput. Med. Imag. Grap. 32(8), 685–698 (2008).
[Crossref]

Wang, K.

Wang, L.

Wang, S.

Wang, W.

Wang, X.

X. Wang and C. Chen, “Ship Detection for Complex Background SAR Images Based on a Multiscale Variance Weighted Image Entropy Method,” IEEE Geosci. Remote Sensing Lett. 14(2), 184–187 (2017).
[Crossref]

Wang, Z.

Weber, U.

G. Pedrini, V. Martínez-García, P. Weidmann, M. Wenzdburger, A. Killinger, U. Weber, S. Schmauder, R. Gadow, and W. Osten, “Residual Stress Analysis of Ceramic Coating by Laser Ablation and Digital Holography,” Exp. Mech. 56(5), 683–701 (2016).
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Weidmann, P.

G. Pedrini, V. Martínez-García, P. Weidmann, M. Wenzdburger, A. Killinger, U. Weber, S. Schmauder, R. Gadow, and W. Osten, “Residual Stress Analysis of Ceramic Coating by Laser Ablation and Digital Holography,” Exp. Mech. 56(5), 683–701 (2016).
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Wenzdburger, M.

G. Pedrini, V. Martínez-García, P. Weidmann, M. Wenzdburger, A. Killinger, U. Weber, S. Schmauder, R. Gadow, and W. Osten, “Residual Stress Analysis of Ceramic Coating by Laser Ablation and Digital Holography,” Exp. Mech. 56(5), 683–701 (2016).
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Wu, J.

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M. Chen, C. Tang, M. Xu, and Z. Lei, “Binarization of optical fringe patterns with intensity inhomogeneities based on modified FCM algorithm,” Opt. Laser. Eng. 123, 14–19 (2019).
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M. Chen, C. Tang, M. Xu, and Z. Lei, “The oriented bilateral filtering method for removal of speckle noise in electronic speckle pattern interferometry fringes,” Appl. Phys. B: Lasers Opt. 125(7), 121 (2019).
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F. Hao, C. Tang, M. Xu, and Z. Lei, “Batch denoising of ESPI fringe patterns based on convolutional neural network,” Appl. Opt. 58(13), 3338–3346 (2019).
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M. Chen, C. Tang, M. Xu, and Z. Lei, “A clustering framework based on FCM and texture features for denoising ESPI fringe patterns with variable density,” Opt. Laser. Eng. 119, 77–86 (2019).
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Xu, Z.

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C. Yan, N. Sang, and T. Zhang, “Local entropy-based transition region extraction and thresholding,” Pattern Recognit. Lett. 24(16), 2935–2941 (2003).
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Yan, S.

Yan, X.

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W. Huo, Y. Huang, J. Pei, Q. Zhang, Q. Gu, and J. Yang, “Ship Detection from Ocean SAR Image Based on Local Contrast Variance Weighted Information Entropy,” Sensors 18(4), 1196 (2018).
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Zhang, B.

J. Wang, J. Kong, Y. Lu, M. Qi, and B. Zhang, “A modified FCM algorithm for MRI brain image segmentation using both local and non-local spatial constraints,” Comput. Med. Imag. Grap. 32(8), 685–698 (2008).
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W. Huo, Y. Huang, J. Pei, Q. Zhang, Q. Gu, and J. Yang, “Ship Detection from Ocean SAR Image Based on Local Contrast Variance Weighted Information Entropy,” Sensors 18(4), 1196 (2018).
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Zhang, T.

C. Yan, N. Sang, and T. Zhang, “Local entropy-based transition region extraction and thresholding,” Pattern Recognit. Lett. 24(16), 2935–2941 (2003).
[Crossref]

Zhang, Z.

Zheng, T.

B. Li, C. Tang, T. Zheng, and Z. Lei, “Fully automated extraction of the fringe skeletons in dynamic electronic speckle pattern interferometry using a U-Net convolutional neural network,” Opt. Eng. 58(2), 023105 (2019).
[Crossref]

Zhou, H. C.

Zhou, Q.

Q. Zhou, C. Tang, B. Li, and Z. Lei, “Adaptive oriented PDEs filtering methods based on new controlling speed function for discontinuous optical fringe patterns,” Opt. Laser. Eng. 100, 111–117 (2018).
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J. Zong, T. Qiu, W. Li, and D. Guo, “Automatic ultrasound image segmentation based on local entropy and active contour model,” Comput. Math. Appl., (to be published).

Appl. Math. Inf. Sci. (1)

C. Qi, “Maximum entropy for image segmentation based on an adaptive particle swarm optimization,” Appl. Math. Inf. Sci. 8(6), 3129–3135 (2014).
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Appl. Opt. (9)

P. D. Ruiz, J. M. Huntley, and R. D. Wildman, “Depth-resolved whole-field displacement measurement by wavelength-scanning electronic speckle pattern interferometry,” Appl. Opt. 44(19), 3945–3953 (2005).
[Crossref]

X. Zhu, Z. Chen, C. Tang, Q. Mi, and X. Yan, “Application of two oriented partial differential equation filtering models on speckle fringes with poor quality and their numerically fast algorithms,” Appl. Opt. 52(9), 1814–1823 (2013).
[Crossref]

F. Hao, C. Tang, M. Xu, and Z. Lei, “Batch denoising of ESPI fringe patterns based on convolutional neural network,” Appl. Opt. 58(13), 3338–3346 (2019).
[Crossref]

B. Li, C. Tang, G. Gao, M. Chen, S. Tang, and Z. Lei, “General filtering method for electronic speckle pattern interferometry fringe images with various densities based on variational image decomposition,” Appl. Opt. 56(16), 4843–4853 (2017).
[Crossref]

C. Tang, F. Zhang, B. Li, and H. Yan, “Performance evaluation of partial differential equation models in electronic speckle pattern interferometry and the delta-mollification phase map method,” Appl. Opt. 45(28), 7392–7400 (2006).
[Crossref]

C. Tang, W. Lu, S. Chen, , Z. Zhang, B. Li, W. Wang, and L. Han, “Denoising by coupled partial differential equations and extracting phase by backpropagation neural networks for electronic speckle pattern interferometry,” Appl. Opt. 46(30), 7475–7484 (2007).
[Crossref]

G. Wang, Y. J. Li, and H. C. Zhou, “Application of the radial basis function interpolation to phase extraction from a single electronic speckle pattern interferometric fringe,” Appl. Opt. 50(19), 3110–3117 (2011).
[Crossref]

X. Chen, C. Tang, B. Li, and Y. Su, “Gradient vector fields based on variational image decomposition for skeletonization of electronic speckle pattern interferometry fringe patterns with variable density and their applications,” Appl. Opt. 55(25), 6893–6902 (2016).
[Crossref]

C. Tang, H. Ren, L. Wang, Z. Wang, L. Han, and T. Gao, “Oriented couple gradient vector fields for skeletonization of gray-scale optical fringe patterns with high density,” Appl. Opt. 49(16), 2979–2984 (2010).
[Crossref]

Appl. Phys. B: Lasers Opt. (1)

M. Chen, C. Tang, M. Xu, and Z. Lei, “The oriented bilateral filtering method for removal of speckle noise in electronic speckle pattern interferometry fringes,” Appl. Phys. B: Lasers Opt. 125(7), 121 (2019).
[Crossref]

Auk (1)

C. Accadia, S. Mariani, M. Casaioli, A. Lavagnini, and A. Speranza, “Speranza. Sensitivity of Precipitation Forecast Skill Scores to Bilinear Interpolation and a Simple Nearest-Neighbor Average Method on High-Resolution Verification Grids,” Auk 133(2), 129–130 (2003).

Biomed. Opt. Express (1)

Chin. Opt. Lett. (1)

Comput. Geosci. (1)

C. Bezdek, R. Ehrlich, and W. Full, “FCM: The fuzzy c-means clustering algorithm,” Comput. Geosci. 10(2-3), 191–203 (1984).
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Comput. Med. Imag. Grap. (1)

J. Wang, J. Kong, Y. Lu, M. Qi, and B. Zhang, “A modified FCM algorithm for MRI brain image segmentation using both local and non-local spatial constraints,” Comput. Med. Imag. Grap. 32(8), 685–698 (2008).
[Crossref]

Exp. Mech. (1)

G. Pedrini, V. Martínez-García, P. Weidmann, M. Wenzdburger, A. Killinger, U. Weber, S. Schmauder, R. Gadow, and W. Osten, “Residual Stress Analysis of Ceramic Coating by Laser Ablation and Digital Holography,” Exp. Mech. 56(5), 683–701 (2016).
[Crossref]

IEEE Geosci. Remote Sensing Lett. (1)

X. Wang and C. Chen, “Ship Detection for Complex Background SAR Images Based on a Multiscale Variance Weighted Image Entropy Method,” IEEE Geosci. Remote Sensing Lett. 14(2), 184–187 (2017).
[Crossref]

IEEE Trans. Syst., Man, Cybern. (1)

N. Otsu, “A Threshold Selection Method from Gray-Level Histograms,” IEEE Trans. Syst., Man, Cybern. 9(1), 62–66 (1979).
[Crossref]

J. JSEM (1)

M. Kumar, K. Gaur, and C. Shakher, “Measurement of Material Constants (Young's Modulus and Poisson's Ratio) of Polypropylene Using Digital Speckle Pattern Interferometry (DSPI),” J. JSEM 15(special), 87–91 (2015).

Opt. Eng. (2)

M. Kumar, R. Agarwal, R. Bhutani, R. Bhutani, and C. Shakher, “Measurement of strain distribution in cortical bone around miniscrew implants used for orthodontic anchorage using digital speckle pattern interferometry,” Opt. Eng. 55(5), 054101 (2016).
[Crossref]

B. Li, C. Tang, T. Zheng, and Z. Lei, “Fully automated extraction of the fringe skeletons in dynamic electronic speckle pattern interferometry using a U-Net convolutional neural network,” Opt. Eng. 58(2), 023105 (2019).
[Crossref]

Opt. Express (4)

Opt. Laser Technol. (1)

P. P. Padghan and K. M. Alti, “Quantification of nanoscale deformations using electronic speckle pattern interferometer,” Opt. Laser Technol. 107, 72–79 (2018).
[Crossref]

Opt. Laser. Eng. (7)

D. Manuel, H. Montes, J. M. Flores-Moreno, and F. M. Santoyo, “Laser speckle based digital optical methods in structural mechanics: A review,” Opt. Laser. Eng. 87, 32–58 (2016).
[Crossref]

B. Sharp, “Electronic speckle pattern interferometry (ESPI),” Opt. Laser. Eng. 11(4), 241–255 (1989).
[Crossref]

W. An and T. Carlsson, “Speckle interferometry for measurement of continuous deformations,” Opt. Laser. Eng. 40(5-6), 529–541 (2003).
[Crossref]

M. Kumar and S. Chandra, “Measurement of temperature and temperature distribution in gaseous flames by digital speckle pattern shearing interferometry using holographic optical element,” Opt. Laser. Eng. 73, 33–39 (2015).
[Crossref]

M. Chen, C. Tang, M. Xu, and Z. Lei, “A clustering framework based on FCM and texture features for denoising ESPI fringe patterns with variable density,” Opt. Laser. Eng. 119, 77–86 (2019).
[Crossref]

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Figures (11)

Fig. 1.
Fig. 1. The flowchart of the proposed method.
Fig. 2.
Fig. 2. The computer-simulated fringe patterns.
Fig. 3.
Fig. 3. The corresponding entropy maps of Fig. 2.
Fig. 4.
Fig. 4. The binarization results of different methods.
Fig. 5.
Fig. 5. The corresponding skeleton results of Fig. 4.
Fig. 6.
Fig. 6. The first group of experimentally obtained ESPI fringe patterns.
Fig. 7.
Fig. 7. The binarization results of Fig. 6 of our method.
Fig. 8.
Fig. 8. The corresponding skeleton results of Fig. 7.
Fig. 9.
Fig. 9. The second group of experimentally obtained ESPI fringe patterns.
Fig. 10.
Fig. 10. The binarization results of Fig. 9 of our method.
Fig. 11.
Fig. 11. The corresponding skeleton results of Fig. 10.

Equations (6)

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E ( j ) = g = 1 N P ( g ) l o g 2 P ( g )
J = j = 1 M i = 1 c u i j β E ( j ) v ( i ) 2
u i j = 1 k = 1 c ( E ( j ) v ( i ) E ( j ) v ( k ) ) 2 / ( β 1 )
v i j = j = 1 M u i j β E ( j ) j = 1 M ( u i j β )
U = [ u 11 u 12 u 1 M u 21 u 22 u 2 M u c 1 u c 2 u c M ]
U = [ u 11 u 12 u 1 M u 21 u 22 u 2 M ]

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