Abstract

We evaluate and compare the use of competitive neural networks, self-organizing maps, the expectation-maximization algorithm, K-means, and fuzzy C-means techniques as partitional clustering methods, when the sensitivity of the activity measurement of dynamic speckle images needs to be improved. The temporal history of the acquired intensity generated by each pixel is analyzed in a wavelet decomposition framework, and it is shown that the mean energy of its corresponding wavelet coefficients provides a suited feature space for clustering purposes. The sensitivity obtained by using the evaluated clustering techniques is also compared with the well-known methods of Konishi–Fujii, weighted generalized differences, and wavelet entropy. The performance of the partitional clustering approach is evaluated using simulated dynamic speckle patterns and also experimental data.

© 2010 Optical Society of America

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  1. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer-Verlag, 1975), pp. 9–75.
    [CrossRef]
  2. H. J. Rabal and R. A. Braga, Dynamic Laser Speckle and Applications (CRC, 2009).
  3. R. A. Braga, W. S. Silva, T. Sáfadi, and C. M. B. Nobre, “Time history speckle pattern under statistical view,” Opt. Commun. 281, 2443–2448 (2008).
    [CrossRef]
  4. P. A. Faccia, O. R. Pardini, J. I. Amalvy, N. Cap, E. E. Grumel, R. Arizaga, and M. Trivi, “Differentiation of the drying time of paints by dynamic speckle interferometry,” Prog. Org. Coat. 64, 350–355 (2008).
    [CrossRef]
  5. M. Pajuelo, G. Baldwin, H. J. Rabal, N. Cap, R. Arizaga, and M. Trivi, “Biospeckle assessment of bruising in fruits,” Opt. Laser Eng. 40, 13–24 (2003).
    [CrossRef]
  6. R. A. Braga, G. W. Horgan, A. M. Enes, D. Miron, G. F. Rabelo, and J. B. B. Filho, “Biological feature isolation by wavelets in biospeckle laser images,” Comput. Electron. Agric. 58, 132–132 (2007).
    [CrossRef]
  7. J. D. Briers and S. Webster, “Laser speckle contrast analysis (LASCA): a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt. 1, 174–179 (1996).
    [CrossRef]
  8. I. Passoni, A. D. Pra, H. J. Rabal, M. Trivi, and R. Arizaga, “Dynamic speckle processing using wavelets based entropy,” Opt. Commun. 246, 219–228 (2005).
    [CrossRef]
  9. R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, 2nd ed. (Wiley, 2001).
  10. R. Xu and D. W. II, “Survey of clustering algorithms,” IEEE Trans. Neural Netw. 16, 645–678 (2005).
    [CrossRef] [PubMed]
  11. J. Bilmes, “A gentle tutorial of the em algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models,” Tech. Rep. (International Computer Science Institute, 1998).
  12. B. Kosko, “Stochastic competitive learning,” IEEE Trans. Neural Netw. 2, 522–529 (1991).
    [CrossRef] [PubMed]
  13. T. Kohonen, “The self-organizing map,” Proc. IEEE , 78, 1464–1480 (1990).
    [CrossRef]
  14. S. Mallat, A Wavelet Tour of Signal Processing (Academic Press, 1998).
  15. V. Cherkassky and F. Mulier, Learning from Data: Concepts, Theory, and Methods (Wiley, 1998).
  16. L. Zunino, D. G. Pérez, M. Garavaglia, and O. A. Rosso, “Wavelet entropy of stochastic processes,” Physica A (Amsterdam) 379, 503–512 (2007).
    [CrossRef]
  17. D. D. Duncan and S. J. Kirkpatrick, “The copula: a tool for simulating speckle dynamics,” J. Opt. Soc. Am. A 25, 231–237 (2008).
    [CrossRef]
  18. Q. Huang and B. Dom, “Quantitative methods of evaluating image segmentation,” in Proceedings of the 1995 International Conference on Image Processing (IEEE, 1995), Vol. 3, pp. 3053–3056.
  19. R. R. Roldán, J. F. G. Lopera, C. A. Allah, J. M. Aroza, and P. L. L. Escamilla, “A measure of quality for evaluating methods of segmentation and edge detection,” Patt. Recog. 34, 969–980 (2001).
    [CrossRef]
  20. Z. Wang and A. C. Bovik, “A universal image quality index,” Signal Process. Lett. 9, 81–84 (2002).
    [CrossRef]
  21. B. Zhang, M. Hsu, and G. Forman, “Accurate recasting of parameter estimation algorithms using sufficient statistics for efficient parallel speed-up: demonstrated for center-based data clustering algorithms,” in Proceedings of the 4th European Conference on Principles of Data Mining and Knowledge Discovery (PKDD 2000) (2000), Vol. 1910, pp. 243–254.
    [PubMed]
  22. P. Ozdzynski, A. Lin, M. Liljeholm, and J. Beatty, “A parallel general implementation of Kohonen’s self-organizing map algorithm: performance and scalability,” Neurocomput. Var. Star Bull. 44, 567–571 (2002).
    [CrossRef]

2008 (3)

R. A. Braga, W. S. Silva, T. Sáfadi, and C. M. B. Nobre, “Time history speckle pattern under statistical view,” Opt. Commun. 281, 2443–2448 (2008).
[CrossRef]

P. A. Faccia, O. R. Pardini, J. I. Amalvy, N. Cap, E. E. Grumel, R. Arizaga, and M. Trivi, “Differentiation of the drying time of paints by dynamic speckle interferometry,” Prog. Org. Coat. 64, 350–355 (2008).
[CrossRef]

D. D. Duncan and S. J. Kirkpatrick, “The copula: a tool for simulating speckle dynamics,” J. Opt. Soc. Am. A 25, 231–237 (2008).
[CrossRef]

2007 (2)

L. Zunino, D. G. Pérez, M. Garavaglia, and O. A. Rosso, “Wavelet entropy of stochastic processes,” Physica A (Amsterdam) 379, 503–512 (2007).
[CrossRef]

R. A. Braga, G. W. Horgan, A. M. Enes, D. Miron, G. F. Rabelo, and J. B. B. Filho, “Biological feature isolation by wavelets in biospeckle laser images,” Comput. Electron. Agric. 58, 132–132 (2007).
[CrossRef]

2005 (2)

I. Passoni, A. D. Pra, H. J. Rabal, M. Trivi, and R. Arizaga, “Dynamic speckle processing using wavelets based entropy,” Opt. Commun. 246, 219–228 (2005).
[CrossRef]

R. Xu and D. W. II, “Survey of clustering algorithms,” IEEE Trans. Neural Netw. 16, 645–678 (2005).
[CrossRef] [PubMed]

2003 (1)

M. Pajuelo, G. Baldwin, H. J. Rabal, N. Cap, R. Arizaga, and M. Trivi, “Biospeckle assessment of bruising in fruits,” Opt. Laser Eng. 40, 13–24 (2003).
[CrossRef]

2002 (2)

Z. Wang and A. C. Bovik, “A universal image quality index,” Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

P. Ozdzynski, A. Lin, M. Liljeholm, and J. Beatty, “A parallel general implementation of Kohonen’s self-organizing map algorithm: performance and scalability,” Neurocomput. Var. Star Bull. 44, 567–571 (2002).
[CrossRef]

2001 (1)

R. R. Roldán, J. F. G. Lopera, C. A. Allah, J. M. Aroza, and P. L. L. Escamilla, “A measure of quality for evaluating methods of segmentation and edge detection,” Patt. Recog. 34, 969–980 (2001).
[CrossRef]

1996 (1)

J. D. Briers and S. Webster, “Laser speckle contrast analysis (LASCA): a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt. 1, 174–179 (1996).
[CrossRef]

1991 (1)

B. Kosko, “Stochastic competitive learning,” IEEE Trans. Neural Netw. 2, 522–529 (1991).
[CrossRef] [PubMed]

1990 (1)

T. Kohonen, “The self-organizing map,” Proc. IEEE , 78, 1464–1480 (1990).
[CrossRef]

Allah, C. A.

R. R. Roldán, J. F. G. Lopera, C. A. Allah, J. M. Aroza, and P. L. L. Escamilla, “A measure of quality for evaluating methods of segmentation and edge detection,” Patt. Recog. 34, 969–980 (2001).
[CrossRef]

Amalvy, J. I.

P. A. Faccia, O. R. Pardini, J. I. Amalvy, N. Cap, E. E. Grumel, R. Arizaga, and M. Trivi, “Differentiation of the drying time of paints by dynamic speckle interferometry,” Prog. Org. Coat. 64, 350–355 (2008).
[CrossRef]

Arizaga, R.

P. A. Faccia, O. R. Pardini, J. I. Amalvy, N. Cap, E. E. Grumel, R. Arizaga, and M. Trivi, “Differentiation of the drying time of paints by dynamic speckle interferometry,” Prog. Org. Coat. 64, 350–355 (2008).
[CrossRef]

I. Passoni, A. D. Pra, H. J. Rabal, M. Trivi, and R. Arizaga, “Dynamic speckle processing using wavelets based entropy,” Opt. Commun. 246, 219–228 (2005).
[CrossRef]

M. Pajuelo, G. Baldwin, H. J. Rabal, N. Cap, R. Arizaga, and M. Trivi, “Biospeckle assessment of bruising in fruits,” Opt. Laser Eng. 40, 13–24 (2003).
[CrossRef]

Aroza, J. M.

R. R. Roldán, J. F. G. Lopera, C. A. Allah, J. M. Aroza, and P. L. L. Escamilla, “A measure of quality for evaluating methods of segmentation and edge detection,” Patt. Recog. 34, 969–980 (2001).
[CrossRef]

Baldwin, G.

M. Pajuelo, G. Baldwin, H. J. Rabal, N. Cap, R. Arizaga, and M. Trivi, “Biospeckle assessment of bruising in fruits,” Opt. Laser Eng. 40, 13–24 (2003).
[CrossRef]

Beatty, J.

P. Ozdzynski, A. Lin, M. Liljeholm, and J. Beatty, “A parallel general implementation of Kohonen’s self-organizing map algorithm: performance and scalability,” Neurocomput. Var. Star Bull. 44, 567–571 (2002).
[CrossRef]

Bilmes, J.

J. Bilmes, “A gentle tutorial of the em algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models,” Tech. Rep. (International Computer Science Institute, 1998).

Bovik, A. C.

Z. Wang and A. C. Bovik, “A universal image quality index,” Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

Braga, R. A.

R. A. Braga, W. S. Silva, T. Sáfadi, and C. M. B. Nobre, “Time history speckle pattern under statistical view,” Opt. Commun. 281, 2443–2448 (2008).
[CrossRef]

R. A. Braga, G. W. Horgan, A. M. Enes, D. Miron, G. F. Rabelo, and J. B. B. Filho, “Biological feature isolation by wavelets in biospeckle laser images,” Comput. Electron. Agric. 58, 132–132 (2007).
[CrossRef]

H. J. Rabal and R. A. Braga, Dynamic Laser Speckle and Applications (CRC, 2009).

Briers, J. D.

J. D. Briers and S. Webster, “Laser speckle contrast analysis (LASCA): a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt. 1, 174–179 (1996).
[CrossRef]

Cap, N.

P. A. Faccia, O. R. Pardini, J. I. Amalvy, N. Cap, E. E. Grumel, R. Arizaga, and M. Trivi, “Differentiation of the drying time of paints by dynamic speckle interferometry,” Prog. Org. Coat. 64, 350–355 (2008).
[CrossRef]

M. Pajuelo, G. Baldwin, H. J. Rabal, N. Cap, R. Arizaga, and M. Trivi, “Biospeckle assessment of bruising in fruits,” Opt. Laser Eng. 40, 13–24 (2003).
[CrossRef]

Cherkassky, V.

V. Cherkassky and F. Mulier, Learning from Data: Concepts, Theory, and Methods (Wiley, 1998).

Dom, B.

Q. Huang and B. Dom, “Quantitative methods of evaluating image segmentation,” in Proceedings of the 1995 International Conference on Image Processing (IEEE, 1995), Vol. 3, pp. 3053–3056.

Duda, R. O.

R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, 2nd ed. (Wiley, 2001).

Duncan, D. D.

Enes, A. M.

R. A. Braga, G. W. Horgan, A. M. Enes, D. Miron, G. F. Rabelo, and J. B. B. Filho, “Biological feature isolation by wavelets in biospeckle laser images,” Comput. Electron. Agric. 58, 132–132 (2007).
[CrossRef]

Escamilla, P. L. L.

R. R. Roldán, J. F. G. Lopera, C. A. Allah, J. M. Aroza, and P. L. L. Escamilla, “A measure of quality for evaluating methods of segmentation and edge detection,” Patt. Recog. 34, 969–980 (2001).
[CrossRef]

Faccia, P. A.

P. A. Faccia, O. R. Pardini, J. I. Amalvy, N. Cap, E. E. Grumel, R. Arizaga, and M. Trivi, “Differentiation of the drying time of paints by dynamic speckle interferometry,” Prog. Org. Coat. 64, 350–355 (2008).
[CrossRef]

Filho, J. B. B.

R. A. Braga, G. W. Horgan, A. M. Enes, D. Miron, G. F. Rabelo, and J. B. B. Filho, “Biological feature isolation by wavelets in biospeckle laser images,” Comput. Electron. Agric. 58, 132–132 (2007).
[CrossRef]

Forman, G.

B. Zhang, M. Hsu, and G. Forman, “Accurate recasting of parameter estimation algorithms using sufficient statistics for efficient parallel speed-up: demonstrated for center-based data clustering algorithms,” in Proceedings of the 4th European Conference on Principles of Data Mining and Knowledge Discovery (PKDD 2000) (2000), Vol. 1910, pp. 243–254.
[PubMed]

Garavaglia, M.

L. Zunino, D. G. Pérez, M. Garavaglia, and O. A. Rosso, “Wavelet entropy of stochastic processes,” Physica A (Amsterdam) 379, 503–512 (2007).
[CrossRef]

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer-Verlag, 1975), pp. 9–75.
[CrossRef]

Grumel, E. E.

P. A. Faccia, O. R. Pardini, J. I. Amalvy, N. Cap, E. E. Grumel, R. Arizaga, and M. Trivi, “Differentiation of the drying time of paints by dynamic speckle interferometry,” Prog. Org. Coat. 64, 350–355 (2008).
[CrossRef]

Hart, P. E.

R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, 2nd ed. (Wiley, 2001).

Horgan, G. W.

R. A. Braga, G. W. Horgan, A. M. Enes, D. Miron, G. F. Rabelo, and J. B. B. Filho, “Biological feature isolation by wavelets in biospeckle laser images,” Comput. Electron. Agric. 58, 132–132 (2007).
[CrossRef]

Hsu, M.

B. Zhang, M. Hsu, and G. Forman, “Accurate recasting of parameter estimation algorithms using sufficient statistics for efficient parallel speed-up: demonstrated for center-based data clustering algorithms,” in Proceedings of the 4th European Conference on Principles of Data Mining and Knowledge Discovery (PKDD 2000) (2000), Vol. 1910, pp. 243–254.
[PubMed]

Huang, Q.

Q. Huang and B. Dom, “Quantitative methods of evaluating image segmentation,” in Proceedings of the 1995 International Conference on Image Processing (IEEE, 1995), Vol. 3, pp. 3053–3056.

Kirkpatrick, S. J.

Kohonen, T.

T. Kohonen, “The self-organizing map,” Proc. IEEE , 78, 1464–1480 (1990).
[CrossRef]

Kosko, B.

B. Kosko, “Stochastic competitive learning,” IEEE Trans. Neural Netw. 2, 522–529 (1991).
[CrossRef] [PubMed]

Liljeholm, M.

P. Ozdzynski, A. Lin, M. Liljeholm, and J. Beatty, “A parallel general implementation of Kohonen’s self-organizing map algorithm: performance and scalability,” Neurocomput. Var. Star Bull. 44, 567–571 (2002).
[CrossRef]

Lin, A.

P. Ozdzynski, A. Lin, M. Liljeholm, and J. Beatty, “A parallel general implementation of Kohonen’s self-organizing map algorithm: performance and scalability,” Neurocomput. Var. Star Bull. 44, 567–571 (2002).
[CrossRef]

Lopera, J. F. G.

R. R. Roldán, J. F. G. Lopera, C. A. Allah, J. M. Aroza, and P. L. L. Escamilla, “A measure of quality for evaluating methods of segmentation and edge detection,” Patt. Recog. 34, 969–980 (2001).
[CrossRef]

Mallat, S.

S. Mallat, A Wavelet Tour of Signal Processing (Academic Press, 1998).

Miron, D.

R. A. Braga, G. W. Horgan, A. M. Enes, D. Miron, G. F. Rabelo, and J. B. B. Filho, “Biological feature isolation by wavelets in biospeckle laser images,” Comput. Electron. Agric. 58, 132–132 (2007).
[CrossRef]

Mulier, F.

V. Cherkassky and F. Mulier, Learning from Data: Concepts, Theory, and Methods (Wiley, 1998).

Nobre, C. M. B.

R. A. Braga, W. S. Silva, T. Sáfadi, and C. M. B. Nobre, “Time history speckle pattern under statistical view,” Opt. Commun. 281, 2443–2448 (2008).
[CrossRef]

Ozdzynski, P.

P. Ozdzynski, A. Lin, M. Liljeholm, and J. Beatty, “A parallel general implementation of Kohonen’s self-organizing map algorithm: performance and scalability,” Neurocomput. Var. Star Bull. 44, 567–571 (2002).
[CrossRef]

Pajuelo, M.

M. Pajuelo, G. Baldwin, H. J. Rabal, N. Cap, R. Arizaga, and M. Trivi, “Biospeckle assessment of bruising in fruits,” Opt. Laser Eng. 40, 13–24 (2003).
[CrossRef]

Pardini, O. R.

P. A. Faccia, O. R. Pardini, J. I. Amalvy, N. Cap, E. E. Grumel, R. Arizaga, and M. Trivi, “Differentiation of the drying time of paints by dynamic speckle interferometry,” Prog. Org. Coat. 64, 350–355 (2008).
[CrossRef]

Passoni, I.

I. Passoni, A. D. Pra, H. J. Rabal, M. Trivi, and R. Arizaga, “Dynamic speckle processing using wavelets based entropy,” Opt. Commun. 246, 219–228 (2005).
[CrossRef]

Pérez, D. G.

L. Zunino, D. G. Pérez, M. Garavaglia, and O. A. Rosso, “Wavelet entropy of stochastic processes,” Physica A (Amsterdam) 379, 503–512 (2007).
[CrossRef]

Pra, A. D.

I. Passoni, A. D. Pra, H. J. Rabal, M. Trivi, and R. Arizaga, “Dynamic speckle processing using wavelets based entropy,” Opt. Commun. 246, 219–228 (2005).
[CrossRef]

Rabal, H. J.

I. Passoni, A. D. Pra, H. J. Rabal, M. Trivi, and R. Arizaga, “Dynamic speckle processing using wavelets based entropy,” Opt. Commun. 246, 219–228 (2005).
[CrossRef]

M. Pajuelo, G. Baldwin, H. J. Rabal, N. Cap, R. Arizaga, and M. Trivi, “Biospeckle assessment of bruising in fruits,” Opt. Laser Eng. 40, 13–24 (2003).
[CrossRef]

H. J. Rabal and R. A. Braga, Dynamic Laser Speckle and Applications (CRC, 2009).

Rabelo, G. F.

R. A. Braga, G. W. Horgan, A. M. Enes, D. Miron, G. F. Rabelo, and J. B. B. Filho, “Biological feature isolation by wavelets in biospeckle laser images,” Comput. Electron. Agric. 58, 132–132 (2007).
[CrossRef]

Roldán, R. R.

R. R. Roldán, J. F. G. Lopera, C. A. Allah, J. M. Aroza, and P. L. L. Escamilla, “A measure of quality for evaluating methods of segmentation and edge detection,” Patt. Recog. 34, 969–980 (2001).
[CrossRef]

Rosso, O. A.

L. Zunino, D. G. Pérez, M. Garavaglia, and O. A. Rosso, “Wavelet entropy of stochastic processes,” Physica A (Amsterdam) 379, 503–512 (2007).
[CrossRef]

Sáfadi, T.

R. A. Braga, W. S. Silva, T. Sáfadi, and C. M. B. Nobre, “Time history speckle pattern under statistical view,” Opt. Commun. 281, 2443–2448 (2008).
[CrossRef]

Silva, W. S.

R. A. Braga, W. S. Silva, T. Sáfadi, and C. M. B. Nobre, “Time history speckle pattern under statistical view,” Opt. Commun. 281, 2443–2448 (2008).
[CrossRef]

Stork, D. G.

R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, 2nd ed. (Wiley, 2001).

Trivi, M.

P. A. Faccia, O. R. Pardini, J. I. Amalvy, N. Cap, E. E. Grumel, R. Arizaga, and M. Trivi, “Differentiation of the drying time of paints by dynamic speckle interferometry,” Prog. Org. Coat. 64, 350–355 (2008).
[CrossRef]

I. Passoni, A. D. Pra, H. J. Rabal, M. Trivi, and R. Arizaga, “Dynamic speckle processing using wavelets based entropy,” Opt. Commun. 246, 219–228 (2005).
[CrossRef]

M. Pajuelo, G. Baldwin, H. J. Rabal, N. Cap, R. Arizaga, and M. Trivi, “Biospeckle assessment of bruising in fruits,” Opt. Laser Eng. 40, 13–24 (2003).
[CrossRef]

W., D.

R. Xu and D. W. II, “Survey of clustering algorithms,” IEEE Trans. Neural Netw. 16, 645–678 (2005).
[CrossRef] [PubMed]

Wang, Z.

Z. Wang and A. C. Bovik, “A universal image quality index,” Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

Webster, S.

J. D. Briers and S. Webster, “Laser speckle contrast analysis (LASCA): a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt. 1, 174–179 (1996).
[CrossRef]

Xu, R.

R. Xu and D. W. II, “Survey of clustering algorithms,” IEEE Trans. Neural Netw. 16, 645–678 (2005).
[CrossRef] [PubMed]

Zhang, B.

B. Zhang, M. Hsu, and G. Forman, “Accurate recasting of parameter estimation algorithms using sufficient statistics for efficient parallel speed-up: demonstrated for center-based data clustering algorithms,” in Proceedings of the 4th European Conference on Principles of Data Mining and Knowledge Discovery (PKDD 2000) (2000), Vol. 1910, pp. 243–254.
[PubMed]

Zunino, L.

L. Zunino, D. G. Pérez, M. Garavaglia, and O. A. Rosso, “Wavelet entropy of stochastic processes,” Physica A (Amsterdam) 379, 503–512 (2007).
[CrossRef]

Comput. Electron. Agric. (1)

R. A. Braga, G. W. Horgan, A. M. Enes, D. Miron, G. F. Rabelo, and J. B. B. Filho, “Biological feature isolation by wavelets in biospeckle laser images,” Comput. Electron. Agric. 58, 132–132 (2007).
[CrossRef]

IEEE Trans. Neural Netw. (2)

B. Kosko, “Stochastic competitive learning,” IEEE Trans. Neural Netw. 2, 522–529 (1991).
[CrossRef] [PubMed]

R. Xu and D. W. II, “Survey of clustering algorithms,” IEEE Trans. Neural Netw. 16, 645–678 (2005).
[CrossRef] [PubMed]

J. Biomed. Opt. (1)

J. D. Briers and S. Webster, “Laser speckle contrast analysis (LASCA): a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt. 1, 174–179 (1996).
[CrossRef]

J. Opt. Soc. Am. A (1)

Neurocomput. Var. Star Bull. (1)

P. Ozdzynski, A. Lin, M. Liljeholm, and J. Beatty, “A parallel general implementation of Kohonen’s self-organizing map algorithm: performance and scalability,” Neurocomput. Var. Star Bull. 44, 567–571 (2002).
[CrossRef]

Opt. Commun. (2)

I. Passoni, A. D. Pra, H. J. Rabal, M. Trivi, and R. Arizaga, “Dynamic speckle processing using wavelets based entropy,” Opt. Commun. 246, 219–228 (2005).
[CrossRef]

R. A. Braga, W. S. Silva, T. Sáfadi, and C. M. B. Nobre, “Time history speckle pattern under statistical view,” Opt. Commun. 281, 2443–2448 (2008).
[CrossRef]

Opt. Laser Eng. (1)

M. Pajuelo, G. Baldwin, H. J. Rabal, N. Cap, R. Arizaga, and M. Trivi, “Biospeckle assessment of bruising in fruits,” Opt. Laser Eng. 40, 13–24 (2003).
[CrossRef]

Patt. Recog. (1)

R. R. Roldán, J. F. G. Lopera, C. A. Allah, J. M. Aroza, and P. L. L. Escamilla, “A measure of quality for evaluating methods of segmentation and edge detection,” Patt. Recog. 34, 969–980 (2001).
[CrossRef]

Physica A (Amsterdam) (1)

L. Zunino, D. G. Pérez, M. Garavaglia, and O. A. Rosso, “Wavelet entropy of stochastic processes,” Physica A (Amsterdam) 379, 503–512 (2007).
[CrossRef]

Proc. IEEE (1)

T. Kohonen, “The self-organizing map,” Proc. IEEE , 78, 1464–1480 (1990).
[CrossRef]

Prog. Org. Coat. (1)

P. A. Faccia, O. R. Pardini, J. I. Amalvy, N. Cap, E. E. Grumel, R. Arizaga, and M. Trivi, “Differentiation of the drying time of paints by dynamic speckle interferometry,” Prog. Org. Coat. 64, 350–355 (2008).
[CrossRef]

Signal Process. Lett. (1)

Z. Wang and A. C. Bovik, “A universal image quality index,” Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

Other (8)

B. Zhang, M. Hsu, and G. Forman, “Accurate recasting of parameter estimation algorithms using sufficient statistics for efficient parallel speed-up: demonstrated for center-based data clustering algorithms,” in Proceedings of the 4th European Conference on Principles of Data Mining and Knowledge Discovery (PKDD 2000) (2000), Vol. 1910, pp. 243–254.
[PubMed]

Q. Huang and B. Dom, “Quantitative methods of evaluating image segmentation,” in Proceedings of the 1995 International Conference on Image Processing (IEEE, 1995), Vol. 3, pp. 3053–3056.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer-Verlag, 1975), pp. 9–75.
[CrossRef]

H. J. Rabal and R. A. Braga, Dynamic Laser Speckle and Applications (CRC, 2009).

R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, 2nd ed. (Wiley, 2001).

S. Mallat, A Wavelet Tour of Signal Processing (Academic Press, 1998).

V. Cherkassky and F. Mulier, Learning from Data: Concepts, Theory, and Methods (Wiley, 1998).

J. Bilmes, “A gentle tutorial of the em algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models,” Tech. Rep. (International Computer Science Institute, 1998).

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Figures (4)

Fig. 1
Fig. 1

Four dynamic speckle sequences that were used to assemble the low- and high-speckle activities are illustrated by the corresponding gray levels of the image A placed in the bottom right, where the darker spots correspond to higher correlation values.

Fig. 2
Fig. 2

Speckle activity obtained using the known methods when they were applied to simulated series of dynamic speckle images generated with the values given in Table 1. Low activity: (a) Konishi–Fujii, (b) WGDs, (c) wavelet entropy with 10-tap Daubechies filter. High activity: (d) Konishi–Fujii, (e) WGDs, and (f) wavelet entropy with 10-tap Daubechies filter.

Fig. 3
Fig. 3

Segmented images obtained using simulated series of dynamic speckle patterns generated with the values given in Table 1. Low activity: (a) K-means clustering (5 clusters—Haar), (b) CNN (six neurons—10-tap Daubechies), (c) EM algorithm (six clusters—10-tap Daubechies). High activity (10-tap Daubechies): (d) K-means clustering (five clusters), (e) SOM (eight clusters), and (f) EM algorithm (four clusters).

Fig. 4
Fig. 4

Segmented images obtained using the experimental data produced by a bruised apple: (a) wavelet entropy and (b) EM algorithm (two clusters) with 10-tap Daubechies filter.

Tables (5)

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Table 1 Parameter Values Used in Simulations Corresponding to High- and Low-Activity Series of N = 256 Dynamic Speckle Images

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Table 2 Edge Quality Values Determined Using Already Known Methods

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Table 3 Image Quality Index Values Determined Using Already Known Methods

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Table 4 Edge Quality Values Determined Using Proposed Clustering Methods

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Table 5 Image Quality Index Values Determined Using Proposed Clustering Methods

Equations (22)

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B R ( a , b ) = 1 N n = 1 N I a , b ( t n ) 1 N n = 1 N | I a , b ( t n ) 1 N n = 1 N I a , b ( t n ) | ,
I WGD ( a , b ) = n = 1 N L l = 1 L | I a , b ( t n ) I a , b ( t n + l ) | p ( l ) ,
J ( X , V ) = i = 1 R min 1 k K { x i v k 2 } ,
x i v k 1 = j = 1 d | x i j v k j | .
J ( X , V ) = i = 1 R k = 1 K ( μ k i ) b x i v k 2 ,
v k = i = 1 R μ k i b x i / i = 1 R μ k i b ,
μ k i = x i v k 2 / ( b 1 ) j = 1 K x i v j 2 / ( b 1 ) .
p ( x i | Θ ) = k = 1 K π k p k ( x i | θ k ) ,
Q ( Θ , Θ j 1 ) = E [ L ( Θ | X , Y ) | X , Θ j 1 ] ,
Θ j M [ Q ( Θ , Θ j 1 ) ] = argmax Θ [ Q ( Θ , Θ j 1 ) ] .
Q ( Θ , Θ j 1 ) = i = 1 R k = 1 K log [ π k p k ( x i | θ k ) ] p ( k | x i , Θ j 1 ) ,
π k j = 1 R i = 1 R p ( k | x i , Θ j 1 ) ,
μ k j = i = 1 R p ( k | x i , Θ j 1 ) x i i = 1 R p ( k | x i , Θ j 1 ) ,
Ω k j = i = 1 R p ( k | x i , Θ j 1 ) ( x i μ k j ) ( x i μ k j ) T i = 1 R p ( k | x i , Θ j 1 ) ,
p ( k | x i , Θ j 1 ) = π k j 1 p k ( x i | Ω k j 1 , μ k j 1 ) k π k j 1 p k ( x i | Ω k j 1 , μ k j 1 ) .
m w = m w + λ ( x i m w ) ,
m u ( τ + 1 ) = m u ( τ ) + H ( τ , d u w ) [ x i ( τ ) m u ( τ ) ] ,
H ( τ , d u w ) = { α ( τ ) if d u w = 0 α ( τ ) / 2 if 0 < d u w NS ( τ ) 0 if d u w > NS ( τ ) ,
α ( τ ) = { α ( 0 ) [ α T / α ( 0 ) ] τ / τ T τ < τ T α T τ τ T ,
NS ( τ ) = { NS ( 0 ) [ NS T / NS ( 0 ) ] τ / τ T τ < τ T NS T τ τ T .
ε a , b ( j ) = 1 N j τ = 1 N j | C a , b j ( τ ) | 2 ,
Q j = 4 σ A B A ¯ B ¯ ( σ A 2 + σ B 2 ) [ A ¯ 2 + B ¯ 2 ] ,

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