Abstract

Biospeckle is a technique whose purpose is to observe and study the underlying activity of some material. It has its roots in optical physics, and its first step is an image acquisition process that produces a video sequence of the reflection of a laser. The video content can be analyzed to have an interpretation of the activity of the observed material. The literature on this subject presents several different measures for analyzing the video sequence. Three of the most popular measures are the generalized difference (GD), the weighted generalized difference (WGD), and Fujii’s method. These measures have drawbacks such as high computation time or limited visual quality of the results. In this paper, we propose (i) an alternative O(n) algorithm for the computation of the GD, (ii) an alternative measure based on the GD, (iii) an alternative measure based on the WGD, and (iv) a generalized definition of the Fujii’s method with better visual quality. We discuss the similarities between the new measures and the existent ones, showing when they are applicable. We prove the gain in time computation. The proposed measures will help researchers to gain time during their research and to be able to develop faster tools based on biospeckle application.

© 2012 Optical Society of America

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  1. J. D. Briers, “Wavelength dependence of intensity fluctuations in laser speckle patterns from biological specimens,” Opt. Commun. 13, 324–326 (1975).
    [CrossRef]
  2. K. Wårdell, A. Jakobsson, and G. Nilsson, “Laser Doppler perfusion imaging by dynamic light scattering,” IEEE Trans. Biomed. Eng. 40, 309–316 (1993).
    [CrossRef]
  3. A. Zdunek, L. Frankevych, K. Konstankiewicz, and Z. Ranachowski, “Comparison of puncture test, acoustic emission and spatial-temporal speckle correlation technique as methods for apple quality evaluation,” Acta Agrophysica 11, 303–315 (2008).
  4. A. Zdunek and J. Cybulska, “Relation of biospeckle activity with quality attributes of apples,” Sensors 11, 6317–6327 (2011).
    [CrossRef]
  5. J. W. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am. 66, 1145 (1976).
    [CrossRef]
  6. J. W. Goodman, Laser Speckle and Related Phenomena, 2nd ed. (Springer Verlag, 1984).
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    [CrossRef]
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    [CrossRef]
  11. S. E. Murialdo, G. H. Sendra, I. P. Lucía, R. Arizaga, J. F. Gonzalez, H. Rabal, and M. Trivi, “Analysis of bacterial chemotactic response using dynamic laser speckle,” J. Biomed. Opt. 14, 064015 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. G. Romero, E. Alanís, and H. Rabal, “Statistics of the dynamic speckle produced by a rotating diffuser and its application to the assessment of paint drying,” Opt. Eng. 39, 1652–1658 (2000).
    [CrossRef]
  18. R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).
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    [CrossRef]
  20. R. A. Braga, C. M. B. Nobre, A. G. Costa, T. Sáfadi, and F. M. da Costa, “Evaluation of activity through dynamic laser speckle using the absolute value of the differences,” Opt. Commun. 284, 646–650 (2011).
    [CrossRef]
  21. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
    [CrossRef]
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    [CrossRef]

2011 (2)

A. Zdunek and J. Cybulska, “Relation of biospeckle activity with quality attributes of apples,” Sensors 11, 6317–6327 (2011).
[CrossRef]

R. A. Braga, C. M. B. Nobre, A. G. Costa, T. Sáfadi, and F. M. da Costa, “Evaluation of activity through dynamic laser speckle using the absolute value of the differences,” Opt. Commun. 284, 646–650 (2011).
[CrossRef]

2010 (1)

A. M. Núñez, M. F. Limia, M. Trivi, H. Rabal, and R. Arizaga, “Characterization of a paint drying process through granulometric analysis of speckle dynamic patterns,” Signal Process. 90, 1623–1630 (2010).
[CrossRef]

2009 (2)

S. E. Murialdo, G. H. Sendra, I. P. Lucía, R. Arizaga, J. F. Gonzalez, H. Rabal, and M. Trivi, “Analysis of bacterial chemotactic response using dynamic laser speckle,” J. Biomed. Opt. 14, 064015 (2009).
[CrossRef]

C. M. B. Nobre, R. A. Braga, A. G. Costa, R. R. Cardoso, W. S. da Silva, and T. Sáfadi, “Biospeckle laser spectral analysis under inertia moment, entropy and cross-spectrum methods,” Opt. Commun. 282, 2236–2242 (2009).
[CrossRef]

2008 (1)

A. Zdunek, L. Frankevych, K. Konstankiewicz, and Z. Ranachowski, “Comparison of puncture test, acoustic emission and spatial-temporal speckle correlation technique as methods for apple quality evaluation,” Acta Agrophysica 11, 303–315 (2008).

2006 (1)

2004 (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

2003 (2)

2002 (1)

R. Arizaga, N. Cap, H. Rabal, and M. Trivi, “Display of the local activity using dynamical speckle patterns,” Opt. Eng. 41, 287–294 (2002).
[CrossRef]

2000 (1)

G. Romero, E. Alanís, and H. Rabal, “Statistics of the dynamic speckle produced by a rotating diffuser and its application to the assessment of paint drying,” Opt. Eng. 39, 1652–1658 (2000).
[CrossRef]

1993 (1)

K. Wårdell, A. Jakobsson, and G. Nilsson, “Laser Doppler perfusion imaging by dynamic light scattering,” IEEE Trans. Biomed. Eng. 40, 309–316 (1993).
[CrossRef]

1987 (1)

1985 (1)

1976 (1)

1975 (1)

J. D. Briers, “Wavelength dependence of intensity fluctuations in laser speckle patterns from biological specimens,” Opt. Commun. 13, 324–326 (1975).
[CrossRef]

Alanís, E.

G. Romero, E. Alanís, and H. Rabal, “Statistics of the dynamic speckle produced by a rotating diffuser and its application to the assessment of paint drying,” Opt. Eng. 39, 1652–1658 (2000).
[CrossRef]

Andermann, M.

Arizaga, R.

A. M. Núñez, M. F. Limia, M. Trivi, H. Rabal, and R. Arizaga, “Characterization of a paint drying process through granulometric analysis of speckle dynamic patterns,” Signal Process. 90, 1623–1630 (2010).
[CrossRef]

S. E. Murialdo, G. H. Sendra, I. P. Lucía, R. Arizaga, J. F. Gonzalez, H. Rabal, and M. Trivi, “Analysis of bacterial chemotactic response using dynamic laser speckle,” J. Biomed. Opt. 14, 064015 (2009).
[CrossRef]

H. Rabal, N. Cap, M. Trivi, R. Arizaga, A. Federico, G. E. Galizzi, and G. H. Kaufmann, “Speckle activity images based on the spatial variance of the phase,” Appl. Opt. 45, 8733–8738 (2006).
[CrossRef]

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

R. Arizaga, N. Cap, H. Rabal, and M. Trivi, “Display of the local activity using dynamical speckle patterns,” Opt. Eng. 41, 287–294 (2002).
[CrossRef]

Asakura, T.

Baldwin, G.

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

Boas, D.

Bolay, H.

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Braga, R. A.

R. A. Braga, C. M. B. Nobre, A. G. Costa, T. Sáfadi, and F. M. da Costa, “Evaluation of activity through dynamic laser speckle using the absolute value of the differences,” Opt. Commun. 284, 646–650 (2011).
[CrossRef]

C. M. B. Nobre, R. A. Braga, A. G. Costa, R. R. Cardoso, W. S. da Silva, and T. Sáfadi, “Biospeckle laser spectral analysis under inertia moment, entropy and cross-spectrum methods,” Opt. Commun. 282, 2236–2242 (2009).
[CrossRef]

A. V. Saúde, F. S. Menezes, P. L. S. Freitas, G. F. Rabelo, and R. A. Braga, “On generalized differences for biospeckle image analysis,” in Conference on Graphics, Patterns and Images (SIBGRAPI), 2010 23rd SIBGRAPI (2010), pp. 209–215.

Briers, J. D.

J. D. Briers, “Wavelength dependence of intensity fluctuations in laser speckle patterns from biological specimens,” Opt. Commun. 13, 324–326 (1975).
[CrossRef]

Brigham, E. O.

E. O. Brigham, The Fast Fourier Transform and Its Applications (Prentice Hall, 1988).

Cap, N.

H. Rabal, N. Cap, M. Trivi, R. Arizaga, A. Federico, G. E. Galizzi, and G. H. Kaufmann, “Speckle activity images based on the spatial variance of the phase,” Appl. Opt. 45, 8733–8738 (2006).
[CrossRef]

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

R. Arizaga, N. Cap, H. Rabal, and M. Trivi, “Display of the local activity using dynamical speckle patterns,” Opt. Eng. 41, 287–294 (2002).
[CrossRef]

Cardoso, R. R.

C. M. B. Nobre, R. A. Braga, A. G. Costa, R. R. Cardoso, W. S. da Silva, and T. Sáfadi, “Biospeckle laser spectral analysis under inertia moment, entropy and cross-spectrum methods,” Opt. Commun. 282, 2236–2242 (2009).
[CrossRef]

Costa, A. G.

R. A. Braga, C. M. B. Nobre, A. G. Costa, T. Sáfadi, and F. M. da Costa, “Evaluation of activity through dynamic laser speckle using the absolute value of the differences,” Opt. Commun. 284, 646–650 (2011).
[CrossRef]

C. M. B. Nobre, R. A. Braga, A. G. Costa, R. R. Cardoso, W. S. da Silva, and T. Sáfadi, “Biospeckle laser spectral analysis under inertia moment, entropy and cross-spectrum methods,” Opt. Commun. 282, 2236–2242 (2009).
[CrossRef]

Cybulska, J.

A. Zdunek and J. Cybulska, “Relation of biospeckle activity with quality attributes of apples,” Sensors 11, 6317–6327 (2011).
[CrossRef]

da Costa, F. M.

R. A. Braga, C. M. B. Nobre, A. G. Costa, T. Sáfadi, and F. M. da Costa, “Evaluation of activity through dynamic laser speckle using the absolute value of the differences,” Opt. Commun. 284, 646–650 (2011).
[CrossRef]

da Silva, W. S.

C. M. B. Nobre, R. A. Braga, A. G. Costa, R. R. Cardoso, W. S. da Silva, and T. Sáfadi, “Biospeckle laser spectral analysis under inertia moment, entropy and cross-spectrum methods,” Opt. Commun. 282, 2236–2242 (2009).
[CrossRef]

Dale, A.

Devor, A.

Dunn, A.

Federico, A.

Frankevych, L.

A. Zdunek, L. Frankevych, K. Konstankiewicz, and Z. Ranachowski, “Comparison of puncture test, acoustic emission and spatial-temporal speckle correlation technique as methods for apple quality evaluation,” Acta Agrophysica 11, 303–315 (2008).

Freitas, P. L. S.

A. V. Saúde, F. S. Menezes, P. L. S. Freitas, G. F. Rabelo, and R. A. Braga, “On generalized differences for biospeckle image analysis,” in Conference on Graphics, Patterns and Images (SIBGRAPI), 2010 23rd SIBGRAPI (2010), pp. 209–215.

Fujii, H.

Galizzi, G. E.

Gonzalez, J. F.

S. E. Murialdo, G. H. Sendra, I. P. Lucía, R. Arizaga, J. F. Gonzalez, H. Rabal, and M. Trivi, “Analysis of bacterial chemotactic response using dynamic laser speckle,” J. Biomed. Opt. 14, 064015 (2009).
[CrossRef]

Gonzalez, R. C.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).

Goodman, J. W.

J. W. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am. 66, 1145 (1976).
[CrossRef]

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2007).

J. W. Goodman, Laser Speckle and Related Phenomena, 2nd ed. (Springer Verlag, 1984).

Ikawa, H.

Jakobsson, A.

K. Wårdell, A. Jakobsson, and G. Nilsson, “Laser Doppler perfusion imaging by dynamic light scattering,” IEEE Trans. Biomed. Eng. 40, 309–316 (1993).
[CrossRef]

Kaufmann, G. H.

Konstankiewicz, K.

A. Zdunek, L. Frankevych, K. Konstankiewicz, and Z. Ranachowski, “Comparison of puncture test, acoustic emission and spatial-temporal speckle correlation technique as methods for apple quality evaluation,” Acta Agrophysica 11, 303–315 (2008).

Limia, M. F.

A. M. Núñez, M. F. Limia, M. Trivi, H. Rabal, and R. Arizaga, “Characterization of a paint drying process through granulometric analysis of speckle dynamic patterns,” Signal Process. 90, 1623–1630 (2010).
[CrossRef]

Lucía, I. P.

S. E. Murialdo, G. H. Sendra, I. P. Lucía, R. Arizaga, J. F. Gonzalez, H. Rabal, and M. Trivi, “Analysis of bacterial chemotactic response using dynamic laser speckle,” J. Biomed. Opt. 14, 064015 (2009).
[CrossRef]

Menezes, F. S.

A. V. Saúde, F. S. Menezes, P. L. S. Freitas, G. F. Rabelo, and R. A. Braga, “On generalized differences for biospeckle image analysis,” in Conference on Graphics, Patterns and Images (SIBGRAPI), 2010 23rd SIBGRAPI (2010), pp. 209–215.

Moskowicz, M.

Murialdo, S. E.

S. E. Murialdo, G. H. Sendra, I. P. Lucía, R. Arizaga, J. F. Gonzalez, H. Rabal, and M. Trivi, “Analysis of bacterial chemotactic response using dynamic laser speckle,” J. Biomed. Opt. 14, 064015 (2009).
[CrossRef]

Nilsson, G.

K. Wårdell, A. Jakobsson, and G. Nilsson, “Laser Doppler perfusion imaging by dynamic light scattering,” IEEE Trans. Biomed. Eng. 40, 309–316 (1993).
[CrossRef]

Nobre, C. M. B.

R. A. Braga, C. M. B. Nobre, A. G. Costa, T. Sáfadi, and F. M. da Costa, “Evaluation of activity through dynamic laser speckle using the absolute value of the differences,” Opt. Commun. 284, 646–650 (2011).
[CrossRef]

C. M. B. Nobre, R. A. Braga, A. G. Costa, R. R. Cardoso, W. S. da Silva, and T. Sáfadi, “Biospeckle laser spectral analysis under inertia moment, entropy and cross-spectrum methods,” Opt. Commun. 282, 2236–2242 (2009).
[CrossRef]

Nohira, K.

Núñez, A. M.

A. M. Núñez, M. F. Limia, M. Trivi, H. Rabal, and R. Arizaga, “Characterization of a paint drying process through granulometric analysis of speckle dynamic patterns,” Signal Process. 90, 1623–1630 (2010).
[CrossRef]

Ohura, T.

Pajuelo, M.

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

Rabal, H.

A. M. Núñez, M. F. Limia, M. Trivi, H. Rabal, and R. Arizaga, “Characterization of a paint drying process through granulometric analysis of speckle dynamic patterns,” Signal Process. 90, 1623–1630 (2010).
[CrossRef]

S. E. Murialdo, G. H. Sendra, I. P. Lucía, R. Arizaga, J. F. Gonzalez, H. Rabal, and M. Trivi, “Analysis of bacterial chemotactic response using dynamic laser speckle,” J. Biomed. Opt. 14, 064015 (2009).
[CrossRef]

H. Rabal, N. Cap, M. Trivi, R. Arizaga, A. Federico, G. E. Galizzi, and G. H. Kaufmann, “Speckle activity images based on the spatial variance of the phase,” Appl. Opt. 45, 8733–8738 (2006).
[CrossRef]

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

R. Arizaga, N. Cap, H. Rabal, and M. Trivi, “Display of the local activity using dynamical speckle patterns,” Opt. Eng. 41, 287–294 (2002).
[CrossRef]

G. Romero, E. Alanís, and H. Rabal, “Statistics of the dynamic speckle produced by a rotating diffuser and its application to the assessment of paint drying,” Opt. Eng. 39, 1652–1658 (2000).
[CrossRef]

Rabal, H. J.

H. J. Rabal, Dynamic Laser Speckle and Applications (CRC Press, 2008), pp. 115–136.

Rabelo, G. F.

A. V. Saúde, F. S. Menezes, P. L. S. Freitas, G. F. Rabelo, and R. A. Braga, “On generalized differences for biospeckle image analysis,” in Conference on Graphics, Patterns and Images (SIBGRAPI), 2010 23rd SIBGRAPI (2010), pp. 209–215.

Ranachowski, Z.

A. Zdunek, L. Frankevych, K. Konstankiewicz, and Z. Ranachowski, “Comparison of puncture test, acoustic emission and spatial-temporal speckle correlation technique as methods for apple quality evaluation,” Acta Agrophysica 11, 303–315 (2008).

Romero, G.

G. Romero, E. Alanís, and H. Rabal, “Statistics of the dynamic speckle produced by a rotating diffuser and its application to the assessment of paint drying,” Opt. Eng. 39, 1652–1658 (2000).
[CrossRef]

Sáfadi, T.

R. A. Braga, C. M. B. Nobre, A. G. Costa, T. Sáfadi, and F. M. da Costa, “Evaluation of activity through dynamic laser speckle using the absolute value of the differences,” Opt. Commun. 284, 646–650 (2011).
[CrossRef]

C. M. B. Nobre, R. A. Braga, A. G. Costa, R. R. Cardoso, W. S. da Silva, and T. Sáfadi, “Biospeckle laser spectral analysis under inertia moment, entropy and cross-spectrum methods,” Opt. Commun. 282, 2236–2242 (2009).
[CrossRef]

Saúde, A. V.

A. V. Saúde, F. S. Menezes, P. L. S. Freitas, G. F. Rabelo, and R. A. Braga, “On generalized differences for biospeckle image analysis,” in Conference on Graphics, Patterns and Images (SIBGRAPI), 2010 23rd SIBGRAPI (2010), pp. 209–215.

Sendra, G. H.

S. E. Murialdo, G. H. Sendra, I. P. Lucía, R. Arizaga, J. F. Gonzalez, H. Rabal, and M. Trivi, “Analysis of bacterial chemotactic response using dynamic laser speckle,” J. Biomed. Opt. 14, 064015 (2009).
[CrossRef]

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Shintomi, Y.

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Trivi, M.

A. M. Núñez, M. F. Limia, M. Trivi, H. Rabal, and R. Arizaga, “Characterization of a paint drying process through granulometric analysis of speckle dynamic patterns,” Signal Process. 90, 1623–1630 (2010).
[CrossRef]

S. E. Murialdo, G. H. Sendra, I. P. Lucía, R. Arizaga, J. F. Gonzalez, H. Rabal, and M. Trivi, “Analysis of bacterial chemotactic response using dynamic laser speckle,” J. Biomed. Opt. 14, 064015 (2009).
[CrossRef]

H. Rabal, N. Cap, M. Trivi, R. Arizaga, A. Federico, G. E. Galizzi, and G. H. Kaufmann, “Speckle activity images based on the spatial variance of the phase,” Appl. Opt. 45, 8733–8738 (2006).
[CrossRef]

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

R. Arizaga, N. Cap, H. Rabal, and M. Trivi, “Display of the local activity using dynamical speckle patterns,” Opt. Eng. 41, 287–294 (2002).
[CrossRef]

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Wårdell, K.

K. Wårdell, A. Jakobsson, and G. Nilsson, “Laser Doppler perfusion imaging by dynamic light scattering,” IEEE Trans. Biomed. Eng. 40, 309–316 (1993).
[CrossRef]

Woods, R. E.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).

Yamamoto, Y.

Zdunek, A.

A. Zdunek and J. Cybulska, “Relation of biospeckle activity with quality attributes of apples,” Sensors 11, 6317–6327 (2011).
[CrossRef]

A. Zdunek, L. Frankevych, K. Konstankiewicz, and Z. Ranachowski, “Comparison of puncture test, acoustic emission and spatial-temporal speckle correlation technique as methods for apple quality evaluation,” Acta Agrophysica 11, 303–315 (2008).

Acta Agrophysica (1)

A. Zdunek, L. Frankevych, K. Konstankiewicz, and Z. Ranachowski, “Comparison of puncture test, acoustic emission and spatial-temporal speckle correlation technique as methods for apple quality evaluation,” Acta Agrophysica 11, 303–315 (2008).

Appl. Opt. (2)

IEEE Trans. Biomed. Eng. (1)

K. Wårdell, A. Jakobsson, and G. Nilsson, “Laser Doppler perfusion imaging by dynamic light scattering,” IEEE Trans. Biomed. Eng. 40, 309–316 (1993).
[CrossRef]

IEEE Trans. Image Process. (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

J. Biomed. Opt. (1)

S. E. Murialdo, G. H. Sendra, I. P. Lucía, R. Arizaga, J. F. Gonzalez, H. Rabal, and M. Trivi, “Analysis of bacterial chemotactic response using dynamic laser speckle,” J. Biomed. Opt. 14, 064015 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (3)

J. D. Briers, “Wavelength dependence of intensity fluctuations in laser speckle patterns from biological specimens,” Opt. Commun. 13, 324–326 (1975).
[CrossRef]

C. M. B. Nobre, R. A. Braga, A. G. Costa, R. R. Cardoso, W. S. da Silva, and T. Sáfadi, “Biospeckle laser spectral analysis under inertia moment, entropy and cross-spectrum methods,” Opt. Commun. 282, 2236–2242 (2009).
[CrossRef]

R. A. Braga, C. M. B. Nobre, A. G. Costa, T. Sáfadi, and F. M. da Costa, “Evaluation of activity through dynamic laser speckle using the absolute value of the differences,” Opt. Commun. 284, 646–650 (2011).
[CrossRef]

Opt. Eng. (2)

R. Arizaga, N. Cap, H. Rabal, and M. Trivi, “Display of the local activity using dynamical speckle patterns,” Opt. Eng. 41, 287–294 (2002).
[CrossRef]

G. Romero, E. Alanís, and H. Rabal, “Statistics of the dynamic speckle produced by a rotating diffuser and its application to the assessment of paint drying,” Opt. Eng. 39, 1652–1658 (2000).
[CrossRef]

Opt. Lasers Eng. (1)

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

Opt. Lett. (2)

Sensors (1)

A. Zdunek and J. Cybulska, “Relation of biospeckle activity with quality attributes of apples,” Sensors 11, 6317–6327 (2011).
[CrossRef]

Signal Process. (1)

A. M. Núñez, M. F. Limia, M. Trivi, H. Rabal, and R. Arizaga, “Characterization of a paint drying process through granulometric analysis of speckle dynamic patterns,” Signal Process. 90, 1623–1630 (2010).
[CrossRef]

Other (7)

H. J. Rabal, Dynamic Laser Speckle and Applications (CRC Press, 2008), pp. 115–136.

A. V. Saúde, F. S. Menezes, P. L. S. Freitas, G. F. Rabelo, and R. A. Braga, “On generalized differences for biospeckle image analysis,” in Conference on Graphics, Patterns and Images (SIBGRAPI), 2010 23rd SIBGRAPI (2010), pp. 209–215.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2007).

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).

J. W. Goodman, Laser Speckle and Related Phenomena, 2nd ed. (Springer Verlag, 1984).

H. J. Rabal and R. A. Braga, eds., Dynamic Laser Speckle and Applications (CRC Press, 2008).

E. O. Brigham, The Fast Fourier Transform and Its Applications (Prentice Hall, 1988).

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Figures (11)

Fig. 1.
Fig. 1.

Schema of the experimental setup to acquire the speckle pattern. It can be seen that the laser (monochromatic light) passes through the lens, reflects on the mirror, and reaches the sample (object). The laser is scattered by the sample (object), and it is acquired on a CCD camera. The video frame sequence is stored on the computer.

Fig. 2.
Fig. 2.

Original object (coin), in (a), and two randomly selected frames of the video sequence, in (b) and (c). It is not possible to differentiate such frames by visual inspection.

Fig. 3.
Fig. 3.

One pixel activity evolution. The activity of pixel p at frame i(i=0,1,,n1) is represented by xi. The activity evolution of pixel p is thus represented by the sequence sp=[x0,x1,,xn1].

Fig. 4.
Fig. 4.

GD of paint drying over a coin. Each pixel p of the image is the value GD(sp), where sp is the sequence of the values sp=[x0,x1,,xn1] of the intensities (xi) of pixel p along time.

Fig. 5.
Fig. 5.

Comparison between GD and GD*. The GD* is in (a), and GD is in (b). In (c), we present GD* with the contrast adjusted by the contrast function in (d). Each pixel p is the value GD*(sp) in (a), GD*(sp) in (b), or GD*(sp) with adjusted contrast in (c), where sp is the sequence of gray levels of the pixel p along time.

Fig. 6.
Fig. 6.

Comparison between GD and MWD for w=4. The GD is in (a), and the MWD is in (b). Each pixel p is the value GD(sp) in (a), or MWD(w,sp) in (b), where sp is the sequence of the values of the pixel p along time.

Fig. 7.
Fig. 7.

Comparison between MWD Eq. (17) and MWD Eq. (18) for w=4 and w=20. The MWD is in (a), for w=4, and (c), for w=20, and MWD is in (b), for w=4, and (d), for w=20. Each pixel p is the value MWD(w,sp) in (a) and (c), or MWD(w,sp) in (b) and (d), where sp is the sequence of the values of the pixel p along time, and w is the window size. The difference between MWD and MWD remains difficult to observe by visual inspection even for the small window size w=4 and the large window size w=20.

Fig. 8.
Fig. 8.

Difference between MWD Eq. (17) and MWD Eq. (18) for (a) w=4 and (b) w=20, normalized in the interval [0…255].

Fig. 9.
Fig. 9.

Fujii result. Each pixel p of the image is the value F(sp), where sp is the sequence of the values sp=[x0,x1,,xn1] of the intensities (xi) of pixel p along time.

Fig. 10.
Fig. 10.

Inverse Fujii result. Each pixel p of the image is the value Fi(sp), where sp is the sequence of the values sp=[x0,x1,,xn1] of the intensities (xi) of pixel p along time.

Fig. 11.
Fig. 11.

Parameterized Fujii result with reference gray level gr=190. Each pixel p of the image is the value Fp(sp,gr), where sp is the sequence of the values sp=[x0,x1,,xn1] of the intensities (xi) of pixel p along time.

Tables (2)

Tables Icon

Table 1. Numerical Comparison between the MWD Eq. (17) and the MWD Eq. (18) for w=4, 8, 12, 16, and 20, Where X=MWD and X=MWD, max(y) Is the Maximum Value in y, min(y) Is the Minimum Value in y, mean(y) Is the Mean Value in y, stddev(y) Is the Standard Deviation in y, peakratio(y,y)=mean(yy)/max({y,y}) Is the Percentage of the Mean Difference over the Peak Value of the Samples Union, and peakstdratio(y,y)=stddev(yy)/max({y,y}) Is the Percentage of the Mean Standard Deviation over the Peak Value of the Samples Uniona

Tables Icon

Table 2. Numerical Comparison between the MWD and the MWD for w=4, 8, 12, 16, and 20, Where X=MWD and X=MWD, Both Normalized to the Interval 0…255, max(y) Is the Maximum Value in y, min(y) Is the Minimum Value in y, mean(y) Is the Mean Value in y, stddev(y) Is the Standard Deviation in y, peakratio(y,y)=mean(yy)/max({y,y}) Is the Percentage of the Mean Difference over the Peak Value of the Samples Union, and peakstdratio(y,y)=stddev(yy)/max({y,y}) Is the Percentage of the Mean Standard Deviation over the Peak Value of the Samples Uniona

Equations (54)

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GD(s)=i=0n1j=i+1n1|xixj|.
(n1)+(n2)++1=n2n2.
|xixj|=|xjxi|,
GD(s)=12i=0n1j=0n1|xixj|,
GD(s)=12[j=0n1|x0xj|+j=0n1|x1xj|++j=0n1|xn1xj|].
j=0n1|x0xj|=l=0m1|x0l|gl,
GD(s)=12i=0n1l=0m1|xil|gl.
GD(s)=12k=0m1(l=0m1|kl|gl)gk
GD(s)=k=0m1(l=k+1m1|kl|gl)gk.
Pk=l=k+1m1|kl|gl,
GD(s)=k=0m1Pkgk.
P0=g1+2g2+3g3++(m1)gm1,P1=g2+2g3+3g4++(m2)gm1,P2=g3+2g4+3g5++(m3)gm1,
P1=P0[g1+g2++gm1],P2=P1[g2+g3++gm1],
P1=P0l=1m1gl,P2=P1l=2m1gl.
Sk=l=km1gl,
Pk+1=PkSk+1.
S0=k=0m1gk=n
Sk+1=l=k+1m1gl=Skgk,
GDh(s)=k=0hPkgk.
GDh+1(s)=GDh(s)+Ph+1gh+1.
S0=n,P0=k=1m1kgk,GD0(s)=P0g0.
Sk+1=Skgk,Pk+1=PkSk+1,GDk+1(s)=GDk(s)+Pk+1gk+1.
k=m1.
f(x)>f(x)g(x)>g(x).
GD*(s)=i=0n1j=i+1n1(xixj)2.
GD(s)=|11|+|110|+|110|=18,GD(s)=|15|+|111|+|511|=20,GD*(s)=(11)2+(110)2+(110)2=162,GD*(s)=(15)2+(111)2+(511)2=152.
(xixj)2=(xjxi)2,
GD*(s)=12i=0n1j=0n1(xixj)2
GD*(s)=12i=0n1j=0n1xi22xixj+xj2
GD*(s)=12i=0n1nxi22xi(nx¯)+nx¯2=12i=0n1nxi22nxix¯+nx¯2,
GD*(s)=12(n(nx¯2)2n(nx¯)x¯+n(nx¯2))=12(n2x¯22n2x¯2+n2x¯2)=12(2n2x¯22n2x¯2),
GD*(s)=n2(x¯2x¯2).
σ2(s)=1ni=0n1(xix¯)2.
σ2(s)=1ni=0n1(xi22xix¯+x¯2)
σ2(s)=1n(nx¯22nx¯2+nx¯2)
σ2(s)=x¯2x¯2.
GD*(s)=n2σ2(s),
WGD(w,s)=i=0nj=i+1i+w|xixj|pj,
MWD(w,s)=i=0nw1j=i+1i+w|xixj|,
MWD(w,s)=i=0nw1|j=i+1i+w(xixj)|.
|xixi+1|+|xixi+2|+|xixi+3|+|xixi+4|,
|(xixi+1)+(xixi+2)+(xixi+3)+(xixi+4)|.
|x1+x2||x1|+|x2|,
|x1+x2++xw+1||x1|+|x2|++|xw+1|.
|4xixi+1xi+2xi+3xi+4|,
f4=[4,1,1,1,1]
si,4=[xi,xi+1,xi+2,xi+3,xi+4]
cw=s*fw,
MWD(w,cw)=i=0n1|cw(i)|,
f*g=F1{F{f}·F{g}},
cw=F1{F{s}·F{fw}}.
F(s)=i=0n1|xixi+1|xi+xi+1.
Fi(s)=i=0n1|xixi+1|(xi+xi+1).
Fp(s,gr)=i=0n1|xixi+1|(255|grxi|+255|grxi+1|).

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